Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(1519,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1520.1519");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.g (of order \(2\), degree \(1\), 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: | \(12.1372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 20x^{14} + 271x^{12} - 2000x^{10} + 10645x^{8} - 29570x^{6} + 58816x^{4} - 56840x^{2} + 38416 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1519.2 | ||
Root | \(-2.56586 - 1.48140i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.1519 |
Dual form | 1520.2.g.g.1519.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.96281i | − | 1.71058i | −0.518152 | − | 0.855288i | \(-0.673380\pi\) | ||
0.518152 | − | 0.855288i | \(-0.326620\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.602114 | + | 2.15348i | −0.269274 | + | 0.963064i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.562696 | 0.212679 | 0.106339 | − | 0.994330i | \(-0.466087\pi\) | ||||
0.106339 | + | 0.994330i | \(0.466087\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.77822 | −1.92607 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.19004i | − | 1.26334i | −0.775236 | − | 0.631672i | \(-0.782369\pi\) | ||
0.775236 | − | 0.631672i | \(-0.217631\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500297 | 0.138757 | 0.0693787 | − | 0.997590i | \(-0.477898\pi\) | ||||
0.0693787 | + | 0.997590i | \(0.477898\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.38033 | + | 1.78395i | 1.64739 | + | 0.460613i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.59328i | − | 0.628962i | −0.949264 | − | 0.314481i | \(-0.898170\pi\) | ||
0.949264 | − | 0.314481i | \(-0.101830\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.27492 | − | 2.87662i | 0.751318 | − | 0.659941i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.66716i | − | 0.363804i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.09416 | −1.06221 | −0.531103 | − | 0.847307i | \(-0.678222\pi\) | ||||
−0.531103 | + | 0.847307i | \(0.678222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.27492 | − | 2.59328i | −0.854983 | − | 0.518655i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.23131i | 1.58412i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.71292i | 1.24656i | 0.781999 | + | 0.623279i | \(0.214200\pi\) | ||||
−0.781999 | + | 0.623279i | \(0.785800\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.79577 | 0.861346 | 0.430673 | − | 0.902508i | \(-0.358276\pi\) | ||||
0.430673 | + | 0.902508i | \(0.358276\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.4143 | −2.16105 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.338807 | + | 1.21175i | −0.0572688 | + | 0.204823i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.89142 | −0.639746 | −0.319873 | − | 0.947461i | \(-0.603640\pi\) | ||||
−0.319873 | + | 0.947461i | \(0.603640\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.48228i | − | 0.237355i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.6408i | − | 1.81799i | −0.416804 | − | 0.908997i | \(-0.636850\pi\) | ||
0.416804 | − | 0.908997i | \(-0.363150\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.46045 | −1.29021 | −0.645104 | − | 0.764095i | \(-0.723186\pi\) | ||||
−0.645104 | + | 0.764095i | \(0.723186\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.47915 | − | 12.4432i | 0.518640 | − | 1.85493i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.2635 | −1.49708 | −0.748540 | − | 0.663090i | \(-0.769245\pi\) | ||||
−0.748540 | + | 0.663090i | \(0.769245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.68337 | −0.954768 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.68337 | −1.07589 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.73420 | −0.787653 | −0.393827 | − | 0.919185i | \(-0.628849\pi\) | ||||
−0.393827 | + | 0.919185i | \(0.628849\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.02315 | + | 2.52288i | 1.21668 | + | 0.340185i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.52285 | − | 9.70294i | −1.12888 | − | 1.28519i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.83135 | 0.889366 | 0.444683 | − | 0.895688i | \(-0.353316\pi\) | ||||
0.444683 | + | 0.895688i | \(0.353316\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.25736 | 0.929210 | 0.464605 | − | 0.885518i | \(-0.346196\pi\) | ||||
0.464605 | + | 0.885518i | \(0.346196\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.25138 | −0.409635 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.301236 | + | 1.07738i | −0.0373637 | + | 0.133632i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.43443i | − | 0.541752i | −0.962614 | − | 0.270876i | \(-0.912687\pi\) | ||
0.962614 | − | 0.270876i | \(-0.0873134\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.0930i | 1.81698i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.79577 | −0.569153 | −0.284577 | − | 0.958653i | \(-0.591853\pi\) | ||||
−0.284577 | + | 0.958653i | \(0.591853\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4420i | 1.22214i | 0.791575 | + | 0.611072i | \(0.209261\pi\) | ||||
−0.791575 | + | 0.611072i | \(0.790739\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.68337 | + | 12.6657i | −0.887200 | + | 1.46251i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.35772i | − | 0.268687i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.96489 | −0.896120 | −0.448060 | − | 0.894003i | \(-0.647885\pi\) | ||||
−0.448060 | + | 0.894003i | \(0.647885\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.05313 | 0.783681 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.12599 | −0.233357 | −0.116679 | − | 0.993170i | \(-0.537225\pi\) | ||||
−0.116679 | + | 0.993170i | \(0.537225\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.58456 | + | 1.56145i | 0.605730 | + | 0.169363i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19.8891 | 2.13233 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.67627i | − | 0.919683i | −0.888001 | − | 0.459841i | \(-0.847906\pi\) | ||
0.888001 | − | 0.459841i | \(-0.152094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.281515 | 0.0295108 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 14.2089i | − | 1.47340i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.22285 | + | 8.78451i | 0.433255 | + | 0.901271i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.1549 | 1.43721 | 0.718605 | − | 0.695418i | \(-0.244781\pi\) | ||||
0.718605 | + | 0.695418i | \(0.244781\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 24.2110i | 2.43329i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.29247 | −0.327613 | −0.163807 | − | 0.986492i | \(-0.552377\pi\) | ||||
−0.163807 | + | 0.986492i | \(0.552377\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.7620i | − | 1.45454i | −0.686349 | − | 0.727272i | \(-0.740788\pi\) | ||
0.686349 | − | 0.727272i | \(-0.259212\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.59018 | + | 1.00382i | 0.350366 | + | 0.0979627i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.9715i | 1.44734i | 0.690144 | + | 0.723672i | \(0.257547\pi\) | ||||
−0.690144 | + | 0.723672i | \(0.742453\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.74835i | − | 0.359027i | −0.983755 | − | 0.179514i | \(-0.942548\pi\) | ||
0.983755 | − | 0.179514i | \(-0.0574524\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.5295i | 1.09433i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.52285 | −0.801763 | −0.400881 | − | 0.916130i | \(-0.631296\pi\) | ||||
−0.400881 | + | 0.916130i | \(0.631296\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.06726 | − | 10.9701i | 0.286024 | − | 1.02297i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.89083 | −0.267257 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.45923i | − | 0.133767i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.55643 | −0.596039 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −34.4895 | −3.10982 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.15855 | − | 7.64448i | 0.729723 | − | 0.683743i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.395651i | 0.0351083i | 0.999846 | + | 0.0175542i | \(0.00558795\pi\) | ||||
−0.999846 | + | 0.0175542i | \(0.994412\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 25.0667i | 2.20700i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.79842i | − | 0.593980i | −0.954881 | − | 0.296990i | \(-0.904017\pi\) | ||
0.954881 | − | 0.296990i | \(-0.0959829\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.84278 | − | 1.61866i | 0.159789 | − | 0.140356i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.7259 | − | 4.95619i | −1.52561 | − | 0.426561i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.834074i | 0.0712598i | 0.999365 | + | 0.0356299i | \(0.0113437\pi\) | ||||
−0.999365 | + | 0.0356299i | \(0.988656\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.8211i | 1.00265i | 0.865258 | + | 0.501327i | \(0.167155\pi\) | ||||
−0.865258 | + | 0.501327i | \(0.832845\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 30.4086i | 2.56087i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2.09627i | − | 0.175299i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.4561 | − | 4.04194i | −1.20052 | − | 0.335665i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.8015i | 1.63320i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.63808 | 0.543813 | 0.271906 | − | 0.962324i | \(-0.412346\pi\) | ||||
0.271906 | + | 0.962324i | \(0.412346\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.3667 | 1.25053 | 0.625264 | − | 0.780413i | \(-0.284991\pi\) | ||||
0.625264 | + | 0.780413i | \(0.284991\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.9845i | 1.21143i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.88760 | + | 10.3276i | −0.231938 | + | 0.829531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.42387i | 0.672298i | 0.941809 | + | 0.336149i | \(0.109125\pi\) | ||||
−0.941809 | + | 0.336149i | \(0.890875\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.9893i | 1.34734i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.86646 | −0.225909 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.1919 | 1.03327 | 0.516633 | − | 0.856207i | \(-0.327185\pi\) | ||||
0.516633 | + | 0.856207i | \(0.327185\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.47481 | − | 26.7338i | 0.581913 | − | 2.08123i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.57495i | − | 0.663550i | −0.943359 | − | 0.331775i | \(-0.892353\pi\) | ||
0.943359 | − | 0.331775i | \(-0.107647\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7497 | −0.980746 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.9232 | + | 16.6217i | −1.44709 | + | 1.27109i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.3888 | −1.47410 | −0.737051 | − | 0.675837i | \(-0.763782\pi\) | ||||
−0.737051 | + | 0.675837i | \(0.763782\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.40548 | − | 1.45923i | −0.181837 | − | 0.110307i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 20.2400i | − | 1.52133i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.1063 | 1.80179 | 0.900893 | − | 0.434040i | \(-0.142912\pi\) | ||||
0.900893 | + | 0.434040i | \(0.142912\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.74983i | 0.650370i | 0.945650 | + | 0.325185i | \(0.105427\pi\) | ||||
−0.945650 | + | 0.325185i | \(0.894573\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 21.5022i | − | 1.58948i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.34308 | − | 8.38008i | 0.172267 | − | 0.616116i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.8659 | −0.794596 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.63172i | 0.336908i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 12.3043i | − | 0.890311i | −0.895453 | − | 0.445155i | \(-0.853148\pi\) | ||
0.895453 | − | 0.445155i | \(-0.146852\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.3598 | 1.10562 | 0.552812 | − | 0.833306i | \(-0.313555\pi\) | ||||
0.552812 | + | 0.833306i | \(0.313555\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.19206 | + | 0.892504i | 0.228588 | + | 0.0639135i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.30945i | − | 0.592024i | −0.955184 | − | 0.296012i | \(-0.904343\pi\) | ||
0.955184 | − | 0.296012i | \(-0.0956568\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 21.3137i | − | 1.51089i | −0.655212 | − | 0.755445i | \(-0.727421\pi\) | ||
0.655212 | − | 0.755445i | \(-0.272579\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.1384 | −0.926709 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.77733i | 0.265117i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.0683 | + | 7.00911i | 1.75084 | + | 0.489538i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 29.4351 | 2.04588 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0531 | − | 13.7220i | −0.833733 | − | 0.949173i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.7251 | 0.738345 | 0.369173 | − | 0.929361i | \(-0.379641\pi\) | ||||
0.369173 | + | 0.929361i | \(0.379641\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.2089i | 0.973580i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.09416 | − | 18.2194i | 0.347419 | − | 1.24255i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.69856 | 0.183190 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 30.9376 | 2.09057 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.29741i | − | 0.0872732i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.74014i | − | 0.451353i | −0.974202 | − | 0.225676i | \(-0.927541\pi\) | ||
0.974202 | − | 0.225676i | \(-0.0724592\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 24.7014 | + | 14.9845i | 1.64676 | + | 0.998967i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 28.5558i | − | 1.89531i | −0.319293 | − | 0.947656i | \(-0.603445\pi\) | ||
0.319293 | − | 0.947656i | \(-0.396555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.6030 | −0.700664 | −0.350332 | − | 0.936626i | \(-0.613931\pi\) | ||||
−0.350332 | + | 0.936626i | \(0.613931\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.98546 | −0.459609 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 2.71441i | − | 0.177827i | −0.996039 | − | 0.0889136i | \(-0.971660\pi\) | ||
0.996039 | − | 0.0889136i | \(-0.0283395\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.17977 | − | 22.1021i | 0.403124 | − | 1.44178i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.5984i | 1.53288i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.6023i | − | 1.26797i | −0.773347 | − | 0.633983i | \(-0.781419\pi\) | ||
0.773347 | − | 0.633983i | \(-0.218581\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 23.8871i | − | 1.53870i | −0.638825 | − | 0.769352i | \(-0.720579\pi\) | ||
0.638825 | − | 0.769352i | \(-0.279421\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.79688i | 0.243570i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.02415 | − | 14.3925i | 0.257094 | − | 0.919502i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.63843 | − | 1.43916i | 0.104251 | − | 0.0915717i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.29888i | 0.399175i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4.57367i | − | 0.288688i | −0.989528 | − | 0.144344i | \(-0.953893\pi\) | ||
0.989528 | − | 0.144344i | \(-0.0461071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.3447i | 1.34193i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.62627 | − | 16.5460i | 0.289708 | − | 1.03615i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.28776 | 0.0803282 | 0.0401641 | − | 0.999193i | \(-0.487212\pi\) | ||||
0.0401641 | + | 0.999193i | \(0.487212\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.18969 | −0.136060 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 38.7887i | − | 2.40096i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.921042 | 0.0567939 | 0.0283969 | − | 0.999597i | \(-0.490960\pi\) | ||||
0.0283969 | + | 0.999597i | \(0.490960\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.45264 | − | 12.3485i | 0.212094 | − | 0.758560i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −25.7061 | −1.57319 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.883370i | 0.0538600i | 0.999637 | + | 0.0269300i | \(0.00857312\pi\) | ||||
−0.999637 | + | 0.0269300i | \(0.991427\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.61207i | 0.0979263i | 0.998801 | + | 0.0489631i | \(0.0155917\pi\) | ||||
−0.998801 | + | 0.0489631i | \(0.984408\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 0.834074i | − | 0.0504805i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.8659 | + | 17.9121i | −0.655240 | + | 1.08014i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.1213i | 1.44931i | 0.689112 | + | 0.724655i | \(0.258001\pi\) | ||||
−0.689112 | + | 0.724655i | \(0.741999\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −27.7110 | −1.65901 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.1375i | 1.14165i | 0.821072 | + | 0.570825i | \(0.193377\pi\) | ||||
−0.821072 | + | 0.570825i | \(0.806623\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.2965 | 1.14706 | 0.573529 | − | 0.819186i | \(-0.305574\pi\) | ||||
0.573529 | + | 0.819186i | \(0.305574\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 26.0268 | − | 12.5115i | 1.54169 | − | 0.741116i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 6.55025i | − | 0.386649i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.2749 | 0.604407 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 41.9382i | − | 2.45846i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.3572 | 1.65665 | 0.828323 | − | 0.560251i | \(-0.189295\pi\) | ||||
0.828323 | + | 0.560251i | \(0.189295\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.11325 | + | 14.7111i | −0.239483 | + | 0.856516i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 34.4895 | 2.00129 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.54859 | −0.147389 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.76066 | −0.274400 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.75496i | 0.560408i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.36976 | + | 15.6286i | −0.250212 | + | 0.894888i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.46104i | − | 0.539970i | −0.962865 | − | 0.269985i | \(-0.912981\pi\) | ||
0.962865 | − | 0.269985i | \(-0.0870187\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −43.7370 | −2.48811 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 0.0624374i | − | 0.00354050i | −0.999998 | − | 0.00177025i | \(-0.999437\pi\) | ||
0.999998 | − | 0.00177025i | \(-0.000563488\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.06791i | 0.512549i | 0.966604 | + | 0.256274i | \(0.0824951\pi\) | ||||
−0.966604 | + | 0.256274i | \(0.917505\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.95770 | − | 7.00176i | 0.110304 | − | 0.394505i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −34.3874 | −1.93139 | −0.965693 | − | 0.259686i | \(-0.916381\pi\) | ||||
−0.965693 | + | 0.259686i | \(0.916381\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.1274 | 1.57483 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 44.3575 | 2.47579 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.45986 | − | 8.49277i | −0.415078 | − | 0.472550i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.13873 | − | 1.29741i | −0.118635 | − | 0.0719673i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.1056 | −0.614144 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.77520 | −0.318397 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.0633 | 0.937885 | 0.468942 | − | 0.883229i | \(-0.344635\pi\) | ||||
0.468942 | + | 0.883229i | \(0.344635\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.4855 | 1.23220 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.54945 | + | 2.67004i | 0.521742 | + | 0.145880i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7284 | 0.584413 | 0.292206 | − | 0.956355i | \(-0.405611\pi\) | ||||
0.292206 | + | 0.956355i | \(0.405611\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 25.2516i | 1.37148i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 20.0945i | − | 1.08818i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.69957 | −0.415738 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −32.5024 | − | 9.08771i | −1.74987 | − | 0.489266i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.38766 | 0.503956 | 0.251978 | − | 0.967733i | \(-0.418919\pi\) | ||||
0.251978 | + | 0.967733i | \(0.418919\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.2894 | 0.925478 | 0.462739 | − | 0.886495i | \(-0.346867\pi\) | ||||
0.462739 | + | 0.886495i | \(0.346867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.11810i | 0.219808i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 30.1419i | − | 1.60429i | −0.597127 | − | 0.802147i | \(-0.703691\pi\) | ||
0.597127 | − | 0.802147i | \(-0.296309\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.88760 | − | 10.3276i | 0.153258 | − | 0.548131i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.32340 | −0.228819 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 16.2449i | − | 0.857374i | −0.903453 | − | 0.428687i | \(-0.858976\pi\) | ||
0.903453 | − | 0.428687i | \(-0.141024\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.45017 | − | 18.8414i | 0.128956 | − | 0.991650i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.4254i | 1.01957i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.4866 | − | 6.28728i | −1.17700 | − | 0.329091i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.5651 | −0.760291 | −0.380146 | − | 0.924927i | \(-0.624126\pi\) | ||||
−0.380146 | + | 0.924927i | \(0.624126\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 67.2633i | 3.50159i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.22661 | −0.167517 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.5159 | 0.596268 | 0.298134 | − | 0.954524i | \(-0.403636\pi\) | ||||
0.298134 | + | 0.954524i | \(0.403636\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −22.6491 | − | 24.1722i | −1.16960 | − | 1.24825i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.35846i | 0.172969i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.6549 | −1.36917 | −0.684584 | − | 0.728934i | \(-0.740016\pi\) | ||||
−0.684584 | + | 0.728934i | \(0.740016\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.17224 | 0.0600555 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.3608i | 0.580509i | 0.956949 | + | 0.290254i | \(0.0937400\pi\) | ||||
−0.956949 | + | 0.290254i | \(0.906260\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.07729 | + | 1.41961i | 0.258762 | + | 0.0723503i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 48.8863 | 2.48503 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.4651 | −1.39253 | −0.696267 | − | 0.717783i | \(-0.745157\pi\) | ||||
−0.696267 | + | 0.717783i | \(0.745157\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.2106i | 0.668087i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.1424 | −1.01605 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.79577 | − | 17.1522i | 0.241301 | − | 0.863021i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10.8572i | − | 0.544907i | −0.962169 | − | 0.272454i | \(-0.912165\pi\) | ||
0.962169 | − | 0.272454i | \(-0.0878351\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.79577 | − | 5.45980i | −0.240089 | − | 0.273332i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.67627i | 0.433272i | 0.976252 | + | 0.216636i | \(0.0695085\pi\) | ||||
−0.976252 | + | 0.216636i | \(0.930491\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.39931 | 0.119518 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.24679 | + | 15.1888i | −0.211025 | + | 0.754735i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.3052i | 0.808219i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.9225i | 1.72681i | 0.504514 | + | 0.863403i | \(0.331672\pi\) | ||||
−0.504514 | + | 0.863403i | \(0.668328\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.47120 | 0.121895 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.84397 | 0.189149 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.28009 | − | 4.57826i | 0.0628369 | − | 0.224738i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 35.0237 | 1.71512 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.1341i | 1.08132i | 0.841240 | + | 0.540662i | \(0.181826\pi\) | ||||
−0.841240 | + | 0.540662i | \(0.818174\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 33.9344i | − | 1.65386i | −0.562305 | − | 0.826930i | \(-0.690085\pi\) | ||
0.562305 | − | 0.826930i | \(-0.309915\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 59.3045 | 2.88348 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.72508 | + | 11.0860i | −0.326214 | + | 0.537752i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.08369 | 0.197623 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.21083 | −0.299862 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.6904 | −1.38197 | −0.690985 | − | 0.722869i | \(-0.742823\pi\) | ||||
−0.690985 | + | 0.722869i | \(0.742823\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.8818 | 0.955459 | 0.477729 | − | 0.878507i | \(-0.341460\pi\) | ||||
0.477729 | + | 0.878507i | \(0.341460\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.9755 | + | 42.8307i | −0.574181 | + | 2.05357i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.6829 | + | 14.6539i | −0.798054 | + | 0.700993i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.23274 | 0.202018 | 0.101009 | − | 0.994886i | \(-0.467793\pi\) | ||||
0.101009 | + | 0.994886i | \(0.467793\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 38.6180 | 1.83895 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.43556 | 0.448297 | 0.224149 | − | 0.974555i | \(-0.428040\pi\) | ||||
0.224149 | + | 0.974555i | \(0.428040\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.6841 | + | 5.22410i | 0.885713 | + | 0.247646i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 19.6673i | − | 0.930233i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.5776i | 0.923924i | 0.886900 | + | 0.461962i | \(0.152854\pi\) | ||||
−0.886900 | + | 0.461962i | \(0.847146\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −48.7756 | −2.29675 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 45.5287i | − | 2.13912i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.169504 | + | 0.606236i | −0.00794648 | + | 0.0284208i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.9251i | 0.932057i | 0.884770 | + | 0.466029i | \(0.154316\pi\) | ||||
−0.884770 | + | 0.466029i | \(0.845684\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.3461 | 0.996349 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.4234 | 1.88270 | 0.941352 | − | 0.337427i | \(-0.109557\pi\) | ||||
0.941352 | + | 0.337427i | \(0.109557\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.3760 | 0.900481 | 0.450240 | − | 0.892907i | \(-0.351338\pi\) | ||||
0.450240 | + | 0.892907i | \(0.351338\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 30.5986 | + | 8.55540i | 1.41898 | + | 0.396747i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.4450 | −0.899808 | −0.449904 | − | 0.893077i | \(-0.648542\pi\) | ||||
−0.449904 | + | 0.893077i | \(0.648542\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2.49524i | − | 0.115219i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.9583 | 1.15002 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.4496i | 1.62998i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.4599 | + | 3.80453i | −0.984646 | + | 0.174564i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.1335 | 1.51708 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 42.8444i | 1.95761i | 0.204795 | + | 0.978805i | \(0.434347\pi\) | ||||
−0.204795 | + | 0.978805i | \(0.565653\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.94687 | −0.0887695 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.49277i | 0.386434i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.52285 | + | 30.4822i | −0.387003 | + | 1.38413i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 40.7181i | − | 1.84512i | −0.385859 | − | 0.922558i | \(-0.626095\pi\) | ||
0.385859 | − | 0.922558i | \(-0.373905\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 39.0849i | − | 1.76748i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 9.85124i | − | 0.444580i | −0.974981 | − | 0.222290i | \(-0.928647\pi\) | ||
0.974981 | − | 0.222290i | \(-0.0713532\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.4085 | 0.784038 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −52.1377 | − | 14.5778i | −2.34342 | − | 0.655221i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.69856 | −0.121047 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 32.4805i | − | 1.45403i | −0.686622 | − | 0.727014i | \(-0.740907\pi\) | ||
0.686622 | − | 0.727014i | \(-0.259093\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.4059 | −1.13505 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.7655 | 0.970474 | 0.485237 | − | 0.874383i | \(-0.338733\pi\) | ||||
0.485237 | + | 0.874383i | \(0.338733\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.98244 | − | 7.09026i | 0.0882176 | − | 0.315512i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 37.7749i | 1.67764i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.6015i | 1.57801i | 0.614387 | + | 0.789005i | \(0.289403\pi\) | ||||
−0.614387 | + | 0.789005i | \(0.710597\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.87567i | 0.259924i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 23.6783 | + | 26.9569i | 1.04542 | + | 1.19017i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.7896 | + | 8.88842i | 1.40082 | + | 0.391670i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.0043i | 1.89133i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 57.4452i | 2.52156i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.26345i | − | 0.405839i | −0.979195 | − | 0.202920i | \(-0.934957\pi\) | ||
0.979195 | − | 0.202920i | \(-0.0650430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.75263i | 0.0766371i | 0.999266 | + | 0.0383185i | \(0.0122002\pi\) | ||||
−0.999266 | + | 0.0383185i | \(0.987800\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.32340 | + | 7.12696i | −0.188689 | + | 0.311046i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 12.4368i | − | 0.541754i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.95045 | 0.128281 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −39.4730 | −1.71298 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.82388i | − | 0.252260i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.2407 | − | 9.01452i | −1.39389 | − | 0.389732i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 71.4222i | − | 3.08209i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.0036i | 1.20620i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.8621 | 0.638972 | 0.319486 | − | 0.947591i | \(-0.396490\pi\) | ||||
0.319486 | + | 0.947591i | \(0.396490\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.9240 | 1.11251 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.07199 | + | 2.25694i | 0.345766 | + | 0.0966766i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 3.27398i | − | 0.139985i | −0.997548 | − | 0.0699926i | \(-0.977702\pi\) | ||
0.997548 | − | 0.0699926i | \(-0.0222976\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −41.9346 | −1.78973 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.3105 | + | 21.9843i | 0.822655 | + | 0.936561i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.48181 | −0.190586 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.8285 | − | 6.94209i | −1.05391 | − | 0.294675i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.9218i | 1.60680i | 0.595442 | + | 0.803399i | \(0.296977\pi\) | ||||
−0.595442 | + | 0.803399i | \(0.703023\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.23274 | −0.179026 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.1936i | 1.35922i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.6528i | 1.33400i | 0.745056 | + | 0.667002i | \(0.232423\pi\) | ||||
−0.745056 | + | 0.667002i | \(0.767577\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.13173 | − | 18.3538i | 0.215893 | − | 0.772148i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.96877 | 0.166673 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 3.55695i | − | 0.149115i | −0.997217 | − | 0.0745575i | \(-0.976246\pi\) | ||
0.997217 | − | 0.0745575i | \(-0.0237544\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.42184i | 0.185048i | 0.995710 | + | 0.0925242i | \(0.0294936\pi\) | ||||
−0.995710 | + | 0.0925242i | \(0.970506\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −36.4554 | −1.52294 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.7771 | + | 13.2106i | 0.908168 | + | 0.550919i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.2037i | 0.674569i | 0.941403 | + | 0.337284i | \(0.109508\pi\) | ||||
−0.941403 | + | 0.337284i | \(0.890492\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 45.5082i | − | 1.89125i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.19628 | −0.0496302 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.0265i | 0.995077i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.74061 | − | 6.22532i | 0.0719652 | − | 0.257385i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −41.1470 | −1.69832 | −0.849159 | − | 0.528138i | \(-0.822891\pi\) | ||||
−0.849159 | + | 0.528138i | \(0.822891\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.7058 | − | 13.7956i | 0.647144 | − | 0.568437i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.6193 | −1.01270 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 36.2536i | − | 1.48876i | −0.667757 | − | 0.744379i | \(-0.732746\pi\) | ||
0.667757 | − | 0.744379i | \(-0.267254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.14241 | + | 0.878620i | 0.128826 | + | 0.0360199i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −63.1485 | −2.58449 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5710 | 0.431918 | 0.215959 | − | 0.976402i | \(-0.430712\pi\) | ||||
0.215959 | + | 0.976402i | \(0.430712\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.4010i | 1.15850i | 0.815150 | + | 0.579250i | \(0.196655\pi\) | ||||
−0.815150 | + | 0.579250i | \(0.803345\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.6231i | 1.04345i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.94772 | − | 14.1191i | 0.160498 | − | 0.574024i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.70439i | − | 0.150356i | −0.997170 | − | 0.0751782i | \(-0.976047\pi\) | ||
0.997170 | − | 0.0751782i | \(-0.0239526\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.1915 | 0.453502 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.13478 | −0.207731 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 39.6526i | − | 1.60155i | −0.598964 | − | 0.800776i | \(-0.704421\pi\) | ||
0.598964 | − | 0.800776i | \(-0.295579\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20.7666 | − | 74.2724i | 0.837391 | − | 2.99495i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 13.6104i | − | 0.547935i | −0.961739 | − | 0.273968i | \(-0.911664\pi\) | ||
0.961739 | − | 0.273968i | \(-0.0883361\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.4083i | 0.498732i | 0.968409 | + | 0.249366i | \(0.0802222\pi\) | ||||
−0.968409 | + | 0.249366i | \(0.919778\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 41.9316i | − | 1.68266i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 4.88210i | − | 0.195597i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.5498 | + | 22.1721i | 0.461993 | + | 0.886883i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −40.6557 | + | 35.7111i | −1.62363 | + | 1.42616i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.0915i | 0.402376i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9.61505i | − | 0.382769i | −0.981515 | − | 0.191385i | \(-0.938702\pi\) | ||
0.981515 | − | 0.191385i | \(-0.0612978\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 31.7763i | − | 1.26300i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.852024 | − | 0.238227i | −0.0338115 | − | 0.00945374i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.34367 | −0.132481 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.7110 | 1.09623 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 14.9752i | − | 0.591483i | −0.955268 | − | 0.295741i | \(-0.904433\pi\) | ||
0.955268 | − | 0.295741i | \(-0.0955667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.6413 | 1.28725 | 0.643623 | − | 0.765342i | \(-0.277430\pi\) | ||||
0.643623 | + | 0.765342i | \(0.277430\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −53.9805 | − | 15.0930i | −2.12548 | − | 0.594286i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −45.9678 | −1.80718 | −0.903591 | − | 0.428397i | \(-0.859078\pi\) | ||||
−0.903591 | + | 0.428397i | \(0.859078\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 28.6236i | − | 1.12358i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 7.99531i | − | 0.313361i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 44.0635i | − | 1.72434i | −0.506619 | − | 0.862170i | \(-0.669105\pi\) | ||
0.506619 | − | 0.862170i | \(-0.330895\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.6402 | + | 4.09342i | 0.572041 | + | 0.159943i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 60.3361i | − | 2.35394i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.0144 | 1.01338 | 0.506689 | − | 0.862129i | \(-0.330869\pi\) | ||||
0.506689 | + | 0.862129i | \(0.330869\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.4559i | 1.57355i | 0.617239 | + | 0.786775i | \(0.288251\pi\) | ||||
−0.617239 | + | 0.786775i | \(0.711749\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.84397 | −0.149287 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.37618 | + | 4.94300i | 0.0921442 | + | 0.191681i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 34.1967i | − | 1.32410i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.9697 | −0.772074 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 30.4086i | − | 1.17391i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.1844 | 0.739506 | 0.369753 | − | 0.929130i | \(-0.379442\pi\) | ||||
0.369753 | + | 0.929130i | \(0.379442\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21.3461 | − | 35.1882i | 0.821611 | − | 1.35439i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.22823 | 0.0472045 | 0.0236023 | − | 0.999721i | \(-0.492486\pi\) | ||||
0.0236023 | + | 0.999721i | \(0.492486\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.96489 | 0.305664 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −84.6051 | −3.24208 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.8015i | 0.757685i | 0.925461 | + | 0.378842i | \(0.123678\pi\) | ||||
−0.925461 | + | 0.378842i | \(0.876322\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.79616 | − | 0.502208i | −0.0686277 | − | 0.0191884i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31.4145i | 1.19854i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.86881 | −0.109293 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 14.1103i | − | 0.536779i | −0.963310 | − | 0.268390i | \(-0.913509\pi\) | ||
0.963310 | − | 0.268390i | \(-0.0864915\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.6234i | 0.517510i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.4565 | − | 7.11766i | −0.965620 | − | 0.269988i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.1879 | −1.14345 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.04228 | −0.304187 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.8986 | −0.827097 | −0.413549 | − | 0.910482i | \(-0.635711\pi\) | ||||
−0.413549 | + | 0.910482i | \(0.635711\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.7441 | + | 11.1941i | −0.480652 | + | 0.422194i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −65.4843 | − | 18.3095i | −2.46628 | − | 0.689574i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.85266 | −0.0696765 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.8947 | 1.57339 | 0.786694 | − | 0.617344i | \(-0.211791\pi\) | ||||
0.786694 | + | 0.617344i | \(0.211791\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 46.0228 | 1.72599 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.4304 | −0.914927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.51426 | + | 1.26219i | 0.168824 | + | 0.0472033i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −58.0778 | −2.16895 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 5.29226i | − | 0.197368i | −0.995119 | − | 0.0986840i | \(-0.968537\pi\) | ||
0.995119 | − | 0.0986840i | \(-0.0314633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 8.30652i | − | 0.309351i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −70.7729 | −2.63207 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.4085 | − | 28.6972i | 0.646534 | − | 1.06579i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.5396 | 1.42935 | 0.714677 | − | 0.699454i | \(-0.246573\pi\) | ||||
0.714677 | + | 0.699454i | \(0.246573\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 32.4088 | 1.20033 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.9403i | 0.811491i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.5959i | 0.723792i | 0.932219 | + | 0.361896i | \(0.117870\pi\) | ||||
−0.932219 | + | 0.361896i | \(0.882130\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −42.6421 | − | 11.9228i | −1.57288 | − | 0.439779i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.5805 | −0.684420 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 28.0172i | − | 1.03063i | −0.857001 | − | 0.515314i | \(-0.827675\pi\) | ||
0.857001 | − | 0.515314i | \(-0.172325\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.26396 | − | 4.85436i | −0.156640 | − | 0.178329i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.94590i | 0.254820i | 0.991850 | + | 0.127410i | \(0.0406664\pi\) | ||||
−0.991850 | + | 0.127410i | \(0.959334\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.99688 | + | 14.2949i | −0.146434 | + | 0.523726i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.2844 | 0.449463 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.42437i | 0.307820i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.5933 | 0.860930 | 0.430465 | − | 0.902607i | \(-0.358350\pi\) | ||||
0.430465 | + | 0.902607i | \(0.358350\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.5509 | −0.493822 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.25254 | + | 33.0919i | −0.336734 | + | 1.20434i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 35.5537i | − | 1.29222i | −0.763244 | − | 0.646110i | \(-0.776395\pi\) | ||
0.763244 | − | 0.646110i | \(-0.223605\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 63.2403 | 2.29548 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.7431 | 0.824437 | 0.412218 | − | 0.911085i | \(-0.364754\pi\) | ||||
0.412218 | + | 0.911085i | \(0.364754\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 2.10918i | − | 0.0763575i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −32.2688 | − | 9.02239i | −1.16668 | − | 0.326205i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.41771 | 0.123406 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.6948 | −1.03476 | −0.517380 | − | 0.855756i | \(-0.673093\pi\) | ||||
−0.517380 | + | 0.855756i | \(0.673093\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 3.81538i | − | 0.137408i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.0735 | 1.40538 | 0.702688 | − | 0.711498i | \(-0.251983\pi\) | ||||
0.702688 | + | 0.711498i | \(0.251983\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.5015 | − | 12.4368i | −0.736437 | − | 0.446742i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.48761i | 0.232742i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.4862 | − | 38.1228i | −1.19977 | − | 1.36589i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.0945i | 0.719037i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −55.2562 | −1.97469 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.1406 | − | 5.07213i | −0.647466 | − | 0.181032i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 31.5915i | − | 1.12612i | −0.826418 | − | 0.563058i | \(-0.809625\pi\) | ||
0.826418 | − | 0.563058i | \(-0.190375\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 2.72887i | − | 0.0971502i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.79577 | −0.170518 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.63084 | 0.128935 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −36.5861 | − | 10.2295i | −1.29758 | − | 0.362803i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.3196 | 1.25109 | 0.625543 | − | 0.780190i | \(-0.284878\pi\) | ||||
0.625543 | + | 0.780190i | \(0.284878\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.6160i | 0.941606i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 50.1334i | 1.77138i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 43.7524 | 1.54399 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.72594 | − | 6.17285i | 0.0608313 | − | 0.217565i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.61725 | 0.0921316 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.3527 | −1.06714 | −0.533572 | − | 0.845755i | \(-0.679150\pi\) | ||||
−0.533572 | + | 0.845755i | \(0.679150\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.6197 | 1.21566 | 0.607832 | − | 0.794066i | \(-0.292039\pi\) | ||||
0.607832 | + | 0.794066i | \(0.292039\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.77625 | 0.167510 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.94300 | + | 28.4083i | −0.278231 | + | 0.995101i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.7073 | + | 24.3375i | −0.969355 | + | 0.851460i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.62665 | −0.0568399 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.7467 | 0.654264 | 0.327132 | − | 0.944979i | \(-0.393918\pi\) | ||||
0.327132 | + | 0.944979i | \(0.393918\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.3454 | −0.848627 | −0.424314 | − | 0.905515i | \(-0.639485\pi\) | ||||
−0.424314 | + | 0.905515i | \(0.639485\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 53.0700 | + | 32.1936i | 1.84766 | + | 1.12084i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.2470i | 0.877925i | 0.898505 | + | 0.438962i | \(0.144654\pi\) | ||||
−0.898505 | + | 0.438962i | \(0.855346\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 22.9562i | − | 0.797302i | −0.917103 | − | 0.398651i | \(-0.869478\pi\) | ||
0.917103 | − | 0.398651i | \(-0.130522\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 71.4668 | 2.47915 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.3318i | 0.600513i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.4659 | + | 5.16310i | 0.639041 | + | 0.178676i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 39.4755i | 1.36447i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.8530 | −1.68659 | −0.843296 | − | 0.537450i | \(-0.819388\pi\) | ||||
−0.843296 | + | 0.537450i | \(0.819388\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.0633 | −0.553907 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 56.7008 | 1.95288 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.67678 | − | 27.4562i | 0.264089 | − | 0.944521i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.68928 | −0.126765 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 57.1717i | − | 1.96213i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.8235 | 0.679541 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 18.3596i | − | 0.628621i | −0.949320 | − | 0.314311i | \(-0.898227\pi\) | ||
0.949320 | − | 0.314311i | \(-0.101773\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24.4005 | − | 50.7588i | −0.834481 | − | 1.73591i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.9587 | 1.29664 | 0.648322 | − | 0.761367i | \(-0.275471\pi\) | ||||
0.648322 | + | 0.761367i | \(0.275471\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.6267i | 0.396700i | 0.980131 | + | 0.198350i | \(0.0635582\pi\) | ||||
−0.980131 | + | 0.198350i | \(0.936442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.4071 | −0.661393 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 28.1889i | − | 0.959561i | −0.877389 | − | 0.479781i | \(-0.840716\pi\) | ||
0.877389 | − | 0.479781i | \(-0.159284\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.6743 | − | 41.7533i | 0.396937 | − | 1.41965i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 30.4426i | − | 1.03388i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.3732i | 1.13211i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.21854i | − | 0.0751722i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −81.7900 | −2.76817 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.59078 | − | 4.30152i | 0.155197 | − | 0.145418i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.0914 | 1.82654 | 0.913269 | − | 0.407357i | \(-0.133549\pi\) | ||||
0.913269 | + | 0.407357i | \(0.133549\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 84.0169i | − | 2.83382i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.1111 | −1.14923 | −0.574616 | − | 0.818423i | \(-0.694849\pi\) | ||||
−0.574616 | + | 0.818423i | \(0.694849\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.1513 | 0.610841 | 0.305421 | − | 0.952218i | \(-0.401203\pi\) | ||||
0.305421 | + | 0.952218i | \(0.401203\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 43.5863 | + | 12.1868i | 1.46514 | + | 0.409654i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.3608i | 0.381458i | 0.981643 | + | 0.190729i | \(0.0610851\pi\) | ||||
−0.981643 | + | 0.190729i | \(0.938915\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.222631i | 0.00746680i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 29.5529i | − | 0.990060i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.6120 | + | 29.5240i | −1.12478 | + | 0.987984i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.5147 | + | 51.9123i | −0.485174 | + | 1.73524i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.55099i | 0.252120i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.1936i | 1.07372i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.8704i | 0.495404i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.1049i | 0.469382i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.8425 | − | 5.26839i | −0.626347 | − | 0.175127i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 13.6572i | − | 0.453481i | −0.973955 | − | 0.226741i | \(-0.927193\pi\) | ||
0.973955 | − | 0.226741i | \(-0.0728070\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.0246 | 0.631007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.70405 | −0.0564576 | −0.0282288 | − | 0.999601i | \(-0.508987\pi\) | ||||
−0.0282288 | + | 0.999601i | \(0.508987\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.90796i | 0.294811i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 46.3044 | + | 12.9467i | 1.53078 | + | 0.428006i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 3.82544i | − | 0.126327i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.7791i | 1.64206i | 0.570884 | + | 0.821031i | \(0.306601\pi\) | ||||
−0.570884 | + | 0.821031i | \(0.693399\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.0312 | −0.923660 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.39931 | −0.0789743 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.6355 | + | 10.0915i | 0.546972 | + | 0.331807i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 85.2981i | 2.80156i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.4229 | −0.735671 | −0.367836 | − | 0.929891i | \(-0.619901\pi\) | ||||
−0.367836 | + | 0.929891i | \(0.619901\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.8875 | + | 19.2255i | −0.717334 | + | 0.630090i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.184990 | −0.00605629 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.54253 | − | 23.3995i | 0.213964 | − | 0.765246i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 30.2982i | − | 0.989800i | −0.868950 | − | 0.494900i | \(-0.835205\pi\) | ||
0.868950 | − | 0.494900i | \(-0.164795\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.8665 | 0.876754 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 20.2859i | − | 0.661301i | −0.943753 | − | 0.330650i | \(-0.892732\pi\) | ||
0.943753 | − | 0.330650i | \(-0.107268\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 59.3003i | 1.93108i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.97431 | − | 2.78883i | −0.324464 | − | 0.0907205i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.88729 | 0.223807 | 0.111903 | − | 0.993719i | \(-0.464305\pi\) | ||||
0.111903 | + | 0.993719i | \(0.464305\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.22410i | 0.169582i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 101.883i | 3.30378i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.2356 | −0.428743 | −0.214371 | − | 0.976752i | \(-0.568770\pi\) | ||||
−0.214371 | + | 0.976752i | \(0.568770\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.4971 | + | 7.40861i | 0.857426 | + | 0.239737i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 83.3360i | − | 2.69387i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.469330i | 0.0151555i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.00057 | −0.258083 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 86.5083i | − | 2.78769i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.24837 | + | 33.0770i | −0.297715 | + | 1.06479i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.65507 | 0.0853813 | 0.0426907 | − | 0.999088i | \(-0.486407\pi\) | ||||
0.0426907 | + | 0.999088i | \(0.486407\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −25.1624 | + | 22.1021i | −0.808333 | + | 0.710022i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.1216 | −0.356909 | −0.178454 | − | 0.983948i | \(-0.557110\pi\) | ||||
−0.178454 | + | 0.983948i | \(0.557110\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.65169i | 0.213244i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.84397 | + | 6.33664i | −0.123106 | + | 0.202935i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.3717 | −1.54755 | −0.773775 | − | 0.633461i | \(-0.781634\pi\) | ||||
−0.773775 | + | 0.633461i | \(0.781634\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.3539 | −1.16188 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.6588i | 0.691512i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.6603i | 0.467590i | 0.972286 | + | 0.233795i | \(0.0751145\pi\) | ||||
−0.972286 | + | 0.233795i | \(0.924885\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.8942 | + | 5.00324i | 0.570157 | + | 0.159416i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.1108i | 0.544643i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43.0989 | 1.37047 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.6331 | −0.750729 | −0.375364 | − | 0.926877i | \(-0.622482\pi\) | ||||
−0.375364 | + | 0.926877i | \(0.622482\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 50.5553i | − | 1.60432i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 45.8986 | + | 12.8333i | 1.45508 | + | 0.406843i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.5810i | 0.715148i | 0.933885 | + | 0.357574i | \(0.116396\pi\) | ||||
−0.933885 | + | 0.357574i | \(0.883604\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 32.0315i | − | 1.01343i |
(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 | 1520.2.g.g.1519.2 | yes | 16 | |
4.3 | odd | 2 | 1520.2.g.e.1519.15 | yes | 16 | ||
5.4 | even | 2 | inner | 1520.2.g.g.1519.15 | yes | 16 | |
19.18 | odd | 2 | 1520.2.g.e.1519.16 | yes | 16 | ||
20.19 | odd | 2 | 1520.2.g.e.1519.2 | yes | 16 | ||
76.75 | even | 2 | inner | 1520.2.g.g.1519.1 | yes | 16 | |
95.94 | odd | 2 | 1520.2.g.e.1519.1 | ✓ | 16 | ||
380.379 | even | 2 | inner | 1520.2.g.g.1519.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1520.2.g.e.1519.1 | ✓ | 16 | 95.94 | odd | 2 | ||
1520.2.g.e.1519.2 | yes | 16 | 20.19 | odd | 2 | ||
1520.2.g.e.1519.15 | yes | 16 | 4.3 | odd | 2 | ||
1520.2.g.e.1519.16 | yes | 16 | 19.18 | odd | 2 | ||
1520.2.g.g.1519.1 | yes | 16 | 76.75 | even | 2 | inner | |
1520.2.g.g.1519.2 | yes | 16 | 1.1 | even | 1 | trivial | |
1520.2.g.g.1519.15 | yes | 16 | 5.4 | even | 2 | inner | |
1520.2.g.g.1519.16 | yes | 16 | 380.379 | even | 2 | inner |