Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1044,2,Mod(109,1044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1044, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([0, 0, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1044.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1044 = 2^{2} \cdot 3^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1044.z (of order \(14\), degree \(6\), 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: | \(8.33638197102\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{14})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{14}]$ |
Embedding invariants
Embedding label | 325.1 | ||
Character | \(\chi\) | \(=\) | 1044.325 |
Dual form | 1044.2.z.c.469.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1044\mathbb{Z}\right)^\times\).
\(n\) | \(523\) | \(901\) | \(929\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.81616 | + | 2.27739i | −0.812210 | + | 1.01848i | 0.187136 | + | 0.982334i | \(0.440079\pi\) |
−0.999347 | + | 0.0361456i | \(0.988492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.620985 | + | 2.72071i | −0.234710 | + | 1.02833i | 0.710967 | + | 0.703225i | \(0.248258\pi\) |
−0.945677 | + | 0.325107i | \(0.894600\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.64877 | − | 3.42372i | −0.497124 | − | 1.03229i | −0.987033 | − | 0.160515i | \(-0.948684\pi\) |
0.489909 | − | 0.871773i | \(-0.337030\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.43161 | + | 2.61573i | −1.50646 | + | 0.725472i | −0.991300 | − | 0.131623i | \(-0.957981\pi\) |
−0.515158 | + | 0.857095i | \(0.672267\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.61615i | − | 1.60465i | −0.596886 | − | 0.802326i | \(-0.703596\pi\) | ||
0.596886 | − | 0.802326i | \(-0.296404\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.85782 | − | 0.652279i | 0.655629 | − | 0.149643i | 0.118250 | − | 0.992984i | \(-0.462272\pi\) |
0.537379 | + | 0.843341i | \(0.319414\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.28906 | − | 1.61643i | −0.268788 | − | 0.337049i | 0.629059 | − | 0.777358i | \(-0.283441\pi\) |
−0.897847 | + | 0.440308i | \(0.854869\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.775470 | − | 3.39756i | −0.155094 | − | 0.679512i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.03013 | − | 4.98784i | 0.376986 | − | 0.926219i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.575797 | + | 0.459183i | 0.103416 | + | 0.0824717i | 0.673833 | − | 0.738884i | \(-0.264647\pi\) |
−0.570417 | + | 0.821356i | \(0.693218\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.06832 | − | 6.35547i | −0.856702 | − | 1.07427i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.51293 | − | 5.21815i | 0.413123 | − | 0.857858i | −0.585755 | − | 0.810488i | \(-0.699202\pi\) |
0.998877 | − | 0.0473696i | \(-0.0150839\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.73867i | 0.271534i | 0.990741 | + | 0.135767i | \(0.0433499\pi\) | ||||
−0.990741 | + | 0.135767i | \(0.956650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.44955 | − | 5.14334i | 0.983547 | − | 0.784352i | 0.00707001 | − | 0.999975i | \(-0.497750\pi\) |
0.976477 | + | 0.215623i | \(0.0691781\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.54934 | + | 3.21723i | 0.225994 | + | 0.469281i | 0.982876 | − | 0.184271i | \(-0.0589924\pi\) |
−0.756882 | + | 0.653552i | \(0.773278\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.709874 | − | 0.341857i | −0.101411 | − | 0.0488368i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.36151 | − | 1.70728i | 0.187018 | − | 0.234513i | −0.679480 | − | 0.733694i | \(-0.737794\pi\) |
0.866497 | + | 0.499182i | \(0.166366\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.7916 | + | 2.46310i | 1.45513 | + | 0.332125i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.5683 | −1.76644 | −0.883218 | − | 0.468963i | \(-0.844628\pi\) | ||||
−0.883218 | + | 0.468963i | \(0.844628\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.3338 | − | 3.04336i | −1.70722 | − | 0.389663i | −0.746111 | − | 0.665822i | \(-0.768081\pi\) |
−0.961112 | + | 0.276159i | \(0.910938\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.90763 | − | 17.1205i | 0.484682 | − | 2.12353i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.97479 | − | 2.39573i | −0.607767 | − | 0.292685i | 0.104576 | − | 0.994517i | \(-0.466652\pi\) |
−0.712343 | + | 0.701832i | \(0.752366\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2131 | + | 5.88150i | −1.44942 | + | 0.698006i | −0.982495 | − | 0.186289i | \(-0.940354\pi\) |
−0.466929 | + | 0.884295i | \(0.654640\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.225677 | − | 0.179972i | 0.0264135 | − | 0.0210641i | −0.610194 | − | 0.792252i | \(-0.708909\pi\) |
0.636608 | + | 0.771188i | \(0.280337\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.3388 | − | 2.35977i | 1.17822 | − | 0.268920i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.36045 | + | 11.1311i | −0.603098 | + | 1.25235i | 0.346257 | + | 0.938140i | \(0.387453\pi\) |
−0.949355 | + | 0.314206i | \(0.898262\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.98190 | − | 8.68327i | −0.217542 | − | 0.953113i | −0.959287 | − | 0.282432i | \(-0.908859\pi\) |
0.741746 | − | 0.670681i | \(-0.233998\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.0676 | + | 12.0160i | 1.63431 | + | 1.30332i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.73977 | − | 6.17226i | −0.820414 | − | 0.654258i | 0.120572 | − | 0.992705i | \(-0.461527\pi\) |
−0.940986 | + | 0.338446i | \(0.890099\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.74369 | − | 16.4022i | −0.392445 | − | 1.71942i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.70476 | + | 7.69302i | −0.380101 | + | 0.789287i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.521674 | − | 0.119069i | 0.0529680 | − | 0.0120896i | −0.195955 | − | 0.980613i | \(-0.562781\pi\) |
0.248923 | + | 0.968523i | \(0.419923\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.5426 | + | 10.0024i | −1.24803 | + | 0.995273i | −0.248388 | + | 0.968661i | \(0.579901\pi\) |
−0.999646 | + | 0.0266128i | \(0.991528\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.6734 | + | 8.02948i | −1.64288 | + | 0.791168i | −0.643202 | + | 0.765697i | \(0.722394\pi\) |
−0.999676 | + | 0.0254715i | \(0.991891\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.31214 | + | 3.03977i | 0.610217 | + | 0.293865i | 0.713356 | − | 0.700802i | \(-0.247174\pi\) |
−0.103139 | + | 0.994667i | \(0.532889\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.93207 | + | 8.46497i | −0.185059 | + | 0.810797i | 0.794114 | + | 0.607769i | \(0.207935\pi\) |
−0.979173 | + | 0.203028i | \(0.934922\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.1630 | + | 3.68910i | 1.52049 | + | 0.347041i | 0.899550 | − | 0.436818i | \(-0.143895\pi\) |
0.620938 | + | 0.783860i | \(0.286752\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.02239 | 0.561590 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.0006 | + | 4.10853i | 1.65012 | + | 0.376628i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.14498 | + | 2.68972i | −0.194998 | + | 0.244520i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.97618 | − | 1.91483i | −0.355640 | − | 0.171267i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.603036 | − | 1.25222i | −0.0535108 | − | 0.111116i | 0.872499 | − | 0.488616i | \(-0.162498\pi\) |
−0.926010 | + | 0.377500i | \(0.876784\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.92580 | + | 7.11809i | −0.779851 | + | 0.621910i | −0.930339 | − | 0.366701i | \(-0.880487\pi\) |
0.150488 | + | 0.988612i | \(0.451916\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.18037i | 0.709328i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.62496 | − | 5.45078i | 0.224265 | − | 0.465692i | −0.758228 | − | 0.651989i | \(-0.773935\pi\) |
0.982493 | + | 0.186298i | \(0.0596489\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.31641 | − | 1.65073i | −0.111656 | − | 0.140013i | 0.722863 | − | 0.690992i | \(-0.242826\pi\) |
−0.834519 | + | 0.550979i | \(0.814254\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.9110 | + | 14.2835i | 1.49779 | + | 1.19445i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.67222 | + | 13.6821i | 0.637143 | + | 1.13624i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.68306 | − | 16.1366i | −0.301728 | − | 1.32196i | −0.867517 | − | 0.497408i | \(-0.834285\pi\) |
0.565788 | − | 0.824550i | \(-0.308572\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.31660 | + | 5.41284i | 0.351280 | + | 0.440491i | 0.925808 | − | 0.377994i | \(-0.123386\pi\) |
−0.574528 | + | 0.818485i | \(0.694815\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.09148 | + | 0.477366i | −0.167991 | + | 0.0383430i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 20.1376i | − | 1.60716i | −0.595198 | − | 0.803579i | \(-0.702927\pi\) | ||
0.595198 | − | 0.803579i | \(-0.297073\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.19834 | − | 2.50339i | 0.409686 | − | 0.197295i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.12740 | − | 8.57063i | −0.323283 | − | 0.671303i | 0.674470 | − | 0.738302i | \(-0.264372\pi\) |
−0.997753 | + | 0.0669984i | \(0.978658\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.479060 | − | 2.09890i | 0.0370707 | − | 0.162418i | −0.953004 | − | 0.302956i | \(-0.902026\pi\) |
0.990075 | + | 0.140539i | \(0.0448835\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.5550 | − | 18.2514i | 1.11962 | − | 1.40395i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.33313 | 0.481499 | 0.240749 | − | 0.970587i | \(-0.422607\pi\) | ||||
0.240749 | + | 0.970587i | \(0.422607\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.72533 | 0.735166 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0764 | + | 15.1434i | −0.902634 | + | 1.13187i | 0.0881078 | + | 0.996111i | \(0.471918\pi\) |
−0.990742 | + | 0.135757i | \(0.956653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.43046 | − | 10.6486i | 0.180655 | − | 0.791501i | −0.800664 | − | 0.599114i | \(-0.795520\pi\) |
0.981319 | − | 0.192387i | \(-0.0616230\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.31988 | + | 15.1999i | 0.538168 | + | 1.11752i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.6518 | + | 10.9085i | −1.65646 | + | 0.797711i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 15.0422i | − | 1.08842i | −0.838950 | − | 0.544208i | \(-0.816830\pi\) | ||
0.838950 | − | 0.544208i | \(-0.183170\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.25071 | − | 1.65493i | 0.521917 | − | 0.119124i | 0.0465574 | − | 0.998916i | \(-0.485175\pi\) |
0.475360 | + | 0.879791i | \(0.342318\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.08478 | + | 3.86819i | 0.219781 | + | 0.275597i | 0.879483 | − | 0.475931i | \(-0.157889\pi\) |
−0.659702 | + | 0.751528i | \(0.729317\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.32601 | − | 14.5722i | −0.235774 | − | 1.03299i | −0.944758 | − | 0.327770i | \(-0.893703\pi\) |
0.708983 | − | 0.705225i | \(-0.249154\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.3098 | + | 8.62078i | 0.863979 | + | 0.605060i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.95962 | − | 3.15769i | −0.276552 | − | 0.220543i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.94512 | − | 8.70891i | −0.480404 | − | 0.602408i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.892716 | − | 1.85374i | 0.0614571 | − | 0.127617i | −0.867978 | − | 0.496603i | \(-0.834581\pi\) |
0.929435 | + | 0.368986i | \(0.120295\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.0293i | 1.63878i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.60687 | + | 1.28143i | −0.109081 | + | 0.0869894i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.3060 | + | 35.9364i | 1.16413 | + | 2.41734i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.2247 | + | 7.81341i | 1.08649 | + | 0.523225i | 0.889385 | − | 0.457158i | \(-0.151133\pi\) |
0.197102 | + | 0.980383i | \(0.436847\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.8582 | + | 21.1395i | −1.11892 | + | 1.40308i | −0.214341 | + | 0.976759i | \(0.568760\pi\) |
−0.904574 | + | 0.426317i | \(0.859811\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.950174 | − | 0.216871i | −0.0627893 | − | 0.0143312i | 0.191011 | − | 0.981588i | \(-0.438823\pi\) |
−0.253800 | + | 0.967257i | \(0.581681\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.10163 | 0.465244 | 0.232622 | − | 0.972567i | \(-0.425270\pi\) | ||||
0.232622 | + | 0.972567i | \(0.425270\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1407 | − | 2.31455i | −0.661508 | − | 0.150985i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.75600 | + | 20.8374i | −0.307640 | + | 1.34786i | 0.550668 | + | 0.834724i | \(0.314373\pi\) |
−0.858308 | + | 0.513134i | \(0.828484\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0959 | − | 5.82510i | −0.779168 | − | 0.375228i | 0.00163978 | − | 0.999999i | \(-0.499478\pi\) |
−0.780808 | + | 0.624771i | \(0.785192\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.06779 | − | 0.995793i | 0.132106 | − | 0.0636189i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.8164 | + | 11.0182i | −0.879116 | + | 0.701072i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.5962 | − | 2.64675i | 0.731945 | − | 0.167062i | 0.159724 | − | 0.987162i | \(-0.448939\pi\) |
0.572220 | + | 0.820100i | \(0.306082\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.40883 | + | 7.07851i | −0.214311 | + | 0.445022i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.76912 | + | 16.5136i | 0.235111 | + | 1.03009i | 0.945332 | + | 0.326110i | \(0.105738\pi\) |
−0.710221 | + | 0.703979i | \(0.751405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.6366 | + | 10.0773i | 0.785199 | + | 0.626176i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.2876 | − | 17.7738i | −1.37431 | − | 1.09598i | −0.984557 | − | 0.175062i | \(-0.943987\pi\) |
−0.389757 | − | 0.920918i | \(-0.627441\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.41542 | + | 6.20137i | 0.0869487 | + | 0.380947i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.39969 | − | 17.4421i | 0.512138 | − | 1.06347i | −0.471258 | − | 0.881995i | \(-0.656200\pi\) |
0.983396 | − | 0.181471i | \(-0.0580858\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.67042 | − | 0.837749i | 0.222962 | − | 0.0508896i | −0.109580 | − | 0.993978i | \(-0.534951\pi\) |
0.332542 | + | 0.943088i | \(0.392094\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.3537 | + | 8.25679i | −0.624351 | + | 0.497903i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.3812 | − | 10.2967i | 1.28467 | − | 0.618667i | 0.338087 | − | 0.941115i | \(-0.390220\pi\) |
0.946587 | + | 0.322448i | \(0.104506\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.61080 | + | 3.18359i | 0.394367 | + | 0.189917i | 0.620549 | − | 0.784168i | \(-0.286910\pi\) |
−0.226182 | + | 0.974085i | \(0.572624\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.753102 | − | 3.29956i | 0.0447673 | − | 0.196138i | −0.947599 | − | 0.319461i | \(-0.896498\pi\) |
0.992367 | + | 0.123323i | \(0.0393552\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.73041 | − | 1.07969i | −0.279227 | − | 0.0637318i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −26.7734 | −1.57491 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.2501 | + | 5.30667i | 1.35828 | + | 0.310019i | 0.838790 | − | 0.544455i | \(-0.183264\pi\) |
0.519493 | + | 0.854475i | \(0.326121\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.6421 | − | 30.9002i | 1.43472 | − | 1.79908i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.2298 | + | 5.40800i | 0.649438 | + | 0.312753i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.98849 | + | 20.7413i | 0.575727 | + | 1.19551i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 31.1473 | − | 24.8391i | 1.78349 | − | 1.42228i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.7787i | 1.69956i | 0.527138 | + | 0.849780i | \(0.323265\pi\) | ||||
−0.527138 | + | 0.849780i | \(0.676735\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.435163 | + | 0.903625i | −0.0246758 | + | 0.0512399i | −0.912942 | − | 0.408088i | \(-0.866196\pi\) |
0.888267 | + | 0.459328i | \(0.151910\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.54595 | + | 10.7163i | 0.483046 | + | 0.605720i | 0.962311 | − | 0.271950i | \(-0.0876685\pi\) |
−0.479266 | + | 0.877670i | \(0.659097\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.08869 | − | 5.65304i | −0.398140 | − | 0.317506i | 0.403870 | − | 0.914816i | \(-0.367665\pi\) |
−0.802010 | + | 0.597310i | \(0.796236\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.4242 | + | 1.27323i | −1.14353 | + | 0.0712873i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.31558 | − | 18.9078i | −0.240125 | − | 1.05206i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.0991 | + | 16.4258i | 0.726609 | + | 0.911139i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.71527 | + | 2.21745i | −0.535620 | + | 0.122252i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0766i | 0.553861i | 0.960890 | + | 0.276930i | \(0.0893172\pi\) | ||||
−0.960890 | + | 0.276930i | \(0.910683\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.4910 | − | 6.97851i | 0.791729 | − | 0.381277i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.47151 | − | 5.13215i | −0.134632 | − | 0.279566i | 0.822743 | − | 0.568413i | \(-0.192442\pi\) |
−0.957375 | + | 0.288847i | \(0.906728\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.622752 | − | 2.72845i | 0.0337239 | − | 0.147754i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.8088 | + | 13.5538i | −0.583621 | + | 0.731838i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.1636 | −1.56558 | −0.782792 | − | 0.622283i | \(-0.786205\pi\) | ||||
−0.782792 | + | 0.622283i | \(0.786205\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.5973 | −1.74489 | −0.872447 | − | 0.488708i | \(-0.837468\pi\) | ||||
−0.872447 | + | 0.488708i | \(0.837468\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.65086 | − | 4.57804i | 0.194316 | − | 0.243664i | −0.675123 | − | 0.737705i | \(-0.735909\pi\) |
0.869439 | + | 0.494041i | \(0.164481\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.78638 | − | 38.4956i | 0.466333 | − | 2.04314i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.675138 | + | 1.40194i | 0.0356324 | + | 0.0739915i | 0.918025 | − | 0.396522i | \(-0.129783\pi\) |
−0.882393 | + | 0.470514i | \(0.844069\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.37673 | + | 4.51559i | −0.493512 | + | 0.237663i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.840812i | 0.0440101i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.37679 | + | 2.14019i | −0.489464 | + | 0.111717i | −0.460128 | − | 0.887853i | \(-0.652197\pi\) |
−0.0293363 | + | 0.999570i | \(0.509339\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.79954 | + | 4.76447i | 0.197262 | + | 0.247359i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.38729 | − | 23.6032i | −0.278943 | − | 1.22213i | −0.899132 | − | 0.437677i | \(-0.855801\pi\) |
0.620189 | − | 0.784452i | \(-0.287056\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.01994 | + | 32.4023i | 0.104032 | + | 1.66880i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.34965 | + | 1.07631i | 0.0693266 | + | 0.0552861i | 0.657540 | − | 0.753420i | \(-0.271597\pi\) |
−0.588213 | + | 0.808706i | \(0.700168\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.0312 | + | 27.6262i | 1.12574 | + | 1.41163i | 0.899149 | + | 0.437642i | \(0.144186\pi\) |
0.226590 | + | 0.973990i | \(0.427242\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.4028 | + | 27.8312i | −0.683070 | + | 1.41841i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 9.84239i | − | 0.499029i | −0.968371 | − | 0.249514i | \(-0.919729\pi\) | ||
0.968371 | − | 0.249514i | \(-0.0802710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.6946 | + | 8.52863i | −0.540847 | + | 0.431311i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.6144 | − | 32.4237i | −0.785646 | − | 1.63141i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.30676 | + | 3.03718i | 0.316527 | + | 0.152431i | 0.585401 | − | 0.810744i | \(-0.300937\pi\) |
−0.268874 | + | 0.963175i | \(0.586651\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.2986 | + | 16.6759i | −0.664100 | + | 0.832755i | −0.993783 | − | 0.111337i | \(-0.964487\pi\) |
0.329683 | + | 0.944092i | \(0.393058\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.32860 | − | 0.987975i | −0.215623 | − | 0.0492146i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.0087 | −1.09093 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.30188 | + | 1.66661i | 0.361055 | + | 0.0824084i | 0.399200 | − | 0.916864i | \(-0.369288\pi\) |
−0.0381454 | + | 0.999272i | \(0.512145\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.42568 | − | 36.9153i | 0.414601 | − | 1.81648i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.3746 | + | 11.2566i | 1.14742 | + | 0.552566i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.0611 | + | 7.25304i | −0.735783 | + | 0.354334i | −0.763956 | − | 0.645269i | \(-0.776745\pi\) |
0.0281729 | + | 0.999603i | \(0.491031\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.5208 | − | 11.5799i | 0.707699 | − | 0.564371i | −0.202128 | − | 0.979359i | \(-0.564786\pi\) |
0.909827 | + | 0.414988i | \(0.136214\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.4788 | + | 5.13063i | −1.09038 | + | 0.248872i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.5602 | − | 34.3877i | 0.801405 | − | 1.66414i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.459881 | − | 2.01487i | −0.0221517 | − | 0.0970528i | 0.962644 | − | 0.270772i | \(-0.0872788\pi\) |
−0.984795 | + | 0.173719i | \(0.944422\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.3543 | − | 12.2447i | −0.737883 | − | 0.588442i | 0.180762 | − | 0.983527i | \(-0.442144\pi\) |
−0.918645 | + | 0.395085i | \(0.870715\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.73828 | − | 3.77865i | −0.226662 | − | 0.180757i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.07736 | − | 39.7705i | −0.433239 | − | 1.89814i | −0.439662 | − | 0.898163i | \(-0.644902\pi\) |
0.00642294 | − | 0.999979i | \(-0.497956\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.8958 | − | 22.6254i | 0.517676 | − | 1.07497i | −0.464250 | − | 0.885704i | \(-0.653676\pi\) |
0.981927 | − | 0.189262i | \(-0.0606095\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.1133 | − | 6.41667i | 1.33270 | − | 0.304180i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.40119 | + | 2.71236i | −0.160512 | + | 0.128004i | −0.700452 | − | 0.713699i | \(-0.747018\pi\) |
0.539940 | + | 0.841703i | \(0.318447\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.95270 | − | 2.86667i | 0.280302 | − | 0.134986i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 44.1533 | + | 21.2631i | 2.06994 | + | 0.996830i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.56895 | + | 6.87400i | −0.0733922 | + | 0.321552i | −0.998276 | − | 0.0586982i | \(-0.981305\pi\) |
0.924884 | + | 0.380250i | \(0.124162\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.7762 | − | 6.79622i | −1.38682 | − | 0.316532i | −0.536987 | − | 0.843590i | \(-0.680438\pi\) |
−0.849829 | + | 0.527059i | \(0.823295\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.0839 | 1.72344 | 0.861718 | − | 0.507387i | \(-0.169388\pi\) | ||||
0.861718 | + | 0.507387i | \(0.169388\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.6548 | − | 7.22501i | −1.46481 | − | 0.334333i | −0.585535 | − | 0.810647i | \(-0.699116\pi\) |
−0.879275 | + | 0.476314i | \(0.841973\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.60737 | − | 12.0473i | 0.443627 | − | 0.556291i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.2432 | − | 13.6012i | −1.29862 | − | 0.625384i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.43231 | − | 9.20379i | −0.203368 | − | 0.422299i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.3383 | − | 11.4344i | 0.655134 | − | 0.522452i | −0.238561 | − | 0.971128i | \(-0.576676\pi\) |
0.893695 | + | 0.448676i | \(0.148104\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.9161i | 1.59204i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.676276 | + | 1.40430i | −0.0307081 | + | 0.0637661i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0513 | + | 15.1118i | 0.546096 | + | 0.684783i | 0.975920 | − | 0.218130i | \(-0.0699958\pi\) |
−0.429824 | + | 0.902913i | \(0.641424\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.31621 | − | 4.23953i | −0.239917 | − | 0.191328i | 0.496149 | − | 0.868238i | \(-0.334747\pi\) |
−0.736066 | + | 0.676910i | \(0.763319\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.0003 | − | 13.4317i | −1.48626 | − | 0.604931i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.41775 | − | 36.8806i | −0.377588 | − | 1.65432i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.2589 | + | 16.6261i | 0.593550 | + | 0.744288i | 0.984357 | − | 0.176184i | \(-0.0563755\pi\) |
−0.390807 | + | 0.920473i | \(0.627804\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.21440 | − | 1.19015i | 0.232499 | − | 0.0530663i | −0.104684 | − | 0.994506i | \(-0.533383\pi\) |
0.337183 | + | 0.941439i | \(0.390526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 46.7302i | − | 2.07947i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.0726 | + | 9.18489i | −0.845379 | + | 0.407113i | −0.805860 | − | 0.592106i | \(-0.798297\pi\) |
−0.0395190 | + | 0.999219i | \(0.512583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.349509 | + | 0.725763i | 0.0154614 | + | 0.0321059i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.9952 | − | 52.5546i | 0.528574 | − | 2.31583i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.46037 | − | 10.6090i | 0.372087 | − | 0.466582i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.731059 | −0.0320283 | −0.0160141 | − | 0.999872i | \(-0.505098\pi\) | ||||
−0.0160141 | + | 0.999872i | \(0.505098\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.2257 | 0.490867 | 0.245433 | − | 0.969413i | \(-0.421070\pi\) | ||||
0.245433 | + | 0.969413i | \(0.421070\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.03802 | − | 3.80956i | 0.132338 | − | 0.165947i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.16681 | − | 18.2560i | 0.181166 | − | 0.793738i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.54787 | − | 9.44376i | −0.196990 | − | 0.409055i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.3866 | + | 8.85450i | −0.794921 | + | 0.382814i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.99405i | 0.128963i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.1334 | + | 6.64951i | −1.25254 | + | 0.285885i | −0.796809 | − | 0.604231i | \(-0.793480\pi\) |
−0.455734 | + | 0.890116i | \(0.650623\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.7691 | − | 19.7738i | −0.675473 | − | 0.847017i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.14511 | + | 40.0673i | 0.391017 | + | 1.71316i | 0.661082 | + | 0.750313i | \(0.270097\pi\) |
−0.270066 | + | 0.962842i | \(0.587045\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.54829 | − | 15.5786i | 0.108561 | − | 0.663670i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.9557 | − | 21.4965i | −1.14628 | − | 0.914124i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.25163 | + | 5.33138i | 0.180148 | + | 0.225898i | 0.863704 | − | 0.504000i | \(-0.168139\pi\) |
−0.683556 | + | 0.729898i | \(0.739567\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.5779 | + | 44.8069i | −0.912646 | + | 1.89513i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 37.7443i | − | 1.59073i | −0.606128 | − | 0.795367i | \(-0.707278\pi\) | ||
0.606128 | − | 0.795367i | \(-0.292722\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.7561 | + | 30.1095i | −1.58841 | + | 1.26671i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.98503 | + | 20.7341i | 0.418594 | + | 0.869220i | 0.998511 | + | 0.0545444i | \(0.0173707\pi\) |
−0.579917 | + | 0.814676i | \(0.696915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.0138 | + | 13.9723i | 1.21419 | + | 0.584723i | 0.927688 | − | 0.373357i | \(-0.121793\pi\) |
0.286502 | + | 0.958080i | \(0.407508\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.49229 | + | 5.63316i | −0.187342 | + | 0.234919i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.86922 | − | 0.883124i | −0.161078 | − | 0.0367649i | 0.141222 | − | 0.989978i | \(-0.454897\pi\) |
−0.302299 | + | 0.953213i | \(0.597754\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.8554 | 1.03118 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.09005 | − | 1.84650i | −0.335056 | − | 0.0764743i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.83792 | + | 34.3402i | −0.323506 | + | 1.41737i | 0.507762 | + | 0.861498i | \(0.330473\pi\) |
−0.831267 | + | 0.555873i | \(0.812384\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.94504 | + | 0.936683i | 0.0801441 | + | 0.0385953i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.33717 | + | 0.643949i | −0.0549112 | + | 0.0264438i | −0.461138 | − | 0.887329i | \(-0.652559\pi\) |
0.406227 | + | 0.913772i | \(0.366844\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −42.0487 | + | 33.5327i | −1.72383 | + | 1.37471i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.8564 | − | 3.39088i | 0.607016 | − | 0.138547i | 0.0920448 | − | 0.995755i | \(-0.470660\pi\) |
0.514971 | + | 0.857207i | \(0.327803\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.81976 | − | 5.85529i | 0.115020 | − | 0.238842i | −0.835509 | − | 0.549477i | \(-0.814827\pi\) |
0.950529 | + | 0.310634i | \(0.100541\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.22992 | − | 9.76991i | −0.0906591 | − | 0.397203i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.4468 | − | 12.3184i | −0.626967 | − | 0.499990i | 0.257692 | − | 0.966227i | \(-0.417038\pi\) |
−0.884660 | + | 0.466237i | \(0.845609\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.8308 | − | 13.4221i | −0.680901 | − | 0.543000i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.991589 | − | 4.34443i | −0.0400499 | − | 0.175470i | 0.950947 | − | 0.309353i | \(-0.100112\pi\) |
−0.990997 | + | 0.133883i | \(0.957255\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.19271 | + | 2.47669i | −0.0480167 | + | 0.0997077i | −0.923597 | − | 0.383365i | \(-0.874765\pi\) |
0.875580 | + | 0.483073i | \(0.160479\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.6750 | − | 5.86014i | 1.03196 | − | 0.235539i | 0.327181 | − | 0.944962i | \(-0.393901\pi\) |
0.704783 | + | 0.709423i | \(0.251044\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.5992 | − | 17.2248i | 0.865355 | − | 0.690098i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 27.2813 | − | 13.1380i | 1.09125 | − | 0.525518i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.5240 | − | 16.6259i | −1.37656 | − | 0.662918i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.40829 | − | 32.4578i | 0.294919 | − | 1.29213i | −0.582669 | − | 0.812710i | \(-0.697991\pi\) |
0.877588 | − | 0.479416i | \(-0.159151\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.94700 | + | 0.900876i | 0.156632 | + | 0.0357502i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.74997 | 0.188201 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.3209 | − | 6.92054i | −1.19760 | − | 0.273345i | −0.423199 | − | 0.906037i | \(-0.639093\pi\) |
−0.774404 | + | 0.632692i | \(0.781950\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.45823 | − | 1.82856i | 0.0575069 | − | 0.0721114i | −0.752246 | − | 0.658882i | \(-0.771030\pi\) |
0.809753 | + | 0.586771i | \(0.199601\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.03444 | + | 4.35075i | 0.355180 | + | 0.171046i | 0.602962 | − | 0.797770i | \(-0.293987\pi\) |
−0.247781 | + | 0.968816i | \(0.579701\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.3710 | + | 46.4538i | 0.878138 | + | 1.82347i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.46804 | − | 4.36062i | 0.213981 | − | 0.170644i | −0.510634 | − | 0.859798i | \(-0.670589\pi\) |
0.724615 | + | 0.689154i | \(0.242018\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 33.2551i | − | 1.29938i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.39394 | − | 11.2006i | 0.210118 | − | 0.436314i | −0.769099 | − | 0.639130i | \(-0.779295\pi\) |
0.979217 | + | 0.202815i | \(0.0650090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.6568 | + | 29.6647i | 0.920143 | + | 1.15382i | 0.987740 | + | 0.156110i | \(0.0498955\pi\) |
−0.0675967 | + | 0.997713i | \(0.521533\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.6299 | − | 14.8568i | −0.722436 | − | 0.576124i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.6795 | + | 3.14807i | −0.413511 | + | 0.121894i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.5649 | + | 50.6691i | 0.446457 | + | 1.95606i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.1911 | + | 17.7951i | 0.547028 | + | 0.685952i | 0.976101 | − | 0.217318i | \(-0.0697309\pi\) |
−0.429072 | + | 0.903270i | \(0.641159\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.1036 | − | 6.41446i | 1.08011 | − | 0.246528i | 0.354793 | − | 0.934945i | \(-0.384551\pi\) |
0.725315 | + | 0.688417i | \(0.241694\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.49326i | 0.0573062i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.1569 | + | 5.85447i | −0.465172 | + | 0.224015i | −0.651763 | − | 0.758423i | \(-0.725970\pi\) |
0.186591 | + | 0.982438i | \(0.440256\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.64622 | + | 15.8775i | 0.292147 | + | 0.606649i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.92941 | + | 12.8346i | −0.111602 | + | 0.488960i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.0186 | + | 13.8169i | −0.419167 | + | 0.525619i | −0.945920 | − | 0.324399i | \(-0.894838\pi\) |
0.526753 | + | 0.850018i | \(0.323409\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.15015 | 0.233289 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.5033 | 0.435718 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.0012 | + | 12.5411i | −0.377740 | + | 0.473671i | −0.933967 | − | 0.357360i | \(-0.883677\pi\) |
0.556227 | + | 0.831030i | \(0.312248\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.77781 | − | 16.5517i | 0.142483 | − | 0.624258i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.4248 | − | 40.3361i | −0.730546 | − | 1.51699i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.26187 | − | 3.01556i | 0.235169 | − | 0.113252i | −0.312588 | − | 0.949889i | \(-0.601196\pi\) |
0.547758 | + | 0.836637i | \(0.315482\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.52265i | − | 0.0570238i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −65.0584 | + | 14.8492i | −2.43305 | + | 0.555327i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.21879 | + | 11.5600i | 0.343803 | + | 0.431115i | 0.923430 | − | 0.383767i | \(-0.125373\pi\) |
−0.579627 | + | 0.814882i | \(0.696802\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.4920 | − | 50.3497i | −0.427984 | − | 1.87512i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.5208 | − | 3.02957i | −0.687845 | − | 0.112515i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.14782 | + | 0.915356i | 0.0425703 | + | 0.0339487i | 0.644544 | − | 0.764567i | \(-0.277047\pi\) |
−0.601974 | + | 0.798516i | \(0.705619\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.0291 | − | 42.6712i | −1.25861 | − | 1.57825i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.39961 | + | 7.05937i | −0.125568 | + | 0.260744i | −0.954270 | − | 0.298945i | \(-0.903365\pi\) |
0.828703 | + | 0.559689i | \(0.189079\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.9823i | 0.772892i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.8651 | − | 30.1964i | 1.39289 | − | 1.11079i | 0.413120 | − | 0.910677i | \(-0.364439\pi\) |
0.979772 | − | 0.200117i | \(-0.0641323\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.51983 | − | 13.5386i | −0.239189 | − | 0.496682i | 0.746472 | − | 0.665417i | \(-0.231746\pi\) |
−0.985661 | + | 0.168735i | \(0.946032\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43.4383 | + | 20.9188i | 1.59145 | + | 0.766404i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.1901 | + | 15.2859i | −0.445415 | + | 0.558533i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0306 | − | 8.22374i | −1.31477 | − | 0.300089i | −0.493063 | − | 0.869993i | \(-0.664123\pi\) |
−0.821711 | + | 0.569905i | \(0.806980\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.1668 | −0.733944 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.5654 | − | 9.48703i | −1.51072 | − | 0.344812i | −0.614677 | − | 0.788779i | \(-0.710714\pi\) |
−0.896043 | + | 0.443967i | \(0.853571\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.50046 | + | 37.2430i | −0.308142 | + | 1.35006i | 0.549365 | + | 0.835583i | \(0.314870\pi\) |
−0.857506 | + | 0.514474i | \(0.827987\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.8310 | − | 10.5132i | −0.790334 | − | 0.380605i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 73.6975 | − | 35.4908i | 2.66106 | − | 1.28150i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.3543 | + | 25.8017i | −1.16673 | + | 0.930432i | −0.998469 | − | 0.0553110i | \(-0.982385\pi\) |
−0.168256 | + | 0.985743i | \(0.553814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.6055 | − | 8.81146i | 1.38854 | − | 0.316926i | 0.538051 | − | 0.842912i | \(-0.319161\pi\) |
0.850493 | + | 0.525986i | \(0.176304\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.11359 | − | 2.31239i | 0.0400012 | − | 0.0830634i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.13410 | + | 4.96880i | 0.0406332 | + | 0.178026i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.2732 | + | 32.1168i | 1.44109 | + | 1.14923i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 45.8612 | + | 36.5731i | 1.63686 | + | 1.30535i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.46773 | − | 32.7183i | −0.266196 | − | 1.16628i | −0.914399 | − | 0.404813i | \(-0.867336\pi\) |
0.648203 | − | 0.761467i | \(-0.275521\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.0740 | + | 41.6840i | −0.713748 | + | 1.48211i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 80.3848 | − | 18.3473i | 2.85455 | − | 0.651532i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.4111 | + | 23.4545i | −1.04179 | + | 0.830802i | −0.985850 | − | 0.167632i | \(-0.946388\pi\) |
−0.0559434 | + | 0.998434i | \(0.517817\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.2857 | − | 10.2506i | 0.753033 | − | 0.362642i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.988262 | − | 0.475922i | −0.0348750 | − | 0.0167949i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.73981 | + | 16.3852i | −0.131811 | + | 0.577502i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.31102 | + | 0.299232i | 0.0460931 | + | 0.0105204i | 0.245505 | − | 0.969395i | \(-0.421046\pi\) |
−0.199412 | + | 0.979916i | \(0.563903\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.06614 | −0.142781 | −0.0713907 | − | 0.997448i | \(-0.522744\pi\) | ||||
−0.0713907 | + | 0.997448i | \(0.522744\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.0147 | + | 6.16592i | 0.946282 | + | 0.215983i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.0768 | − | 18.9057i | 0.527469 | − | 0.661426i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.4095 | − | 21.3865i | −1.54990 | − | 0.746394i | −0.553640 | − | 0.832756i | \(-0.686762\pi\) |
−0.996264 | + | 0.0863616i | \(0.972476\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.1881 | − | 35.6915i | −0.599140 | − | 1.24413i | −0.951323 | − | 0.308195i | \(-0.900275\pi\) |
0.352183 | − | 0.935931i | \(-0.385439\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.2991 | + | 20.9728i | −0.914508 | + | 0.729296i | −0.962993 | − | 0.269528i | \(-0.913132\pi\) |
0.0484842 | + | 0.998824i | \(0.484561\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 45.1571i | − | 1.56837i | −0.620527 | − | 0.784185i | \(-0.713081\pi\) | ||
0.620527 | − | 0.784185i | \(-0.286919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.26178 | + | 4.69663i | −0.0783660 | + | 0.162729i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.90996 | + | 4.90293i | 0.135310 | + | 0.169673i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.3666 | + | 20.2292i | 0.875753 | + | 0.698390i | 0.954406 | − | 0.298512i | \(-0.0964904\pi\) |
−0.0786529 | + | 0.996902i | \(0.525062\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.7571 | − | 20.2520i | −0.715763 | − | 0.698343i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.1314 | + | 66.2949i | 0.520535 | + | 2.28061i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.98596 | − | 7.50615i | −0.205680 | − | 0.257914i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.6741 | + | 2.66454i | −0.400183 | + | 0.0913392i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 37.4830i | − | 1.28339i | −0.766958 | − | 0.641697i | \(-0.778231\pi\) | ||
0.766958 | − | 0.641697i | \(-0.221769\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.5905 | − | 5.58171i | 0.395925 | − | 0.190668i | −0.225318 | − | 0.974285i | \(-0.572342\pi\) |
0.621243 | + | 0.783618i | \(0.286628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.1229 | + | 41.7857i | 0.686586 | + | 1.42571i | 0.894276 | + | 0.447516i | \(0.147691\pi\) |
−0.207690 | + | 0.978195i | \(0.566595\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.27892 | − | 18.7472i | 0.145656 | − | 0.638161i | −0.848406 | − | 0.529346i | \(-0.822437\pi\) |
0.994062 | − | 0.108815i | \(-0.0347055\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.5020 | + | 14.4230i | −0.391078 | + | 0.490397i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.9479 | 1.59260 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.2877 | 1.12791 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.67884 | − | 9.62897i | 0.259592 | − | 0.325518i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.16720 | + | 35.7828i | −0.275787 | + | 1.20830i | 0.627278 | + | 0.778796i | \(0.284169\pi\) |
−0.903064 | + | 0.429505i | \(0.858688\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.1873 | + | 29.4602i | 0.477981 | + | 0.992538i | 0.990963 | + | 0.134138i | \(0.0428267\pi\) |
−0.512982 | + | 0.858400i | \(0.671459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.4062 | + | 14.1613i | −0.989596 | + | 0.476564i | −0.857395 | − | 0.514659i | \(-0.827919\pi\) |
−0.132201 | + | 0.991223i | \(0.542204\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 55.8120i | 1.87398i | 0.349350 | + | 0.936992i | \(0.386402\pi\) | ||||
−0.349350 | + | 0.936992i | \(0.613598\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.78140 | − | 0.863080i | 0.126824 | − | 0.0289468i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.52626 | + | 8.18367i | 0.218393 | + | 0.273856i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.5546 | − | 55.0055i | −0.419655 | − | 1.83863i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.45928 | − | 1.93978i | 0.115373 | − | 0.0646954i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.2956 | − | 9.00795i | −0.376311 | − | 0.300098i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.8368 | + | 24.8746i | 0.659398 | + | 0.826859i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.8304 | + | 32.8722i | −0.525641 | + | 1.09150i | 0.454048 | + | 0.890977i | \(0.349980\pi\) |
−0.979688 | + | 0.200526i | \(0.935735\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.7316i | 0.653736i | 0.945070 | + | 0.326868i | \(0.105993\pi\) | ||||
−0.945070 | + | 0.326868i | \(0.894007\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.4613 | + | 21.1022i | −0.875743 | + | 0.698382i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.8235 | − | 28.7048i | −0.456492 | − | 0.947915i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.08361 | + | 1.96656i | 0.134706 | + | 0.0648709i | 0.500023 | − | 0.866012i | \(-0.333325\pi\) |
−0.365317 | + | 0.930883i | \(0.619039\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 50.9522 | − | 63.8921i | 1.67711 | − | 2.10303i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.6777 | − | 4.49130i | −0.646997 | − | 0.147673i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.6884 | 0.908426 | 0.454213 | − | 0.890893i | \(-0.349920\pi\) | ||||
0.454213 | + | 0.890893i | \(0.349920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.25168 | − | 0.513932i | −0.0737959 | − | 0.0168434i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.2963 | − | 71.3986i | 0.532945 | − | 2.33498i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.5916 | + | 17.1400i | 1.16273 | + | 0.559940i | 0.912833 | − | 0.408333i | \(-0.133890\pi\) |
0.249894 | + | 0.968273i | \(0.419604\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.0837 | + | 15.9323i | −1.07850 | + | 0.519378i | −0.886837 | − | 0.462083i | \(-0.847102\pi\) |
−0.191663 | + | 0.981461i | \(0.561388\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.81044 | − | 2.24125i | 0.0915204 | − | 0.0729851i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.37996 | + | 0.314967i | −0.0448427 | + | 0.0102350i | −0.244883 | − | 0.969553i | \(-0.578750\pi\) |
0.200041 | + | 0.979788i | \(0.435893\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.755035 | + | 1.56785i | −0.0245095 | + | 0.0508944i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.192647 | − | 0.844042i | −0.00624045 | − | 0.0273412i | 0.971712 | − | 0.236170i | \(-0.0758921\pi\) |
−0.977952 | + | 0.208828i | \(0.933035\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.2570 | + | 27.3190i | 1.10853 | + | 0.884023i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.2000 | + | 10.5266i | 0.426249 | + | 0.339922i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.77746 | − | 29.6940i | −0.218628 | − | 0.957870i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.39952 | + | 19.5183i | −0.302581 | + | 0.628316i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.3935 | − | 11.5020i | 1.62055 | − | 0.369879i | 0.686528 | − | 0.727103i | \(-0.259134\pi\) |
0.934019 | + | 0.357224i | \(0.116277\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.0067 | − | 32.7017i | 1.31597 | − | 1.04945i | 0.321229 | − | 0.947002i | \(-0.395904\pi\) |
0.994738 | − | 0.102447i | \(-0.0326674\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.30862 | − | 2.55650i | 0.170187 | − | 0.0819575i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.8957 | − | 5.72866i | −0.380577 | − | 0.183276i | 0.233808 | − | 0.972283i | \(-0.424881\pi\) |
−0.614385 | + | 0.789007i | \(0.710596\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.37093 | + | 36.6754i | −0.267536 | + | 1.17215i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.84891 | + | 1.79146i | 0.250341 | + | 0.0571388i | 0.345850 | − | 0.938290i | \(-0.387591\pi\) |
−0.0955086 | + | 0.995429i | \(0.530448\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.4118 | −0.459198 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.6277 | − | 3.79517i | −0.528731 | − | 0.120679i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0918 | + | 20.1784i | −0.511172 | + | 0.640989i | −0.968708 | − | 0.248202i | \(-0.920160\pi\) |
0.457537 | + | 0.889191i | \(0.348732\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.2271 | + | 18.8908i | 1.24358 | + | 0.598878i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.22270 | − | 10.8451i | −0.165405 | − | 0.343466i | 0.801748 | − | 0.597662i | \(-0.203904\pi\) |
−0.967153 | + | 0.254196i | \(0.918189\pi\) | |||||||
\(998\) | 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 | 1044.2.z.c.325.1 | ✓ | 24 | |
3.2 | odd | 2 | inner | 1044.2.z.c.325.4 | yes | 24 | |
29.5 | even | 14 | inner | 1044.2.z.c.469.1 | yes | 24 | |
87.5 | odd | 14 | inner | 1044.2.z.c.469.4 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1044.2.z.c.325.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1044.2.z.c.325.4 | yes | 24 | 3.2 | odd | 2 | inner | |
1044.2.z.c.469.1 | yes | 24 | 29.5 | even | 14 | inner | |
1044.2.z.c.469.4 | yes | 24 | 87.5 | odd | 14 | inner |