Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(449,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.dc (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} - 18 x^{18} + 232 x^{17} + 208 x^{16} - 3152 x^{15} - 2732 x^{14} + 24552 x^{13} + 30728 x^{12} - 110512 x^{11} - 211368 x^{10} + 231024 x^{9} + \cdots + 414864 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 1368) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1889.6 | ||
Root | \(-2.54394 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1889 |
Dual form | 2736.2.dc.e.449.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.501439 | + | 0.289506i | 0.224250 | + | 0.129471i | 0.607917 | − | 0.794001i | \(-0.292005\pi\) |
−0.383666 | + | 0.923472i | \(0.625339\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.198579 | 0.0750558 | 0.0375279 | − | 0.999296i | \(-0.488052\pi\) | ||||
0.0375279 | + | 0.999296i | \(0.488052\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.48583i | − | 0.749505i | −0.927125 | − | 0.374752i | \(-0.877728\pi\) | ||
0.927125 | − | 0.374752i | \(-0.122272\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.34042 | + | 2.50594i | −1.20382 | + | 0.695024i | −0.961402 | − | 0.275149i | \(-0.911273\pi\) |
−0.242415 | + | 0.970173i | \(0.577939\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.01349 | − | 2.31719i | −0.973415 | − | 0.562001i | −0.0731391 | − | 0.997322i | \(-0.523302\pi\) |
−0.900276 | + | 0.435321i | \(0.856635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.16251 | + | 2.99976i | 0.725529 | + | 0.688191i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.14465 | − | 2.97027i | 1.07273 | − | 0.619344i | 0.143807 | − | 0.989606i | \(-0.454065\pi\) |
0.928927 | + | 0.370262i | \(0.120732\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.33237 | − | 4.03979i | −0.466475 | − | 0.807958i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.51838 | + | 7.82606i | 0.839042 | + | 1.45326i | 0.890696 | + | 0.454599i | \(0.150217\pi\) |
−0.0516543 | + | 0.998665i | \(0.516449\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.41355i | − | 0.253882i | −0.991910 | − | 0.126941i | \(-0.959484\pi\) | ||
0.991910 | − | 0.126941i | \(-0.0405158\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0995752 | + | 0.0574898i | 0.0168313 | + | 0.00971755i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 11.6243i | − | 1.91102i | −0.294951 | − | 0.955512i | \(-0.595303\pi\) | ||
0.294951 | − | 0.955512i | \(-0.404697\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.60914 | − | 6.25122i | 0.563654 | − | 0.976277i | −0.433520 | − | 0.901144i | \(-0.642729\pi\) |
0.997174 | − | 0.0751327i | \(-0.0239380\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.66185 | − | 8.07455i | 0.710925 | − | 1.23136i | −0.253586 | − | 0.967313i | \(-0.581610\pi\) |
0.964510 | − | 0.264045i | \(-0.0850567\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.86260 | + | 1.07537i | −0.271689 | + | 0.156860i | −0.629655 | − | 0.776875i | \(-0.716804\pi\) |
0.357966 | + | 0.933735i | \(0.383470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.96057 | −0.994367 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.62456 | + | 2.81382i | 0.223151 | + | 0.386508i | 0.955763 | − | 0.294138i | \(-0.0950325\pi\) |
−0.732612 | + | 0.680646i | \(0.761699\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.719661 | − | 1.24649i | 0.0970391 | − | 0.168077i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.59275 | − | 7.95487i | 0.597925 | − | 1.03564i | −0.395202 | − | 0.918594i | \(-0.629326\pi\) |
0.993127 | − | 0.117042i | \(-0.0373411\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.46529 | − | 4.27001i | −0.315648 | − | 0.546719i | 0.663927 | − | 0.747798i | \(-0.268889\pi\) |
−0.979575 | + | 0.201079i | \(0.935555\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.90194 | −0.359941 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.17689 | + | 1.83418i | −0.388119 | + | 0.224081i | −0.681345 | − | 0.731963i | \(-0.738605\pi\) |
0.293226 | + | 0.956043i | \(0.405271\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.07974 | − | 13.9945i | 0.958889 | − | 1.66084i | 0.233683 | − | 0.972313i | \(-0.424922\pi\) |
0.725206 | − | 0.688532i | \(-0.241745\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.02871 | + | 8.70999i | −0.588566 | + | 1.01943i | 0.405854 | + | 0.913938i | \(0.366974\pi\) |
−0.994420 | + | 0.105489i | \(0.966359\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.493633i | − | 0.0562547i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.26495 | + | 0.730318i | 0.142318 | + | 0.0821672i | 0.569468 | − | 0.822013i | \(-0.307149\pi\) |
−0.427150 | + | 0.904181i | \(0.640482\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.592477i | 0.0650328i | 0.999471 | + | 0.0325164i | \(0.0103521\pi\) | ||||
−0.999471 | + | 0.0325164i | \(0.989648\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.34168 | − | 2.32386i | −0.145526 | − | 0.252058i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.78657 | + | 4.82649i | 0.295376 | + | 0.511607i | 0.975072 | − | 0.221887i | \(-0.0712216\pi\) |
−0.679696 | + | 0.733494i | \(0.737888\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.861917 | + | 0.497628i | −0.0903534 | + | 0.0521656i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.717358 | + | 2.41976i | 0.0735994 | + | 0.248262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.32474 | − | 5.38364i | −0.946784 | − | 0.546626i | −0.0547037 | − | 0.998503i | \(-0.517421\pi\) |
−0.892081 | + | 0.451876i | \(0.850755\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.3063 | − | 7.10502i | 1.22452 | − | 0.706976i | 0.258640 | − | 0.965974i | \(-0.416726\pi\) |
0.965878 | + | 0.258998i | \(0.0833924\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.3772i | 1.81076i | 0.424607 | + | 0.905378i | \(0.360412\pi\) | ||||
−0.424607 | + | 0.905378i | \(0.639588\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.0687 | 1.36007 | 0.680035 | − | 0.733180i | \(-0.261965\pi\) | ||||
0.680035 | + | 0.733180i | \(0.261965\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.11575 | − | 2.95358i | −0.490000 | − | 0.282902i | 0.234574 | − | 0.972098i | \(-0.424630\pi\) |
−0.724574 | + | 0.689197i | \(0.757964\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.69467 | −0.347566 | −0.173783 | − | 0.984784i | \(-0.555599\pi\) | ||||
−0.173783 | + | 0.984784i | \(0.555599\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.43964 | 0.320748 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.796995 | − | 0.460145i | −0.0730604 | − | 0.0421815i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.82067 | 0.438243 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5.59600i | − | 0.500521i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.90854 | − | 4.56600i | 0.701770 | − | 0.405167i | −0.106237 | − | 0.994341i | \(-0.533880\pi\) |
0.808006 | + | 0.589174i | \(0.200547\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.1576 | − | 7.59655i | −1.14959 | − | 0.663713i | −0.200799 | − | 0.979632i | \(-0.564354\pi\) |
−0.948786 | + | 0.315919i | \(0.897687\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.628008 | + | 0.595689i | 0.0544552 | + | 0.0516527i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.50990 | + | 3.18114i | −0.470742 | + | 0.271783i | −0.716550 | − | 0.697535i | \(-0.754280\pi\) |
0.245808 | + | 0.969319i | \(0.420947\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.45810 | − | 16.3819i | −0.802226 | − | 1.38950i | −0.918148 | − | 0.396238i | \(-0.870316\pi\) |
0.115922 | − | 0.993258i | \(-0.463018\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.22934 | + | 10.7895i | 0.520924 | + | 0.902266i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.23239i | 0.434526i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.73882 | + | 2.15861i | 0.306296 | + | 0.176840i | 0.645268 | − | 0.763956i | \(-0.276746\pi\) |
−0.338972 | + | 0.940797i | \(0.610079\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 13.5536i | − | 1.10298i | −0.834182 | − | 0.551489i | \(-0.814060\pi\) | ||
0.834182 | − | 0.551489i | \(-0.185940\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.409232 | − | 0.708810i | 0.0328703 | − | 0.0569330i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.860138 | + | 1.48980i | −0.0686465 | + | 0.118899i | −0.898306 | − | 0.439371i | \(-0.855201\pi\) |
0.829659 | + | 0.558270i | \(0.188535\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.02162 | − | 0.589833i | 0.0805150 | − | 0.0464853i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.69773 | −0.602933 | −0.301467 | − | 0.953477i | \(-0.597476\pi\) | ||||
−0.301467 | + | 0.953477i | \(0.597476\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.95402 | − | 10.3127i | −0.460736 | − | 0.798017i | 0.538262 | − | 0.842777i | \(-0.319081\pi\) |
−0.998998 | + | 0.0447601i | \(0.985748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.05951 | − | 10.4954i | 0.466116 | − | 0.807336i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.88358 | − | 13.6548i | 0.599377 | − | 1.03815i | −0.393536 | − | 0.919309i | \(-0.628748\pi\) |
0.992913 | − | 0.118842i | \(-0.0379183\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.463160 | − | 0.802217i | −0.0350116 | − | 0.0606419i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.4722 | 1.60491 | 0.802454 | − | 0.596714i | \(-0.203527\pi\) | ||||
0.802454 | + | 0.596714i | \(0.203527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.46463 | − | 3.73236i | 0.480512 | − | 0.277424i | −0.240118 | − | 0.970744i | \(-0.577186\pi\) |
0.720630 | + | 0.693320i | \(0.243853\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.36530 | − | 5.82888i | 0.247422 | − | 0.428548i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.76013 | + | 9.97684i | −0.421223 | + | 0.729579i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.49453i | − | 0.542285i | −0.962539 | − | 0.271143i | \(-0.912598\pi\) | ||
0.962539 | − | 0.271143i | \(-0.0874015\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.51556 | + | 3.76176i | 0.469001 | + | 0.270778i | 0.715821 | − | 0.698284i | \(-0.246053\pi\) |
−0.246821 | + | 0.969061i | \(0.579386\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.30108i | 0.235192i | 0.993062 | + | 0.117596i | \(0.0375188\pi\) | ||||
−0.993062 | + | 0.117596i | \(0.962481\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.08225 | − | 13.9989i | −0.572936 | − | 0.992354i | −0.996263 | − | 0.0863766i | \(-0.972471\pi\) |
0.423327 | − | 0.905977i | \(-0.360862\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.897255 | + | 1.55409i | 0.0629750 | + | 0.109076i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.61953 | − | 2.08974i | 0.252799 | − | 0.145954i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.45687 | − | 7.86145i | 0.515803 | − | 0.543788i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.7050 | + | 6.75788i | 0.805805 | + | 0.465232i | 0.845497 | − | 0.533980i | \(-0.179304\pi\) |
−0.0396918 | + | 0.999212i | \(0.512638\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.67526 | − | 2.69926i | 0.318850 | − | 0.184088i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.280702i | − | 0.0190553i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.2270 | 1.56242 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.1337 | − | 8.73745i | −1.01343 | − | 0.585103i | −0.101234 | − | 0.994863i | \(-0.532279\pi\) |
−0.912193 | + | 0.409760i | \(0.865613\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.5976 | 1.10162 | 0.550810 | − | 0.834630i | \(-0.314319\pi\) | ||||
0.550810 | + | 0.834630i | \(0.314319\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5614 | −0.697916 | −0.348958 | − | 0.937138i | \(-0.613464\pi\) | ||||
−0.348958 | + | 0.937138i | \(0.613464\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.58362 | − | 1.49165i | −0.169258 | − | 0.0977214i | 0.412978 | − | 0.910741i | \(-0.364489\pi\) |
−0.582236 | + | 0.813020i | \(0.697822\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.24531 | −0.0812350 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.8616i | 1.41411i | 0.707158 | + | 0.707056i | \(0.249977\pi\) | ||||
−0.707158 | + | 0.707056i | \(0.750023\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.70550 | + | 3.87142i | −0.431939 | + | 0.249380i | −0.700172 | − | 0.713974i | \(-0.746893\pi\) |
0.268233 | + | 0.963354i | \(0.413560\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.49030 | − | 2.01512i | −0.222987 | − | 0.128742i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.2438 | − | 5.09513i | −1.35171 | − | 0.324196i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.5605 | + | 10.7159i | −1.17153 | + | 0.676383i | −0.954040 | − | 0.299680i | \(-0.903120\pi\) |
−0.217490 | + | 0.976063i | \(0.569787\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.38357 | − | 12.7887i | −0.464201 | − | 0.804020i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.45876 | − | 12.9189i | −0.465265 | − | 0.805862i | 0.533949 | − | 0.845517i | \(-0.320707\pi\) |
−0.999213 | + | 0.0396549i | \(0.987374\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.30834i | − | 0.143433i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.7069 | − | 11.3778i | −1.21518 | − | 0.701586i | −0.251299 | − | 0.967910i | \(-0.580858\pi\) |
−0.963884 | + | 0.266324i | \(0.914191\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.88128i | 0.115566i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.57925 | + | 13.1276i | −0.462115 | + | 0.800407i | −0.999066 | − | 0.0432067i | \(-0.986243\pi\) |
0.536951 | + | 0.843613i | \(0.319576\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.62861 | + | 4.55289i | −0.159677 | + | 0.276568i | −0.934752 | − | 0.355301i | \(-0.884379\pi\) |
0.775075 | + | 0.631869i | \(0.217712\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.0422 | + | 5.79787i | −0.605568 | + | 0.349625i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.8807 | 1.37477 | 0.687384 | − | 0.726294i | \(-0.258759\pi\) | ||||
0.687384 | + | 0.726294i | \(0.258759\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.4022 | − | 18.0171i | −0.620542 | − | 1.07481i | −0.989385 | − | 0.145318i | \(-0.953579\pi\) |
0.368843 | − | 0.929492i | \(-0.379754\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.9479 | + | 18.9622i | −0.650783 | + | 1.12719i | 0.332151 | + | 0.943226i | \(0.392226\pi\) |
−0.982933 | + | 0.183962i | \(0.941108\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.716700 | − | 1.24136i | 0.0423055 | − | 0.0732752i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.23874 | + | 3.87761i | 0.131691 | + | 0.228095i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.84168 | 0.341274 | 0.170637 | − | 0.985334i | \(-0.445417\pi\) | ||||
0.170637 | + | 0.985334i | \(0.445417\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.60596 | − | 2.65925i | 0.268169 | − | 0.154828i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.8866 | + | 25.7844i | −0.860917 | + | 1.49115i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.925745 | − | 1.60344i | 0.0533590 | − | 0.0924206i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.85487i | − | 0.163469i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.3364 | − | 8.27711i | −0.818220 | − | 0.472399i | 0.0315824 | − | 0.999501i | \(-0.489945\pi\) |
−0.849802 | + | 0.527102i | \(0.823279\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.7502i | 0.949817i | 0.880035 | + | 0.474908i | \(0.157519\pi\) | ||||
−0.880035 | + | 0.474908i | \(0.842481\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.6097 | + | 25.3047i | 0.825789 | + | 1.43031i | 0.901315 | + | 0.433165i | \(0.142603\pi\) |
−0.0755253 | + | 0.997144i | \(0.524063\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.77821 | + | 13.4723i | 0.436868 | + | 0.756677i | 0.997446 | − | 0.0714243i | \(-0.0227545\pi\) |
−0.560578 | + | 0.828101i | \(0.689421\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.4542 | − | 11.2319i | 1.08923 | − | 0.628866i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.74170 | − | 19.3676i | −0.319477 | − | 1.07764i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.2470 | + | 11.6896i | 1.12310 | + | 0.648422i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.369874 | + | 0.213547i | −0.0203918 | + | 0.0117732i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 30.0226i | − | 1.65019i | −0.564995 | − | 0.825094i | \(-0.691122\pi\) | ||
0.564995 | − | 0.825094i | \(-0.308878\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.12402 | −0.116048 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.16548 | + | 2.40494i | 0.226908 | + | 0.131005i | 0.609145 | − | 0.793059i | \(-0.291513\pi\) |
−0.382237 | + | 0.924064i | \(0.624846\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.51385 | −0.190285 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.77228 | −0.149689 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.64059 | − | 2.10190i | −0.195437 | − | 0.112836i | 0.399088 | − | 0.916913i | \(-0.369327\pi\) |
−0.594525 | + | 0.804077i | \(0.702660\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.7302 | 1.64495 | 0.822476 | − | 0.568800i | \(-0.192592\pi\) | ||||
0.822476 | + | 0.568800i | \(0.192592\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.32845i | − | 0.123931i | −0.998078 | − | 0.0619653i | \(-0.980263\pi\) | ||
0.998078 | − | 0.0619653i | \(-0.0197368\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.10299 | − | 4.67827i | 0.430062 | − | 0.248297i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.0394 | + | 14.4565i | 1.32153 | + | 0.762985i | 0.983972 | − | 0.178321i | \(-0.0570666\pi\) |
0.337556 | + | 0.941306i | \(0.390400\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00293 | + | 18.9735i | 0.0527858 | + | 0.998606i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.04318 | + | 2.91168i | −0.263972 | + | 0.152404i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.3220 | + | 24.8064i | 0.747601 | + | 1.29488i | 0.948970 | + | 0.315368i | \(0.102128\pi\) |
−0.201368 | + | 0.979516i | \(0.564539\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.322604 | + | 0.558766i | 0.0167488 | + | 0.0290097i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 17.0680i | − | 0.883745i | −0.897078 | − | 0.441873i | \(-0.854314\pi\) | ||
0.897078 | − | 0.441873i | \(-0.145686\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −39.2233 | − | 22.6456i | −2.02011 | − | 1.16631i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.8562i | 1.63634i | 0.574975 | + | 0.818171i | \(0.305012\pi\) | ||||
−0.574975 | + | 0.818171i | \(0.694988\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.84259 | − | 4.92351i | 0.145249 | − | 0.251579i | −0.784217 | − | 0.620487i | \(-0.786935\pi\) |
0.929466 | + | 0.368908i | \(0.120268\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.142910 | − | 0.247527i | 0.00728335 | − | 0.0126151i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.0407 | − | 16.7667i | 1.47242 | − | 0.850104i | 0.472904 | − | 0.881114i | \(-0.343206\pi\) |
0.999519 | + | 0.0310100i | \(0.00987237\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.5307 | −1.39229 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.422863 | + | 0.732420i | 0.0212765 | + | 0.0368520i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.89375 | − | 3.28008i | 0.0950448 | − | 0.164622i | −0.814582 | − | 0.580048i | \(-0.803034\pi\) |
0.909627 | + | 0.415425i | \(0.136367\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0794 | + | 20.9221i | −0.603216 | + | 1.04480i | 0.389115 | + | 0.921189i | \(0.372781\pi\) |
−0.992331 | + | 0.123611i | \(0.960552\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.54228 | + | 6.13541i | 0.176454 | + | 0.305627i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −28.8960 | −1.43232 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.04034 | − | 4.06474i | 0.348122 | − | 0.200988i | −0.315736 | − | 0.948847i | \(-0.602251\pi\) |
0.663858 | + | 0.747859i | \(0.268918\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.912023 | − | 1.57967i | 0.0448777 | − | 0.0777305i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.171526 | + | 0.297091i | −0.00841986 | + | 0.0145836i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 9.73708i | − | 0.475687i | −0.971303 | − | 0.237844i | \(-0.923559\pi\) | ||
0.971303 | − | 0.237844i | \(-0.0764406\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1997 | − | 8.77556i | −0.740789 | − | 0.427695i | 0.0815671 | − | 0.996668i | \(-0.474007\pi\) |
−0.822356 | + | 0.568973i | \(0.807341\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.6182i | 1.04864i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.489555 | − | 0.847935i | −0.0236913 | − | 0.0410344i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.74207 | + | 3.01736i | 0.0839127 | + | 0.145341i | 0.904927 | − | 0.425566i | \(-0.139925\pi\) |
−0.821015 | + | 0.570907i | \(0.806592\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.5893 | + | 13.0419i | −1.08557 | + | 0.626756i | −0.932394 | − | 0.361443i | \(-0.882284\pi\) |
−0.153178 | + | 0.988199i | \(0.548951\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.1801 | + | 6.03921i | 1.20453 | + | 0.288894i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.261898 | + | 0.151207i | 0.0124997 | + | 0.00721671i | 0.506237 | − | 0.862394i | \(-0.331036\pi\) |
−0.493737 | + | 0.869611i | \(0.664369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.28403 | + | 2.47339i | −0.203541 | + | 0.117514i | −0.598306 | − | 0.801268i | \(-0.704159\pi\) |
0.394765 | + | 0.918782i | \(0.370826\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.22692i | 0.152971i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.5597 | −0.875889 | −0.437944 | − | 0.899002i | \(-0.644293\pi\) | ||||
−0.437944 | + | 0.899002i | \(0.644293\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.5394 | − | 8.97170i | −0.731724 | − | 0.422461i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.576265 | −0.0270157 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −39.3948 | −1.84281 | −0.921405 | − | 0.388603i | \(-0.872958\pi\) | ||||
−0.921405 | + | 0.388603i | \(0.872958\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.3706 | + | 12.3383i | 0.995327 | + | 0.574652i | 0.906862 | − | 0.421427i | \(-0.138471\pi\) |
0.0884645 | + | 0.996079i | \(0.471804\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.5320 | 0.954205 | 0.477102 | − | 0.878848i | \(-0.341687\pi\) | ||||
0.477102 | + | 0.878848i | \(0.341687\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.4282i | 0.575111i | 0.957764 | + | 0.287555i | \(0.0928425\pi\) | ||||
−0.957764 | + | 0.287555i | \(0.907157\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.630864 | + | 0.364229i | −0.0291306 | + | 0.0168185i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.0719 | − | 11.5885i | −0.922909 | − | 0.532842i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.74223 | − | 19.7724i | 0.217588 | − | 0.907221i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.1284 | − | 6.42499i | 0.508470 | − | 0.293565i | −0.223735 | − | 0.974650i | \(-0.571825\pi\) |
0.732204 | + | 0.681085i | \(0.238492\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.1299 | + | 50.4544i | 1.32821 | + | 2.30052i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.11719 | − | 5.39913i | −0.141544 | − | 0.245162i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.7617i | 0.532975i | 0.963838 | + | 0.266487i | \(0.0858630\pi\) | ||||
−0.963838 | + | 0.266487i | \(0.914137\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.7058 | + | 7.33571i | 0.573406 | + | 0.331056i | 0.758509 | − | 0.651663i | \(-0.225928\pi\) |
−0.185103 | + | 0.982719i | \(0.559262\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 41.8798i | − | 1.88617i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.60447 | − | 2.77902i | 0.0719702 | − | 0.124656i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.33608 | + | 5.77826i | −0.149343 | + | 0.258670i | −0.930985 | − | 0.365057i | \(-0.881049\pi\) |
0.781642 | + | 0.623728i | \(0.214383\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.07351 | − | 2.92919i | 0.226216 | − | 0.130606i | −0.382609 | − | 0.923910i | \(-0.624974\pi\) |
0.608825 | + | 0.793304i | \(0.291641\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.22777 | 0.366131 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.56376 | + | 9.63672i | 0.246609 | + | 0.427140i | 0.962583 | − | 0.270987i | \(-0.0873502\pi\) |
−0.715973 | + | 0.698128i | \(0.754017\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.998597 | + | 1.72962i | −0.0441753 | + | 0.0765139i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.32029 | + | 9.21502i | −0.234440 | + | 0.406062i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.67319 | + | 4.63011i | 0.117567 | + | 0.203632i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.9945 | −1.40170 | −0.700852 | − | 0.713307i | \(-0.747197\pi\) | ||||
−0.700852 | + | 0.713307i | \(0.747197\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.69847 | − | 4.44471i | 0.336631 | − | 0.194354i | −0.322150 | − | 0.946688i | \(-0.604406\pi\) |
0.658781 | + | 0.752335i | \(0.271072\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.27547 | + | 5.67328i | −0.142682 | + | 0.247132i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.14498 | − | 10.6434i | 0.267173 | − | 0.462757i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.1772i | 1.56701i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.05458 | + | 4.07296i | 0.304996 | + | 0.176090i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.3028i | 0.745283i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0404 | + | 29.5149i | 0.732626 | + | 1.26895i | 0.955757 | + | 0.294157i | \(0.0950389\pi\) |
−0.223131 | + | 0.974788i | \(0.571628\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.71016 | − | 2.96208i | −0.0732551 | − | 0.126882i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.75459 | − | 1.01302i | 0.0750210 | − | 0.0433134i | −0.462020 | − | 0.886869i | \(-0.652875\pi\) |
0.537041 | + | 0.843556i | \(0.319542\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.18686 | + | 38.3040i | −0.391373 | + | 1.63181i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.251192 | + | 0.145026i | 0.0106818 | + | 0.00616713i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.9880 | + | 9.23067i | −0.677433 | + | 0.391116i | −0.798887 | − | 0.601481i | \(-0.794577\pi\) |
0.121454 | + | 0.992597i | \(0.461244\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.7293i | 1.97644i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.3102 | −1.10884 | −0.554421 | − | 0.832237i | \(-0.687060\pi\) | ||||
−0.554421 | + | 0.832237i | \(0.687060\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.85265 | − | 1.06963i | −0.0779417 | − | 0.0449996i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.3661 | 1.14725 | 0.573624 | − | 0.819119i | \(-0.305537\pi\) | ||||
0.573624 | + | 0.819119i | \(0.305537\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.5121 | 1.77908 | 0.889539 | − | 0.456860i | \(-0.151026\pi\) | ||||
0.889539 | + | 0.456860i | \(0.151026\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.9985 | − | 13.8555i | −1.00081 | − | 0.577816i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.8052 | −1.28244 | −0.641219 | − | 0.767358i | \(-0.721571\pi\) | ||||
−0.641219 | + | 0.767358i | \(0.721571\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.117654i | 0.00488109i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.99467 | − | 4.03838i | 0.289690 | − | 0.167253i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.0210 | − | 11.5592i | −0.826357 | − | 0.477097i | 0.0262466 | − | 0.999655i | \(-0.491644\pi\) |
−0.852604 | + | 0.522558i | \(0.824978\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.24031 | − | 4.47037i | 0.174719 | − | 0.184199i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.8849 | + | 16.0993i | −1.14509 | + | 0.661121i | −0.947687 | − | 0.319201i | \(-0.896586\pi\) |
−0.197408 | + | 0.980321i | \(0.563252\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.266429 | − | 0.461469i | −0.0109225 | − | 0.0189184i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.17822 | − | 5.50484i | −0.129859 | − | 0.224922i | 0.793763 | − | 0.608227i | \(-0.208119\pi\) |
−0.923622 | + | 0.383305i | \(0.874786\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.82631i | − | 0.156079i | −0.996950 | − | 0.0780393i | \(-0.975134\pi\) | ||
0.996950 | − | 0.0780393i | \(-0.0248660\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.41727 | + | 1.39561i | 0.0982760 | + | 0.0567397i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.1802i | 0.616146i | 0.951363 | + | 0.308073i | \(0.0996842\pi\) | ||||
−0.951363 | + | 0.308073i | \(0.900316\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.38966 | − | 9.33516i | 0.218042 | − | 0.377660i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.68177 | − | 6.37702i | 0.148705 | − | 0.257565i | −0.782044 | − | 0.623223i | \(-0.785823\pi\) |
0.930749 | + | 0.365658i | \(0.119156\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.93545 | + | 5.15888i | −0.359728 | + | 0.207689i | −0.668961 | − | 0.743297i | \(-0.733261\pi\) |
0.309234 | + | 0.950986i | \(0.399927\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.5742 | 0.545594 | 0.272797 | − | 0.962072i | \(-0.412051\pi\) | ||||
0.272797 | + | 0.962072i | \(0.412051\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.553355 | + | 0.958439i | 0.0221697 | + | 0.0383991i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.0418 | + | 17.3929i | −0.401672 | + | 0.695716i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26.9357 | + | 46.6541i | −1.07400 | + | 1.86022i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.8122 | + | 20.4593i | 0.470236 | + | 0.814472i | 0.999421 | − | 0.0340341i | \(-0.0108355\pi\) |
−0.529185 | + | 0.848507i | \(0.677502\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.28753 | 0.209829 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.2118 | − | 17.4428i | 1.19703 | − | 0.691108i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.65587 | + | 8.06420i | −0.183896 | + | 0.318517i | −0.943204 | − | 0.332215i | \(-0.892204\pi\) |
0.759308 | + | 0.650731i | \(0.225538\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.52083 | + | 11.2944i | −0.257156 | + | 0.445408i | −0.965479 | − | 0.260481i | \(-0.916119\pi\) |
0.708323 | + | 0.705889i | \(0.249452\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 39.2031i | − | 1.54123i | −0.637298 | − | 0.770617i | \(-0.719948\pi\) | ||
0.637298 | − | 0.770617i | \(-0.280052\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.7744 | − | 11.4168i | −0.776214 | − | 0.448147i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 3.23276i | − | 0.126508i | −0.997997 | − | 0.0632539i | \(-0.979852\pi\) | ||
0.997997 | − | 0.0632539i | \(-0.0201478\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.39849 | − | 7.61841i | −0.171863 | − | 0.297676i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.0326 | − | 36.4295i | −0.819312 | − | 1.41909i | −0.906190 | − | 0.422872i | \(-0.861022\pi\) |
0.0868772 | − | 0.996219i | \(-0.472311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.6185 | + | 18.2549i | −1.22982 | + | 0.710035i | −0.966991 | − | 0.254809i | \(-0.917987\pi\) |
−0.262825 | + | 0.964844i | \(0.584654\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.142452 | + | 0.480513i | 0.00552406 | + | 0.0186335i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 46.4910 | + | 26.8416i | 1.80014 | + | 1.03931i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.6145 | + | 6.12829i | −0.409769 | + | 0.236580i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 27.9597i | − | 1.07777i | −0.842381 | − | 0.538883i | \(-0.818847\pi\) | ||
0.842381 | − | 0.538883i | \(-0.181153\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.3400 | −1.55039 | −0.775196 | − | 0.631720i | \(-0.782349\pi\) | ||||
−0.775196 | + | 0.631720i | \(0.782349\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.85170 | − | 1.06908i | −0.0710617 | − | 0.0410275i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.5412 | 1.89564 | 0.947820 | − | 0.318805i | \(-0.103282\pi\) | ||||
0.947820 | + | 0.318805i | \(0.103282\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.68384 | −0.140752 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.1026 | − | 8.14212i | −0.537265 | − | 0.310190i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.1533 | −0.652544 | −0.326272 | − | 0.945276i | \(-0.605793\pi\) | ||||
−0.326272 | + | 0.945276i | \(0.605793\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 10.9527i | − | 0.415460i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.9705 | + | 16.7261i | −1.09734 | + | 0.633548i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.98145 | − | 1.72134i | −0.112608 | − | 0.0650143i | 0.442638 | − | 0.896700i | \(-0.354043\pi\) |
−0.555246 | + | 0.831686i | \(0.687376\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.8701 | − | 36.7620i | 1.31515 | − | 1.38650i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.44376 | − | 1.41091i | 0.0919072 | − | 0.0530626i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.80569 | + | 6.59164i | 0.142926 | + | 0.247554i | 0.928597 | − | 0.371090i | \(-0.121016\pi\) |
−0.785671 | + | 0.618644i | \(0.787682\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.19863 | − | 7.27224i | −0.157240 | − | 0.272348i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.21372i | 0.269778i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.05303 | + | 4.64942i | 0.300328 | + | 0.173394i | 0.642590 | − | 0.766210i | \(-0.277860\pi\) |
−0.342263 | + | 0.939604i | \(0.611193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.64932i | 0.135908i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.0771 | − | 36.5066i | 0.782784 | − | 1.35582i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.3374 | − | 26.5652i | 0.568834 | − | 0.985249i | −0.427848 | − | 0.903851i | \(-0.640728\pi\) |
0.996682 | − | 0.0813982i | \(-0.0259385\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.4206 | + | 21.6048i | −1.38405 | + | 0.799081i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.63651 | 0.318997 | 0.159498 | − | 0.987198i | \(-0.449012\pi\) | ||||
0.159498 | + | 0.987198i | \(0.449012\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.55945 | + | 7.89720i | 0.167949 | + | 0.290897i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0042 | + | 25.9880i | −0.551938 | + | 0.955985i | 0.446197 | + | 0.894935i | \(0.352778\pi\) |
−0.998135 | + | 0.0610498i | \(0.980555\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.2894 | + | 19.5538i | −0.414167 | + | 0.717358i | −0.995341 | − | 0.0964216i | \(-0.969260\pi\) |
0.581174 | + | 0.813779i | \(0.302594\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.24986 | + | 2.16482i | 0.0457913 | + | 0.0793128i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.79374 | 0.102081 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.1212 | + | 8.73023i | −0.551780 | + | 0.318571i | −0.749840 | − | 0.661619i | \(-0.769869\pi\) |
0.198059 | + | 0.980190i | \(0.436536\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.92385 | − | 6.79632i | 0.142804 | − | 0.247343i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.82310 | + | 17.0141i | −0.357027 | + | 0.618388i | −0.987463 | − | 0.157853i | \(-0.949543\pi\) |
0.630436 | + | 0.776241i | \(0.282876\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.6922i | 1.51134i | 0.654953 | + | 0.755670i | \(0.272688\pi\) | ||||
−0.654953 | + | 0.755670i | \(0.727312\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.01588 | − | 0.586519i | −0.0367773 | − | 0.0212334i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 46.0366i | 1.66229i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.69363 | − | 9.86165i | −0.205317 | − | 0.355620i | 0.744916 | − | 0.667158i | \(-0.232489\pi\) |
−0.950234 | + | 0.311538i | \(0.899156\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.94814 | + | 17.2307i | 0.357810 | + | 0.619745i | 0.987595 | − | 0.157025i | \(-0.0501903\pi\) |
−0.629785 | + | 0.776770i | \(0.716857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.71045 | + | 3.29693i | −0.205126 | + | 0.118429i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.1661 | − | 8.94299i | 1.08081 | − | 0.320416i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.7880 | − | 20.0848i | −1.24481 | − | 0.718692i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.862613 | + | 0.498030i | −0.0307880 | + | 0.0177755i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.6451i | 1.27061i | 0.772262 | + | 0.635305i | \(0.219125\pi\) | ||||
−0.772262 | + | 0.635305i | \(0.780875\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.733685 | −0.0260868 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.4008 | + | 12.3558i | 0.759966 | + | 0.438766i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.904874 | −0.0320523 | −0.0160261 | − | 0.999872i | \(-0.505101\pi\) | ||||
−0.0160261 | + | 0.999872i | \(0.505101\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.96739 | 0.352621 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.6515 | + | 12.5005i | 0.764065 | + | 0.441133i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.683040 | 0.0240740 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.9234i | 0.384048i | 0.981390 | + | 0.192024i | \(0.0615051\pi\) | ||||
−0.981390 | + | 0.192024i | \(0.938495\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.9919 | − | 16.1611i | 0.982929 | − | 0.567494i | 0.0797760 | − | 0.996813i | \(-0.474579\pi\) |
0.903153 | + | 0.429318i | \(0.141246\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.85994 | − | 2.22854i | −0.135208 | − | 0.0780623i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.9648 | − | 11.5515i | 1.36321 | − | 0.404134i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.3396 | − | 7.70160i | 0.465554 | − | 0.268788i | −0.248823 | − | 0.968549i | \(-0.580044\pi\) |
0.714377 | + | 0.699761i | \(0.246710\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.5572 | + | 18.2857i | 0.368002 | + | 0.637398i | 0.989253 | − | 0.146213i | \(-0.0467086\pi\) |
−0.621251 | + | 0.783612i | \(0.713375\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.58148 | + | 11.3995i | 0.228861 | + | 0.396398i | 0.957471 | − | 0.288531i | \(-0.0931667\pi\) |
−0.728610 | + | 0.684929i | \(0.759833\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.92198i | 0.101485i | 0.998712 | + | 0.0507423i | \(0.0161587\pi\) | ||||
−0.998712 | + | 0.0507423i | \(0.983841\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.9362 | + | 16.1290i | 0.967931 | + | 0.558835i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 6.89489i | − | 0.238607i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.5472 | − | 26.9286i | 0.536750 | − | 0.929678i | −0.462326 | − | 0.886710i | \(-0.652985\pi\) |
0.999076 | − | 0.0429685i | \(-0.0136815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3315 | + | 45.6075i | −0.907983 | + | 1.57267i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.07694 | − | 3.50852i | 0.209053 | − | 0.120697i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.957283 | 0.0328926 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.5273 | − | 59.8030i | −1.18358 | − | 2.05002i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.4673 | − | 28.5222i | 0.563829 | − | 0.976580i | −0.433329 | − | 0.901236i | \(-0.642661\pi\) |
0.997158 | − | 0.0753440i | \(-0.0240055\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.5980 | + | 23.5524i | −0.464499 | + | 0.804535i | −0.999179 | − | 0.0405194i | \(-0.987099\pi\) |
0.534680 | + | 0.845054i | \(0.320432\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.09525 | + | 15.7534i | 0.310326 | + | 0.537500i | 0.978433 | − | 0.206565i | \(-0.0662285\pi\) |
−0.668107 | + | 0.744065i | \(0.732895\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.4199 | 0.592980 | 0.296490 | − | 0.955036i | \(-0.404184\pi\) | ||||
0.296490 | + | 0.955036i | \(0.404184\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.90626 | − | 4.56468i | 0.268821 | − | 0.155204i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.81544 | − | 3.14444i | 0.0615847 | − | 0.106668i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.19270 | − | 15.9222i | 0.311483 | − | 0.539504i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 1.11125i | − | 0.0375670i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.65733 | − | 0.956862i | −0.0559642 | − | 0.0323109i | 0.471757 | − | 0.881729i | \(-0.343620\pi\) |
−0.527721 | + | 0.849418i | \(0.676953\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13.2316i | − | 0.445785i | −0.974843 | − | 0.222893i | \(-0.928450\pi\) | ||
0.974843 | − | 0.222893i | \(-0.0715499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.2127 | − | 41.9377i | −0.814823 | − | 1.41131i | −0.909455 | − | 0.415802i | \(-0.863501\pi\) |
0.0946321 | − | 0.995512i | \(-0.469833\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.8340 | − | 43.0138i | −0.833846 | − | 1.44426i | −0.894967 | − | 0.446133i | \(-0.852801\pi\) |
0.0611211 | − | 0.998130i | \(-0.480532\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.57047 | − | 0.906712i | 0.0526719 | − | 0.0304101i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.11636 | − | 2.18647i | −0.305067 | − | 0.0731675i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.7670 | + | 6.21633i | 0.359901 | + | 0.207789i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.0626 | − | 6.38697i | 0.368957 | − | 0.213017i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 15.0577i | − | 0.501644i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.32216 | 0.143673 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.6301 | + | 28.6540i | 1.64794 | + | 0.951439i | 0.977889 | + | 0.209125i | \(0.0670616\pi\) |
0.670052 | + | 0.742314i | \(0.266272\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.1726 | 1.09906 | 0.549528 | − | 0.835475i | \(-0.314808\pi\) | ||||
0.549528 | + | 0.835475i | \(0.314808\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.47280 | 0.0487424 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.61282 | − | 1.50851i | −0.0862831 | − | 0.0498156i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.32773 | 0.0767847 | 0.0383924 | − | 0.999263i | \(-0.487776\pi\) | ||||
0.0383924 | + | 0.999263i | \(0.487776\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 80.9895i | 2.66580i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −46.9597 | + | 27.1122i | −1.54403 | + | 0.891444i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.5417 | − | 26.2935i | −1.49418 | − | 0.862663i | −0.494199 | − | 0.869349i | \(-0.664538\pi\) |
−0.999978 | + | 0.00668592i | \(0.997872\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.0129 | − | 20.8800i | −0.721442 | − | 0.684314i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.77671 | + | 3.33518i | −0.188919 | + | 0.109072i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.0863 | − | 20.9342i | −0.394844 | − | 0.683889i | 0.598238 | − | 0.801319i | \(-0.295868\pi\) |
−0.993081 | + | 0.117429i | \(0.962535\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.9700 | + | 25.9289i | 0.488009 | + | 0.845257i | 0.999905 | − | 0.0137909i | \(-0.00438992\pi\) |
−0.511896 | + | 0.859048i | \(0.671057\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 42.8805i | − | 1.39638i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.4249 | − | 13.5244i | −0.761206 | − | 0.439482i | 0.0685227 | − | 0.997650i | \(-0.478171\pi\) |
−0.829729 | + | 0.558167i | \(0.811505\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 50.4067i | − | 1.63627i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.04170 | + | 5.26838i | −0.0985304 | + | 0.170660i | −0.911077 | − | 0.412237i | \(-0.864748\pi\) |
0.812546 | + | 0.582897i | \(0.198081\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.16971 | − | 3.75805i | 0.0702102 | − | 0.121608i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.09415 | + | 0.631708i | −0.0353320 | + | 0.0203989i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.0019 | 0.935544 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.17810 | + | 3.77259i | 0.0701157 | + | 0.121444i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.9763 | + | 44.9923i | −0.835343 | + | 1.44686i | 0.0584083 | + | 0.998293i | \(0.481397\pi\) |
−0.893751 | + | 0.448563i | \(0.851936\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.3108 | + | 24.7870i | −0.459254 | + | 0.795451i | −0.998922 | − | 0.0464267i | \(-0.985217\pi\) |
0.539668 | + | 0.841878i | \(0.318550\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.87818 | − | 3.25310i | −0.0602117 | − | 0.104290i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.5032 | −1.61574 | −0.807870 | − | 0.589361i | \(-0.799380\pi\) | ||||
−0.807870 | + | 0.589361i | \(0.799380\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.9978 | − | 6.92694i | 0.383452 | − | 0.221386i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.1280 | − | 31.3986i | 0.578193 | − | 1.00146i | −0.417494 | − | 0.908680i | \(-0.637091\pi\) |
0.995687 | − | 0.0927799i | \(-0.0295753\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.955681 | + | 1.65529i | −0.0304505 | + | 0.0527419i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 55.3877i | − | 1.76123i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.4701 | − | 25.6748i | −1.41264 | − | 0.815588i | −0.417004 | − | 0.908905i | \(-0.636920\pi\) |
−0.995637 | + | 0.0933161i | \(0.970253\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 9.35944i | − | 0.296714i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.24043 | − | 7.34464i | −0.134296 | − | 0.232607i | 0.791032 | − | 0.611774i | \(-0.209544\pi\) |
−0.925328 | + | 0.379167i | \(0.876211\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2736.2.dc.e.1889.6 | 20 | ||
3.2 | odd | 2 | 2736.2.dc.f.1889.5 | 20 | |||
4.3 | odd | 2 | 1368.2.cu.a.521.6 | yes | 20 | ||
12.11 | even | 2 | 1368.2.cu.b.521.5 | yes | 20 | ||
19.12 | odd | 6 | 2736.2.dc.f.449.5 | 20 | |||
57.50 | even | 6 | inner | 2736.2.dc.e.449.6 | 20 | ||
76.31 | even | 6 | 1368.2.cu.b.449.5 | yes | 20 | ||
228.107 | odd | 6 | 1368.2.cu.a.449.6 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.cu.a.449.6 | ✓ | 20 | 228.107 | odd | 6 | ||
1368.2.cu.a.521.6 | yes | 20 | 4.3 | odd | 2 | ||
1368.2.cu.b.449.5 | yes | 20 | 76.31 | even | 6 | ||
1368.2.cu.b.521.5 | yes | 20 | 12.11 | even | 2 | ||
2736.2.dc.e.449.6 | 20 | 57.50 | even | 6 | inner | ||
2736.2.dc.e.1889.6 | 20 | 1.1 | even | 1 | trivial | ||
2736.2.dc.f.449.5 | 20 | 19.12 | odd | 6 | |||
2736.2.dc.f.1889.5 | 20 | 3.2 | odd | 2 |