Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4176,2,Mod(289,4176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4176.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4176 = 2^{4} \cdot 3^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4176.o (of order \(2\), degree \(1\), 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: | \(33.3455278841\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 87) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4176.289 |
Dual form | 4176.2.o.l.289.1 |
$q$-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 \(\left(\mathbb{Z}/4176\mathbb{Z}\right)^\times\).
\(n\) | \(929\) | \(1045\) | \(1567\) | \(4033\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.23607 | −1.44721 | −0.723607 | − | 0.690212i | \(-0.757517\pi\) | ||||
−0.723607 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.23607 | 1.60108 | 0.800542 | − | 0.599277i | \(-0.204545\pi\) | ||||
0.800542 | + | 0.599277i | \(0.204545\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.23607i | 0.674200i | 0.941469 | + | 0.337100i | \(0.109446\pi\) | ||||
−0.941469 | + | 0.337100i | \(0.890554\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000i | 0.727607i | 0.931476 | + | 0.363803i | \(0.118522\pi\) | ||||
−0.931476 | + | 0.363803i | \(0.881478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.70820i | − | 1.76838i | −0.467124 | − | 0.884192i | \(-0.654710\pi\) | ||
0.467124 | − | 0.884192i | \(-0.345290\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.23607 | 0.257738 | 0.128869 | − | 0.991662i | \(-0.458865\pi\) | ||||
0.128869 | + | 0.991662i | \(0.458865\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | − | 3.00000i | 0.830455 | − | 0.557086i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.23607i | 1.29964i | 0.760090 | + | 0.649818i | \(0.225155\pi\) | ||||
−0.760090 | + | 0.649818i | \(0.774845\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −13.7082 | −2.31711 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.76393i | 0.783186i | 0.920139 | + | 0.391593i | \(0.128076\pi\) | ||||
−0.920139 | + | 0.391593i | \(0.871924\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.47214i | 0.698430i | 0.937043 | + | 0.349215i | \(0.113552\pi\) | ||||
−0.937043 | + | 0.349215i | \(0.886448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.472136i | 0.0720001i | 0.999352 | + | 0.0360000i | \(0.0114616\pi\) | ||||
−0.999352 | + | 0.0360000i | \(0.988538\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.2361i | − | 1.49308i | −0.665338 | − | 0.746542i | \(-0.731713\pi\) | ||
0.665338 | − | 0.746542i | \(-0.268287\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.9443 | 1.56347 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.76393 | −0.929098 | −0.464549 | − | 0.885548i | \(-0.653783\pi\) | ||||
−0.464549 | + | 0.885548i | \(0.653783\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.23607i | − | 0.975711i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.94427 | 1.16445 | 0.582223 | − | 0.813029i | \(-0.302183\pi\) | ||||
0.582223 | + | 0.813029i | \(0.302183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.76393i | 0.353885i | 0.984221 | + | 0.176943i | \(0.0566207\pi\) | ||||
−0.984221 | + | 0.176943i | \(0.943379\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.23607 | 0.401385 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.70820 | −0.575199 | −0.287599 | − | 0.957751i | \(-0.592857\pi\) | ||||
−0.287599 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.76393 | 0.565375 | 0.282687 | − | 0.959212i | \(-0.408774\pi\) | ||||
0.282687 | + | 0.959212i | \(0.408774\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.70820i | − | 0.902177i | −0.892479 | − | 0.451089i | \(-0.851036\pi\) | ||
0.892479 | − | 0.451089i | \(-0.148964\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.47214i | 1.07945i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.29180i | 0.257847i | 0.991655 | + | 0.128924i | \(0.0411522\pi\) | ||||
−0.991655 | + | 0.128924i | \(0.958848\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 9.70820i | − | 1.05300i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.0557281i | 0.00590717i | 0.999996 | + | 0.00295358i | \(0.000940156\pi\) | ||||
−0.999996 | + | 0.00295358i | \(0.999060\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.23607 | −0.444061 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 24.9443i | 2.55923i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.1803i | 1.84593i | 0.384879 | + | 0.922967i | \(0.374243\pi\) | ||||
−0.384879 | + | 0.922967i | \(0.625757\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.94427i | 0.392470i | 0.980557 | + | 0.196235i | \(0.0628715\pi\) | ||||
−0.980557 | + | 0.196235i | \(0.937129\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.4164 | 1.91316 | 0.956578 | − | 0.291477i | \(-0.0941468\pi\) | ||||
0.956578 | + | 0.291477i | \(0.0941468\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.763932 | 0.0738521 | 0.0369260 | − | 0.999318i | \(-0.488243\pi\) | ||||
0.0369260 | + | 0.999318i | \(0.488243\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.52786i | − | 0.425946i | −0.977058 | − | 0.212973i | \(-0.931685\pi\) | ||
0.977058 | − | 0.212973i | \(-0.0683146\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.7082i | 1.16496i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.00000 | 0.545455 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.4721i | 1.10672i | 0.832941 | + | 0.553362i | \(0.186655\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.2361i | 1.06907i | 0.845146 | + | 0.534535i | \(0.179513\pi\) | ||||
−0.845146 | + | 0.534535i | \(0.820487\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 32.6525i | − | 2.83133i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.52786i | 0.301406i | 0.988579 | + | 0.150703i | \(0.0481537\pi\) | ||||
−0.988579 | + | 0.150703i | \(0.951846\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.70820 | 0.568982 | 0.284491 | − | 0.958679i | \(-0.408175\pi\) | ||||
0.284491 | + | 0.958679i | \(0.408175\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2.23607i | − | 0.186989i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.4721 | + | 9.70820i | −1.20185 | + | 0.806222i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.52786 | 0.452860 | 0.226430 | − | 0.974027i | \(-0.427295\pi\) | ||||
0.226430 | + | 0.974027i | \(0.427295\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 23.4164i | − | 1.88085i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000i | 0.159617i | 0.996810 | + | 0.0798087i | \(0.0254309\pi\) | ||||
−0.996810 | + | 0.0798087i | \(0.974569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.23607 | 0.412660 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.41641i | − | 0.580898i | −0.956890 | − | 0.290449i | \(-0.906195\pi\) | ||
0.956890 | − | 0.290449i | \(-0.0938046\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.8885 | 1.22949 | 0.614746 | − | 0.788725i | \(-0.289258\pi\) | ||||
0.614746 | + | 0.788725i | \(0.289258\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23.1803 | 1.75227 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.2361 | −1.28828 | −0.644142 | − | 0.764906i | \(-0.722785\pi\) | ||||
−0.644142 | + | 0.764906i | \(0.722785\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.4164 | 1.51754 | 0.758770 | − | 0.651359i | \(-0.225801\pi\) | ||||
0.758770 | + | 0.651359i | \(0.225801\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 15.4164i | − | 1.13344i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.70820 | −0.490552 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.94427i | 0.647185i | 0.946197 | + | 0.323592i | \(0.104891\pi\) | ||||
−0.946197 | + | 0.323592i | \(0.895109\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.4164i | 1.25366i | 0.779156 | + | 0.626830i | \(0.215648\pi\) | ||||
−0.779156 | + | 0.626830i | \(0.784352\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.70820 | 0.264199 | 0.132099 | − | 0.991236i | \(-0.457828\pi\) | ||||
0.132099 | + | 0.991236i | \(0.457828\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.1246 | 1.42660 | 0.713298 | − | 0.700861i | \(-0.247201\pi\) | ||||
0.713298 | + | 0.700861i | \(0.247201\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.9443 | − | 12.7082i | 1.32963 | − | 0.891941i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 14.4721i | − | 1.01078i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.2361 | 1.19224 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.0000i | − | 0.688428i | −0.938891 | − | 0.344214i | \(-0.888145\pi\) | ||
0.938891 | − | 0.344214i | \(-0.111855\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.52786i | − | 0.104199i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.6525i | 2.08083i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.00000i | − | 0.201802i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.7082 | 0.851004 | 0.425502 | − | 0.904957i | \(-0.360097\pi\) | ||||
0.425502 | + | 0.904957i | \(0.360097\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.05573 | 0.601050 | 0.300525 | − | 0.953774i | \(-0.402838\pi\) | ||||
0.300525 | + | 0.953774i | \(0.402838\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.1803i | 1.46572i | 0.680380 | + | 0.732859i | \(0.261815\pi\) | ||||
−0.680380 | + | 0.732859i | \(0.738185\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.4721 | 0.686052 | 0.343026 | − | 0.939326i | \(-0.388548\pi\) | ||||
0.343026 | + | 0.939326i | \(0.388548\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.1246i | 2.16081i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.1803 | 1.69347 | 0.846733 | − | 0.532019i | \(-0.178566\pi\) | ||||
0.846733 | + | 0.532019i | \(0.178566\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.00000 | −0.193247 | −0.0966235 | − | 0.995321i | \(-0.530804\pi\) | ||||
−0.0966235 | + | 0.995321i | \(0.530804\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −35.4164 | −2.26267 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.70820i | 0.490461i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 12.2361i | − | 0.772334i | −0.922429 | − | 0.386167i | \(-0.873799\pi\) | ||
0.922429 | − | 0.386167i | \(-0.126201\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.76393i | 0.173767i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.4721 | 1.65129 | 0.825643 | − | 0.564193i | \(-0.190812\pi\) | ||||
0.825643 | + | 0.564193i | \(0.190812\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.1803i | 1.25395i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.94427i | − | 0.304877i | −0.988313 | − | 0.152438i | \(-0.951287\pi\) | ||
0.988313 | − | 0.152438i | \(-0.0487126\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.8885 | 1.34460 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.3607i | 1.30238i | 0.758913 | + | 0.651192i | \(0.225731\pi\) | ||||
−0.758913 | + | 0.651192i | \(0.774269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.4164i | 1.42245i | 0.702967 | + | 0.711223i | \(0.251858\pi\) | ||||
−0.702967 | + | 0.711223i | \(0.748142\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.2361i | 0.737863i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.41641 | 0.385525 | 0.192762 | − | 0.981245i | \(-0.438255\pi\) | ||||
0.192762 | + | 0.981245i | \(0.438255\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.41641 | 0.0844958 | 0.0422479 | − | 0.999107i | \(-0.486548\pi\) | ||||
0.0422479 | + | 0.999107i | \(0.486548\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.8885 | 0.825588 | 0.412794 | − | 0.910824i | \(-0.364553\pi\) | ||||
0.412794 | + | 0.910824i | \(0.364553\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.9443i | 1.11825i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.9443i | 1.74936i | 0.484698 | + | 0.874682i | \(0.338929\pi\) | ||||
−0.484698 | + | 0.874682i | \(0.661071\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.9443 | −1.68520 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.23607 | −0.0714837 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000i | 0.115278i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8.94427i | − | 0.512148i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 28.1803i | − | 1.60834i | −0.594401 | − | 0.804168i | \(-0.702611\pi\) | ||
0.594401 | − | 0.804168i | \(-0.297389\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 15.6525i | − | 0.887570i | −0.896133 | − | 0.443785i | \(-0.853635\pi\) | ||
0.896133 | − | 0.443785i | \(-0.146365\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.47214 | −0.309303 | −0.154652 | − | 0.987969i | \(-0.549426\pi\) | ||||
−0.154652 | + | 0.987969i | \(0.549426\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 23.8328i | − | 1.33858i | −0.742999 | − | 0.669292i | \(-0.766597\pi\) | ||
0.742999 | − | 0.669292i | \(-0.233403\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.70820 | + | 10.0000i | 0.375587 | + | 0.559893i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.1246 | 1.28669 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.47214 | −0.303539 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 43.3607i | − | 2.39055i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.29180i | 0.455758i | 0.973689 | + | 0.227879i | \(0.0731791\pi\) | ||||
−0.973689 | + | 0.227879i | \(0.926821\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.2361 | 0.832435 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.2361i | 1.04786i | 0.851763 | + | 0.523928i | \(0.175534\pi\) | ||||
−0.851763 | + | 0.523928i | \(0.824466\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.1803 | −0.876215 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7082 | 0.902158 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.6525 | −1.21605 | −0.608024 | − | 0.793918i | \(-0.708038\pi\) | ||||
−0.608024 | + | 0.793918i | \(0.708038\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.65248 | −0.247626 | −0.123813 | − | 0.992306i | \(-0.539512\pi\) | ||||
−0.123813 | + | 0.992306i | \(0.539512\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.4164 | −0.818218 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 25.3050i | − | 1.33554i | −0.744366 | − | 0.667772i | \(-0.767248\pi\) | ||
0.744366 | − | 0.667772i | \(-0.232752\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −40.4164 | −2.12718 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.9443i | 1.30564i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.0000i | 0.939592i | 0.882775 | + | 0.469796i | \(0.155673\pi\) | ||||
−0.882775 | + | 0.469796i | \(0.844327\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.6525 | −1.48756 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.88854 | −0.201341 | −0.100671 | − | 0.994920i | \(-0.532099\pi\) | ||||
−0.100671 | + | 0.994920i | \(0.532099\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.47214 | + | 3.00000i | −0.230327 | + | 0.154508i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 14.2918i | − | 0.734120i | −0.930197 | − | 0.367060i | \(-0.880364\pi\) | ||
0.930197 | − | 0.367060i | \(-0.119636\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.34752 | −0.273246 | −0.136623 | − | 0.990623i | \(-0.543625\pi\) | ||||
−0.136623 | + | 0.990623i | \(0.543625\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 30.6525i | − | 1.56219i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.4721i | 0.683064i | 0.939870 | + | 0.341532i | \(0.110946\pi\) | ||||
−0.939870 | + | 0.341532i | \(0.889054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.70820i | 0.187532i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 7.41641i | − | 0.373160i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.94427 | 0.348523 | 0.174262 | − | 0.984699i | \(-0.444246\pi\) | ||||
0.174262 | + | 0.984699i | \(0.444246\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.7082 | −1.68331 | −0.841654 | − | 0.540018i | \(-0.818418\pi\) | ||||
−0.841654 | + | 0.540018i | \(0.818418\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.23607i | − | 0.360454i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.6525 | −0.528024 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.5836i | − | 0.523325i | −0.965159 | − | 0.261662i | \(-0.915729\pi\) | ||
0.965159 | − | 0.261662i | \(-0.0842707\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 37.8885 | 1.86437 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.4164 | 0.953114 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.81966 | 0.186603 | 0.0933013 | − | 0.995638i | \(-0.470258\pi\) | ||||
0.0933013 | + | 0.995638i | \(0.470258\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000i | 0.974740i | 0.873195 | + | 0.487370i | \(0.162044\pi\) | ||||
−0.873195 | + | 0.487370i | \(0.837956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.4164i | 0.796313i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.7082i | 0.566600i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.3607 | 0.691730 | 0.345865 | − | 0.938284i | \(-0.387586\pi\) | ||||
0.345865 | + | 0.938284i | \(0.387586\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 14.2918i | − | 0.686820i | −0.939186 | − | 0.343410i | \(-0.888418\pi\) | ||
0.939186 | − | 0.343410i | \(-0.111582\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 9.52786i | − | 0.455780i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.2918 | −0.634383 | −0.317191 | − | 0.948362i | \(-0.602740\pi\) | ||||
−0.317191 | + | 0.948362i | \(0.602740\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.65248i | 0.458603i | 0.973355 | + | 0.229301i | \(0.0736442\pi\) | ||||
−0.973355 | + | 0.229301i | \(0.926356\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 0.180340i | − | 0.00854893i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 18.8885i | − | 0.891405i | −0.895181 | − | 0.445703i | \(-0.852954\pi\) | ||
0.895181 | − | 0.445703i | \(-0.147046\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0000 | −0.470882 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.7082 | 0.642651 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.41641 | 0.300147 | 0.150073 | − | 0.988675i | \(-0.452049\pi\) | ||||
0.150073 | + | 0.988675i | \(0.452049\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.9443i | 0.882323i | 0.897428 | + | 0.441161i | \(0.145433\pi\) | ||||
−0.897428 | + | 0.441161i | \(0.854567\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.708204 | −0.0329130 | −0.0164565 | − | 0.999865i | \(-0.505239\pi\) | ||||
−0.0164565 | + | 0.999865i | \(0.505239\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 13.5279i | − | 0.625995i | −0.949754 | − | 0.312997i | \(-0.898667\pi\) | ||
0.949754 | − | 0.312997i | \(-0.101333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.9443 | −0.920941 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.05573 | −0.0485424 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 42.1803i | − | 1.93537i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.4721i | 0.478484i | 0.970960 | + | 0.239242i | \(0.0768989\pi\) | ||||
−0.970960 | + | 0.239242i | \(0.923101\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 4.76393i | − | 0.217217i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 58.8328i | − | 2.67146i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.3607 | −0.922630 | −0.461315 | − | 0.887236i | \(-0.652622\pi\) | ||||
−0.461315 | + | 0.887236i | \(0.652622\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | + | 13.4164i | 0.405340 | + | 0.604245i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.1803 | 0.905212 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.1803 | −0.948162 | −0.474081 | − | 0.880481i | \(-0.657220\pi\) | ||||
−0.474081 | + | 0.880481i | \(0.657220\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.1803i | 1.12274i | 0.827566 | + | 0.561368i | \(0.189725\pi\) | ||||
−0.827566 | + | 0.561368i | \(0.810275\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 12.7639i | − | 0.567988i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.8328 | 1.18934 | 0.594672 | − | 0.803969i | \(-0.297282\pi\) | ||||
0.594672 | + | 0.803969i | \(0.297282\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 32.6525i | − | 1.44446i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −62.8328 | −2.76874 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.8885 | 1.00664 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.52786 | 0.154559 | 0.0772793 | − | 0.997009i | \(-0.475377\pi\) | ||||
0.0772793 | + | 0.997009i | \(0.475377\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.0689 | −1.44600 | −0.723001 | − | 0.690847i | \(-0.757238\pi\) | ||||
−0.723001 | + | 0.690847i | \(0.757238\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.7082 | −0.945624 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.4721 | −0.933571 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.47214i | − | 0.193710i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.47214 | −0.106880 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.4721i | 1.05409i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 10.6525i | − | 0.457986i | −0.973428 | − | 0.228993i | \(-0.926457\pi\) | ||
0.973428 | − | 0.228993i | \(-0.0735432\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.1803 | −0.693090 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.34752 | 0.271401 | 0.135700 | − | 0.990750i | \(-0.456672\pi\) | ||||
0.135700 | + | 0.990750i | \(0.456672\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.1246 | − | 34.4721i | −0.985142 | − | 1.46856i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.70820i | 0.412835i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.4721 | 0.697947 | 0.348973 | − | 0.937133i | \(-0.386530\pi\) | ||||
0.348973 | + | 0.937133i | \(0.386530\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.472136i | − | 0.0199692i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.0689i | 0.550788i | 0.961331 | + | 0.275394i | \(0.0888083\pi\) | ||||
−0.961331 | + | 0.275394i | \(0.911192\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.6525i | 0.616434i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 21.0000i | − | 0.880366i | −0.897908 | − | 0.440183i | \(-0.854914\pi\) | ||
0.897908 | − | 0.440183i | \(-0.145086\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.8328 | −0.788129 | −0.394064 | − | 0.919083i | \(-0.628931\pi\) | ||||
−0.394064 | + | 0.919083i | \(0.628931\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.76393 | 0.282075 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 24.8328i | − | 1.03380i | −0.856045 | − | 0.516902i | \(-0.827085\pi\) | ||
0.856045 | − | 0.516902i | \(-0.172915\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.4164 | −1.05445 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 15.1246i | − | 0.626397i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.944272 | −0.0389743 | −0.0194871 | − | 0.999810i | \(-0.506203\pi\) | ||||
−0.0194871 | + | 0.999810i | \(0.506203\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 55.7771 | 2.29825 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.1803 | −1.65001 | −0.825004 | − | 0.565126i | \(-0.808827\pi\) | ||||
−0.825004 | + | 0.565126i | \(0.808827\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 41.1246i | − | 1.68594i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.76393i | − | 0.0720723i | −0.999350 | − | 0.0360362i | \(-0.988527\pi\) | ||
0.999350 | − | 0.0360362i | \(-0.0114731\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 18.5410i | − | 0.756304i | −0.925744 | − | 0.378152i | \(-0.876560\pi\) | ||
0.925744 | − | 0.378152i | \(-0.123440\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.4164 | −0.789389 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 25.4164i | − | 1.03162i | −0.856703 | − | 0.515810i | \(-0.827491\pi\) | ||
0.856703 | − | 0.515810i | \(-0.172509\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.2361i | 0.414107i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.4164 | −0.986169 | −0.493085 | − | 0.869981i | \(-0.664131\pi\) | ||||
−0.493085 | + | 0.869981i | \(0.664131\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 19.8885i | − | 0.800683i | −0.916366 | − | 0.400341i | \(-0.868892\pi\) | ||
0.916366 | − | 0.400341i | \(-0.131108\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.5410i | 1.30793i | 0.756523 | + | 0.653967i | \(0.226896\pi\) | ||||
−0.756523 | + | 0.653967i | \(0.773104\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.236068i | 0.00945786i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.2918 | −0.569851 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.7082 | −1.14286 | −0.571428 | − | 0.820652i | \(-0.693610\pi\) | ||||
−0.571428 | + | 0.820652i | \(0.693610\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 40.3607i | − | 1.60166i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.9443 | −0.433628 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.4721i | 0.769103i | 0.923104 | + | 0.384552i | \(0.125644\pi\) | ||||
−0.923104 | + | 0.384552i | \(0.874356\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.708204 | −0.0279288 | −0.0139644 | − | 0.999902i | \(-0.504445\pi\) | ||||
−0.0139644 | + | 0.999902i | \(0.504445\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.5967 | 0.691800 | 0.345900 | − | 0.938271i | \(-0.387574\pi\) | ||||
0.345900 | + | 0.938271i | \(0.387574\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.0000i | 0.785069i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.3050i | 1.26419i | 0.774891 | + | 0.632095i | \(0.217805\pi\) | ||||
−0.774891 | + | 0.632095i | \(0.782195\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 39.5967i | − | 1.54717i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 26.2361i | − | 1.02201i | −0.859577 | − | 0.511006i | \(-0.829273\pi\) | ||
0.859577 | − | 0.511006i | \(-0.170727\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.8328 | −1.16036 | −0.580181 | − | 0.814488i | \(-0.697018\pi\) | ||||
−0.580181 | + | 0.814488i | \(0.697018\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 105.666i | 4.09754i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.52786 | − | 3.70820i | 0.214040 | − | 0.143582i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.18034 | −0.238589 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.41641 | −0.170240 | −0.0851200 | − | 0.996371i | \(-0.527127\pi\) | ||||
−0.0851200 | + | 0.996371i | \(0.527127\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 18.0557i | − | 0.693938i | −0.937877 | − | 0.346969i | \(-0.887211\pi\) | ||
0.937877 | − | 0.346969i | \(-0.112789\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 77.0132i | 2.95549i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.9443 | 1.26058 | 0.630289 | − | 0.776361i | \(-0.282936\pi\) | ||||
0.630289 | + | 0.776361i | \(0.282936\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 11.4164i | − | 0.436199i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.76393 | 0.257685 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.2361 | 1.15023 | 0.575117 | − | 0.818071i | \(-0.304956\pi\) | ||||
0.575117 | + | 0.818071i | \(0.304956\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.7082 | −0.823439 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.4164 | −0.508183 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.18034 | −0.308967 | −0.154484 | − | 0.987995i | \(-0.549371\pi\) | ||||
−0.154484 | + | 0.987995i | \(0.549371\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.7214 | 1.38497 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.7082i | 0.628377i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.4164 | −0.503864 | −0.251932 | − | 0.967745i | \(-0.581066\pi\) | ||||
−0.251932 | + | 0.967745i | \(0.581066\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.94427i | 0.334966i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.23607i | 0.270614i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.0000 | −1.11881 | −0.559406 | − | 0.828894i | \(-0.688971\pi\) | ||||
−0.559406 | + | 0.828894i | \(0.688971\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 82.2492 | 3.06312 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.4721 | − | 16.4164i | 0.908872 | − | 0.609690i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 5.81966i | − | 0.215839i | −0.994160 | − | 0.107920i | \(-0.965581\pi\) | ||
0.994160 | − | 0.107920i | \(-0.0344189\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.41641 | −0.0523877 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.47214i | 0.312925i | 0.987684 | + | 0.156463i | \(0.0500091\pi\) | ||||
−0.987684 | + | 0.156463i | \(0.949991\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 10.5279i | − | 0.387799i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 12.1803i | − | 0.448061i | −0.974582 | − | 0.224031i | \(-0.928078\pi\) | ||
0.974582 | − | 0.224031i | \(-0.0719215\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.0689i | 1.58004i | 0.613078 | + | 0.790022i | \(0.289931\pi\) | ||||
−0.613078 | + | 0.790022i | \(0.710069\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.8885 | −0.655386 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.23607 | 0.118243 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 26.8328i | − | 0.979143i | −0.871963 | − | 0.489572i | \(-0.837153\pi\) | ||
0.871963 | − | 0.489572i | \(-0.162847\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.8328 | 1.41327 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 38.0000i | − | 1.38113i | −0.723269 | − | 0.690567i | \(-0.757361\pi\) | ||
0.723269 | − | 0.690567i | \(-0.242639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.65248 | −0.0961522 | −0.0480761 | − | 0.998844i | \(-0.515309\pi\) | ||||
−0.0480761 | + | 0.998844i | \(0.515309\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.1803 | 0.766780 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.94427 | −0.322959 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 40.1803i | − | 1.44894i | −0.689306 | − | 0.724470i | \(-0.742085\pi\) | ||
0.689306 | − | 0.724470i | \(-0.257915\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 31.8885i | − | 1.14695i | −0.819223 | − | 0.573476i | \(-0.805595\pi\) | ||
0.819223 | − | 0.573476i | \(-0.194405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.5967i | 1.42236i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.4721 | 1.23509 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.6525i | 0.381176i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 6.47214i | − | 0.231000i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.0000 | 0.427754 | 0.213877 | − | 0.976861i | \(-0.431391\pi\) | ||||
0.213877 | + | 0.976861i | \(0.431391\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 19.1803i | − | 0.681974i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.76393i | − | 0.0981501i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.8328i | 1.58806i | 0.607879 | + | 0.794030i | \(0.292021\pi\) | ||||
−0.607879 | + | 0.794030i | \(0.707979\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.7082 | 1.08638 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.2361 | 0.608248 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.9443 | −0.597207 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 43.3607i | − | 1.52448i | −0.647294 | − | 0.762240i | \(-0.724100\pi\) | ||
0.647294 | − | 0.762240i | \(-0.275900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.5967 | −1.63623 | −0.818117 | − | 0.575052i | \(-0.804982\pi\) | ||||
−0.818117 | + | 0.575052i | \(0.804982\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.0000i | 0.840683i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.63932 | 0.127324 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.4721 | 0.435281 | 0.217640 | − | 0.976029i | \(-0.430164\pi\) | ||||
0.217640 | + | 0.976029i | \(0.430164\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26.3607i | − | 0.918876i | −0.888210 | − | 0.459438i | \(-0.848051\pi\) | ||
0.888210 | − | 0.459438i | \(-0.151949\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.8885i | 1.03933i | 0.854371 | + | 0.519663i | \(0.173943\pi\) | ||||
−0.854371 | + | 0.519663i | \(0.826057\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.3050i | 0.948340i | 0.880433 | + | 0.474170i | \(0.157252\pi\) | ||||
−0.880433 | + | 0.474170i | \(0.842748\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32.8328i | 1.13759i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −51.4164 | −1.77934 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 0.708204i | − | 0.0244499i | −0.999925 | − | 0.0122250i | \(-0.996109\pi\) | ||
0.999925 | − | 0.0122250i | \(-0.00389142\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0000 | − | 26.8328i | 0.379310 | − | 0.925270i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 38.8328 | 1.33589 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.4164 | 0.873318 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.88854i | 0.201857i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 45.1935i | − | 1.54740i | −0.633555 | − | 0.773698i | \(-0.718405\pi\) | ||
0.633555 | − | 0.773698i | \(-0.281595\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.5967 | −1.28428 | −0.642140 | − | 0.766587i | \(-0.721953\pi\) | ||||
−0.642140 | + | 0.766587i | \(0.721953\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.3607i | 1.24061i | 0.784361 | + | 0.620305i | \(0.212991\pi\) | ||||
−0.784361 | + | 0.620305i | \(0.787009\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.6525 | −1.58807 | −0.794034 | − | 0.607873i | \(-0.792023\pi\) | ||||
−0.794034 | + | 0.607873i | \(0.792023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.4164 | −0.660178 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.12461 | −0.173841 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.70820 | 0.159531 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.47214 | −0.218798 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.4721 | 1.09651 | 0.548253 | − | 0.836312i | \(-0.315293\pi\) | ||||
0.548253 | + | 0.836312i | \(0.315293\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 55.2492i | 1.86139i | 0.365792 | + | 0.930697i | \(0.380798\pi\) | ||||
−0.365792 | + | 0.930697i | \(0.619202\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.2492 | −1.15258 | −0.576289 | − | 0.817246i | \(-0.695500\pi\) | ||||
−0.576289 | + | 0.817246i | \(0.695500\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 17.0689i | − | 0.573117i | −0.958063 | − | 0.286559i | \(-0.907489\pi\) | ||
0.958063 | − | 0.286559i | \(-0.0925113\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 52.8328i | 1.77196i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −78.9017 | −2.64034 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 55.7771 | 1.86442 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.7082 | + | 32.3607i | 0.724009 | + | 1.07929i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 20.2918i | − | 0.676018i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −66.0689 | −2.19620 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 26.4721i | − | 0.878993i | −0.898244 | − | 0.439496i | \(-0.855157\pi\) | ||
0.898244 | − | 0.439496i | \(-0.144843\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 51.1803i | − | 1.69568i | −0.530252 | − | 0.847840i | \(-0.677903\pi\) | ||
0.530252 | − | 0.847840i | \(-0.322097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 13.4164i | − | 0.444018i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 51.8328i | 1.71167i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.6525 | 0.846197 | 0.423099 | − | 0.906084i | \(-0.360942\pi\) | ||||
0.423099 | + | 0.906084i | \(0.360942\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.76393 | −0.156807 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.0689i | 0.857140i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.3607 | 1.06172 | 0.530860 | − | 0.847460i | \(-0.321869\pi\) | ||||
0.530860 | + | 0.847460i | \(0.321869\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 84.3607i | − | 2.76481i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.7082 | 0.709934 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.0000 | 1.07806 | 0.539032 | − | 0.842286i | \(-0.318790\pi\) | ||||
0.539032 | + | 0.842286i | \(0.318790\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.8328 | 1.46151 | 0.730754 | − | 0.682641i | \(-0.239169\pi\) | ||||
0.730754 | + | 0.682641i | \(0.239169\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.52786i | 0.180012i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 16.8197i | − | 0.546566i | −0.961934 | − | 0.273283i | \(-0.911891\pi\) | ||
0.961934 | − | 0.273283i | \(-0.0881095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.70820i | 0.250219i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 59.6656 | 1.93276 | 0.966380 | − | 0.257119i | \(-0.0827733\pi\) | ||||
0.966380 | + | 0.257119i | \(0.0827733\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 28.9443i | − | 0.936615i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.9443i | 0.482576i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.3607 | −0.689054 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 56.3607i | − | 1.81431i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 27.1246i | − | 0.872269i | −0.899882 | − | 0.436134i | \(-0.856347\pi\) | ||
0.899882 | − | 0.436134i | \(-0.143653\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.5836i | 0.532193i | 0.963946 | + | 0.266096i | \(0.0857340\pi\) | ||||
−0.963946 | + | 0.266096i | \(0.914266\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.4164 | 0.910988 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.0132 | −1.63206 | −0.816028 | − | 0.578013i | \(-0.803828\pi\) | ||||
−0.816028 | + | 0.578013i | \(0.803828\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.124612 | −0.00398261 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 13.8885i | − | 0.442976i | −0.975163 | − | 0.221488i | \(-0.928909\pi\) | ||
0.975163 | − | 0.221488i | \(-0.0710913\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0000 | −0.382352 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.583592i | 0.0185572i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.2918 | 0.676356 | 0.338178 | − | 0.941082i | \(-0.390189\pi\) | ||||
0.338178 | + | 0.941082i | \(0.390189\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −65.1246 | −2.06459 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 24.5836i | − | 0.778570i | −0.921117 | − | 0.389285i | \(-0.872722\pi\) | ||
0.921117 | − | 0.389285i | \(-0.127278\pi\) | |||||||
\(998\) | 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 | 4176.2.o.l.289.2 | 4 | ||
3.2 | odd | 2 | 1392.2.o.i.289.2 | 4 | |||
4.3 | odd | 2 | 261.2.c.b.28.4 | 4 | |||
12.11 | even | 2 | 87.2.c.a.28.1 | ✓ | 4 | ||
29.28 | even | 2 | inner | 4176.2.o.l.289.1 | 4 | ||
60.23 | odd | 4 | 2175.2.f.a.724.2 | 4 | |||
60.47 | odd | 4 | 2175.2.f.b.724.3 | 4 | |||
60.59 | even | 2 | 2175.2.d.e.376.4 | 4 | |||
87.86 | odd | 2 | 1392.2.o.i.289.4 | 4 | |||
116.75 | even | 4 | 7569.2.a.n.1.2 | 2 | |||
116.99 | even | 4 | 7569.2.a.f.1.1 | 2 | |||
116.115 | odd | 2 | 261.2.c.b.28.1 | 4 | |||
348.191 | odd | 4 | 2523.2.a.d.1.1 | 2 | |||
348.215 | odd | 4 | 2523.2.a.e.1.2 | 2 | |||
348.347 | even | 2 | 87.2.c.a.28.4 | yes | 4 | ||
1740.347 | odd | 4 | 2175.2.f.a.724.1 | 4 | |||
1740.1043 | odd | 4 | 2175.2.f.b.724.4 | 4 | |||
1740.1739 | even | 2 | 2175.2.d.e.376.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
87.2.c.a.28.1 | ✓ | 4 | 12.11 | even | 2 | ||
87.2.c.a.28.4 | yes | 4 | 348.347 | even | 2 | ||
261.2.c.b.28.1 | 4 | 116.115 | odd | 2 | |||
261.2.c.b.28.4 | 4 | 4.3 | odd | 2 | |||
1392.2.o.i.289.2 | 4 | 3.2 | odd | 2 | |||
1392.2.o.i.289.4 | 4 | 87.86 | odd | 2 | |||
2175.2.d.e.376.1 | 4 | 1740.1739 | even | 2 | |||
2175.2.d.e.376.4 | 4 | 60.59 | even | 2 | |||
2175.2.f.a.724.1 | 4 | 1740.347 | odd | 4 | |||
2175.2.f.a.724.2 | 4 | 60.23 | odd | 4 | |||
2175.2.f.b.724.3 | 4 | 60.47 | odd | 4 | |||
2175.2.f.b.724.4 | 4 | 1740.1043 | odd | 4 | |||
2523.2.a.d.1.1 | 2 | 348.191 | odd | 4 | |||
2523.2.a.e.1.2 | 2 | 348.215 | odd | 4 | |||
4176.2.o.l.289.1 | 4 | 29.28 | even | 2 | inner | ||
4176.2.o.l.289.2 | 4 | 1.1 | even | 1 | trivial | ||
7569.2.a.f.1.1 | 2 | 116.99 | even | 4 | |||
7569.2.a.n.1.2 | 2 | 116.75 | even | 4 |