Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(361,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.h (of order \(3\), 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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 882) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.3 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.667 |
Dual form | 2646.2.h.q.361.3 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.517638 | 0.231495 | 0.115747 | − | 0.993279i | \(-0.463074\pi\) | ||||
0.115747 | + | 0.993279i | \(0.463074\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.258819 | − | 0.448288i | −0.0818458 | − | 0.141761i | ||||
\(11\) | 1.46410 | 0.441443 | 0.220722 | − | 0.975337i | \(-0.429159\pi\) | ||||
0.220722 | + | 0.975337i | \(0.429159\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.22474 | − | 2.12132i | −0.339683 | − | 0.588348i | 0.644690 | − | 0.764444i | \(-0.276986\pi\) |
−0.984373 | + | 0.176096i | \(0.943653\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.74238 | + | 3.01790i | 0.422590 | + | 0.731947i | 0.996192 | − | 0.0871869i | \(-0.0277877\pi\) |
−0.573602 | + | 0.819134i | \(0.694454\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.258819 | − | 0.448288i | 0.0593772 | − | 0.102844i | −0.834809 | − | 0.550540i | \(-0.814422\pi\) |
0.894186 | + | 0.447696i | \(0.147755\pi\) | |||||||
\(20\) | −0.258819 | + | 0.448288i | −0.0578737 | + | 0.100240i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.732051 | − | 1.26795i | −0.156074 | − | 0.270328i | ||||
\(23\) | −7.92820 | −1.65314 | −0.826572 | − | 0.562831i | \(-0.809712\pi\) | ||||
−0.826572 | + | 0.562831i | \(0.809712\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.73205 | −0.946410 | ||||||||
\(26\) | −1.22474 | + | 2.12132i | −0.240192 | + | 0.416025i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.36603 | − | 2.36603i | 0.253665 | − | 0.439360i | −0.710867 | − | 0.703326i | \(-0.751697\pi\) |
0.964532 | + | 0.263966i | \(0.0850307\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.67423 | − | 6.36396i | 0.659912 | − | 1.14300i | −0.320726 | − | 0.947172i | \(-0.603927\pi\) |
0.980638 | − | 0.195829i | \(-0.0627398\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.74238 | − | 3.01790i | 0.298816 | − | 0.517565i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | − | 6.92820i | 0.657596 | − | 1.13899i | −0.323640 | − | 0.946180i | \(-0.604907\pi\) |
0.981236 | − | 0.192809i | \(-0.0617599\pi\) | |||||||
\(38\) | −0.517638 | −0.0839720 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.517638 | 0.0818458 | ||||||||
\(41\) | −2.82843 | − | 4.89898i | −0.441726 | − | 0.765092i | 0.556092 | − | 0.831121i | \(-0.312300\pi\) |
−0.997818 | + | 0.0660290i | \(0.978967\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.09808 | − | 10.5622i | 0.929948 | − | 1.61072i | 0.146544 | − | 0.989204i | \(-0.453185\pi\) |
0.783404 | − | 0.621513i | \(-0.213482\pi\) | |||||||
\(44\) | −0.732051 | + | 1.26795i | −0.110361 | + | 0.191151i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.96410 | + | 6.86603i | 0.584475 | + | 1.01234i | ||||
\(47\) | 2.31079 | + | 4.00240i | 0.337063 | + | 0.583811i | 0.983879 | − | 0.178836i | \(-0.0572331\pi\) |
−0.646816 | + | 0.762646i | \(0.723900\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.36603 | + | 4.09808i | 0.334607 | + | 0.579555i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.44949 | 0.339683 | ||||||||
\(53\) | 3.36603 | + | 5.83013i | 0.462359 | + | 0.800830i | 0.999078 | − | 0.0429316i | \(-0.0136698\pi\) |
−0.536719 | + | 0.843761i | \(0.680336\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.757875 | 0.102192 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.73205 | −0.358736 | ||||||||
\(59\) | −7.39924 | + | 12.8159i | −0.963299 | + | 1.66848i | −0.249180 | + | 0.968457i | \(0.580161\pi\) |
−0.714118 | + | 0.700025i | \(0.753172\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.19067 | + | 3.79435i | 0.280487 | + | 0.485817i | 0.971505 | − | 0.237020i | \(-0.0761708\pi\) |
−0.691018 | + | 0.722838i | \(0.742837\pi\) | |||||||
\(62\) | −7.34847 | −0.933257 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.633975 | − | 1.09808i | −0.0786349 | − | 0.136200i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.90192 | − | 3.29423i | 0.232357 | − | 0.402454i | −0.726144 | − | 0.687542i | \(-0.758690\pi\) |
0.958501 | + | 0.285088i | \(0.0920229\pi\) | |||||||
\(68\) | −3.48477 | −0.422590 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.803848 | 0.0953992 | 0.0476996 | − | 0.998862i | \(-0.484811\pi\) | ||||
0.0476996 | + | 0.998862i | \(0.484811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.31079 | + | 4.00240i | 0.270457 | + | 0.468446i | 0.968979 | − | 0.247143i | \(-0.0794917\pi\) |
−0.698522 | + | 0.715589i | \(0.746158\pi\) | |||||||
\(74\) | −8.00000 | −0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.258819 | + | 0.448288i | 0.0296886 | + | 0.0514221i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.06218 | − | 12.2321i | −0.794557 | − | 1.37621i | −0.923120 | − | 0.384512i | \(-0.874370\pi\) |
0.128563 | − | 0.991701i | \(-0.458964\pi\) | |||||||
\(80\) | −0.258819 | − | 0.448288i | −0.0289368 | − | 0.0501201i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.82843 | + | 4.89898i | −0.312348 | + | 0.541002i | ||||
\(83\) | 4.94975 | − | 8.57321i | 0.543305 | − | 0.941033i | −0.455406 | − | 0.890284i | \(-0.650506\pi\) |
0.998711 | − | 0.0507487i | \(-0.0161607\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.901924 | + | 1.56218i | 0.0978274 | + | 0.169442i | ||||
\(86\) | −12.1962 | −1.31514 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.46410 | 0.156074 | ||||||||
\(89\) | 8.05558 | − | 13.9527i | 0.853889 | − | 1.47898i | −0.0237822 | − | 0.999717i | \(-0.507571\pi\) |
0.877672 | − | 0.479263i | \(-0.159096\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.96410 | − | 6.86603i | 0.413286 | − | 0.715833i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.31079 | − | 4.00240i | 0.238340 | − | 0.412816i | ||||
\(95\) | 0.133975 | − | 0.232051i | 0.0137455 | − | 0.0238079i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.517638 | + | 0.896575i | −0.0525582 | + | 0.0910334i | −0.891108 | − | 0.453792i | \(-0.850071\pi\) |
0.838549 | + | 0.544826i | \(0.183404\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.36603 | − | 4.09808i | 0.236603 | − | 0.409808i | ||||
\(101\) | 5.79555 | 0.576679 | 0.288340 | − | 0.957528i | \(-0.406897\pi\) | ||||
0.288340 | + | 0.957528i | \(0.406897\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.2122 | 1.10477 | 0.552384 | − | 0.833590i | \(-0.313718\pi\) | ||||
0.552384 | + | 0.833590i | \(0.313718\pi\) | |||||||
\(104\) | −1.22474 | − | 2.12132i | −0.120096 | − | 0.208013i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.36603 | − | 5.83013i | 0.326937 | − | 0.566272i | ||||
\(107\) | 1.53590 | − | 2.66025i | 0.148481 | − | 0.257176i | −0.782185 | − | 0.623046i | \(-0.785895\pi\) |
0.930666 | + | 0.365869i | \(0.119228\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.29423 | − | 9.16987i | −0.507095 | − | 0.878315i | −0.999966 | − | 0.00821222i | \(-0.997386\pi\) |
0.492871 | − | 0.870102i | \(-0.335947\pi\) | |||||||
\(110\) | −0.378937 | − | 0.656339i | −0.0361303 | − | 0.0625794i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.33013 | − | 12.6962i | −0.689560 | − | 1.19435i | −0.971980 | − | 0.235063i | \(-0.924470\pi\) |
0.282420 | − | 0.959291i | \(-0.408863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.10394 | −0.382694 | ||||||||
\(116\) | 1.36603 | + | 2.36603i | 0.126832 | + | 0.219680i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.7985 | 1.36231 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.85641 | −0.805128 | ||||||||
\(122\) | 2.19067 | − | 3.79435i | 0.198334 | − | 0.343525i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.67423 | + | 6.36396i | 0.329956 | + | 0.571501i | ||||
\(125\) | −5.03768 | −0.450584 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.92820 | −0.526043 | −0.263021 | − | 0.964790i | \(-0.584719\pi\) | ||||
−0.263021 | + | 0.964790i | \(0.584719\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.633975 | + | 1.09808i | −0.0556033 | + | 0.0963077i | ||||
\(131\) | 12.4877 | 1.09105 | 0.545527 | − | 0.838093i | \(-0.316330\pi\) | ||||
0.545527 | + | 0.838093i | \(0.316330\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.80385 | −0.328602 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.74238 | + | 3.01790i | 0.149408 | + | 0.258782i | ||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.1075 | − | 17.5068i | −0.857311 | − | 1.48491i | −0.874485 | − | 0.485053i | \(-0.838800\pi\) |
0.0171736 | − | 0.999853i | \(-0.494533\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.401924 | − | 0.696152i | −0.0337287 | − | 0.0584198i | ||||
\(143\) | −1.79315 | − | 3.10583i | −0.149951 | − | 0.259722i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.707107 | − | 1.22474i | 0.0587220 | − | 0.101710i | ||||
\(146\) | 2.31079 | − | 4.00240i | 0.191242 | − | 0.331241i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.00000 | + | 6.92820i | 0.328798 | + | 0.569495i | ||||
\(149\) | 2.39230 | 0.195985 | 0.0979926 | − | 0.995187i | \(-0.468758\pi\) | ||||
0.0979926 | + | 0.995187i | \(0.468758\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3923 | −1.41537 | −0.707683 | − | 0.706530i | \(-0.750259\pi\) | ||||
−0.707683 | + | 0.706530i | \(0.750259\pi\) | |||||||
\(152\) | 0.258819 | − | 0.448288i | 0.0209930 | − | 0.0363609i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.90192 | − | 3.29423i | 0.152766 | − | 0.264599i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.64256 | + | 14.9694i | −0.689752 | + | 1.19469i | 0.282166 | + | 0.959366i | \(0.408947\pi\) |
−0.971918 | + | 0.235320i | \(0.924386\pi\) | |||||||
\(158\) | −7.06218 | + | 12.2321i | −0.561837 | + | 0.973130i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.258819 | + | 0.448288i | −0.0204614 | + | 0.0354403i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.53590 | − | 6.12436i | 0.276953 | − | 0.479697i | −0.693673 | − | 0.720290i | \(-0.744009\pi\) |
0.970626 | + | 0.240593i | \(0.0773421\pi\) | |||||||
\(164\) | 5.65685 | 0.441726 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.89949 | −0.768350 | ||||||||
\(167\) | −6.64136 | − | 11.5032i | −0.513924 | − | 0.890143i | −0.999870 | − | 0.0161534i | \(-0.994858\pi\) |
0.485945 | − | 0.873989i | \(-0.338475\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.50000 | − | 6.06218i | 0.269231 | − | 0.466321i | ||||
\(170\) | 0.901924 | − | 1.56218i | 0.0691744 | − | 0.119814i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.09808 | + | 10.5622i | 0.464974 | + | 0.805359i | ||||
\(173\) | 9.71003 | + | 16.8183i | 0.738240 | + | 1.27867i | 0.953287 | + | 0.302065i | \(0.0976760\pi\) |
−0.215048 | + | 0.976604i | \(0.568991\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.732051 | − | 1.26795i | −0.0551804 | − | 0.0955753i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.1112 | −1.20758 | ||||||||
\(179\) | −4.09808 | − | 7.09808i | −0.306305 | − | 0.530535i | 0.671246 | − | 0.741234i | \(-0.265759\pi\) |
−0.977551 | + | 0.210699i | \(0.932426\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.9730 | 1.55891 | 0.779454 | − | 0.626459i | \(-0.215497\pi\) | ||||
0.779454 | + | 0.626459i | \(0.215497\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.92820 | −0.584475 | ||||||||
\(185\) | 2.07055 | − | 3.58630i | 0.152230 | − | 0.263670i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.55103 | + | 4.41851i | 0.186549 | + | 0.323113i | ||||
\(188\) | −4.62158 | −0.337063 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.267949 | −0.0194391 | ||||||||
\(191\) | −3.59808 | − | 6.23205i | −0.260348 | − | 0.450935i | 0.705987 | − | 0.708225i | \(-0.250504\pi\) |
−0.966334 | + | 0.257290i | \(0.917171\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.8660 | − | 20.5526i | 0.854135 | − | 1.47941i | −0.0233098 | − | 0.999728i | \(-0.507420\pi\) |
0.877445 | − | 0.479677i | \(-0.159246\pi\) | |||||||
\(194\) | 1.03528 | 0.0743285 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.66025 | −0.688265 | −0.344132 | − | 0.938921i | \(-0.611827\pi\) | ||||
−0.344132 | + | 0.938921i | \(0.611827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.79555 | + | 10.0382i | 0.410836 | + | 0.711589i | 0.994981 | − | 0.100060i | \(-0.0319035\pi\) |
−0.584145 | + | 0.811649i | \(0.698570\pi\) | |||||||
\(200\) | −4.73205 | −0.334607 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.89778 | − | 5.01910i | −0.203887 | − | 0.353142i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.46410 | − | 2.53590i | −0.102257 | − | 0.177115i | ||||
\(206\) | −5.60609 | − | 9.71003i | −0.390595 | − | 0.676530i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.22474 | + | 2.12132i | −0.0849208 | + | 0.147087i | ||||
\(209\) | 0.378937 | − | 0.656339i | 0.0262116 | − | 0.0453999i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.633975 | − | 1.09808i | −0.0436446 | − | 0.0755947i | 0.843378 | − | 0.537321i | \(-0.180564\pi\) |
−0.887022 | + | 0.461726i | \(0.847230\pi\) | |||||||
\(212\) | −6.73205 | −0.462359 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.07180 | −0.209984 | ||||||||
\(215\) | 3.15660 | − | 5.46739i | 0.215278 | − | 0.372873i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.29423 | + | 9.16987i | −0.358570 | + | 0.621062i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.378937 | + | 0.656339i | −0.0255480 | + | 0.0442504i | ||||
\(221\) | 4.26795 | − | 7.39230i | 0.287093 | − | 0.497260i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.88108 | − | 3.25813i | 0.125967 | − | 0.218181i | −0.796144 | − | 0.605108i | \(-0.793130\pi\) |
0.922110 | + | 0.386927i | \(0.126463\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.33013 | + | 12.6962i | −0.487593 | + | 0.844535i | ||||
\(227\) | 3.34607 | 0.222086 | 0.111043 | − | 0.993816i | \(-0.464581\pi\) | ||||
0.111043 | + | 0.993816i | \(0.464581\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.8004 | −0.911954 | −0.455977 | − | 0.889992i | \(-0.650710\pi\) | ||||
−0.455977 | + | 0.889992i | \(0.650710\pi\) | |||||||
\(230\) | 2.05197 | + | 3.55412i | 0.135303 | + | 0.234351i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.36603 | − | 2.36603i | 0.0896840 | − | 0.155337i | ||||
\(233\) | 0.696152 | − | 1.20577i | 0.0456065 | − | 0.0789927i | −0.842321 | − | 0.538976i | \(-0.818811\pi\) |
0.887928 | + | 0.459983i | \(0.152145\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.19615 | + | 2.07180i | 0.0780284 | + | 0.135149i | ||||
\(236\) | −7.39924 | − | 12.8159i | −0.481649 | − | 0.834241i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.23205 | − | 10.7942i | −0.403118 | − | 0.698221i | 0.590983 | − | 0.806684i | \(-0.298740\pi\) |
−0.994100 | + | 0.108464i | \(0.965407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.7279 | −0.819878 | −0.409939 | − | 0.912113i | \(-0.634450\pi\) | ||||
−0.409939 | + | 0.912113i | \(0.634450\pi\) | |||||||
\(242\) | 4.42820 | + | 7.66987i | 0.284656 | + | 0.493038i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.38134 | −0.280487 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.26795 | −0.0806777 | ||||||||
\(248\) | 3.67423 | − | 6.36396i | 0.233314 | − | 0.404112i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.51884 | + | 4.36276i | 0.159305 | + | 0.275925i | ||||
\(251\) | −0.517638 | −0.0326730 | −0.0163365 | − | 0.999867i | \(-0.505200\pi\) | ||||
−0.0163365 | + | 0.999867i | \(0.505200\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.6077 | −0.729770 | ||||||||
\(254\) | 2.96410 | + | 5.13397i | 0.185984 | + | 0.322134i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3.76217 | 0.234678 | 0.117339 | − | 0.993092i | \(-0.462564\pi\) | ||||
0.117339 | + | 0.993092i | \(0.462564\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.26795 | 0.0786349 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.24384 | − | 10.8147i | −0.385746 | − | 0.668131i | ||||
\(263\) | −2.66025 | −0.164038 | −0.0820191 | − | 0.996631i | \(-0.526137\pi\) | ||||
−0.0820191 | + | 0.996631i | \(0.526137\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.74238 | + | 3.01790i | 0.107034 | + | 0.185388i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.90192 | + | 3.29423i | 0.116178 | + | 0.201227i | ||||
\(269\) | −13.4536 | − | 23.3023i | −0.820281 | − | 1.42077i | −0.905473 | − | 0.424404i | \(-0.860484\pi\) |
0.0851918 | − | 0.996365i | \(-0.472850\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.39924 | − | 12.8159i | 0.449472 | − | 0.778508i | −0.548880 | − | 0.835901i | \(-0.684946\pi\) |
0.998352 | + | 0.0573934i | \(0.0182789\pi\) | |||||||
\(272\) | 1.74238 | − | 3.01790i | 0.105647 | − | 0.182987i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.92820 | −0.417786 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.1962 | −0.973132 | −0.486566 | − | 0.873644i | \(-0.661751\pi\) | ||||
−0.486566 | + | 0.873644i | \(0.661751\pi\) | |||||||
\(278\) | −10.1075 | + | 17.5068i | −0.606210 | + | 1.04999i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.69615 | + | 15.0622i | −0.518769 | + | 0.898534i | 0.480993 | + | 0.876724i | \(0.340276\pi\) |
−0.999762 | + | 0.0218099i | \(0.993057\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.88040 | − | 8.45310i | 0.290109 | − | 0.502484i | −0.683726 | − | 0.729739i | \(-0.739642\pi\) |
0.973835 | + | 0.227255i | \(0.0729749\pi\) | |||||||
\(284\) | −0.401924 | + | 0.696152i | −0.0238498 | + | 0.0413090i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.79315 | + | 3.10583i | −0.106031 | + | 0.183651i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.42820 | − | 4.20577i | 0.142835 | − | 0.247398i | ||||
\(290\) | −1.41421 | −0.0830455 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.62158 | −0.270457 | ||||||||
\(293\) | 1.48356 | + | 2.56961i | 0.0866707 | + | 0.150118i | 0.906102 | − | 0.423059i | \(-0.139044\pi\) |
−0.819431 | + | 0.573178i | \(0.805711\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.83013 | + | 6.63397i | −0.222999 | + | 0.386245i | ||||
\(296\) | 4.00000 | − | 6.92820i | 0.232495 | − | 0.402694i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.19615 | − | 2.07180i | −0.0692912 | − | 0.120016i | ||||
\(299\) | 9.71003 | + | 16.8183i | 0.561545 | + | 0.972625i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.69615 | + | 15.0622i | 0.500407 | + | 0.866731i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.517638 | −0.0296886 | ||||||||
\(305\) | 1.13397 | + | 1.96410i | 0.0649312 | + | 0.112464i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.9329 | 0.681046 | 0.340523 | − | 0.940236i | \(-0.389396\pi\) | ||||
0.340523 | + | 0.940236i | \(0.389396\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.80385 | −0.216044 | ||||||||
\(311\) | −9.09085 | + | 15.7458i | −0.515495 | + | 0.892863i | 0.484343 | + | 0.874878i | \(0.339059\pi\) |
−0.999838 | + | 0.0179854i | \(0.994275\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.34607 | − | 5.79555i | −0.189131 | − | 0.327584i | 0.755830 | − | 0.654768i | \(-0.227234\pi\) |
−0.944961 | + | 0.327184i | \(0.893900\pi\) | |||||||
\(314\) | 17.2851 | 0.975456 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.1244 | 0.794557 | ||||||||
\(317\) | 16.2942 | + | 28.2224i | 0.915175 | + | 1.58513i | 0.806645 | + | 0.591037i | \(0.201281\pi\) |
0.108530 | + | 0.994093i | \(0.465386\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | − | 3.46410i | 0.111979 | − | 0.193952i | ||||
\(320\) | 0.517638 | 0.0289368 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.80385 | 0.100369 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.79555 | + | 10.0382i | 0.321480 | + | 0.556819i | ||||
\(326\) | −7.07180 | −0.391671 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.82843 | − | 4.89898i | −0.156174 | − | 0.270501i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.02628 | + | 10.4378i | 0.331234 | + | 0.573715i | 0.982754 | − | 0.184917i | \(-0.0592016\pi\) |
−0.651520 | + | 0.758632i | \(0.725868\pi\) | |||||||
\(332\) | 4.94975 | + | 8.57321i | 0.271653 | + | 0.470516i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.64136 | + | 11.5032i | −0.363399 | + | 0.629426i | ||||
\(335\) | 0.984508 | − | 1.70522i | 0.0537894 | − | 0.0931660i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.6603 | + | 18.4641i | 0.580701 | + | 1.00580i | 0.995396 | + | 0.0958434i | \(0.0305548\pi\) |
−0.414695 | + | 0.909960i | \(0.636112\pi\) | |||||||
\(338\) | −7.00000 | −0.380750 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.80385 | −0.0978274 | ||||||||
\(341\) | 5.37945 | − | 9.31749i | 0.291314 | − | 0.504570i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.09808 | − | 10.5622i | 0.328786 | − | 0.569474i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.71003 | − | 16.8183i | 0.522014 | − | 0.904155i | ||||
\(347\) | 10.8564 | − | 18.8038i | 0.582802 | − | 1.00944i | −0.412343 | − | 0.911029i | \(-0.635289\pi\) |
0.995145 | − | 0.0984148i | \(-0.0313772\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.2987 | + | 29.9623i | −0.925980 | + | 1.60384i | −0.136002 | + | 0.990709i | \(0.543425\pi\) |
−0.789978 | + | 0.613136i | \(0.789908\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.732051 | + | 1.26795i | −0.0390184 | + | 0.0675819i | ||||
\(353\) | 0.101536 | 0.00540421 | 0.00270211 | − | 0.999996i | \(-0.499140\pi\) | ||||
0.00270211 | + | 0.999996i | \(0.499140\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.416102 | 0.0220844 | ||||||||
\(356\) | 8.05558 | + | 13.9527i | 0.426945 | + | 0.739490i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.09808 | + | 7.09808i | −0.216590 | + | 0.375145i | ||||
\(359\) | −6.96410 | + | 12.0622i | −0.367551 | + | 0.636617i | −0.989182 | − | 0.146693i | \(-0.953137\pi\) |
0.621631 | + | 0.783310i | \(0.286470\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.36603 | + | 16.2224i | 0.492949 | + | 0.853812i | ||||
\(362\) | −10.4865 | − | 18.1631i | −0.551157 | − | 0.954632i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.19615 | + | 2.07180i | 0.0626095 | + | 0.108443i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.277401 | 0.0144802 | 0.00724012 | − | 0.999974i | \(-0.497695\pi\) | ||||
0.00724012 | + | 0.999974i | \(0.497695\pi\) | |||||||
\(368\) | 3.96410 | + | 6.86603i | 0.206643 | + | 0.357916i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.14110 | −0.215286 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.1244 | 0.990222 | 0.495111 | − | 0.868830i | \(-0.335127\pi\) | ||||
0.495111 | + | 0.868830i | \(0.335127\pi\) | |||||||
\(374\) | 2.55103 | − | 4.41851i | 0.131910 | − | 0.228476i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.31079 | + | 4.00240i | 0.119170 | + | 0.206408i | ||||
\(377\) | −6.69213 | −0.344662 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.5167 | −1.41344 | −0.706718 | − | 0.707495i | \(-0.749825\pi\) | ||||
−0.706718 | + | 0.707495i | \(0.749825\pi\) | |||||||
\(380\) | 0.133975 | + | 0.232051i | 0.00687275 | + | 0.0119040i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.59808 | + | 6.23205i | −0.184094 | + | 0.318859i | ||||
\(383\) | −34.2185 | −1.74849 | −0.874243 | − | 0.485489i | \(-0.838641\pi\) | ||||
−0.874243 | + | 0.485489i | \(0.838641\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.7321 | −1.20793 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.517638 | − | 0.896575i | −0.0262791 | − | 0.0455167i | ||||
\(389\) | 4.87564 | 0.247205 | 0.123602 | − | 0.992332i | \(-0.460555\pi\) | ||||
0.123602 | + | 0.992332i | \(0.460555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.8140 | − | 23.9265i | −0.698602 | − | 1.21001i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.83013 | + | 8.36603i | 0.243338 | + | 0.421474i | ||||
\(395\) | −3.65565 | − | 6.33178i | −0.183936 | − | 0.318586i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.1948 | − | 22.8541i | 0.662228 | − | 1.14701i | −0.317801 | − | 0.948157i | \(-0.602945\pi\) |
0.980029 | − | 0.198855i | \(-0.0637222\pi\) | |||||||
\(398\) | 5.79555 | − | 10.0382i | 0.290505 | − | 0.503169i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.36603 | + | 4.09808i | 0.118301 | + | 0.204904i | ||||
\(401\) | 25.0526 | 1.25107 | 0.625533 | − | 0.780198i | \(-0.284882\pi\) | ||||
0.625533 | + | 0.780198i | \(0.284882\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.0000 | −0.896644 | ||||||||
\(404\) | −2.89778 | + | 5.01910i | −0.144170 | + | 0.249709i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.85641 | − | 10.1436i | 0.290291 | − | 0.502799i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.90138 | − | 15.4176i | 0.440145 | − | 0.762354i | −0.557555 | − | 0.830140i | \(-0.688260\pi\) |
0.997700 | + | 0.0677865i | \(0.0215937\pi\) | |||||||
\(410\) | −1.46410 | + | 2.53590i | −0.0723068 | + | 0.125239i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.60609 | + | 9.71003i | −0.276192 | + | 0.478379i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.56218 | − | 4.43782i | 0.125772 | − | 0.217844i | ||||
\(416\) | 2.44949 | 0.120096 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.757875 | −0.0370689 | ||||||||
\(419\) | 11.3323 | + | 19.6281i | 0.553619 | + | 0.958896i | 0.998010 | + | 0.0630626i | \(0.0200868\pi\) |
−0.444391 | + | 0.895833i | \(0.646580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0263 | + | 24.2942i | −0.683599 | + | 1.18403i | 0.290276 | + | 0.956943i | \(0.406253\pi\) |
−0.973875 | + | 0.227085i | \(0.927080\pi\) | |||||||
\(422\) | −0.633975 | + | 1.09808i | −0.0308614 | + | 0.0534535i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.36603 | + | 5.83013i | 0.163469 | + | 0.283136i | ||||
\(425\) | −8.24504 | − | 14.2808i | −0.399943 | − | 0.692722i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.53590 | + | 2.66025i | 0.0742405 | + | 0.128588i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.31319 | −0.304449 | ||||||||
\(431\) | −13.3923 | − | 23.1962i | −0.645085 | − | 1.11732i | −0.984282 | − | 0.176604i | \(-0.943489\pi\) |
0.339197 | − | 0.940715i | \(-0.389845\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.2523 | 0.973261 | 0.486631 | − | 0.873608i | \(-0.338226\pi\) | ||||
0.486631 | + | 0.873608i | \(0.338226\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.5885 | 0.507095 | ||||||||
\(437\) | −2.05197 | + | 3.55412i | −0.0981590 | + | 0.170016i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.14162 | + | 15.8338i | 0.436306 | + | 0.755704i | 0.997401 | − | 0.0720474i | \(-0.0229533\pi\) |
−0.561095 | + | 0.827751i | \(0.689620\pi\) | |||||||
\(440\) | 0.757875 | 0.0361303 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.53590 | −0.406011 | ||||||||
\(443\) | −18.4904 | − | 32.0263i | −0.878505 | − | 1.52161i | −0.852982 | − | 0.521940i | \(-0.825208\pi\) |
−0.0255224 | − | 0.999674i | \(-0.508125\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.16987 | − | 7.22243i | 0.197671 | − | 0.342376i | ||||
\(446\) | −3.76217 | −0.178144 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.7846 | 1.12247 | 0.561233 | − | 0.827658i | \(-0.310327\pi\) | ||||
0.561233 | + | 0.827658i | \(0.310327\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.14110 | − | 7.17260i | −0.194997 | − | 0.337745i | ||||
\(452\) | 14.6603 | 0.689560 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.67303 | − | 2.89778i | −0.0785193 | − | 0.135999i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.1340 | + | 19.2846i | 0.520825 | + | 0.902096i | 0.999707 | + | 0.0242164i | \(0.00770906\pi\) |
−0.478881 | + | 0.877880i | \(0.658958\pi\) | |||||||
\(458\) | 6.90018 | + | 11.9515i | 0.322424 | + | 0.558455i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.05197 | − | 3.55412i | 0.0956736 | − | 0.165712i | ||||
\(461\) | −19.4894 | + | 33.7566i | −0.907712 | + | 1.57220i | −0.0904771 | + | 0.995899i | \(0.528839\pi\) |
−0.817235 | + | 0.576305i | \(0.804494\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.33013 | − | 5.76795i | −0.154764 | − | 0.268059i | 0.778209 | − | 0.628005i | \(-0.216128\pi\) |
−0.932973 | + | 0.359946i | \(0.882795\pi\) | |||||||
\(464\) | −2.73205 | −0.126832 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.39230 | −0.0644973 | ||||||||
\(467\) | −12.2982 | + | 21.3011i | −0.569094 | + | 0.985699i | 0.427562 | + | 0.903986i | \(0.359372\pi\) |
−0.996656 | + | 0.0817131i | \(0.973961\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.19615 | − | 2.07180i | 0.0551744 | − | 0.0955649i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.39924 | + | 12.8159i | −0.340577 | + | 0.589898i | ||||
\(473\) | 8.92820 | − | 15.4641i | 0.410519 | − | 0.711040i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.22474 | + | 2.12132i | −0.0561951 | + | 0.0973329i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.23205 | + | 10.7942i | −0.285047 | + | 0.493717i | ||||
\(479\) | −13.2827 | −0.606903 | −0.303452 | − | 0.952847i | \(-0.598139\pi\) | ||||
−0.303452 | + | 0.952847i | \(0.598139\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.5959 | −0.893497 | ||||||||
\(482\) | 6.36396 | + | 11.0227i | 0.289870 | + | 0.502070i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.42820 | − | 7.66987i | 0.201282 | − | 0.348631i | ||||
\(485\) | −0.267949 | + | 0.464102i | −0.0121669 | + | 0.0210738i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.1603 | + | 27.9904i | 0.732291 | + | 1.26837i | 0.955902 | + | 0.293687i | \(0.0948822\pi\) |
−0.223611 | + | 0.974679i | \(0.571784\pi\) | |||||||
\(488\) | 2.19067 | + | 3.79435i | 0.0991670 | + | 0.171762i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.53590 | − | 4.39230i | −0.114443 | − | 0.198222i | 0.803114 | − | 0.595826i | \(-0.203175\pi\) |
−0.917557 | + | 0.397604i | \(0.869842\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.52056 | 0.428784 | ||||||||
\(494\) | 0.633975 | + | 1.09808i | 0.0285239 | + | 0.0494048i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.34847 | −0.329956 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.32051 | 0.327711 | 0.163855 | − | 0.986484i | \(-0.447607\pi\) | ||||
0.163855 | + | 0.986484i | \(0.447607\pi\) | |||||||
\(500\) | 2.51884 | − | 4.36276i | 0.112646 | − | 0.195109i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.258819 | + | 0.448288i | 0.0115517 | + | 0.0200081i | ||||
\(503\) | 28.9406 | 1.29040 | 0.645199 | − | 0.764015i | \(-0.276774\pi\) | ||||
0.645199 | + | 0.764015i | \(0.276774\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.00000 | 0.133498 | ||||||||
\(506\) | 5.80385 | + | 10.0526i | 0.258012 | + | 0.446891i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.96410 | − | 5.13397i | 0.131511 | − | 0.227783i | ||||
\(509\) | −7.62587 | −0.338011 | −0.169005 | − | 0.985615i | \(-0.554056\pi\) | ||||
−0.169005 | + | 0.985615i | \(0.554056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.88108 | − | 3.25813i | −0.0829710 | − | 0.143710i | ||||
\(515\) | 5.80385 | 0.255748 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.38323 | + | 5.85993i | 0.148794 | + | 0.257719i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.633975 | − | 1.09808i | −0.0278016 | − | 0.0481538i | ||||
\(521\) | 16.2635 | + | 28.1691i | 0.712515 | + | 1.23411i | 0.963910 | + | 0.266228i | \(0.0857773\pi\) |
−0.251395 | + | 0.967885i | \(0.580889\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.6281 | − | 33.9969i | 0.858277 | − | 1.48658i | −0.0152941 | − | 0.999883i | \(-0.504868\pi\) |
0.873571 | − | 0.486696i | \(-0.161798\pi\) | |||||||
\(524\) | −6.24384 | + | 10.8147i | −0.272764 | + | 0.472440i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.33013 | + | 2.30385i | 0.0579963 | + | 0.100453i | ||||
\(527\) | 25.6077 | 1.11549 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39.8564 | 1.73289 | ||||||||
\(530\) | 1.74238 | − | 3.01790i | 0.0756843 | − | 0.131089i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.92820 | + | 12.0000i | −0.300094 | + | 0.519778i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.795040 | − | 1.37705i | 0.0343726 | − | 0.0595350i | ||||
\(536\) | 1.90192 | − | 3.29423i | 0.0821506 | − | 0.142289i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13.4536 | + | 23.3023i | −0.580026 | + | 1.00464i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.3660 | + | 17.9545i | −0.445670 | + | 0.771924i | −0.998099 | − | 0.0616369i | \(-0.980368\pi\) |
0.552428 | + | 0.833560i | \(0.313701\pi\) | |||||||
\(542\) | −14.7985 | −0.635649 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.48477 | −0.149408 | ||||||||
\(545\) | −2.74049 | − | 4.74668i | −0.117390 | − | 0.203325i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.73205 | − | 9.92820i | 0.245085 | − | 0.424499i | −0.717071 | − | 0.697000i | \(-0.754518\pi\) |
0.962155 | + | 0.272501i | \(0.0878509\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.46410 | + | 6.00000i | 0.147710 | + | 0.255841i | ||||
\(551\) | −0.707107 | − | 1.22474i | −0.0301238 | − | 0.0521759i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.09808 | + | 14.0263i | 0.344054 | + | 0.595920i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.2151 | 0.857311 | ||||||||
\(557\) | 1.43782 | + | 2.49038i | 0.0609225 | + | 0.105521i | 0.894878 | − | 0.446311i | \(-0.147262\pi\) |
−0.833956 | + | 0.551832i | \(0.813929\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.8744 | −1.26355 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.3923 | 0.733650 | ||||||||
\(563\) | 0.637756 | − | 1.10463i | 0.0268782 | − | 0.0465545i | −0.852273 | − | 0.523097i | \(-0.824777\pi\) |
0.879152 | + | 0.476542i | \(0.158110\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.79435 | − | 6.57201i | −0.159630 | − | 0.276487i | ||||
\(566\) | −9.76079 | −0.410277 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.803848 | 0.0337287 | ||||||||
\(569\) | 13.4641 | + | 23.3205i | 0.564445 | + | 0.977647i | 0.997101 | + | 0.0760878i | \(0.0242429\pi\) |
−0.432657 | + | 0.901559i | \(0.642424\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.00000 | + | 3.46410i | −0.0836974 | + | 0.144968i | −0.904835 | − | 0.425762i | \(-0.860006\pi\) |
0.821138 | + | 0.570730i | \(0.193340\pi\) | |||||||
\(572\) | 3.58630 | 0.149951 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 37.5167 | 1.56455 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.1440 | + | 22.7661i | 0.547193 | + | 0.947766i | 0.998465 | + | 0.0553797i | \(0.0176369\pi\) |
−0.451272 | + | 0.892386i | \(0.649030\pi\) | |||||||
\(578\) | −4.85641 | −0.202000 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.707107 | + | 1.22474i | 0.0293610 | + | 0.0508548i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.92820 | + | 8.53590i | 0.204105 | + | 0.353521i | ||||
\(584\) | 2.31079 | + | 4.00240i | 0.0956211 | + | 0.165621i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.48356 | − | 2.56961i | 0.0612855 | − | 0.106150i | ||||
\(587\) | −1.76097 | + | 3.05008i | −0.0726828 | + | 0.125890i | −0.900076 | − | 0.435732i | \(-0.856489\pi\) |
0.827393 | + | 0.561623i | \(0.189823\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.90192 | − | 3.29423i | −0.0783674 | − | 0.135736i | ||||
\(590\) | 7.66025 | 0.315368 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.00000 | −0.328798 | ||||||||
\(593\) | 3.39683 | − | 5.88349i | 0.139491 | − | 0.241606i | −0.787813 | − | 0.615915i | \(-0.788787\pi\) |
0.927304 | + | 0.374309i | \(0.122120\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.19615 | + | 2.07180i | −0.0489963 | + | 0.0848641i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.71003 | − | 16.8183i | 0.397073 | − | 0.687750i | ||||
\(599\) | −6.19615 | + | 10.7321i | −0.253168 | + | 0.438500i | −0.964396 | − | 0.264461i | \(-0.914806\pi\) |
0.711228 | + | 0.702961i | \(0.248139\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.9730 | + | 36.3262i | −0.855505 | + | 1.48178i | 0.0206704 | + | 0.999786i | \(0.493420\pi\) |
−0.876176 | + | 0.481992i | \(0.839913\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.69615 | − | 15.0622i | 0.353841 | − | 0.612871i | ||||
\(605\) | −4.58441 | −0.186383 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.3891 | 0.868156 | 0.434078 | − | 0.900875i | \(-0.357074\pi\) | ||||
0.434078 | + | 0.900875i | \(0.357074\pi\) | |||||||
\(608\) | 0.258819 | + | 0.448288i | 0.0104965 | + | 0.0181805i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.13397 | − | 1.96410i | 0.0459133 | − | 0.0795241i | ||||
\(611\) | 5.66025 | − | 9.80385i | 0.228989 | − | 0.396621i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.2224 | − | 17.7058i | −0.412880 | − | 0.715129i | 0.582323 | − | 0.812957i | \(-0.302144\pi\) |
−0.995203 | + | 0.0978280i | \(0.968810\pi\) | |||||||
\(614\) | −5.96644 | − | 10.3342i | −0.240786 | − | 0.417054i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.1962 | + | 36.7128i | 0.853325 | + | 1.47800i | 0.878190 | + | 0.478311i | \(0.158751\pi\) |
−0.0248653 | + | 0.999691i | \(0.507916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.48717 | 0.300935 | 0.150467 | − | 0.988615i | \(-0.451922\pi\) | ||||
0.150467 | + | 0.988615i | \(0.451922\pi\) | |||||||
\(620\) | 1.90192 | + | 3.29423i | 0.0763831 | + | 0.132299i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.1817 | 0.729020 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.0526 | 0.842102 | ||||||||
\(626\) | −3.34607 | + | 5.79555i | −0.133736 | + | 0.231637i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.64256 | − | 14.9694i | −0.344876 | − | 0.597343i | ||||
\(629\) | 27.8781 | 1.11157 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.87564 | −0.154287 | −0.0771435 | − | 0.997020i | \(-0.524580\pi\) | ||||
−0.0771435 | + | 0.997020i | \(0.524580\pi\) | |||||||
\(632\) | −7.06218 | − | 12.2321i | −0.280918 | − | 0.486565i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.2942 | − | 28.2224i | 0.647126 | − | 1.12086i | ||||
\(635\) | −3.06866 | −0.121776 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.00000 | −0.158362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.258819 | − | 0.448288i | −0.0102307 | − | 0.0177201i | ||||
\(641\) | 3.05256 | 0.120569 | 0.0602844 | − | 0.998181i | \(-0.480799\pi\) | ||||
0.0602844 | + | 0.998181i | \(0.480799\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.845807 | − | 1.46498i | −0.0333554 | − | 0.0577732i | 0.848866 | − | 0.528608i | \(-0.177286\pi\) |
−0.882221 | + | 0.470835i | \(0.843953\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.901924 | − | 1.56218i | −0.0354857 | − | 0.0614631i | ||||
\(647\) | 7.91688 | + | 13.7124i | 0.311244 | + | 0.539091i | 0.978632 | − | 0.205619i | \(-0.0659209\pi\) |
−0.667388 | + | 0.744711i | \(0.732588\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.8332 | + | 18.7637i | −0.425242 | + | 0.736540i | ||||
\(650\) | 5.79555 | − | 10.0382i | 0.227320 | − | 0.393730i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.53590 | + | 6.12436i | 0.138476 | + | 0.239848i | ||||
\(653\) | 41.3205 | 1.61700 | 0.808498 | − | 0.588499i | \(-0.200281\pi\) | ||||
0.808498 | + | 0.588499i | \(0.200281\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.46410 | 0.252573 | ||||||||
\(656\) | −2.82843 | + | 4.89898i | −0.110432 | + | 0.191273i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.5622 | + | 33.8827i | −0.762034 | + | 1.31988i | 0.179766 | + | 0.983709i | \(0.442466\pi\) |
−0.941800 | + | 0.336173i | \(0.890867\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.7267 | − | 18.5792i | 0.417221 | − | 0.722648i | −0.578438 | − | 0.815727i | \(-0.696337\pi\) |
0.995659 | + | 0.0930785i | \(0.0296708\pi\) | |||||||
\(662\) | 6.02628 | − | 10.4378i | 0.234218 | − | 0.405677i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.94975 | − | 8.57321i | 0.192087 | − | 0.332705i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.8301 | + | 18.7583i | −0.419344 | + | 0.726325i | ||||
\(668\) | 13.2827 | 0.513924 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.96902 | −0.0760697 | ||||||||
\(671\) | 3.20736 | + | 5.55532i | 0.123819 | + | 0.214461i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0885 | − | 34.7942i | 0.774353 | − | 1.34122i | −0.160804 | − | 0.986986i | \(-0.551409\pi\) |
0.935157 | − | 0.354233i | \(-0.115258\pi\) | |||||||
\(674\) | 10.6603 | − | 18.4641i | 0.410618 | − | 0.711211i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.50000 | + | 6.06218i | 0.134615 | + | 0.233161i | ||||
\(677\) | −0.568406 | − | 0.984508i | −0.0218456 | − | 0.0378377i | 0.854896 | − | 0.518800i | \(-0.173621\pi\) |
−0.876742 | + | 0.480962i | \(0.840288\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.901924 | + | 1.56218i | 0.0345872 | + | 0.0599068i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.7589 | −0.411980 | ||||||||
\(683\) | −6.80385 | − | 11.7846i | −0.260342 | − | 0.450926i | 0.705991 | − | 0.708221i | \(-0.250502\pi\) |
−0.966333 | + | 0.257295i | \(0.917169\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12.1962 | −0.464974 | ||||||||
\(689\) | 8.24504 | − | 14.2808i | 0.314111 | − | 0.544057i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.4913 | − | 32.0279i | −0.703442 | − | 1.21840i | −0.967251 | − | 0.253822i | \(-0.918312\pi\) |
0.263809 | − | 0.964575i | \(-0.415021\pi\) | |||||||
\(692\) | −19.4201 | −0.738240 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.7128 | −0.824207 | ||||||||
\(695\) | −5.23205 | − | 9.06218i | −0.198463 | − | 0.343748i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.85641 | − | 17.0718i | 0.373338 | − | 0.646640i | ||||
\(698\) | 34.5975 | 1.30953 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.5359 | −0.775630 | −0.387815 | − | 0.921737i | \(-0.626770\pi\) | ||||
−0.387815 | + | 0.921737i | \(0.626770\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.07055 | − | 3.58630i | −0.0780924 | − | 0.135260i | ||||
\(704\) | 1.46410 | 0.0551804 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.0507680 | − | 0.0879327i | −0.00191068 | − | 0.00330939i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.2679 | + | 19.5167i | 0.423177 | + | 0.732964i | 0.996248 | − | 0.0865418i | \(-0.0275816\pi\) |
−0.573072 | + | 0.819505i | \(0.694248\pi\) | |||||||
\(710\) | −0.208051 | − | 0.360355i | −0.00780802 | − | 0.0135239i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.05558 | − | 13.9527i | 0.301895 | − | 0.522898i | ||||
\(713\) | −29.1301 | + | 50.4548i | −1.09093 | + | 1.88955i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.928203 | − | 1.60770i | −0.0347128 | − | 0.0601244i | ||||
\(716\) | 8.19615 | 0.306305 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.9282 | 0.519796 | ||||||||
\(719\) | 17.0077 | − | 29.4582i | 0.634281 | − | 1.09861i | −0.352386 | − | 0.935855i | \(-0.614629\pi\) |
0.986667 | − | 0.162752i | \(-0.0520372\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.36603 | − | 16.2224i | 0.348567 | − | 0.603736i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.4865 | + | 18.1631i | −0.389727 | + | 0.675027i | ||||
\(725\) | −6.46410 | + | 11.1962i | −0.240071 | + | 0.415815i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.8864 | + | 25.7840i | −0.552106 | + | 0.956276i | 0.446016 | + | 0.895025i | \(0.352842\pi\) |
−0.998122 | + | 0.0612512i | \(0.980491\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.19615 | − | 2.07180i | 0.0442716 | − | 0.0766806i | ||||
\(731\) | 42.5007 | 1.57195 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.1146 | −1.11231 | −0.556154 | − | 0.831079i | \(-0.687723\pi\) | ||||
−0.556154 | + | 0.831079i | \(0.687723\pi\) | |||||||
\(734\) | −0.138701 | − | 0.240237i | −0.00511954 | − | 0.00886730i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.96410 | − | 6.86603i | 0.146119 | − | 0.253085i | ||||
\(737\) | 2.78461 | − | 4.82309i | 0.102572 | − | 0.177661i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.07180 | + | 13.9808i | 0.296926 | + | 0.514291i | 0.975431 | − | 0.220305i | \(-0.0707052\pi\) |
−0.678505 | + | 0.734596i | \(0.737372\pi\) | |||||||
\(740\) | 2.07055 | + | 3.58630i | 0.0761150 | + | 0.131835i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.1244 | − | 24.4641i | −0.518172 | − | 0.897501i | −0.999777 | − | 0.0211123i | \(-0.993279\pi\) |
0.481605 | − | 0.876389i | \(-0.340054\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.23835 | 0.0453696 | ||||||||
\(746\) | −9.56218 | − | 16.5622i | −0.350096 | − | 0.606384i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.10205 | −0.186549 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.1769 | −1.83098 | −0.915491 | − | 0.402339i | \(-0.868197\pi\) | ||||
−0.915491 | + | 0.402339i | \(0.868197\pi\) | |||||||
\(752\) | 2.31079 | − | 4.00240i | 0.0842658 | − | 0.145953i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.34607 | + | 5.79555i | 0.121857 | + | 0.211062i | ||||
\(755\) | −9.00292 | −0.327650 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.2487 | 0.735952 | 0.367976 | − | 0.929835i | \(-0.380051\pi\) | ||||
0.367976 | + | 0.929835i | \(0.380051\pi\) | |||||||
\(758\) | 13.7583 | + | 23.8301i | 0.499725 | + | 0.865549i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.133975 | − | 0.232051i | 0.00485977 | − | 0.00841737i | ||||
\(761\) | −39.7738 | −1.44180 | −0.720900 | − | 0.693039i | \(-0.756271\pi\) | ||||
−0.720900 | + | 0.693039i | \(0.756271\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7.19615 | 0.260348 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.1093 | + | 29.6341i | 0.618183 | + | 1.07072i | ||||
\(767\) | 36.2487 | 1.30887 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.9372 | + | 25.8719i | 0.538648 | + | 0.932966i | 0.998977 | + | 0.0452178i | \(0.0143982\pi\) |
−0.460329 | + | 0.887748i | \(0.652268\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.8660 | + | 20.5526i | 0.427068 | + | 0.739703i | ||||
\(773\) | −6.76148 | − | 11.7112i | −0.243194 | − | 0.421224i | 0.718429 | − | 0.695601i | \(-0.244862\pi\) |
−0.961622 | + | 0.274377i | \(0.911528\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.3867 | + | 30.1146i | −0.624547 | + | 1.08175i | ||||
\(776\) | −0.517638 | + | 0.896575i | −0.0185821 | + | 0.0321852i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.43782 | − | 4.22243i | −0.0874002 | − | 0.151382i | ||||
\(779\) | −2.92820 | −0.104914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.17691 | 0.0421133 | ||||||||
\(782\) | −13.8140 | + | 23.9265i | −0.493986 | + | 0.855610i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.47372 | + | 7.74871i | −0.159674 | + | 0.276563i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.0938 | + | 31.3393i | −0.644973 | + | 1.11713i | 0.339334 | + | 0.940666i | \(0.389798\pi\) |
−0.984308 | + | 0.176461i | \(0.943535\pi\) | |||||||
\(788\) | 4.83013 | − | 8.36603i | 0.172066 | − | 0.298027i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.65565 | + | 6.33178i | −0.130062 | + | 0.225274i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.36603 | − | 9.29423i | 0.190553 | − | 0.330048i | ||||
\(794\) | −26.3896 | −0.936531 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.5911 | −0.410836 | ||||||||
\(797\) | −12.2796 | − | 21.2690i | −0.434967 | − | 0.753385i | 0.562326 | − | 0.826916i | \(-0.309907\pi\) |
−0.997293 | + | 0.0735308i | \(0.976573\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.05256 | + | 13.9474i | −0.284879 | + | 0.493425i | ||||
\(800\) | 2.36603 | − | 4.09808i | 0.0836516 | − | 0.144889i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.5263 | − | 21.6962i | −0.442318 | − | 0.766118i | ||||
\(803\) | 3.38323 | + | 5.85993i | 0.119392 | + | 0.206792i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.00000 | + | 15.5885i | 0.317011 | + | 0.549080i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.79555 | 0.203887 | ||||||||
\(809\) | 16.6603 | + | 28.8564i | 0.585743 | + | 1.01454i | 0.994782 | + | 0.102020i | \(0.0325307\pi\) |
−0.409039 | + | 0.912517i | \(0.634136\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.82894 | −0.274911 | −0.137456 | − | 0.990508i | \(-0.543892\pi\) | ||||
−0.137456 | + | 0.990508i | \(0.543892\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.7128 | −0.410534 | ||||||||
\(815\) | 1.83032 | − | 3.17020i | 0.0641132 | − | 0.111047i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.15660 | − | 5.46739i | −0.110435 | − | 0.191280i | ||||
\(818\) | −17.8028 | −0.622459 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.92820 | 0.102257 | ||||||||
\(821\) | −3.33975 | − | 5.78461i | −0.116558 | − | 0.201884i | 0.801844 | − | 0.597534i | \(-0.203853\pi\) |
−0.918401 | + | 0.395650i | \(0.870519\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.66025 | − | 6.33975i | 0.127588 | − | 0.220990i | −0.795153 | − | 0.606408i | \(-0.792610\pi\) |
0.922742 | + | 0.385419i | \(0.125943\pi\) | |||||||
\(824\) | 11.2122 | 0.390595 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.7321 | 1.83367 | 0.916837 | − | 0.399263i | \(-0.130734\pi\) | ||||
0.916837 | + | 0.399263i | \(0.130734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.947343 | − | 1.64085i | −0.0329026 | − | 0.0569890i | 0.849105 | − | 0.528224i | \(-0.177142\pi\) |
−0.882008 | + | 0.471235i | \(0.843808\pi\) | |||||||
\(830\) | −5.12436 | −0.177869 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.22474 | − | 2.12132i | −0.0424604 | − | 0.0735436i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.43782 | − | 5.95448i | −0.118971 | − | 0.206063i | ||||
\(836\) | 0.378937 | + | 0.656339i | 0.0131058 | + | 0.0227000i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.3323 | − | 19.6281i | 0.391467 | − | 0.678042i | ||||
\(839\) | 22.4751 | − | 38.9280i | 0.775927 | − | 1.34395i | −0.158345 | − | 0.987384i | \(-0.550616\pi\) |
0.934272 | − | 0.356561i | \(-0.116051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7679 | + | 18.6506i | 0.371309 | + | 0.643125i | ||||
\(842\) | 28.0526 | 0.966755 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.26795 | 0.0436446 | ||||||||
\(845\) | 1.81173 | − | 3.13801i | 0.0623255 | − | 0.107951i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.36603 | − | 5.83013i | 0.115590 | − | 0.200207i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.24504 | + | 14.2808i | −0.282803 | + | 0.489829i | ||||
\(851\) | −31.7128 | + | 54.9282i | −1.08710 | + | 1.88291i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.7992 | − | 20.4367i | 0.403996 | − | 0.699741i | −0.590208 | − | 0.807251i | \(-0.700954\pi\) |
0.994204 | + | 0.107510i | \(0.0342878\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.53590 | − | 2.66025i | 0.0524959 | − | 0.0909256i | ||||
\(857\) | 5.45378 | 0.186298 | 0.0931488 | − | 0.995652i | \(-0.470307\pi\) | ||||
0.0931488 | + | 0.995652i | \(0.470307\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.69642 | −0.330838 | −0.165419 | − | 0.986223i | \(-0.552898\pi\) | ||||
−0.165419 | + | 0.986223i | \(0.552898\pi\) | |||||||
\(860\) | 3.15660 | + | 5.46739i | 0.107639 | + | 0.186436i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.3923 | + | 23.1962i | −0.456144 | + | 0.790064i | ||||
\(863\) | 10.5981 | − | 18.3564i | 0.360763 | − | 0.624859i | −0.627324 | − | 0.778758i | \(-0.715850\pi\) |
0.988087 | + | 0.153899i | \(0.0491831\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.02628 | + | 8.70577i | 0.170899 | + | 0.296005i | ||||
\(866\) | −10.1261 | − | 17.5390i | −0.344100 | − | 0.595998i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.3397 | − | 17.9090i | −0.350752 | − | 0.607520i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.31749 | −0.315711 | ||||||||
\(872\) | −5.29423 | − | 9.16987i | −0.179285 | − | 0.310531i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.10394 | 0.138818 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.0526 | 0.812197 | 0.406099 | − | 0.913829i | \(-0.366889\pi\) | ||||
0.406099 | + | 0.913829i | \(0.366889\pi\) | |||||||
\(878\) | 9.14162 | − | 15.8338i | 0.308515 | − | 0.534363i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.378937 | − | 0.656339i | −0.0127740 | − | 0.0221252i | ||||
\(881\) | 0.480473 | 0.0161876 | 0.00809378 | − | 0.999967i | \(-0.497424\pi\) | ||||
0.00809378 | + | 0.999967i | \(0.497424\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.2487 | 1.28717 | 0.643586 | − | 0.765374i | \(-0.277446\pi\) | ||||
0.643586 | + | 0.765374i | \(0.277446\pi\) | |||||||
\(884\) | 4.26795 | + | 7.39230i | 0.143547 | + | 0.248630i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.4904 | + | 32.0263i | −0.621197 | + | 1.07594i | ||||
\(887\) | 26.9716 | 0.905617 | 0.452809 | − | 0.891608i | \(-0.350422\pi\) | ||||
0.452809 | + | 0.891608i | \(0.350422\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.33975 | −0.279549 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.88108 | + | 3.25813i | 0.0629833 | + | 0.109090i | ||||
\(893\) | 2.39230 | 0.0800554 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.12132 | − | 3.67423i | −0.0709079 | − | 0.122816i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.8923 | − | 20.5981i | −0.396851 | − | 0.687367i | ||||
\(899\) | −10.0382 | − | 17.3867i | −0.334793 | − | 0.579878i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.7298 | + | 20.3166i | −0.390777 | + | 0.676845i | ||||
\(902\) | −4.14110 | + | 7.17260i | −0.137884 | + | 0.238822i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.33013 | − | 12.6962i | −0.243796 | − | 0.422268i | ||||
\(905\) | 10.8564 | 0.360879 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.12436 | −0.170151 | −0.0850757 | − | 0.996374i | \(-0.527113\pi\) | ||||
−0.0850757 | + | 0.996374i | \(0.527113\pi\) | |||||||
\(908\) | −1.67303 | + | 2.89778i | −0.0555215 | + | 0.0961661i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.8923 | − | 24.0622i | 0.460273 | − | 0.797216i | −0.538702 | − | 0.842497i | \(-0.681085\pi\) |
0.998974 | + | 0.0452811i | \(0.0144183\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.24693 | − | 12.5521i | 0.239838 | − | 0.415412i | ||||
\(914\) | 11.1340 | − | 19.2846i | 0.368279 | − | 0.637878i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.90018 | − | 11.9515i | 0.227988 | − | 0.394888i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.18653 | + | 14.1795i | −0.270049 | + | 0.467738i | −0.968874 | − | 0.247554i | \(-0.920373\pi\) |
0.698825 | + | 0.715292i | \(0.253707\pi\) | |||||||
\(920\) | −4.10394 | −0.135303 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 38.9788 | 1.28370 | ||||||||
\(923\) | −0.984508 | − | 1.70522i | −0.0324055 | − | 0.0561279i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.9282 | + | 32.7846i | −0.622355 | + | 1.07795i | ||||
\(926\) | −3.33013 | + | 5.76795i | −0.109435 | + | 0.189547i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.36603 | + | 2.36603i | 0.0448420 | + | 0.0776686i | ||||
\(929\) | −2.01978 | − | 3.49837i | −0.0662670 | − | 0.114778i | 0.830988 | − | 0.556290i | \(-0.187776\pi\) |
−0.897255 | + | 0.441512i | \(0.854442\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.696152 | + | 1.20577i | 0.0228032 | + | 0.0394964i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 24.5964 | 0.804820 | ||||||||
\(935\) | 1.32051 | + | 2.28719i | 0.0431852 | + | 0.0747990i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.7690 | −1.03785 | −0.518925 | − | 0.854820i | \(-0.673667\pi\) | ||||
−0.518925 | + | 0.854820i | \(0.673667\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.39230 | −0.0780284 | ||||||||
\(941\) | 29.1994 | − | 50.5749i | 0.951874 | − | 1.64869i | 0.210510 | − | 0.977592i | \(-0.432488\pi\) |
0.741364 | − | 0.671103i | \(-0.234179\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.4243 | + | 38.8401i | 0.730237 | + | 1.26481i | ||||
\(944\) | 14.7985 | 0.481649 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.8564 | −0.580562 | ||||||||
\(947\) | −17.8301 | − | 30.8827i | −0.579401 | − | 1.00355i | −0.995548 | − | 0.0942550i | \(-0.969953\pi\) |
0.416147 | − | 0.909297i | \(-0.363380\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.66025 | − | 9.80385i | 0.183740 | − | 0.318246i | ||||
\(950\) | 2.44949 | 0.0794719 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.7128 | −0.768133 | −0.384067 | − | 0.923305i | \(-0.625477\pi\) | ||||
−0.384067 | + | 0.923305i | \(0.625477\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.86250 | − | 3.22595i | −0.0602691 | − | 0.104389i | ||||
\(956\) | 12.4641 | 0.403118 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.64136 | + | 11.5032i | 0.214573 | + | 0.371651i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.5000 | − | 19.9186i | −0.370968 | − | 0.642535i | ||||
\(962\) | 9.79796 | + | 16.9706i | 0.315899 | + | 0.547153i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.36396 | − | 11.0227i | 0.204969 | − | 0.355017i | ||||
\(965\) | 6.14231 | − | 10.6388i | 0.197728 | − | 0.342475i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.232051 | + | 0.401924i | 0.00746225 | + | 0.0129250i | 0.869732 | − | 0.493524i | \(-0.164291\pi\) |
−0.862270 | + | 0.506449i | \(0.830958\pi\) | |||||||
\(968\) | −8.85641 | −0.284656 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.535898 | 0.0172067 | ||||||||
\(971\) | −14.2994 | + | 24.7673i | −0.458890 | + | 0.794821i | −0.998903 | − | 0.0468359i | \(-0.985086\pi\) |
0.540012 | + | 0.841657i | \(0.318420\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.1603 | − | 27.9904i | 0.517808 | − | 0.896870i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.19067 | − | 3.79435i | 0.0701217 | − | 0.121454i | ||||
\(977\) | −8.07180 | + | 13.9808i | −0.258240 | + | 0.447284i | −0.965770 | − | 0.259398i | \(-0.916476\pi\) |
0.707531 | + | 0.706683i | \(0.249809\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.7942 | − | 20.4281i | 0.376944 | − | 0.652886i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.53590 | + | 4.39230i | −0.0809238 | + | 0.140164i | ||||
\(983\) | −23.6355 | −0.753855 | −0.376927 | − | 0.926243i | \(-0.623019\pi\) | ||||
−0.376927 | + | 0.926243i | \(0.623019\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.00052 | −0.159330 | ||||||||
\(986\) | −4.76028 | − | 8.24504i | −0.151598 | − | 0.262576i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.633975 | − | 1.09808i | 0.0201694 | − | 0.0349345i | ||||
\(989\) | −48.3468 | + | 83.7391i | −1.53734 | + | 2.66275i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.33975 | − | 12.7128i | −0.233155 | − | 0.403836i | 0.725580 | − | 0.688138i | \(-0.241572\pi\) |
−0.958735 | + | 0.284302i | \(0.908238\pi\) | |||||||
\(992\) | 3.67423 | + | 6.36396i | 0.116657 | + | 0.202056i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.00000 | + | 5.19615i | 0.0951064 | + | 0.164729i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.8778 | −1.38962 | −0.694812 | − | 0.719192i | \(-0.744512\pi\) | ||||
−0.694812 | + | 0.719192i | \(0.744512\pi\) | |||||||
\(998\) | −3.66025 | − | 6.33975i | −0.115863 | − | 0.200681i | ||||
\(999\) | 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 | 2646.2.h.q.667.3 | 8 | ||
3.2 | odd | 2 | 882.2.h.t.79.1 | 8 | |||
7.2 | even | 3 | 2646.2.f.q.883.2 | 8 | |||
7.3 | odd | 6 | 2646.2.e.t.2125.3 | 8 | |||
7.4 | even | 3 | 2646.2.e.t.2125.2 | 8 | |||
7.5 | odd | 6 | 2646.2.f.q.883.3 | 8 | |||
7.6 | odd | 2 | inner | 2646.2.h.q.667.2 | 8 | ||
9.4 | even | 3 | 2646.2.e.t.1549.2 | 8 | |||
9.5 | odd | 6 | 882.2.e.q.373.3 | 8 | |||
21.2 | odd | 6 | 882.2.f.s.295.3 | yes | 8 | ||
21.5 | even | 6 | 882.2.f.s.295.2 | ✓ | 8 | ||
21.11 | odd | 6 | 882.2.e.q.655.3 | 8 | |||
21.17 | even | 6 | 882.2.e.q.655.2 | 8 | |||
21.20 | even | 2 | 882.2.h.t.79.4 | 8 | |||
63.2 | odd | 6 | 7938.2.a.cj.1.2 | 4 | |||
63.4 | even | 3 | inner | 2646.2.h.q.361.3 | 8 | ||
63.5 | even | 6 | 882.2.f.s.589.1 | yes | 8 | ||
63.13 | odd | 6 | 2646.2.e.t.1549.3 | 8 | |||
63.16 | even | 3 | 7938.2.a.co.1.3 | 4 | |||
63.23 | odd | 6 | 882.2.f.s.589.4 | yes | 8 | ||
63.31 | odd | 6 | inner | 2646.2.h.q.361.2 | 8 | ||
63.32 | odd | 6 | 882.2.h.t.67.1 | 8 | |||
63.40 | odd | 6 | 2646.2.f.q.1765.3 | 8 | |||
63.41 | even | 6 | 882.2.e.q.373.2 | 8 | |||
63.47 | even | 6 | 7938.2.a.cj.1.3 | 4 | |||
63.58 | even | 3 | 2646.2.f.q.1765.2 | 8 | |||
63.59 | even | 6 | 882.2.h.t.67.4 | 8 | |||
63.61 | odd | 6 | 7938.2.a.co.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.e.q.373.2 | 8 | 63.41 | even | 6 | |||
882.2.e.q.373.3 | 8 | 9.5 | odd | 6 | |||
882.2.e.q.655.2 | 8 | 21.17 | even | 6 | |||
882.2.e.q.655.3 | 8 | 21.11 | odd | 6 | |||
882.2.f.s.295.2 | ✓ | 8 | 21.5 | even | 6 | ||
882.2.f.s.295.3 | yes | 8 | 21.2 | odd | 6 | ||
882.2.f.s.589.1 | yes | 8 | 63.5 | even | 6 | ||
882.2.f.s.589.4 | yes | 8 | 63.23 | odd | 6 | ||
882.2.h.t.67.1 | 8 | 63.32 | odd | 6 | |||
882.2.h.t.67.4 | 8 | 63.59 | even | 6 | |||
882.2.h.t.79.1 | 8 | 3.2 | odd | 2 | |||
882.2.h.t.79.4 | 8 | 21.20 | even | 2 | |||
2646.2.e.t.1549.2 | 8 | 9.4 | even | 3 | |||
2646.2.e.t.1549.3 | 8 | 63.13 | odd | 6 | |||
2646.2.e.t.2125.2 | 8 | 7.4 | even | 3 | |||
2646.2.e.t.2125.3 | 8 | 7.3 | odd | 6 | |||
2646.2.f.q.883.2 | 8 | 7.2 | even | 3 | |||
2646.2.f.q.883.3 | 8 | 7.5 | odd | 6 | |||
2646.2.f.q.1765.2 | 8 | 63.58 | even | 3 | |||
2646.2.f.q.1765.3 | 8 | 63.40 | odd | 6 | |||
2646.2.h.q.361.2 | 8 | 63.31 | odd | 6 | inner | ||
2646.2.h.q.361.3 | 8 | 63.4 | even | 3 | inner | ||
2646.2.h.q.667.2 | 8 | 7.6 | odd | 2 | inner | ||
2646.2.h.q.667.3 | 8 | 1.1 | even | 1 | trivial | ||
7938.2.a.cj.1.2 | 4 | 63.2 | odd | 6 | |||
7938.2.a.cj.1.3 | 4 | 63.47 | even | 6 | |||
7938.2.a.co.1.2 | 4 | 63.61 | odd | 6 | |||
7938.2.a.co.1.3 | 4 | 63.16 | even | 3 |