Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(81,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.r (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 737.15 | ||
Character | \(\chi\) | \(=\) | 1148.737 |
Dual form | 1148.2.r.a.81.15 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.294024 | − | 0.169755i | 0.169755 | − | 0.0980079i | −0.412715 | − | 0.910860i | \(-0.635420\pi\) |
0.582470 | + | 0.812852i | \(0.302086\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.09216 | + | 3.62373i | −0.935643 | + | 1.62058i | −0.162161 | + | 0.986764i | \(0.551846\pi\) |
−0.773483 | + | 0.633817i | \(0.781487\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0873039 | − | 2.64431i | −0.0329978 | − | 0.999455i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.44237 | + | 2.49825i | −0.480789 | + | 0.832751i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.02680 | + | 1.74752i | −0.912614 | + | 0.526898i | −0.881271 | − | 0.472611i | \(-0.843312\pi\) |
−0.0313427 | + | 0.999509i | \(0.509978\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.69474i | − | 1.30209i | −0.759040 | − | 0.651044i | \(-0.774331\pi\) | ||
0.759040 | − | 0.651044i | \(-0.225669\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.42062i | 0.366802i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.513708 | − | 0.296589i | 0.124592 | − | 0.0719335i | −0.436408 | − | 0.899749i | \(-0.643750\pi\) |
0.561001 | + | 0.827815i | \(0.310416\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.364147 | + | 0.210240i | 0.0835411 | + | 0.0482325i | 0.541189 | − | 0.840901i | \(-0.317975\pi\) |
−0.457648 | + | 0.889134i | \(0.651308\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.474554 | − | 0.762670i | −0.103556 | − | 0.166428i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.40916 | − | 4.17279i | 0.502345 | − | 0.870087i | −0.497651 | − | 0.867377i | \(-0.665804\pi\) |
0.999996 | − | 0.00270972i | \(-0.000862532\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.25428 | − | 10.8327i | −1.25086 | − | 2.16655i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.99792i | 0.384500i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.24692i | − | 0.974328i | −0.873311 | − | 0.487164i | \(-0.838031\pi\) | ||
0.873311 | − | 0.487164i | \(-0.161969\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.176817 | − | 0.306255i | −0.0317572 | − | 0.0550051i | 0.849710 | − | 0.527250i | \(-0.176777\pi\) |
−0.881467 | + | 0.472245i | \(0.843444\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.593301 | + | 1.02763i | −0.103280 | + | 0.178887i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.76492 | + | 5.21596i | 1.65057 | + | 0.881658i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.33617 | − | 2.31431i | 0.219664 | − | 0.380470i | −0.735041 | − | 0.678023i | \(-0.762837\pi\) |
0.954705 | + | 0.297553i | \(0.0961705\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.796955 | − | 1.38037i | −0.127615 | − | 0.221036i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.27959 | − | 5.49948i | −0.512186 | − | 0.858875i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.13438 | −0.172992 | −0.0864959 | − | 0.996252i | \(-0.527567\pi\) | ||||
−0.0864959 | + | 0.996252i | \(0.527567\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.03533 | − | 10.4535i | −0.899694 | − | 1.55832i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.07940 | + | 1.20054i | 0.303311 | + | 0.175117i | 0.643929 | − | 0.765085i | \(-0.277303\pi\) |
−0.340618 | + | 0.940202i | \(0.610636\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.98476 | + | 0.461717i | −0.997822 | + | 0.0659596i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.100695 | − | 0.174409i | 0.0141001 | − | 0.0244221i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.65391 | + | 3.26429i | −0.776624 | + | 0.448384i | −0.835232 | − | 0.549897i | \(-0.814667\pi\) |
0.0586085 | + | 0.998281i | \(0.481334\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 14.6244i | − | 1.97195i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.142757 | 0.0189087 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.0567409 | + | 0.0982782i | 0.00738704 | + | 0.0127947i | 0.869695 | − | 0.493589i | \(-0.164315\pi\) |
−0.862308 | + | 0.506384i | \(0.830982\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.54050 | − | 2.66823i | 0.197241 | − | 0.341632i | −0.750392 | − | 0.660993i | \(-0.770135\pi\) |
0.947633 | + | 0.319361i | \(0.103468\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.73208 | + | 3.59596i | 0.848162 | + | 0.453048i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.0125 | + | 9.82216i | 2.11014 | + | 1.21829i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.74960 | − | 3.31954i | 0.702426 | − | 0.405546i | −0.105824 | − | 0.994385i | \(-0.533748\pi\) |
0.808250 | + | 0.588839i | \(0.200415\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.63587i | − | 0.196935i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.06848i | 0.957552i | 0.877937 | + | 0.478776i | \(0.158919\pi\) | ||||
−0.877937 | + | 0.478776i | \(0.841081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.25368 | − | 3.90348i | −0.263773 | − | 0.456868i | 0.703468 | − | 0.710727i | \(-0.251634\pi\) |
−0.967241 | + | 0.253858i | \(0.918300\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.67782 | − | 2.12339i | −0.424678 | − | 0.245188i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.88524 | + | 7.85123i | 0.556725 | + | 0.894731i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.1141 | − | 6.41672i | −1.25043 | − | 0.721937i | −0.279236 | − | 0.960222i | \(-0.590081\pi\) |
−0.971195 | + | 0.238285i | \(0.923415\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.98794 | − | 6.90732i | −0.443105 | − | 0.767480i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.34427 | 0.806138 | 0.403069 | − | 0.915170i | \(-0.367943\pi\) | ||||
0.403069 | + | 0.915170i | \(0.367943\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.48205i | 0.269216i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.890689 | − | 1.54272i | −0.0954919 | − | 0.165397i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.69457 | − | 3.28776i | −0.603623 | − | 0.348502i | 0.166843 | − | 0.985984i | \(-0.446643\pi\) |
−0.770465 | + | 0.637482i | \(0.779976\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.4144 | + | 0.409869i | −1.30138 | + | 0.0429660i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.103977 | − | 0.0600309i | −0.0107819 | − | 0.00622491i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.52371 | + | 0.879714i | −0.156329 | + | 0.0902568i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 16.0169i | − | 1.62627i | −0.582074 | − | 0.813136i | \(-0.697758\pi\) | ||
0.582074 | − | 0.813136i | \(-0.302242\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 10.0823i | − | 1.01331i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.47921 | + | 2.58607i | −0.445698 | + | 0.257324i | −0.706012 | − | 0.708200i | \(-0.749507\pi\) |
0.260313 | + | 0.965524i | \(0.416174\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.68488 | + | 8.11445i | −0.461615 | + | 0.799541i | −0.999042 | − | 0.0437699i | \(-0.986063\pi\) |
0.537427 | + | 0.843310i | \(0.319396\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.75655 | − | 0.124025i | 0.366602 | − | 0.0121036i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.68469 | + | 13.3103i | −0.742907 | + | 1.28675i | 0.208260 | + | 0.978074i | \(0.433220\pi\) |
−0.951166 | + | 0.308678i | \(0.900113\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.79035 | + | 3.92041i | −0.650397 | + | 0.375507i | −0.788608 | − | 0.614896i | \(-0.789198\pi\) |
0.138211 | + | 0.990403i | \(0.455865\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.907282i | − | 0.0861154i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.6306 | −1.18819 | −0.594094 | − | 0.804395i | \(-0.702489\pi\) | ||||
−0.594094 | + | 0.804395i | \(0.702489\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.0807 | + | 17.4603i | 0.940031 | + | 1.62818i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.7287 | + | 6.77154i | 1.08431 | + | 0.626029i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.829123 | − | 1.33251i | −0.0760056 | − | 0.122151i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.607671 | − | 1.05252i | 0.0552428 | − | 0.0956834i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.89784 | − | 1.06025i | −0.171123 | − | 0.0955997i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 31.4183 | 2.81014 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.65473 | −0.501777 | −0.250888 | − | 0.968016i | \(-0.580723\pi\) | ||||
−0.250888 | + | 0.968016i | \(0.580723\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.333536 | + | 0.192567i | −0.0293662 | + | 0.0169546i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.46402 | − | 16.3922i | 0.826875 | − | 1.43219i | −0.0736020 | − | 0.997288i | \(-0.523449\pi\) |
0.900477 | − | 0.434903i | \(-0.143217\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.524149 | − | 0.981273i | 0.0454495 | − | 0.0850871i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.23994 | − | 4.17998i | −0.623114 | − | 0.359755i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.0288 | + | 8.67688i | −1.28400 | + | 0.741316i | −0.977577 | − | 0.210580i | \(-0.932465\pi\) |
−0.306421 | + | 0.951896i | \(0.599131\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.2679 | −1.54946 | −0.774730 | − | 0.632293i | \(-0.782114\pi\) | ||||
−0.774730 | + | 0.632293i | \(0.782114\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.815190 | 0.0686514 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.20417 | + | 14.2100i | 0.686067 | + | 1.18830i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.0134 | + | 10.9774i | 1.57898 | + | 0.911623i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.97531 | + | 1.32145i | −0.162921 | + | 0.108991i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.1062 | + | 8.14421i | 1.15562 | + | 0.667200i | 0.950251 | − | 0.311484i | \(-0.100826\pi\) |
0.205373 | + | 0.978684i | \(0.434159\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.44092 | + | 4.87336i | −0.686912 | + | 0.396589i | −0.802454 | − | 0.596714i | \(-0.796473\pi\) |
0.115542 | + | 0.993303i | \(0.463139\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.71116i | 0.138339i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.47972 | 0.118854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.1066 | − | 6.41237i | 0.886400 | − | 0.511763i | 0.0136364 | − | 0.999907i | \(-0.495659\pi\) |
0.872763 | + | 0.488144i | \(0.162326\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.10826 | + | 1.91956i | −0.0878904 | + | 0.152231i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.2445 | − | 6.00627i | −0.886189 | − | 0.473360i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.70745 | + | 9.88559i | −0.447042 | + | 0.774299i | −0.998192 | − | 0.0601069i | \(-0.980856\pi\) |
0.551150 | + | 0.834406i | \(0.314189\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.48256 | − | 4.29992i | −0.193267 | − | 0.334749i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.80882i | − | 0.681647i | −0.940127 | − | 0.340823i | \(-0.889294\pi\) | ||
0.940127 | − | 0.340823i | \(-0.110706\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.04061 | −0.695432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.05047 | + | 0.606488i | −0.0803312 | + | 0.0463793i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.68920 | − | 9.85398i | 0.432542 | − | 0.749184i | −0.564550 | − | 0.825399i | \(-0.690950\pi\) |
0.997091 | + | 0.0762150i | \(0.0242835\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −28.0991 | + | 17.4840i | −2.12409 | + | 1.32167i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0333664 | + | 0.0192641i | 0.00250797 | + | 0.00144798i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.9361 | + | 12.0875i | −1.56484 | + | 0.903461i | −0.568086 | + | 0.822969i | \(0.692316\pi\) |
−0.996755 | + | 0.0804918i | \(0.974351\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1837i | 0.979940i | 0.871739 | + | 0.489970i | \(0.162992\pi\) | ||||
−0.871739 | + | 0.489970i | \(0.837008\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.04603i | − | 0.0773249i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.59095 | + | 9.68381i | 0.411055 | + | 0.711968i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.03659 | + | 1.79543i | −0.0758032 | + | 0.131295i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.28313 | − | 0.174426i | 0.384291 | − | 0.0126877i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.8508 | − | 8.57414i | −1.07457 | − | 0.620403i | −0.145143 | − | 0.989411i | \(-0.546364\pi\) |
−0.929426 | + | 0.369008i | \(0.879698\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.8507 | − | 12.0382i | 1.50087 | − | 0.866527i | 0.500869 | − | 0.865523i | \(-0.333014\pi\) |
0.999999 | − | 0.00100383i | \(-0.000319529\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.66944 | 0.477608 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.46342 | 0.674241 | 0.337120 | − | 0.941462i | \(-0.390547\pi\) | ||||
0.337120 | + | 0.941462i | \(0.390547\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0359 | − | 9.25832i | 1.13675 | − | 0.656305i | 0.191129 | − | 0.981565i | \(-0.438785\pi\) |
0.945625 | + | 0.325260i | \(0.105452\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.12701 | − | 1.95205i | 0.0794934 | − | 0.137687i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.8745 | + | 0.458076i | −0.973797 | + | 0.0321506i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 26.7901 | − | 0.378552i | 1.87110 | − | 0.0264392i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.94979 | + | 12.0374i | 0.483044 | + | 0.836656i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.46960 | −0.101654 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.563983i | 0.0388262i | 0.999812 | + | 0.0194131i | \(0.00617977\pi\) | ||||
−0.999812 | + | 0.0194131i | \(0.993820\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.36966 | + | 2.37232i | 0.0938477 | + | 0.162549i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.37331 | − | 4.11070i | 0.161859 | − | 0.280347i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.794397 | + | 0.494295i | −0.0539272 | + | 0.0335549i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.32527 | − | 0.765145i | −0.0895535 | − | 0.0517037i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.39241 | − | 2.41173i | −0.0936637 | − | 0.162230i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.7194 | 1.11962 | 0.559808 | − | 0.828623i | \(-0.310875\pi\) | ||||
0.559808 | + | 0.828623i | \(0.310875\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 36.0839 | 2.40559 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.19247 | − | 2.42052i | 0.278264 | − | 0.160656i | −0.354373 | − | 0.935104i | \(-0.615306\pi\) |
0.632637 | + | 0.774448i | \(0.281972\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0330 | − | 5.79257i | −0.663001 | − | 0.382784i | 0.130419 | − | 0.991459i | \(-0.458368\pi\) |
−0.793419 | + | 0.608675i | \(0.791701\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.76916 | + | 1.47916i | 0.182197 | + | 0.0973213i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.3937 | + | 6.00079i | 0.680912 | + | 0.393125i | 0.800199 | − | 0.599735i | \(-0.204727\pi\) |
−0.119286 | + | 0.992860i | \(0.538061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.70087 | + | 5.02345i | −0.567582 | + | 0.327694i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.35707 | −0.283022 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.45645i | 0.288264i | 0.989559 | + | 0.144132i | \(0.0460389\pi\) | ||||
−0.989559 | + | 0.144132i | \(0.953961\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.4069 | − | 19.7573i | −0.734783 | − | 1.27268i | −0.954818 | − | 0.297190i | \(-0.903951\pi\) |
0.220035 | − | 0.975492i | \(-0.429383\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.53586 | − | 4.35083i | −0.483425 | − | 0.279106i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.9401 | − | 26.2769i | 0.826713 | − | 1.67877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.987025 | − | 1.70958i | 0.0628029 | − | 0.108778i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.15939 | − | 1.24672i | 0.136846 | − | 0.0790080i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.0358 | 1.07529 | 0.537644 | − | 0.843172i | \(-0.319314\pi\) | ||||
0.537644 | + | 0.843172i | \(0.319314\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.8403i | 1.05874i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.421340 | + | 0.729783i | 0.0263853 | + | 0.0457008i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.3130 | − | 14.0371i | −1.51660 | − | 0.875612i | −0.999810 | − | 0.0195016i | \(-0.993792\pi\) |
−0.516794 | − | 0.856110i | \(-0.672875\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.23640 | − | 3.33119i | −0.387511 | − | 0.206990i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.1081 | + | 7.56798i | 0.811372 | + | 0.468446i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.0136 | − | 12.7096i | 1.35742 | − | 0.783705i | 0.368142 | − | 0.929770i | \(-0.379994\pi\) |
0.989275 | + | 0.146065i | \(0.0466607\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 27.3177i | − | 1.67811i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.23245 | −0.136624 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.4165 | + | 18.0418i | 0.635103 | + | 1.10003i | 0.986493 | + | 0.163801i | \(0.0523755\pi\) |
−0.351391 | + | 0.936229i | \(0.614291\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.42979 | + | 11.1367i | −0.390582 | + | 0.676507i | −0.992526 | − | 0.122030i | \(-0.961059\pi\) |
0.601945 | + | 0.798538i | \(0.294393\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.58054 | + | 2.22791i | −0.216704 | + | 0.134839i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 37.8609 | + | 21.8590i | 2.28310 | + | 1.31815i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.9628 | + | 25.9162i | 0.899025 | + | 1.55716i | 0.828743 | + | 0.559629i | \(0.189056\pi\) |
0.0702814 | + | 0.997527i | \(0.477610\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.02014 | 0.0610740 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 11.4220i | − | 0.681381i | −0.940176 | − | 0.340690i | \(-0.889339\pi\) | ||
0.940176 | − | 0.340690i | \(-0.110661\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3348 | + | 19.6325i | 0.673787 | + | 1.16703i | 0.976822 | + | 0.214054i | \(0.0686667\pi\) |
−0.303035 | + | 0.952979i | \(0.598000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.298671 | + | 0.517314i | −0.0176918 | + | 0.0306430i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.2560 | + | 9.15238i | −0.841506 | + | 0.540248i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.32407 | + | 14.4177i | −0.489651 | + | 0.848101i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.71895 | − | 4.70936i | −0.159388 | − | 0.276067i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.8416i | 0.925474i | 0.886496 | + | 0.462737i | \(0.153133\pi\) | ||||
−0.886496 | + | 0.462737i | \(0.846867\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.474845 | −0.0276465 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.49142 | − | 6.04731i | −0.202592 | − | 0.350900i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.5902 | − | 11.3104i | −1.13293 | − | 0.654097i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0990360 | + | 2.99966i | 0.00570834 | + | 0.172897i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.877997 | + | 1.52074i | −0.0504396 | + | 0.0873640i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.44597 | + | 11.1647i | 0.369095 | + | 0.639291i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.7706 | −1.01422 | −0.507111 | − | 0.861881i | \(-0.669286\pi\) | ||||
−0.507111 | + | 0.861881i | \(0.669286\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.18112i | 0.180968i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.1694 | − | 15.6862i | 1.54063 | − | 0.889485i | 0.541834 | − | 0.840486i | \(-0.317730\pi\) |
0.998799 | − | 0.0489990i | \(-0.0156031\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.48992 | − | 3.16961i | −0.310309 | − | 0.179157i | 0.336756 | − | 0.941592i | \(-0.390670\pi\) |
−0.647065 | + | 0.762435i | \(0.724004\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −27.1154 | + | 16.8719i | −1.52778 | + | 0.950625i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.3736 | − | 10.0306i | −0.975797 | − | 0.563377i | −0.0747986 | − | 0.997199i | \(-0.523831\pi\) |
−0.900999 | + | 0.433822i | \(0.857165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.16910 | + | 15.8814i | 0.513371 | + | 0.889185i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.21805i | 0.291243i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.249420 | 0.0138781 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −50.8569 | + | 29.3623i | −2.82103 | + | 1.62873i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.33102 | + | 2.30539i | −0.0736054 | + | 0.127488i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.99306 | − | 5.60338i | 0.165013 | − | 0.308925i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.7442 | + | 9.66729i | 0.920347 | + | 0.531362i | 0.883746 | − | 0.467968i | \(-0.155014\pi\) |
0.0366010 | + | 0.999330i | \(0.488347\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.85448 | + | 6.67616i | 0.211224 | + | 0.365851i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.7800i | 1.51779i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.72087 | −0.366109 | −0.183055 | − | 0.983103i | \(-0.558599\pi\) | ||||
−0.183055 | + | 0.983103i | \(0.558599\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.71370 | + | 2.14411i | −0.201701 | + | 0.116452i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.07038 | + | 0.617982i | 0.0579641 | + | 0.0334656i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.83072 | + | 18.4296i | 0.0988496 | + | 0.995102i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.92794 | + | 3.42250i | 0.319150 | + | 0.184261i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.2089 | + | 13.3996i | −1.24592 | + | 0.719331i | −0.970293 | − | 0.241935i | \(-0.922218\pi\) |
−0.275625 | + | 0.961265i | \(0.588885\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.09042 | −0.111897 | −0.0559487 | − | 0.998434i | \(-0.517818\pi\) | ||||
−0.0559487 | + | 0.998434i | \(0.517818\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.37973 | 0.500653 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.8452 | − | 23.9805i | −0.736904 | − | 1.27636i | −0.953883 | − | 0.300179i | \(-0.902953\pi\) |
0.216978 | − | 0.976176i | \(-0.430380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.2380 | − | 16.8806i | −1.55179 | − | 0.895927i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.469982 | − | 0.251042i | −0.0248741 | − | 0.0132866i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.4361 | + | 19.8080i | −0.603576 | + | 1.04542i | 0.388699 | + | 0.921365i | \(0.372925\pi\) |
−0.992275 | + | 0.124060i | \(0.960409\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.41160 | − | 16.3014i | −0.495347 | − | 0.857967i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 0.412620i | − | 0.0216569i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.8602 | 0.987190 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0035 | + | 25.9869i | 0.783178 | + | 1.35650i | 0.930081 | + | 0.367353i | \(0.119736\pi\) |
−0.146904 | + | 0.989151i | \(0.546931\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.4695 | − | 0.260979i | 0.961482 | − | 0.0135860i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.12539 | + | 14.6657i | 0.473767 | + | 0.761405i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.8866 | + | 25.7843i | −0.770796 | + | 1.33506i | 0.166330 | + | 0.986070i | \(0.446808\pi\) |
−0.937127 | + | 0.348989i | \(0.886525\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.23773 | − | 5.33340i | 0.477034 | − | 0.275416i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.6329 | −1.26866 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.7944 | 1.68454 | 0.842268 | − | 0.539059i | \(-0.181220\pi\) | ||||
0.842268 | + | 0.539059i | \(0.181220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.66263 | + | 0.959918i | −0.0851790 | + | 0.0491781i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.8601 | − | 11.4662i | −1.01480 | − | 0.585896i | −0.102208 | − | 0.994763i | \(-0.532591\pi\) |
−0.912594 | + | 0.408867i | \(0.865924\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −38.6715 | + | 1.27677i | −1.97088 | + | 0.0650701i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.63620 | − | 2.83397i | 0.0831725 | − | 0.144059i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.17937 | − | 10.7030i | −0.313306 | − | 0.542662i | 0.665770 | − | 0.746157i | \(-0.268103\pi\) |
−0.979076 | + | 0.203495i | \(0.934770\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.85813i | − | 0.144542i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.42625i | − | 0.324161i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 46.5049 | − | 26.8496i | 2.33992 | − | 1.35095i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.5979 | − | 14.7789i | −1.28472 | − | 0.741733i | −0.307013 | − | 0.951705i | \(-0.599329\pi\) |
−0.977707 | + | 0.209972i | \(0.932663\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0124633 | − | 0.377494i | −0.000623943 | − | 0.0188984i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.24277 | + | 14.2769i | −0.411624 | + | 0.712954i | −0.995068 | − | 0.0992000i | \(-0.968372\pi\) |
0.583443 | + | 0.812154i | \(0.301705\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.43779 | + | 0.830108i | −0.0716214 | + | 0.0413506i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 33.3737 | 1.65835 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.33992i | 0.462962i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.06901 | − | 8.77979i | −0.250647 | − | 0.434133i | 0.713057 | − | 0.701106i | \(-0.247310\pi\) |
−0.963704 | + | 0.266973i | \(0.913977\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.94588 | + | 5.10242i | −0.145310 | + | 0.251684i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.254924 | − | 0.158621i | 0.0125440 | − | 0.00780522i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.3654 | + | 26.6137i | −0.754258 | + | 1.30641i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.37119 | + | 3.10106i | −0.263028 | + | 0.151859i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.1068 | −0.738018 | −0.369009 | − | 0.929426i | \(-0.620303\pi\) | ||||
−0.369009 | + | 0.929426i | \(0.620303\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 28.1611i | − | 1.37249i | −0.727370 | − | 0.686245i | \(-0.759258\pi\) | ||
0.727370 | − | 0.686245i | \(-0.240742\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.99851 | + | 3.46324i | −0.291657 | + | 0.168388i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.42575 | − | 3.70991i | −0.311695 | − | 0.179957i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.19012 | − | 3.84062i | −0.347954 | − | 0.185861i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.82444 | + | 2.78539i | 0.232926 | + | 0.134480i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.6842 | − | 25.4339i | −0.707315 | − | 1.22511i | −0.965850 | − | 0.259104i | \(-0.916573\pi\) |
0.258534 | − | 0.966002i | \(-0.416760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.54692 | −0.266568 | −0.133284 | − | 0.991078i | \(-0.542552\pi\) | ||||
−0.133284 | + | 0.991078i | \(0.542552\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.45386 | 0.357385 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.75458 | − | 1.01301i | 0.0839329 | − | 0.0484587i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.8508 | + | 16.0797i | 1.32925 | + | 0.767442i | 0.985183 | − | 0.171504i | \(-0.0548628\pi\) |
0.344065 | + | 0.938946i | \(0.388196\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.92109 | − | 18.1156i | 0.424814 | − | 0.862650i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.6302 | − | 23.6082i | 0.647591 | − | 1.12166i | −0.336105 | − | 0.941824i | \(-0.609110\pi\) |
0.983697 | − | 0.179837i | \(-0.0575569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.8279 | − | 13.7571i | 1.12955 | − | 0.652147i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.53007 | 0.261564 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.00100 | −0.188819 | −0.0944095 | − | 0.995533i | \(-0.530096\pi\) | ||||
−0.0944095 | + | 0.995533i | \(0.530096\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.5371 | + | 10.9147i | 0.919967 | + | 0.513951i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.65455 | + | 2.86577i | −0.0777377 | + | 0.134646i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24.4876 | − | 45.8438i | 1.14800 | − | 2.14919i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.3377 | + | 8.27785i | 0.670687 | + | 0.387222i | 0.796337 | − | 0.604853i | \(-0.206768\pi\) |
−0.125650 | + | 0.992075i | \(0.540102\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.592563 | + | 1.02635i | 0.0276585 | + | 0.0479059i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.76219 | −0.0820732 | −0.0410366 | − | 0.999158i | \(-0.513066\pi\) | ||||
−0.0410366 | + | 0.999158i | \(0.513066\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 40.0312i | − | 1.86041i | −0.367042 | − | 0.930204i | \(-0.619629\pi\) | ||
0.367042 | − | 0.930204i | \(-0.380371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.435072 | − | 0.251189i | 0.0201760 | − | 0.0116486i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.2164 | − | 17.6953i | 0.472758 | − | 0.818841i | −0.526756 | − | 0.850017i | \(-0.676592\pi\) |
0.999514 | + | 0.0311756i | \(0.00992511\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.27985 | − | 14.9139i | −0.428504 | − | 0.688661i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.17706 | − | 3.77078i | 0.100314 | − | 0.173748i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.43355 | − | 1.98236i | 0.157875 | − | 0.0911490i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.25961i | − | 0.241328i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 18.8332i | − | 0.862312i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.9075 | + | 8.60685i | −0.681141 | + | 0.393257i | −0.800285 | − | 0.599620i | \(-0.795318\pi\) |
0.119144 | + | 0.992877i | \(0.461985\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.8651 | − | 6.27295i | −0.495405 | − | 0.286022i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.32574 | + | 0.142817i | −0.196828 | + | 0.00649842i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 58.0410 | + | 33.5100i | 2.63551 | + | 1.52161i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.8130 | − | 27.3890i | −0.716558 | − | 1.24111i | −0.962356 | − | 0.271793i | \(-0.912383\pi\) |
0.245798 | − | 0.969321i | \(-0.420950\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.87547i | 0.175255i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.6941 | −0.798524 | −0.399262 | − | 0.916837i | \(-0.630734\pi\) | ||||
−0.399262 | + | 0.916837i | \(0.630734\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.55618 | − | 2.69538i | −0.0700868 | − | 0.121394i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 36.5354 | + | 21.0938i | 1.64215 | + | 0.948094i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.3356 | − | 0.704409i | 0.957031 | − | 0.0315971i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.4272 | − | 7.17486i | −0.556319 | − | 0.321191i | 0.195348 | − | 0.980734i | \(-0.437416\pi\) |
−0.751667 | + | 0.659543i | \(0.770750\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.49534 | − | 2.59000i | −0.0668068 | − | 0.115713i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.34019i | 0.238107i | 0.992888 | + | 0.119054i | \(0.0379860\pi\) | ||||
−0.992888 | + | 0.119054i | \(0.962014\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 21.6420i | − | 0.963054i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.65816 | + | 1.53469i | −0.118053 | + | 0.0681578i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.9828 | + | 15.0012i | 1.15167 | + | 0.664915i | 0.949293 | − | 0.314393i | \(-0.101801\pi\) |
0.202374 | + | 0.979308i | \(0.435134\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.1253 | + | 6.30021i | −0.447916 | + | 0.278705i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.420044 | + | 0.727538i | −0.0185454 | + | 0.0321216i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.6031 | − | 33.9535i | −0.863814 | − | 1.49617i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.39189 | −0.369075 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 3.86307i | − | 0.169570i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.9614 | − | 16.7209i | 1.26882 | − | 0.732555i | 0.294058 | − | 0.955788i | \(-0.404994\pi\) |
0.974765 | + | 0.223232i | \(0.0716608\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.89239 | − | 11.9380i | 0.301383 | − | 0.522011i | −0.675066 | − | 0.737757i | \(-0.735885\pi\) |
0.976450 | + | 0.215746i | \(0.0692183\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.29381 | + | 9.91067i | −0.231041 | + | 0.432537i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.181664 | − | 0.104884i | −0.00791341 | − | 0.00456881i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.108116 | − | 0.187263i | −0.00470070 | − | 0.00814185i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.327365 | −0.0142064 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25.8186 | + | 15.3968i | −1.11833 | + | 0.666911i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.1552 | − | 55.6945i | −1.39019 | − | 2.40788i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.10382 | + | 7.10802i | −0.177093 | + | 0.306734i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.3346 | − | 13.6035i | 0.875873 | − | 0.585946i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.1515 | − | 17.5830i | 0.436448 | − | 0.755951i | −0.560964 | − | 0.827840i | \(-0.689569\pi\) |
0.997413 | + | 0.0718893i | \(0.0229028\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.23800 | + | 3.87634i | 0.0960419 | + | 0.166350i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 32.8085i | − | 1.40536i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.94543i | 0.211451i | 0.994395 | + | 0.105726i | \(0.0337165\pi\) | ||||
−0.994395 | + | 0.105726i | \(0.966283\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.44394 | + | 7.69714i | 0.189663 | + | 0.328506i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.10311 | − | 1.91065i | 0.0469942 | − | 0.0813964i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.9975 | + | 29.9493i | −0.680282 | + | 1.27357i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.28774 | + | 1.89818i | 0.139557 | + | 0.0805733i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.65247 | − | 2.10875i | 0.154760 | − | 0.0893507i | −0.420620 | − | 0.907237i | \(-0.638187\pi\) |
0.575380 | + | 0.817886i | \(0.304854\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.32563i | 0.225250i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.703867i | 0.0297173i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.289260 | + | 0.167004i | −0.0121909 | + | 0.00703839i | −0.506083 | − | 0.862485i | \(-0.668907\pi\) |
0.493892 | + | 0.869523i | \(0.335574\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.4253 | − | 45.7700i | 1.11172 | − | 1.92556i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.9169 | + | 11.1484i | −0.752441 | + | 0.468189i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.1104 | + | 38.2964i | −0.926917 | + | 1.60547i | −0.138469 | + | 0.990367i | \(0.544218\pi\) |
−0.788449 | + | 0.615101i | \(0.789115\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.59195 | + | 3.80587i | −0.275865 | + | 0.159271i | −0.631550 | − | 0.775335i | \(-0.717581\pi\) |
0.355685 | + | 0.934606i | \(0.384248\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.82200 | −0.243218 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −60.2703 | −2.51345 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.367907 | − | 0.212411i | 0.0153162 | − | 0.00884280i | −0.492322 | − | 0.870413i | \(-0.663852\pi\) |
0.507639 | + | 0.861570i | \(0.330519\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.08708 | − | 7.07902i | 0.169853 | − | 0.294194i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.641183 | − | 19.4205i | −0.0266008 | − | 0.805699i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.4088 | − | 19.7607i | 0.472505 | − | 0.818403i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −49.0765 | + | 28.3343i | −2.02906 | + | 1.17148i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 33.5213i | − | 1.38357i | −0.722103 | − | 0.691785i | \(-0.756824\pi\) | ||
0.722103 | − | 0.691785i | \(-0.243176\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.148696i | − | 0.00612691i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.78247 | − | 1.60646i | 0.114456 | − | 0.0660809i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.4301 | − | 22.7650i | −1.61920 | − | 0.934847i | −0.987127 | − | 0.159940i | \(-0.948870\pi\) |
−0.632075 | − | 0.774907i | \(-0.717797\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.56332 | − | 0.216693i | 0.269070 | − | 0.00888354i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.14329 | − | 5.44433i | 0.128646 | − | 0.222822i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.01805 | + | 5.22741i | 0.123314 | + | 0.213586i | 0.921073 | − | 0.389391i | \(-0.127314\pi\) |
−0.797759 | + | 0.602977i | \(0.793981\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.91508i | 0.0781177i | 0.999237 | + | 0.0390588i | \(0.0124360\pi\) | ||||
−0.999237 | + | 0.0390588i | \(0.987564\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.1520i | 0.779928i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.54269 | + | 4.40407i | 0.103375 | + | 0.179051i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.5421 | + | 26.9198i | −0.630836 | + | 1.09264i | 0.356545 | + | 0.934278i | \(0.383955\pi\) |
−0.987381 | + | 0.158362i | \(0.949379\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.00167 | + | 2.48994i | −0.162156 | + | 0.100898i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.63623 | − | 9.76224i | 0.228017 | − | 0.394938i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.2562 | − | 21.2283i | −0.495021 | − | 0.857402i | 0.504962 | − | 0.863141i | \(-0.331506\pi\) |
−0.999984 | + | 0.00573943i | \(0.998173\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.81266 | − | 4.65905i | 0.315037 | − | 0.187871i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.04873 | −0.283771 | −0.141886 | − | 0.989883i | \(-0.545316\pi\) | ||||
−0.141886 | + | 0.989883i | \(0.545316\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.673139 | − | 1.16591i | −0.0270557 | − | 0.0468619i | 0.852181 | − | 0.523248i | \(-0.175280\pi\) |
−0.879236 | + | 0.476386i | \(0.841946\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.33691 | + | 4.81332i | 0.334549 | + | 0.193152i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.19670 | + | 15.3452i | −0.328394 | + | 0.614794i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −34.4607 | + | 59.6877i | −1.37843 | + | 2.38751i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.432097 | + | 0.249471i | −0.0172563 | + | 0.00996293i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.58517i | − | 0.0632049i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.5849 | 1.17776 | 0.588879 | − | 0.808222i | \(-0.299570\pi\) | ||||
0.588879 | + | 0.808222i | \(0.299570\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.0957388 | + | 0.165824i | 0.00380527 | + | 0.00659093i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.8306 | − | 20.4912i | 0.469484 | − | 0.813170i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.16764 | + | 32.7916i | 0.0858852 | + | 1.29925i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −20.1571 | − | 11.6377i | −0.797402 | − | 0.460380i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.6214 | − | 16.5246i | 1.13048 | − | 0.652681i | 0.186422 | − | 0.982470i | \(-0.440311\pi\) |
0.944055 | + | 0.329789i | \(0.106977\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 14.2295i | − | 0.561155i | −0.959831 | − | 0.280578i | \(-0.909474\pi\) | ||
0.959831 | − | 0.280578i | \(-0.0905260\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.61152i | − | 0.0634537i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.63959 | + | 8.03601i | 0.182401 | + | 0.315928i | 0.942698 | − | 0.333648i | \(-0.108280\pi\) |
−0.760297 | + | 0.649576i | \(0.774946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.343487 | − | 0.198312i | −0.0134830 | − | 0.00778443i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.149663 | + | 0.280187i | −0.00586575 | + | 0.0109814i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.5493 | − | 8.40002i | −0.569356 | − | 0.328718i | 0.187536 | − | 0.982258i | \(-0.439950\pi\) |
−0.756892 | + | 0.653540i | \(0.773283\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.6005 | + | 68.5901i | 1.54732 | + | 2.68004i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.0025 | 0.507277 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.20966i | 0.0471216i | 0.999722 | + | 0.0235608i | \(0.00750033\pi\) | ||||
−0.999722 | + | 0.0235608i | \(0.992500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.3689 | − | 37.0120i | −0.831153 | − | 1.43960i | −0.897125 | − | 0.441777i | \(-0.854348\pi\) |
0.0659721 | − | 0.997821i | \(-0.478985\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.818804 | − | 0.472737i | −0.0317997 | − | 0.0183596i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.45926 | + | 3.95236i | 0.0953661 | + | 0.153266i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.8943 | − | 12.6407i | −0.847750 | − | 0.489449i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.91591 | − | 2.83820i | 0.190060 | − | 0.109731i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.7683i | 0.415704i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 11.2114i | − | 0.432169i | −0.976375 | − | 0.216085i | \(-0.930671\pi\) | ||
0.976375 | − | 0.216085i | \(-0.0693287\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21.6430 | − | 12.4956i | 0.833039 | − | 0.480955i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.2563 | + | 21.2286i | −0.471049 | + | 0.815880i | −0.999452 | − | 0.0331133i | \(-0.989458\pi\) |
0.528403 | + | 0.848994i | \(0.322791\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −42.3537 | + | 1.39834i | −1.62539 | + | 0.0536634i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.821791 | − | 1.42338i | 0.0314911 | − | 0.0545442i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.2539 | + | 12.8483i | −0.851522 | + | 0.491627i | −0.861164 | − | 0.508327i | \(-0.830264\pi\) |
0.00964183 | + | 0.999954i | \(0.496931\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 72.6138i | − | 2.77443i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.93326 | −0.150063 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.3250 | + | 26.5436i | 0.583835 | + | 1.01123i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.7856 | + | 10.2685i | 0.676597 | + | 0.390633i | 0.798572 | − | 0.601900i | \(-0.205589\pi\) |
−0.121975 | + | 0.992533i | \(0.538923\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −26.6607 | + | 0.880222i | −1.01275 | + | 0.0334369i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 38.2193 | − | 66.1978i | 1.44974 | − | 2.51103i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.31584 | − | 1.85243i | −0.125596 | − | 0.0701660i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.07465 | 0.154117 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.12245 | 0.155703 | 0.0778513 | − | 0.996965i | \(-0.475194\pi\) | ||||
0.0778513 | + | 0.996965i | \(0.475194\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.973121 | − | 0.561832i | 0.0367020 | − | 0.0211899i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.70551 | + | 2.95403i | −0.0642332 | + | 0.111255i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.22944 | + | 11.6187i | 0.271891 | + | 0.436965i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.781214 | − | 0.451034i | −0.0293391 | − | 0.0169389i | 0.485259 | − | 0.874371i | \(-0.338725\pi\) |
−0.514598 | + | 0.857432i | \(0.672059\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 32.0612 | − | 18.5105i | 1.20239 | − | 0.694199i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.70392 | −0.0638122 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −68.6578 | −2.56766 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.756503 | + | 1.31030i | 0.0282521 | + | 0.0489341i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.58744 | − | 2.64856i | −0.171083 | − | 0.0987747i | 0.412014 | − | 0.911178i | \(-0.364826\pi\) |
−0.583096 | + | 0.812403i | \(0.698159\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.8661 | + | 11.6799i | 0.814337 | + | 0.434981i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.70780 | − | 3.87275i | −0.249466 | − | 0.144029i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −56.8385 | + | 32.8157i | −2.11093 | + | 1.21874i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.9678i | 1.22271i | 0.791357 | + | 0.611354i | \(0.209375\pi\) | ||||
−0.791357 | + | 0.611354i | \(0.790625\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.9734 | 0.776791 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.582741 | + | 0.336446i | −0.0215535 | + | 0.0124439i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.53214 | + | 2.65374i | −0.0565908 | + | 0.0980182i | −0.892933 | − | 0.450190i | \(-0.851356\pi\) |
0.836342 | + | 0.548208i | \(0.184690\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.655924 | − | 9.92267i | −0.0241941 | − | 0.366003i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.6019 | + | 20.0951i | −0.427363 | + | 0.740214i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.0637 | − | 29.5552i | −0.627697 | − | 1.08720i | −0.988013 | − | 0.154373i | \(-0.950664\pi\) |
0.360315 | − | 0.932831i | \(-0.382669\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.670209i | − | 0.0246207i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.8675 | −0.802242 | −0.401121 | − | 0.916025i | \(-0.631379\pi\) | ||||
−0.401121 | + | 0.916025i | \(0.631379\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −59.0249 | + | 34.0780i | −2.16250 | + | 1.24852i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.5931 | + | 18.3478i | −0.387582 | + | 0.671312i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35.8674 | + | 19.1587i | 1.31057 | + | 0.700042i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.1252 | + | 7.00051i | 0.442457 | + | 0.255452i | 0.704639 | − | 0.709566i | \(-0.251109\pi\) |
−0.262183 | + | 0.965018i | \(0.584442\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.00892 | − | 2.89190i | 0.182535 | − | 0.105387i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 40.7835i | − | 1.48426i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 18.5806i | − | 0.675323i | −0.941268 | − | 0.337662i | \(-0.890364\pi\) | ||
0.941268 | − | 0.337662i | \(-0.109636\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.85871 | + | 4.95144i | 0.103765 | + | 0.179726i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.88037 | + | 13.6492i | −0.285663 | + | 0.494783i | −0.972770 | − | 0.231773i | \(-0.925547\pi\) |
0.687107 | + | 0.726557i | \(0.258881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.9596 | + | 17.6135i | 0.396764 | + | 0.637652i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.20079 | − | 3.58003i | −0.224190 | − | 0.129436i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.461391 | − | 0.266384i | 0.0166599 | − | 0.00961857i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.52930 | 0.235453 | 0.117726 | − | 0.993046i | \(-0.462439\pi\) | ||||
0.117726 | + | 0.993046i | \(0.462439\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.53147 | −0.343268 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.4930 | − | 11.2543i | 0.701113 | − | 0.404788i | −0.106649 | − | 0.994297i | \(-0.534012\pi\) |
0.807762 | + | 0.589509i | \(0.200679\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.21172 | + | 3.83082i | −0.0794474 | + | 0.137607i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.39913 | + | 0.0792092i | −0.0860685 | + | 0.00284161i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0380406 | − | 2.69212i | −0.00136294 | − | 0.0964553i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.0998 | − | 24.4217i | −0.504532 | − | 0.873875i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.4829 | 0.374629 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 53.6629i | 1.91531i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.4455 | + | 30.2165i | 0.621865 | + | 1.07710i | 0.989138 | + | 0.146988i | \(0.0469580\pi\) |
−0.367273 | + | 0.930113i | \(0.619709\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.31502 | − | 7.47383i | 0.153619 | − | 0.266075i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.10270 | + | 33.3993i | 0.0392076 | + | 1.18754i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.5267 | − | 7.23227i | −0.444835 | − | 0.256825i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.63730 | − | 8.03204i | −0.164468 | − | 0.284867i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.0410 | 1.06411 | 0.532053 | − | 0.846711i | \(-0.321421\pi\) | ||||
0.532053 | + | 0.846711i | \(0.321421\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.42427 | 0.0503871 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.4273 | − | 9.48431i | 0.580430 | − | 0.335112i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.6429 | + | 7.87671i | 0.481446 | + | 0.277963i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 45.2904 | − | 28.1809i | 1.59628 | − | 0.993246i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.12537 | + | 3.53649i | 0.215623 | + | 0.124490i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.7648 | + | 18.9168i | −1.15195 | + | 0.665079i | −0.949362 | − | 0.314185i | \(-0.898269\pi\) |
−0.202589 | + | 0.979264i | \(0.564935\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.5682 | 0.406215 | 0.203107 | − | 0.979156i | \(-0.434896\pi\) | ||||
0.203107 | + | 0.979156i | \(0.434896\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.36595i | 0.153120i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.8818 | − | 41.3645i | −0.836544 | − | 1.44894i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.413082 | − | 0.238493i | −0.0144519 | − | 0.00834382i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.8821 | − | 31.6054i | 0.589908 | − | 1.10438i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.3163 | − | 26.5287i | 0.534544 | − | 0.925857i | −0.464641 | − | 0.885499i | \(-0.653817\pi\) |
0.999185 | − | 0.0403581i | \(-0.0128499\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.8684 | − | 9.73895i | 0.587994 | − | 0.339479i | −0.176310 | − | 0.984335i | \(-0.556416\pi\) |
0.764304 | + | 0.644856i | \(0.223083\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.8427 | 0.516756 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.2885i | 1.05324i | 0.850102 | + | 0.526618i | \(0.176540\pi\) | ||||
−0.850102 | + | 0.526618i | \(0.823460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.92108 | − | 8.52356i | −0.170916 | − | 0.296035i | 0.767824 | − | 0.640661i | \(-0.221339\pi\) |
−0.938740 | + | 0.344625i | \(0.888006\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.79881 | + | 5.08000i | 0.305227 | + | 0.176223i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.45118 | + | 2.30879i | −0.119576 | + | 0.0799949i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31.9208 | + | 18.4295i | 1.10466 | + | 0.637778i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.611874 | − | 0.353266i | 0.0211495 | − | 0.0122107i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.67304i | 0.264903i | 0.991190 | + | 0.132451i | \(0.0422848\pi\) | ||||
−0.991190 | + | 0.132451i | \(0.957715\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.46988 | 0.0506855 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.93894 | − | 3.35835i | −0.0667807 | − | 0.115668i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.9144 | − | 32.7607i | 0.650676 | − | 1.12700i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.83623 | − | 1.51498i | −0.0974541 | − | 0.0520554i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.66543 | + | 3.84829i | 0.228757 | + | 0.132073i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.43808 | − | 11.1511i | −0.220694 | − | 0.382254i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.4075 | 0.801459 | 0.400729 | − | 0.916196i | \(-0.368757\pi\) | ||||
0.400729 | + | 0.916196i | \(0.368757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 5.07548i | − | 0.173578i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.29565 | − | 2.24414i | −0.0442587 | − | 0.0766583i | 0.843047 | − | 0.537839i | \(-0.180759\pi\) |
−0.887306 | + | 0.461181i | \(0.847426\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.1249 | + | 22.7329i | −0.447814 | + | 0.775637i | −0.998243 | − | 0.0592446i | \(-0.981131\pi\) |
0.550429 | + | 0.834882i | \(0.314464\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.63795 | + | 5.11104i | −0.0899010 | + | 0.174184i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.23479 | + | 9.06692i | −0.178194 | + | 0.308642i | −0.941262 | − | 0.337677i | \(-0.890359\pi\) |
0.763068 | + | 0.646318i | \(0.223692\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.8054 | + | 41.2322i | 0.809409 | + | 1.40194i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.65220i | 0.191959i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.8534 | 1.52155 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.5844 | − | 26.9929i | −0.528056 | − | 0.914620i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 40.0143 | + | 23.1023i | 1.35428 | + | 0.781894i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.74294 | − | 83.0797i | −0.0927283 | − | 2.80861i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.03604 | − | 6.99063i | 0.136287 | − | 0.236057i | −0.789801 | − | 0.613363i | \(-0.789816\pi\) |
0.926089 | + | 0.377306i | \(0.123150\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.68918 | + | 4.65780i | 0.0907038 | + | 0.157104i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.3701 | −1.05688 | −0.528442 | − | 0.848969i | \(-0.677224\pi\) | ||||
−0.528442 | + | 0.848969i | \(0.677224\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.24853i | 0.311238i | 0.987817 | + | 0.155619i | \(0.0497372\pi\) | ||||
−0.987817 | + | 0.155619i | \(0.950263\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.139616 | + | 0.0806072i | −0.00469313 | + | 0.00270958i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.6503 | + | 25.7789i | 1.49921 | + | 0.865569i | 1.00000 | 0.000911288i | \(-0.000290072\pi\) | |
0.499211 | + | 0.866481i | \(0.333623\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.493680 | + | 14.9529i | 0.0165575 | + | 0.501503i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.1414 | + | 13.9380i | 0.808767 | + | 0.466942i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.504804 | + | 0.874347i | 0.0168926 | + | 0.0292589i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 101.156i | − | 3.38127i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.67997 | −0.256427 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.60690 | + | 0.927741i | −0.0535930 | + | 0.0309419i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.93630 | + | 3.35378i | −0.0645077 | + | 0.111731i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.538325 | + | 0.865160i | 0.0179143 | + | 0.0287907i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −47.7744 | − | 27.5825i | −1.58807 | − | 0.916875i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.133323 | + | 0.230922i | 0.00442692 | + | 0.00766764i | 0.868230 | − | 0.496161i | \(-0.165258\pi\) |
−0.863803 | + | 0.503829i | \(0.831924\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 14.9203i | − | 0.494874i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.9639 | 1.68851 | 0.844255 | − | 0.535942i | \(-0.180044\pi\) | ||||
0.844255 | + | 0.535942i | \(0.180044\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.2296 | + | 12.8343i | −0.735693 | + | 0.424753i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.79054 | + | 2.18847i | 0.125311 | + | 0.0723485i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.1722 | − | 23.5947i | −1.45870 | − | 0.779166i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.0626 | − | 27.1716i | −1.55245 | − | 0.896309i | −0.997941 | − | 0.0641328i | \(-0.979572\pi\) |
−0.554511 | − | 0.832176i | \(-0.687095\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.22498 | + | 3.01664i | −0.172169 | + | 0.0994017i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.8794 | 1.24682 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −33.4270 | −1.09907 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.5146 | − | 23.4080i | −0.443879 | − | 0.768820i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.77731 | + | 1.60348i | 0.0911207 | + | 0.0526085i | 0.544868 | − | 0.838522i | \(-0.316580\pi\) |
−0.453747 | + | 0.891130i | \(0.649913\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.64055 | − | 1.30035i | −0.0865405 | − | 0.0426171i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.32562 | − | 9.22425i | 0.174353 | − | 0.301988i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.33744 | − | 7.51267i | −0.141850 | − | 0.245691i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.33380i | 0.304922i | 0.988309 | + | 0.152461i | \(0.0487198\pi\) | ||||
−0.988309 | + | 0.152461i | \(0.951280\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.15222 | −0.0702352 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.8479 | + | 44.7698i | 0.842616 | + | 1.45945i | 0.887676 | + | 0.460469i | \(0.152319\pi\) |
−0.0450599 | + | 0.998984i | \(0.514348\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.8492 | + | 0.435910i | −1.00459 | + | 0.0141952i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.4211 | + | 19.5096i | −0.338998 | + | 0.634646i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.340654 | + | 0.590030i | −0.0110698 | + | 0.0191734i | −0.871507 | − | 0.490383i | \(-0.836857\pi\) |
0.860437 | + | 0.509556i | \(0.170190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.3259 | + | 10.5804i | −0.594883 | + | 0.343456i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.81099 | −0.220862 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.1209 | 0.716566 | 0.358283 | − | 0.933613i | \(-0.383362\pi\) | ||||
0.358283 | + | 0.933613i | \(0.383362\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 62.1408 | − | 35.8770i | 2.01083 | − | 1.16095i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.39187 | + | 3.11300i | 0.174294 | + | 0.100629i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.2564 | + | 38.9833i | 0.783281 | + | 1.25884i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4375 | − | 26.7385i | 0.497983 | − | 0.862532i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.1683 | − | 38.3966i | −0.714362 | − | 1.23731i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 100.743i | 3.24304i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.55641i | 0.275156i | 0.990491 | + | 0.137578i | \(0.0439317\pi\) | ||||
−0.990491 | + | 0.137578i | \(0.956068\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0733355 | − | 0.0423403i | 0.00235588 | − | 0.00136017i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.5630 | + | 18.8003i | 1.04500 | + | 0.603329i | 0.921244 | − | 0.388984i | \(-0.127174\pi\) |
0.123752 | + | 0.992313i | \(0.460507\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.59486 | + | 48.3059i | 0.0511287 | + | 1.54862i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.96877 | + | 17.2664i | −0.319256 | + | 0.552968i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.2023 | + | 13.3959i | −0.742308 | + | 0.428572i | −0.822908 | − | 0.568175i | \(-0.807650\pi\) |
0.0805997 | + | 0.996747i | \(0.474316\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.9817 | 0.734499 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 22.6187i | − | 0.722159i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.65553 | + | 11.5277i | 0.212278 | + | 0.367677i | 0.952427 | − | 0.304766i | \(-0.0985783\pi\) |
−0.740149 | + | 0.672443i | \(0.765245\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.7990 | + | 34.2929i | −0.630849 | + | 1.09266i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.0711692 | − | 2.15561i | −0.00226534 | − | 0.0686140i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.73291 | + | 4.73354i | −0.0869015 | + | 0.150518i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.1601 | + | 22.0317i | −1.21219 | + | 0.699861i | −0.963237 | − | 0.268653i | \(-0.913421\pi\) |
−0.248958 | + | 0.968514i | \(0.580088\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.56427 | 0.208311 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 77.4796i | 2.45627i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.4632 | − | 29.1350i | 1.59819 | − | 0.922713i | 0.606349 | − | 0.795198i | \(-0.292633\pi\) |
0.991837 | − | 0.127515i | \(-0.0407000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.62381 | + | 2.66956i | 0.146291 | + | 0.0844610i |
(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 | 1148.2.r.a.737.15 | yes | 56 | |
7.4 | even | 3 | inner | 1148.2.r.a.81.14 | ✓ | 56 | |
41.40 | even | 2 | inner | 1148.2.r.a.737.14 | yes | 56 | |
287.81 | even | 6 | inner | 1148.2.r.a.81.15 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.r.a.81.14 | ✓ | 56 | 7.4 | even | 3 | inner | |
1148.2.r.a.81.15 | yes | 56 | 287.81 | even | 6 | inner | |
1148.2.r.a.737.14 | yes | 56 | 41.40 | even | 2 | inner | |
1148.2.r.a.737.15 | yes | 56 | 1.1 | even | 1 | trivial |