Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(201,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.i (of order \(3\), 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: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} + 20 x^{18} + 261 x^{16} + 1994 x^{14} + 11074 x^{12} + 39211 x^{10} + 99376 x^{8} + 134299 x^{6} + \cdots + 4096 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.9 | ||
Root | \(-1.21562 - 2.10552i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.201 |
Dual form | 1900.2.i.g.501.9 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.21562 | − | 2.10552i | 0.701841 | − | 1.21562i | −0.265979 | − | 0.963979i | \(-0.585695\pi\) |
0.967820 | − | 0.251645i | \(-0.0809715\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.663818 | −0.250900 | −0.125450 | − | 0.992100i | \(-0.540037\pi\) | ||||
−0.125450 | + | 0.992100i | \(0.540037\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.45548 | − | 2.52097i | −0.485161 | − | 0.840323i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.80905 | −0.545450 | −0.272725 | − | 0.962092i | \(-0.587925\pi\) | ||||
−0.272725 | + | 0.962092i | \(0.587925\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.15197 | − | 1.99526i | −0.319498 | − | 0.553386i | 0.660886 | − | 0.750487i | \(-0.270181\pi\) |
−0.980383 | + | 0.197100i | \(0.936847\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.18033 | − | 3.77643i | 0.528807 | − | 0.915920i | −0.470629 | − | 0.882331i | \(-0.655973\pi\) |
0.999436 | − | 0.0335887i | \(-0.0106936\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.21168 | − | 1.12329i | 0.966225 | − | 0.257699i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.806953 | + | 1.39768i | −0.176092 | + | 0.305000i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.04716 | − | 1.81374i | −0.218349 | − | 0.378191i | 0.735955 | − | 0.677031i | \(-0.236734\pi\) |
−0.954303 | + | 0.298840i | \(0.903400\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.216466 | 0.0416588 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.974621 | − | 1.68809i | −0.180983 | − | 0.313471i | 0.761233 | − | 0.648479i | \(-0.224594\pi\) |
−0.942215 | + | 0.335008i | \(0.891261\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.52527 | −1.71079 | −0.855394 | − | 0.517977i | \(-0.826685\pi\) | ||||
−0.855394 | + | 0.517977i | \(0.826685\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.19913 | + | 3.80900i | −0.382819 | + | 0.663062i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.97461 | −0.489023 | −0.244511 | − | 0.969646i | \(-0.578628\pi\) | ||||
−0.244511 | + | 0.969646i | \(0.578628\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.60143 | −0.896946 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.247657 | + | 0.428954i | −0.0386775 | + | 0.0669914i | −0.884716 | − | 0.466130i | \(-0.845648\pi\) |
0.846039 | + | 0.533122i | \(0.178981\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.93588 | − | 6.81715i | 0.600216 | − | 1.03960i | −0.392572 | − | 0.919721i | \(-0.628415\pi\) |
0.992788 | − | 0.119884i | \(-0.0382521\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.28772 | − | 5.69449i | −0.479563 | − | 0.830627i | 0.520163 | − | 0.854067i | \(-0.325871\pi\) |
−0.999725 | + | 0.0234403i | \(0.992538\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.55935 | −0.937049 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.30091 | − | 9.18145i | −0.742276 | − | 1.28566i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.15225 | − | 1.99575i | −0.158273 | − | 0.274137i | 0.775973 | − | 0.630766i | \(-0.217259\pi\) |
−0.934246 | + | 0.356629i | \(0.883926\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.75471 | − | 10.2333i | 0.364871 | − | 1.35543i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.88559 | + | 6.73003i | −0.505860 | + | 0.876176i | 0.494117 | + | 0.869396i | \(0.335492\pi\) |
−0.999977 | + | 0.00678007i | \(0.997842\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.36021 | − | 9.28415i | −0.686304 | − | 1.18871i | −0.973025 | − | 0.230700i | \(-0.925899\pi\) |
0.286721 | − | 0.958014i | \(-0.407435\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.966176 | + | 1.67347i | 0.121727 | + | 0.210837i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.29199 | + | 3.96984i | 0.280011 | + | 0.484993i | 0.971387 | − | 0.237502i | \(-0.0763286\pi\) |
−0.691376 | + | 0.722495i | \(0.742995\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.09182 | −0.612984 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.95914 | + | 5.12538i | −0.351185 | + | 0.608270i | −0.986457 | − | 0.164018i | \(-0.947554\pi\) |
0.635272 | + | 0.772288i | \(0.280888\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.80773 | + | 4.86313i | −0.328620 | + | 0.569187i | −0.982238 | − | 0.187638i | \(-0.939917\pi\) |
0.653618 | + | 0.756824i | \(0.273250\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.20088 | 0.136853 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.99810 | − | 5.19286i | 0.337312 | − | 0.584242i | −0.646614 | − | 0.762817i | \(-0.723815\pi\) |
0.983926 | + | 0.178575i | \(0.0571488\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.62959 | − | 8.01868i | 0.514399 | − | 0.890965i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.20090 | 0.680638 | 0.340319 | − | 0.940310i | \(-0.389465\pi\) | ||||
0.340319 | + | 0.940310i | \(0.389465\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.73909 | −0.508084 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.65028 | + | 11.5186i | 0.704928 | + | 1.22097i | 0.966717 | + | 0.255847i | \(0.0823542\pi\) |
−0.261789 | + | 0.965125i | \(0.584312\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.764696 | + | 1.32449i | 0.0801619 | + | 0.138844i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.5791 | + | 20.0557i | −1.20070 | + | 2.07968i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.08470 | + | 8.80695i | −0.516273 | + | 0.894211i | 0.483549 | + | 0.875317i | \(0.339348\pi\) |
−0.999822 | + | 0.0188932i | \(0.993986\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.63305 | + | 4.56057i | 0.264631 | + | 0.458354i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.48770 | − | 12.9691i | −0.745054 | − | 1.29047i | −0.950170 | − | 0.311733i | \(-0.899091\pi\) |
0.205116 | − | 0.978738i | \(-0.434243\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.1501 | 1.78839 | 0.894193 | − | 0.447681i | \(-0.147750\pi\) | ||||
0.894193 | + | 0.447681i | \(0.147750\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.9698 | 1.35051 | 0.675256 | − | 0.737584i | \(-0.264033\pi\) | ||||
0.675256 | + | 0.737584i | \(0.264033\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.20544 | − | 15.9443i | 0.881721 | − | 1.52719i | 0.0322945 | − | 0.999478i | \(-0.489719\pi\) |
0.849426 | − | 0.527707i | \(-0.176948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.61601 | + | 6.26311i | −0.343216 | + | 0.594468i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.8946 | −1.02487 | −0.512437 | − | 0.858725i | \(-0.671257\pi\) | ||||
−0.512437 | + | 0.858725i | \(0.671257\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.35333 | + | 5.80814i | −0.310016 | + | 0.536963i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.44734 | + | 2.50687i | −0.132677 | + | 0.229804i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.72733 | −0.702484 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.602115 | + | 1.04289i | 0.0542909 | + | 0.0940346i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.65262 | − | 2.86242i | −0.146646 | − | 0.253998i | 0.783340 | − | 0.621594i | \(-0.213514\pi\) |
−0.929986 | + | 0.367595i | \(0.880181\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.56910 | − | 16.5742i | −0.842512 | − | 1.45927i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.646627 | + | 1.11999i | −0.0564961 | + | 0.0978541i | −0.892890 | − | 0.450274i | \(-0.851326\pi\) |
0.836394 | + | 0.548128i | \(0.184660\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.79579 | + | 0.745658i | −0.242426 | + | 0.0646567i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.29920 | + | 12.6426i | 0.623613 | + | 1.08013i | 0.988807 | + | 0.149197i | \(0.0476690\pi\) |
−0.365195 | + | 0.930931i | \(0.618998\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.87915 | + | 3.25478i | 0.159387 | + | 0.276067i | 0.934648 | − | 0.355575i | \(-0.115715\pi\) |
−0.775261 | + | 0.631641i | \(0.782382\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.9865 | −1.34631 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.08397 | + | 3.60954i | 0.174270 | + | 0.301844i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.97370 | + | 13.8108i | −0.657659 | + | 1.13910i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.83653 | + | 6.64507i | −0.314301 | + | 0.544385i | −0.979289 | − | 0.202469i | \(-0.935103\pi\) |
0.664988 | + | 0.746854i | \(0.268437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.62643 | 0.132357 | 0.0661785 | − | 0.997808i | \(-0.478919\pi\) | ||||
0.0661785 | + | 0.997808i | \(0.478919\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.6937 | −1.02622 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.32729 | + | 2.29893i | −0.105929 | + | 0.183474i | −0.914117 | − | 0.405450i | \(-0.867115\pi\) |
0.808188 | + | 0.588924i | \(0.200448\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.60279 | −0.444331 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.695126 | + | 1.20399i | 0.0547836 | + | 0.0948880i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.8052 | 1.55127 | 0.775633 | − | 0.631184i | \(-0.217431\pi\) | ||||
0.775633 | + | 0.631184i | \(0.217431\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.0448558 | + | 0.0776925i | 0.00347105 | + | 0.00601203i | 0.867756 | − | 0.496991i | \(-0.165562\pi\) |
−0.864285 | + | 0.503003i | \(0.832228\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.84595 | − | 6.66139i | 0.295842 | − | 0.512414i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.96179 | − | 8.98259i | −0.685325 | − | 0.686916i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.91662 | − | 13.7120i | 0.601889 | − | 1.04250i | −0.390646 | − | 0.920541i | \(-0.627748\pi\) |
0.992535 | − | 0.121962i | \(-0.0389185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.44682 | + | 16.3624i | 0.710067 | + | 1.22987i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.5051 | −1.00942 | −0.504709 | − | 0.863290i | \(-0.668400\pi\) | ||||
−0.504709 | + | 0.863290i | \(0.668400\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.78591 | + | 8.28945i | 0.355734 | + | 0.616150i | 0.987243 | − | 0.159219i | \(-0.0508975\pi\) |
−0.631509 | + | 0.775368i | \(0.717564\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −26.0640 | −1.92670 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.94432 | + | 6.83177i | −0.288438 | + | 0.499588i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.143694 | −0.0104522 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.9010 | 1.94649 | 0.973243 | − | 0.229778i | \(-0.0738000\pi\) | ||||
0.973243 | + | 0.229778i | \(0.0738000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4137 | − | 19.7692i | 0.821579 | − | 1.42302i | −0.0829272 | − | 0.996556i | \(-0.526427\pi\) |
0.904506 | − | 0.426461i | \(-0.140240\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.4172 | −0.742192 | −0.371096 | − | 0.928594i | \(-0.621018\pi\) | ||||
−0.371096 | + | 0.928594i | \(0.621018\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.782081 | − | 1.35460i | −0.0554403 | − | 0.0960254i | 0.836973 | − | 0.547244i | \(-0.184323\pi\) |
−0.892414 | + | 0.451218i | \(0.850990\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.1448 | 0.786092 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.646971 | + | 1.12059i | 0.0454085 | + | 0.0786498i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.04825 | + | 5.27973i | −0.211868 | + | 0.366967i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.61915 | + | 2.03208i | −0.527028 | + | 0.140562i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.4253 | + | 18.0571i | −0.717704 | + | 1.24310i | 0.244203 | + | 0.969724i | \(0.421474\pi\) |
−0.961907 | + | 0.273376i | \(0.911860\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.19439 | + | 12.4611i | 0.492952 | + | 0.853818i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.32305 | 0.429236 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.82629 | + | 11.8235i | 0.461278 | + | 0.798957i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.0466 | −0.675810 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.2856 | − | 19.5472i | 0.755740 | − | 1.30898i | −0.189266 | − | 0.981926i | \(-0.560611\pi\) |
0.945006 | − | 0.327054i | \(-0.106056\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.4187 | 0.757883 | 0.378941 | − | 0.925421i | \(-0.376288\pi\) | ||||
0.378941 | + | 0.925421i | \(0.376288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8237 | −1.04566 | −0.522829 | − | 0.852438i | \(-0.675123\pi\) | ||||
−0.522829 | + | 0.852438i | \(0.675123\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.45982 | − | 2.52849i | 0.0960492 | − | 0.166362i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.73314 | + | 11.6621i | −0.441103 | + | 0.764013i | −0.997772 | − | 0.0667219i | \(-0.978746\pi\) |
0.556669 | + | 0.830735i | \(0.312079\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.28912 | − | 12.6251i | −0.473479 | − | 0.820090i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.7437 | 1.27711 | 0.638557 | − | 0.769574i | \(-0.279532\pi\) | ||||
0.638557 | + | 0.769574i | \(0.279532\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.69793 | + | 4.67295i | 0.173789 | + | 0.301011i | 0.939742 | − | 0.341886i | \(-0.111066\pi\) |
−0.765953 | + | 0.642897i | \(0.777732\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.9310 | − | 18.9330i | −0.701223 | − | 1.21455i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.09296 | − | 7.10942i | −0.451314 | − | 0.452361i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.53797 | − | 13.0561i | 0.477699 | − | 0.827399i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.78646 | + | 3.09424i | 0.112760 | + | 0.195306i | 0.916882 | − | 0.399158i | \(-0.130697\pi\) |
−0.804122 | + | 0.594464i | \(0.797364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.89437 | + | 3.28115i | 0.119098 | + | 0.206284i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.26649 | − | 16.0500i | −0.578028 | − | 1.00117i | −0.995705 | − | 0.0925780i | \(-0.970489\pi\) |
0.417678 | − | 0.908595i | \(-0.362844\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.97460 | 0.122696 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.83709 | + | 4.91398i | −0.175611 | + | 0.304168i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.37288 | + | 9.30609i | −0.331306 | + | 0.573838i | −0.982768 | − | 0.184843i | \(-0.940822\pi\) |
0.651462 | + | 0.758681i | \(0.274156\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 32.3370 | 1.97899 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.05027 | − | 10.4794i | 0.368892 | − | 0.638939i | −0.620501 | − | 0.784206i | \(-0.713071\pi\) |
0.989393 | + | 0.145267i | \(0.0464040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.34472 | − | 16.1855i | 0.567651 | − | 0.983201i | −0.429146 | − | 0.903235i | \(-0.641185\pi\) |
0.996798 | − | 0.0799661i | \(-0.0254812\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.71833 | 0.225044 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.94922 | −0.357454 | −0.178727 | − | 0.983899i | \(-0.557198\pi\) | ||||
−0.178727 | + | 0.983899i | \(0.557198\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.8639 | + | 24.0129i | 0.830008 | + | 1.43762i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.78943 | + | 15.2237i | 0.524333 | + | 0.908172i | 0.999599 | + | 0.0283294i | \(0.00901874\pi\) |
−0.475265 | + | 0.879843i | \(0.657648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.7056 | + | 27.2029i | −0.933603 | + | 1.61705i | −0.156495 | + | 0.987679i | \(0.550020\pi\) |
−0.777107 | + | 0.629368i | \(0.783314\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.164399 | − | 0.284748i | 0.00970418 | − | 0.0168081i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00764 | − | 1.74528i | −0.0592727 | − | 0.102663i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.3622 | + | 21.4119i | 0.724682 | + | 1.25519i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.1435 | 1.64416 | 0.822080 | − | 0.569372i | \(-0.192814\pi\) | ||||
0.822080 | + | 0.569372i | \(0.192814\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.391598 | −0.0227228 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.41259 | + | 4.17873i | −0.139524 | + | 0.241662i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.61271 | + | 4.52535i | −0.150594 | + | 0.260837i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −36.4089 | −2.09164 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.4862 | − | 23.3588i | 0.769698 | − | 1.33316i | −0.168028 | − | 0.985782i | \(-0.553740\pi\) |
0.937727 | − | 0.347374i | \(-0.112927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.0637 | − | 38.2155i | 1.25516 | − | 2.17401i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.99721 | −0.283366 | −0.141683 | − | 0.989912i | \(-0.545251\pi\) | ||||
−0.141683 | + | 0.989912i | \(0.545251\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.0761 | − | 22.6484i | −0.739104 | − | 1.28017i | −0.952899 | − | 0.303287i | \(-0.901916\pi\) |
0.213795 | − | 0.976878i | \(-0.431417\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.0085 | − | 22.5314i | −0.730632 | − | 1.26549i | −0.956614 | − | 0.291359i | \(-0.905892\pi\) |
0.225982 | − | 0.974131i | \(-0.427441\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.76314 | + | 3.05385i | 0.0987169 | + | 0.170983i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.9820 | − | 29.4137i | 0.947844 | − | 1.64171i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.94081 | − | 18.3543i | 0.274914 | − | 1.02126i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.3807 | − | 38.7645i | −1.23766 | − | 2.14368i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.18245 | + | 3.78011i | 0.120322 | + | 0.208404i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.97402 | 0.438292 | 0.219146 | − | 0.975692i | \(-0.429673\pi\) | ||||
0.219146 | + | 0.975692i | \(0.429673\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.32949 | + | 7.49890i | 0.237255 | + | 0.410937i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.97951 | + | 3.42862i | −0.107831 | + | 0.186769i | −0.914891 | − | 0.403700i | \(-0.867724\pi\) |
0.807060 | + | 0.590469i | \(0.201057\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.2437 | + | 22.9387i | −0.719299 | + | 1.24586i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.2317 | 0.933150 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.00094 | 0.486005 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.40205 | − | 4.16047i | 0.128949 | − | 0.223345i | −0.794321 | − | 0.607498i | \(-0.792173\pi\) |
0.923269 | + | 0.384153i | \(0.125506\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.02058 | 0.482861 | 0.241430 | − | 0.970418i | \(-0.422383\pi\) | ||||
0.241430 | + | 0.970418i | \(0.422383\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.249361 | − | 0.431906i | −0.0133099 | − | 0.0230534i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0910 | 0.962889 | 0.481444 | − | 0.876477i | \(-0.340112\pi\) | ||||
0.481444 | + | 0.876477i | \(0.340112\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.51884 | + | 6.09481i | 0.186237 | + | 0.322572i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.4849 | + | 30.2848i | −0.922820 | + | 1.59837i | −0.127791 | + | 0.991801i | \(0.540789\pi\) |
−0.795030 | + | 0.606571i | \(0.792545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.4765 | − | 9.46183i | 0.867182 | − | 0.497991i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.39352 | + | 16.2701i | −0.493032 | + | 0.853957i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.93819 | − | 8.55319i | −0.257771 | − | 0.446473i | 0.707873 | − | 0.706339i | \(-0.249655\pi\) |
−0.965645 | + | 0.259866i | \(0.916321\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.44184 | 0.0750593 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.764883 | + | 1.32482i | 0.0397107 | + | 0.0687810i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.9698 | 0.982220 | 0.491110 | − | 0.871098i | \(-0.336591\pi\) | ||||
0.491110 | + | 0.871098i | \(0.336591\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.24546 | + | 3.88925i | −0.115647 | + | 0.200306i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.93773 | 0.459101 | 0.229550 | − | 0.973297i | \(-0.426274\pi\) | ||||
0.229550 | + | 0.973297i | \(0.426274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.03584 | −0.411689 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.06230 | − | 13.9643i | 0.411964 | − | 0.713543i | −0.583140 | − | 0.812371i | \(-0.698176\pi\) |
0.995104 | + | 0.0988287i | \(0.0315096\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −22.9144 | −1.16481 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.0603 | + | 17.4249i | 0.510075 | + | 0.883476i | 0.999932 | + | 0.0116730i | \(0.00371573\pi\) |
−0.489857 | + | 0.871803i | \(0.662951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.13262 | −0.461857 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.57211 | + | 2.72298i | 0.0793025 | + | 0.137356i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.00633 | − | 13.8674i | 0.401826 | − | 0.695983i | −0.592120 | − | 0.805850i | \(-0.701709\pi\) |
0.993946 | + | 0.109866i | \(0.0350423\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.82863 | + | 6.79304i | −0.0915460 | + | 0.340077i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.83602 | − | 11.8403i | 0.341375 | − | 0.591278i | −0.643313 | − | 0.765603i | \(-0.722441\pi\) |
0.984688 | + | 0.174324i | \(0.0557741\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.9728 | + | 19.0054i | 0.546593 | + | 0.946727i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.38123 | 0.266738 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.03518 | − | 5.25709i | −0.150080 | − | 0.259946i | 0.781177 | − | 0.624310i | \(-0.214620\pi\) |
−0.931257 | + | 0.364364i | \(0.881287\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 35.4923 | 1.75071 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.57932 | − | 4.46752i | 0.126920 | − | 0.219832i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.13735 | 0.447458 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.33985 | −0.309722 | −0.154861 | − | 0.987936i | \(-0.549493\pi\) | ||||
−0.154861 | + | 0.987936i | \(0.549493\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.52768 | − | 6.11011i | 0.171928 | − | 0.297789i | −0.767166 | − | 0.641449i | \(-0.778334\pi\) |
0.939094 | + | 0.343660i | \(0.111667\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.57043 | + | 16.5765i | −0.465330 | + | 0.805975i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.55820 | + | 6.16299i | 0.172194 | + | 0.298248i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.1333 | 0.489239 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.0390 | + | 22.5843i | 0.628069 | + | 1.08785i | 0.987939 | + | 0.154845i | \(0.0494877\pi\) |
−0.359870 | + | 0.933002i | \(0.617179\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.1278 | − | 29.6662i | −0.823109 | − | 1.42567i | −0.903356 | − | 0.428892i | \(-0.858904\pi\) |
0.0802463 | − | 0.996775i | \(-0.474429\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.44766 | − | 6.46262i | −0.308433 | − | 0.309149i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.13427 | + | 5.42872i | −0.149591 | + | 0.259099i | −0.931076 | − | 0.364825i | \(-0.881129\pi\) |
0.781485 | + | 0.623923i | \(0.214462\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.54701 | + | 16.5359i | 0.454620 | + | 0.787424i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.3447 | + | 28.3099i | 0.776561 | + | 1.34504i | 0.933913 | + | 0.357500i | \(0.116371\pi\) |
−0.157352 | + | 0.987543i | \(0.550296\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.32756 | + | 16.1558i | 0.441178 | + | 0.764143i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.0822 | −1.08932 | −0.544659 | − | 0.838658i | \(-0.683341\pi\) | ||||
−0.544659 | + | 0.838658i | \(0.683341\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.448025 | − | 0.776001i | 0.0210967 | − | 0.0365405i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.97713 | − | 3.42448i | 0.0928935 | − | 0.160896i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.9166 | 0.931661 | 0.465830 | − | 0.884874i | \(-0.345756\pi\) | ||||
0.465830 | + | 0.884874i | \(0.345756\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.471966 | − | 0.817468i | 0.0220295 | − | 0.0381562i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.2586 | + | 36.8209i | −0.990111 | + | 1.71492i | −0.373562 | + | 0.927605i | \(0.621864\pi\) |
−0.616548 | + | 0.787317i | \(0.711470\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.2843 | −1.26801 | −0.634005 | − | 0.773329i | \(-0.718590\pi\) | ||||
−0.634005 | + | 0.773329i | \(0.718590\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 39.5912 | 1.83206 | 0.916031 | − | 0.401107i | \(-0.131375\pi\) | ||||
0.916031 | + | 0.401107i | \(0.131375\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.52146 | − | 2.63525i | −0.0702547 | − | 0.121685i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.22696 | + | 5.58927i | 0.148691 | + | 0.257540i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.12022 | + | 12.3326i | −0.327388 | + | 0.567053i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.35415 | + | 5.80956i | −0.153576 | + | 0.266001i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.7954 | + | 23.8943i | 0.630326 | + | 1.09176i | 0.987485 | + | 0.157713i | \(0.0504121\pi\) |
−0.357159 | + | 0.934044i | \(0.616255\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.42665 | + | 5.93513i | 0.156242 | + | 0.270618i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.38005 | 0.153797 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.9289 | −1.35621 | −0.678104 | − | 0.734966i | \(-0.737198\pi\) | ||||
−0.678104 | + | 0.734966i | \(0.737198\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.0757 | − | 41.7004i | 1.08874 | − | 1.88576i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.23550 | + | 12.5323i | −0.326534 | + | 0.565573i | −0.981822 | − | 0.189806i | \(-0.939214\pi\) |
0.655288 | + | 0.755379i | \(0.272547\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.49996 | −0.382819 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.96433 | − | 3.40232i | 0.0881122 | − | 0.152615i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.06799 | − | 15.7062i | 0.405939 | − | 0.703107i | −0.588491 | − | 0.808504i | \(-0.700278\pi\) |
0.994430 | + | 0.105396i | \(0.0336111\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.218111 | 0.00974449 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.48833 | − | 14.7022i | −0.378476 | − | 0.655539i | 0.612365 | − | 0.790575i | \(-0.290218\pi\) |
−0.990841 | + | 0.135036i | \(0.956885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.35046 | − | 16.1955i | −0.415269 | − | 0.719266i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.6888 | + | 28.9058i | 0.739717 | + | 1.28123i | 0.952623 | + | 0.304155i | \(0.0983739\pi\) |
−0.212906 | + | 0.977073i | \(0.568293\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.86382 | − | 3.22824i | 0.0824507 | − | 0.142809i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.911684 | − | 0.243153i | 0.0402518 | − | 0.0107355i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.94765 | + | 10.3016i | 0.261577 | + | 0.453065i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.2473 | − | 33.3372i | −0.844861 | − | 1.46334i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.09359 | 0.0479110 | 0.0239555 | − | 0.999713i | \(-0.492374\pi\) | ||||
0.0239555 | + | 0.999713i | \(0.492374\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.02994 | + | 3.51597i | 0.0887633 | + | 0.153742i | 0.906989 | − | 0.421155i | \(-0.138375\pi\) |
−0.818225 | + | 0.574898i | \(0.805042\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.7682 | + | 35.9715i | −0.904676 | + | 1.56695i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.30690 | − | 16.1200i | 0.404648 | − | 0.700871i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.6216 | 0.981694 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.14117 | 0.0494295 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.4171 | + | 28.4352i | −0.708450 | + | 1.22707i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.8662 | 0.511114 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.65097 | − | 11.5198i | −0.285947 | − | 0.495275i | 0.686891 | − | 0.726760i | \(-0.258975\pi\) |
−0.972838 | + | 0.231485i | \(0.925642\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.2715 | 0.998675 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.1362 | + | 29.6808i | 0.732692 | + | 1.26906i | 0.955729 | + | 0.294250i | \(0.0950698\pi\) |
−0.223036 | + | 0.974810i | \(0.571597\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.6034 | + | 27.0258i | −0.665936 | + | 1.15343i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00100 | − | 6.01493i | −0.255651 | − | 0.256244i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.99019 | + | 3.44712i | −0.0846316 | + | 0.146586i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.3255 | + | 35.2047i | 0.861217 | + | 1.49167i | 0.870755 | + | 0.491717i | \(0.163631\pi\) |
−0.00953795 | + | 0.999955i | \(0.503036\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.1360 | −0.767071 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.58963 | + | 16.6097i | 0.404874 | + | 0.701263i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.7137 | −0.872980 | −0.436490 | − | 0.899709i | \(-0.643779\pi\) | ||||
−0.436490 | + | 0.899709i | \(0.643779\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.07321 | + | 5.32295i | −0.129063 | + | 0.223543i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.0551 | 1.42766 | 0.713831 | − | 0.700318i | \(-0.246958\pi\) | ||||
0.713831 | + | 0.700318i | \(0.246958\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.5413 | 0.775929 | 0.387965 | − | 0.921674i | \(-0.373178\pi\) | ||||
0.387965 | + | 0.921674i | \(0.373178\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.7015 | − | 56.6406i | 1.36612 | − | 2.36620i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.96818 | −0.123567 | −0.0617834 | − | 0.998090i | \(-0.519679\pi\) | ||||
−0.0617834 | + | 0.998090i | \(0.519679\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.7496 | − | 48.0638i | −1.15324 | − | 1.99746i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.11627 | −0.170772 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.08448 | + | 3.61042i | 0.0863302 | + | 0.149528i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.0138 | + | 32.9328i | −0.784781 | + | 1.35928i | 0.144348 | + | 0.989527i | \(0.453892\pi\) |
−0.929130 | + | 0.369754i | \(0.879442\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.1174 | + | 10.6996i | −1.65301 | + | 0.440869i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.6634 | + | 21.9336i | −0.520901 | + | 0.902227i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.9428 | − | 38.0060i | −0.901081 | − | 1.56072i | −0.826093 | − | 0.563533i | \(-0.809442\pi\) |
−0.0749876 | − | 0.997184i | \(-0.523892\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.80287 | −0.155641 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.4883 | + | 30.2906i | 0.714552 | + | 1.23764i | 0.963132 | + | 0.269029i | \(0.0867026\pi\) |
−0.248581 | + | 0.968611i | \(0.579964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.9988 | 1.30526 | 0.652630 | − | 0.757677i | \(-0.273666\pi\) | ||||
0.652630 | + | 0.757677i | \(0.273666\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.67190 | − | 11.5561i | 0.271701 | − | 0.470599i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.10357 | −0.0853814 | −0.0426907 | − | 0.999088i | \(-0.513593\pi\) | ||||
−0.0426907 | + | 0.999088i | \(0.513593\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.14589 | 0.127478 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.57467 | + | 13.1197i | −0.306438 | + | 0.530767i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.4127 | + | 30.1598i | −0.703294 | + | 1.21814i | 0.264010 | + | 0.964520i | \(0.414955\pi\) |
−0.967304 | + | 0.253621i | \(0.918378\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.16726 | − | 15.8782i | −0.369060 | − | 0.639231i | 0.620359 | − | 0.784318i | \(-0.286987\pi\) |
−0.989419 | + | 0.145087i | \(0.953654\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.4325 | 1.30357 | 0.651786 | − | 0.758403i | \(-0.274020\pi\) | ||||
0.651786 | + | 0.758403i | \(0.274020\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.226675 | − | 0.392612i | −0.00909615 | − | 0.0157550i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.41458 | − | 7.64628i | −0.176866 | − | 0.306342i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.98342 | + | 18.5125i | −0.199019 | + | 0.739319i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.48562 | + | 11.2334i | −0.258598 | + | 0.447906i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.25551 | − | 12.5669i | −0.288837 | − | 0.500281i | 0.684695 | − | 0.728830i | \(-0.259935\pi\) |
−0.973532 | + | 0.228549i | \(0.926602\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.3464 | + | 43.9012i | 1.00743 | + | 1.74492i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.55614 | + | 13.0876i | 0.299385 | + | 0.518550i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.2279 | 0.681525 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.8849 | − | 24.0494i | 0.548421 | − | 0.949892i | −0.449962 | − | 0.893048i | \(-0.648563\pi\) |
0.998383 | − | 0.0568449i | \(-0.0181041\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.61539 | + | 9.72615i | −0.221450 | + | 0.383562i | −0.955248 | − | 0.295805i | \(-0.904412\pi\) |
0.733799 | + | 0.679367i | \(0.237745\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.00223 | −0.0787157 | −0.0393578 | − | 0.999225i | \(-0.512531\pi\) | ||||
−0.0393578 | + | 0.999225i | \(0.512531\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.02923 | − | 12.1750i | 0.275921 | − | 0.477910i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.68645 | − | 13.3133i | 0.301256 | − | 0.521790i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.23945 | 0.126770 | 0.0633848 | − | 0.997989i | \(-0.479810\pi\) | ||||
0.0633848 | + | 0.997989i | \(0.479810\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.3464 | 0.637734 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.14745 | + | 5.45154i | 0.122607 | + | 0.212362i | 0.920795 | − | 0.390047i | \(-0.127541\pi\) |
−0.798188 | + | 0.602409i | \(0.794208\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.196536 | − | 0.340410i | −0.00764435 | − | 0.0132404i | 0.862178 | − | 0.506606i | \(-0.169100\pi\) |
−0.869822 | + | 0.493365i | \(0.835767\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.2129 | + | 21.1534i | −0.474311 | + | 0.821530i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.04117 | + | 3.53542i | −0.0790346 | + | 0.136892i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.4381 | − | 47.5242i | −1.06082 | − | 1.83739i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.69690 | + | 16.7955i | 0.374345 | + | 0.648384i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.1041 | 1.66154 | 0.830770 | − | 0.556616i | \(-0.187900\pi\) | ||||
0.830770 | + | 0.556616i | \(0.187900\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.3727 | 0.475522 | 0.237761 | − | 0.971324i | \(-0.423587\pi\) | ||||
0.237761 | + | 0.971324i | \(0.423587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.37532 | − | 5.84622i | 0.129533 | − | 0.224357i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.8808 | − | 24.0422i | 0.531913 | − | 0.921300i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.8415 | −1.25664 | −0.628322 | − | 0.777954i | \(-0.716258\pi\) | ||||
−0.628322 | + | 0.777954i | \(0.716258\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.2356 | + | 33.3171i | −0.733885 | + | 1.27113i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.65470 | + | 4.59807i | −0.101136 | + | 0.175172i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.6704 | −0.634171 | −0.317085 | − | 0.948397i | \(-0.602704\pi\) | ||||
−0.317085 | + | 0.948397i | \(0.602704\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.74786 | − | 3.02739i | −0.0663959 | − | 0.115001i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.07995 | + | 1.87052i | 0.0409059 | + | 0.0708510i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.3699 | + | 28.3536i | 0.619168 | + | 1.07243i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.9399 | + | 27.6087i | −0.602041 | + | 1.04277i | 0.390470 | + | 0.920616i | \(0.372312\pi\) |
−0.992512 | + | 0.122151i | \(0.961021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.5281 | + | 3.34134i | −0.472506 | + | 0.126021i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.97047 | + | 8.60911i | 0.186934 | + | 0.323779i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.99202 | + | 5.18233i | 0.112368 | + | 0.194626i | 0.916724 | − | 0.399520i | \(-0.130823\pi\) |
−0.804357 | + | 0.594147i | \(0.797490\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.4547 | −0.654603 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.97451 | + | 17.2764i | 0.373548 | + | 0.647004i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.0009 | − | 41.5708i | 0.896331 | − | 1.55249i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.345920 | − | 0.599151i | 0.0129006 | − | 0.0223446i | −0.859503 | − | 0.511131i | \(-0.829227\pi\) |
0.872404 | + | 0.488786i | \(0.162560\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0484 | −0.448706 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.1187 | 0.487889 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.0511 | − | 19.1410i | 0.409862 | − | 0.709902i | −0.585012 | − | 0.811025i | \(-0.698910\pi\) |
0.994874 | + | 0.101123i | \(0.0322435\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.3743 | −0.939789 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.1630 | − | 29.7272i | −0.634796 | − | 1.09950i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.0945 | −0.705271 | −0.352635 | − | 0.935761i | \(-0.614714\pi\) | ||||
−0.352635 | + | 0.935761i | \(0.614714\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.14633 | − | 7.18165i | −0.152732 | − | 0.264540i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.05045 | + | 10.4797i | −0.222569 | + | 0.385501i | −0.955587 | − | 0.294708i | \(-0.904778\pi\) |
0.733018 | + | 0.680209i | \(0.238111\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.5914 | + | 6.29200i | −0.866652 | + | 0.231142i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.89364 | − | 13.6722i | 0.289590 | − | 0.501584i | −0.684122 | − | 0.729368i | \(-0.739814\pi\) |
0.973712 | + | 0.227783i | \(0.0731478\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.02531 | − | 15.6323i | −0.330219 | − | 0.571956i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.27341 | −0.338843 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.5848 | − | 30.4578i | −0.641678 | − | 1.11142i | −0.985058 | − | 0.172223i | \(-0.944905\pi\) |
0.343380 | − | 0.939197i | \(-0.388428\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.68664 | 0.316559 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.35917 | − | 12.7465i | 0.267473 | − | 0.463278i | −0.700735 | − | 0.713421i | \(-0.747145\pi\) |
0.968209 | + | 0.250144i | \(0.0804779\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.21138 | 0.334352 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.9486 | −1.44814 | −0.724068 | − | 0.689728i | \(-0.757730\pi\) | ||||
−0.724068 | + | 0.689728i | \(0.757730\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.11074 | + | 10.5841i | −0.221224 | + | 0.383170i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.9042 | 0.646485 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.9729 | − | 43.2544i | −0.900547 | − | 1.55979i | −0.826786 | − | 0.562516i | \(-0.809833\pi\) |
−0.0737605 | − | 0.997276i | \(-0.523500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45.0583 | −1.62273 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.6269 | + | 20.1384i | 0.418190 | + | 0.724327i | 0.995757 | − | 0.0920165i | \(-0.0293312\pi\) |
−0.577567 | + | 0.816343i | \(0.695998\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.40037 | − | 4.15757i | 0.0861129 | − | 0.149152i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.561213 | + | 2.08481i | −0.0201075 | + | 0.0746960i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.35324 | − | 9.27208i | 0.191554 | − | 0.331781i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.210972 | − | 0.365414i | −0.00753952 | − | 0.0130588i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.5711 | 0.697636 | 0.348818 | − | 0.937191i | \(-0.386583\pi\) | ||||
0.348818 | + | 0.937191i | \(0.386583\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.0628 | + | 22.6254i | 0.465048 | + | 0.805486i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.23201 | 0.257141 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.3495 | + | 21.3900i | −0.438545 | + | 0.759582i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −47.6782 | −1.68885 | −0.844424 | − | 0.535676i | \(-0.820057\pi\) | ||||
−0.844424 | + | 0.535676i | \(0.820057\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.6732 | −1.01438 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.3587 | − | 33.5303i | 0.684007 | − | 1.18474i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.07933 | − | 8.79767i | 0.179246 | − | 0.310463i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.7097 | − | 25.4780i | −0.517806 | − | 0.896867i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.4485 | −0.859565 | −0.429782 | − | 0.902933i | \(-0.641410\pi\) | ||||
−0.429782 | + | 0.902933i | \(0.641410\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.38004 | + | 9.31850i | 0.188919 | + | 0.327217i | 0.944890 | − | 0.327388i | \(-0.106168\pi\) |
−0.755971 | + | 0.654605i | \(0.772835\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.7193 | − | 39.3510i | −0.796802 | − | 1.38010i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.91906 | − | 33.1327i | 0.312038 | − | 1.15917i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.22600 | − | 3.85555i | 0.0777828 | − | 0.134724i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.60434 | + | 6.24289i | 0.125792 | + | 0.217879i | 0.922042 | − | 0.387089i | \(-0.126519\pi\) |
−0.796250 | + | 0.604968i | \(0.793186\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.87075 | − | 6.70433i | −0.134926 | − | 0.233698i | 0.790643 | − | 0.612277i | \(-0.209746\pi\) |
−0.925569 | + | 0.378579i | \(0.876413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.3140 | − | 23.0605i | −0.462972 | − | 0.801891i | 0.536136 | − | 0.844132i | \(-0.319884\pi\) |
−0.999107 | + | 0.0422411i | \(0.986550\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.1093 | −0.420572 | −0.210286 | − | 0.977640i | \(-0.567439\pi\) | ||||
−0.210286 | + | 0.977640i | \(0.567439\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.23201 | + | 12.5262i | −0.250876 | + | 0.434530i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.3015 | + | 24.7709i | −0.495518 | + | 0.858262i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.06189 | −0.0712695 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.20591 | − | 2.08869i | 0.0416325 | − | 0.0721096i | −0.844458 | − | 0.535621i | \(-0.820077\pi\) |
0.886091 | + | 0.463512i | \(0.153411\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.6002 | − | 21.8242i | 0.434491 | − | 0.752560i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.7386 | 1.47199 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.12954 | 0.176253 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 38.1843 | + | 66.1371i | 1.31048 | + | 2.26982i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.11490 | + | 5.39517i | 0.106777 | + | 0.184944i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.8401 | + | 23.9717i | −0.473875 | + | 0.820775i | −0.999553 | − | 0.0299085i | \(-0.990478\pi\) |
0.525678 | + | 0.850684i | \(0.323812\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.20245 | − | 14.2071i | 0.280190 | − | 0.485304i | −0.691241 | − | 0.722624i | \(-0.742936\pi\) |
0.971431 | + | 0.237320i | \(0.0762690\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.4715 | + | 30.2616i | 0.596121 | + | 1.03251i | 0.993388 | + | 0.114808i | \(0.0366254\pi\) |
−0.397267 | + | 0.917703i | \(0.630041\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.399695 | − | 0.692293i | −0.0136216 | − | 0.0235933i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.6243 | 0.633979 | 0.316990 | − | 0.948429i | \(-0.397328\pi\) | ||||
0.316990 | + | 0.948429i | \(0.397328\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.89962 | −0.166400 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.42372 | + | 9.39416i | −0.183987 | + | 0.318675i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.28058 | − | 9.14624i | 0.178926 | − | 0.309908i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.6028 | 1.00190 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.1893 | − | 26.3087i | 0.512907 | − | 0.888381i | −0.486981 | − | 0.873413i | \(-0.661902\pi\) |
0.999888 | − | 0.0149683i | \(-0.00476473\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 34.2119 | − | 59.2567i | 1.15394 | − | 1.99868i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.3772 | −0.888670 | −0.444335 | − | 0.895861i | \(-0.646560\pi\) | ||||
−0.444335 | + | 0.895861i | \(0.646560\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.5598 | − | 25.2183i | −0.489977 | − | 0.848664i | 0.509957 | − | 0.860200i | \(-0.329661\pi\) |
−0.999933 | + | 0.0115356i | \(0.996328\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.0100 | − | 17.3379i | −0.336104 | − | 0.582148i | 0.647593 | − | 0.761987i | \(-0.275776\pi\) |
−0.983696 | + | 0.179838i | \(0.942443\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.09704 | + | 1.90012i | 0.0367935 | + | 0.0637281i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.37517 | + | 14.5062i | −0.280579 | + | 0.485977i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.2433 | − | 20.2903i | −0.677418 | − | 0.678990i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.86560 | + | 10.1595i | 0.195847 | + | 0.339217i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.28352 | + | 16.0795i | 0.309623 | + | 0.536283i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0491 | −0.334784 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.35215 | + | 11.0022i | 0.211386 | + | 0.366132i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.75370 | − | 6.50159i | 0.124639 | − | 0.215882i | −0.796952 | − | 0.604042i | \(-0.793556\pi\) |
0.921592 | + | 0.388160i | \(0.126889\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21.7964 | + | 37.7525i | −0.722942 | + | 1.25217i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.3882 | 1.27186 | 0.635929 | − | 0.771748i | \(-0.280617\pi\) | ||||
0.635929 | + | 0.771748i | \(0.280617\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.2178 | −0.371254 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.429243 | − | 0.743471i | 0.0141749 | − | 0.0245516i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.8811 | −1.24958 | −0.624791 | − | 0.780792i | \(-0.714816\pi\) | ||||
−0.624791 | + | 0.780792i | \(0.714816\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.7883 | − | 56.7910i | −1.08041 | − | 1.87133i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.6353 | 0.448811 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −26.4172 | − | 45.7560i | −0.867655 | − | 1.50282i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.96821 | − | 10.3372i | 0.195811 | − | 0.339154i | −0.751355 | − | 0.659898i | \(-0.770600\pi\) |
0.947166 | + | 0.320744i | \(0.103933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.6258 | + | 7.36802i | −0.905401 | + | 0.241477i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.07473 | + | 10.5217i | −0.198878 | + | 0.344466i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.77228 | − | 11.7299i | −0.221241 | − | 0.383200i | 0.733944 | − | 0.679210i | \(-0.237677\pi\) |
−0.955185 | + | 0.296010i | \(0.904344\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −63.5824 | −2.07493 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.04614 | − | 12.2043i | −0.229698 | − | 0.397848i | 0.728021 | − | 0.685555i | \(-0.240440\pi\) |
−0.957718 | + | 0.287707i | \(0.907107\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.03735 | 0.0337807 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.53567 | + | 9.58806i | −0.179885 | + | 0.311570i | −0.941841 | − | 0.336059i | \(-0.890906\pi\) |
0.761956 | + | 0.647629i | \(0.224239\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.9376 | 0.419973 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −63.2539 | −2.05115 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.69507 | − | 6.40004i | 0.119695 | − | 0.207318i | −0.799952 | − | 0.600064i | \(-0.795142\pi\) |
0.919647 | + | 0.392747i | \(0.128475\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.57326 | 0.277134 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.84534 | − | 8.39238i | −0.156464 | − | 0.271004i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 59.7307 | 1.92680 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.3328 | − | 35.2174i | −0.655215 | − | 1.13487i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.760861 | + | 1.31785i | −0.0244676 | + | 0.0423792i | −0.878000 | − | 0.478661i | \(-0.841122\pi\) |
0.853532 | + | 0.521040i | \(0.174456\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32.6391 | − | 32.7149i | −1.04852 | − | 1.05095i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.2897 | − | 47.2671i | 0.875768 | − | 1.51687i | 0.0198254 | − | 0.999803i | \(-0.493689\pi\) |
0.855942 | − | 0.517071i | \(-0.172978\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.24741 | − | 2.16058i | −0.0399902 | − | 0.0692651i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.0130 | −0.416321 | −0.208161 | − | 0.978095i | \(-0.566748\pi\) | ||||
−0.208161 | + | 0.978095i | \(0.566748\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0307 | − | 20.8378i | −0.384503 | − | 0.665979i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −53.5934 | −1.71111 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.1709 | + | 17.6166i | −0.324402 | + | 0.561882i | −0.981391 | − | 0.192019i | \(-0.938497\pi\) |
0.656989 | + | 0.753900i | \(0.271830\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.6121 | 0.337788 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.4860 | −0.524225 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.9449 | + | 29.3495i | −0.538274 | + | 0.932318i | 0.460723 | + | 0.887544i | \(0.347590\pi\) |
−0.998997 | + | 0.0447741i | \(0.985743\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.69341 | − | 16.7895i | 0.307611 | − | 0.532798i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.76185 | + | 3.05162i | 0.0557985 | + | 0.0966458i | 0.892575 | − | 0.450898i | \(-0.148896\pi\) |
−0.836777 | + | 0.547544i | \(0.815563\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.643901 | −0.0203721 |
(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 | 1900.2.i.g.201.9 | 20 | ||
5.2 | odd | 4 | 380.2.r.a.49.2 | ✓ | 20 | ||
5.3 | odd | 4 | 380.2.r.a.49.9 | yes | 20 | ||
5.4 | even | 2 | inner | 1900.2.i.g.201.2 | 20 | ||
15.2 | even | 4 | 3420.2.bj.c.1189.7 | 20 | |||
15.8 | even | 4 | 3420.2.bj.c.1189.1 | 20 | |||
19.7 | even | 3 | inner | 1900.2.i.g.501.9 | 20 | ||
95.7 | odd | 12 | 380.2.r.a.349.9 | yes | 20 | ||
95.64 | even | 6 | inner | 1900.2.i.g.501.2 | 20 | ||
95.83 | odd | 12 | 380.2.r.a.349.2 | yes | 20 | ||
285.83 | even | 12 | 3420.2.bj.c.2629.7 | 20 | |||
285.197 | even | 12 | 3420.2.bj.c.2629.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.r.a.49.2 | ✓ | 20 | 5.2 | odd | 4 | ||
380.2.r.a.49.9 | yes | 20 | 5.3 | odd | 4 | ||
380.2.r.a.349.2 | yes | 20 | 95.83 | odd | 12 | ||
380.2.r.a.349.9 | yes | 20 | 95.7 | odd | 12 | ||
1900.2.i.g.201.2 | 20 | 5.4 | even | 2 | inner | ||
1900.2.i.g.201.9 | 20 | 1.1 | even | 1 | trivial | ||
1900.2.i.g.501.2 | 20 | 95.64 | even | 6 | inner | ||
1900.2.i.g.501.9 | 20 | 19.7 | even | 3 | inner | ||
3420.2.bj.c.1189.1 | 20 | 15.8 | even | 4 | |||
3420.2.bj.c.1189.7 | 20 | 15.2 | even | 4 | |||
3420.2.bj.c.2629.1 | 20 | 285.197 | even | 12 | |||
3420.2.bj.c.2629.7 | 20 | 285.83 | even | 12 |