Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(41,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([0, 33, 53]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.ba (of order \(66\), degree \(20\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{66}]$ |
Embedding invariants
Embedding label | 221.1 | ||
Root | \(0.928368 - 0.371662i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.221 |
Dual form | 804.2.ba.a.593.1 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{17}{66}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.71442 | − | 0.246497i | −0.989821 | − | 0.142315i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.93365 | − | 1.19689i | 1.86474 | − | 0.452382i | 0.865888 | − | 0.500237i | \(-0.166754\pi\) |
0.998854 | + | 0.0478556i | \(0.0152387\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.87848 | + | 0.845198i | 0.959493 | + | 0.281733i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.814576 | − | 0.580057i | \(-0.803030\pi\) | ||||
0.814576 | + | 0.580057i | \(0.196970\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.38028 | + | 1.16993i | −0.937520 | + | 0.324479i | −0.752753 | − | 0.658303i | \(-0.771274\pi\) |
−0.184767 | + | 0.982782i | \(0.559153\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.539964 | + | 2.22576i | −0.123876 | + | 0.510625i | 0.875736 | + | 0.482790i | \(0.160376\pi\) |
−0.999613 | + | 0.0278351i | \(0.991139\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.75337 | + | 0.835846i | −1.91014 | + | 0.182397i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.27430 | − | 3.77875i | 0.654861 | − | 0.755750i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.72659 | − | 2.15856i | −0.909632 | − | 0.415415i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.77569 | + | 3.03729i | 1.57616 | + | 0.545514i | 0.968571 | − | 0.248738i | \(-0.0800157\pi\) |
0.607589 | + | 0.794252i | \(0.292137\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.89230 | − | 10.2058i | 0.968688 | − | 1.67782i | 0.269325 | − | 0.963049i | \(-0.413199\pi\) |
0.699363 | − | 0.714767i | \(-0.253467\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.08360 | − | 1.17252i | 0.974156 | − | 0.187753i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.458227 | − | 0.888835i | \(-0.348485\pi\) | ||||
−0.458227 | + | 0.888835i | \(0.651515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.69843 | + | 7.31091i | 0.716505 | + | 1.11490i | 0.988296 | + | 0.152547i | \(0.0487475\pi\) |
−0.271792 | + | 0.962356i | \(0.587616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.6865 | − | 8.60247i | 2.38378 | − | 1.22892i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.47437 | − | 3.68280i | 0.195285 | − | 0.487798i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00083 | − | 0.712685i | 0.128143 | − | 0.0912500i | −0.514188 | − | 0.857677i | \(-0.671907\pi\) |
0.642331 | + | 0.766427i | \(0.277967\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.2130 | + | 0.724685i | 1.91666 | + | 0.0913017i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.18322 | − | 0.186740i | 0.999740 | − | 0.0228140i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.53832 | − | 9.18178i | −0.765252 | − | 1.07465i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
0.229598 | − | 0.973286i | \(-0.426259\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.54498 | + | 5.67126i | −0.755750 | + | 0.654861i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.356735 | − | 1.85092i | 0.0401358 | − | 0.208244i | −0.956325 | − | 0.292306i | \(-0.905577\pi\) |
0.996461 | + | 0.0840621i | \(0.0267894\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.57128 | + | 4.86577i | 0.841254 | + | 0.540641i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.2768 | + | 9.81781i | −1.60145 | + | 1.02919i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.2965 | − | 7.37038i | −1.48248 | − | 0.764273i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.93786 | − | 1.11882i | −0.196760 | − | 0.113599i | 0.398384 | − | 0.917219i | \(-0.369571\pi\) |
−0.595143 | + | 0.803620i | \(0.702905\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.690079 | − | 0.723734i | \(-0.257576\pi\) | ||||
−0.690079 | + | 0.723734i | \(0.742424\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.59559 | + | 19.0567i | −0.649883 | + | 1.87771i | −0.217355 | + | 0.976093i | \(0.569743\pi\) |
−0.432528 | + | 0.901620i | \(0.642378\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.7805 | − | 13.6739i | −1.51150 | − | 1.30972i | −0.756227 | − | 0.654309i | \(-0.772960\pi\) |
−0.755271 | − | 0.655412i | \(-0.772495\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.6176 | + | 16.0445i | −1.19761 | + | 1.52288i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.0950560 | − | 0.995472i | \(-0.530303\pi\) | ||||
0.0950560 | + | 0.995472i | \(0.469697\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.7189 | + | 0.510603i | −0.990960 | + | 0.0472052i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.59775 | + | 10.3950i | 0.327068 | + | 0.945001i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.09365 | − | 20.9963i | −0.451988 | − | 1.86312i | −0.502784 | − | 0.864412i | \(-0.667691\pi\) |
0.0507955 | − | 0.998709i | \(-0.483824\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.25298 | − | 13.6921i | −0.550544 | − | 1.20552i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.6274i | 1.00822i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.3812 | − | 9.76449i | 1.81353 | − | 0.828213i | 0.873822 | − | 0.486246i | \(-0.161634\pi\) |
0.939712 | − | 0.341967i | \(-0.111093\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −30.7281 | + | 10.6351i | −2.53441 | + | 0.877168i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.829457 | + | 17.4124i | 0.0675003 | + | 1.41700i | 0.737853 | + | 0.674962i | \(0.235840\pi\) |
−0.670352 | + | 0.742043i | \(0.733857\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.95608 | + | 4.68391i | 0.475347 | + | 0.373817i | 0.826898 | − | 0.562352i | \(-0.190103\pi\) |
−0.351551 | + | 0.936169i | \(0.614346\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.9203 | + | 20.6466i | 0.933670 | + | 1.61716i | 0.776989 | + | 0.629514i | \(0.216746\pi\) |
0.156680 | + | 0.987649i | \(0.449921\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.161146 | + | 0.126727i | −0.0123959 | + | 0.00974822i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.43549 | + | 5.95043i | −0.262718 | + | 0.455041i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.6315 | − | 22.5620i | 0.879259 | − | 1.70553i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.9975 | + | 6.00408i | −1.11475 | + | 0.446280i | −0.854599 | − | 0.519288i | \(-0.826197\pi\) |
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.89151 | + | 0.975143i | −0.139825 | + | 0.0720846i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −25.9029 | − | 4.99237i | −1.88416 | − | 0.363141i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.371662 | − | 0.928368i | \(-0.378788\pi\) | ||||
−0.371662 | + | 0.928368i | \(0.621212\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.4715 | − | 15.5469i | −0.969697 | − | 1.11909i | −0.992851 | − | 0.119359i | \(-0.961916\pi\) |
0.0231538 | − | 0.999732i | \(-0.492629\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.998867 | − | 0.0475819i | \(-0.984848\pi\) | ||||
0.998867 | + | 0.0475819i | \(0.0151515\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.1607 | + | 18.2697i | −1.35826 | + | 1.29510i | −0.440622 | + | 0.897693i | \(0.645242\pi\) |
−0.917642 | + | 0.397409i | \(0.869909\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.0755 | − | 1.69698i | −0.992811 | − | 0.119696i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.6468 | − | 5.06300i | −0.870638 | − | 0.348551i | −0.107049 | − | 0.994254i | \(-0.534140\pi\) |
−0.763589 | + | 0.645703i | \(0.776565\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 46.9314 | + | 4.48141i | 3.18591 | + | 0.304218i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.94615 | + | 17.3531i | 0.604525 | + | 1.17261i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.04652 | − | 28.1442i | −0.270975 | − | 1.88467i | −0.438387 | − | 0.898786i | \(-0.644450\pi\) |
0.167412 | − | 0.985887i | \(-0.446459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.6188 | − | 8.10961i | 0.841254 | − | 0.540641i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.22106 | + | 27.0894i | 0.345018 | + | 1.79012i | 0.576304 | + | 0.817235i | \(0.304494\pi\) |
−0.231287 | + | 0.972886i | \(0.574293\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.618159 | − | 0.786053i | \(-0.712121\pi\) | ||||
0.618159 | + | 0.786053i | \(0.287879\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.06784 | + | 3.08532i | −0.0693635 | + | 0.200413i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.7813 | + | 27.9872i | −0.823317 | + | 1.80281i | −0.289605 | + | 0.957146i | \(0.593524\pi\) |
−0.533712 | + | 0.845666i | \(0.679203\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.7810 | − | 10.2083i | −0.755750 | − | 0.654861i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.778747 | − | 8.15541i | −0.0495505 | − | 0.518916i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.998867 | − | 0.0475819i | \(-0.0151515\pi\) | ||||
−0.998867 | + | 0.0475819i | \(0.984848\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.8553 | − | 57.4040i | 1.04734 | − | 3.56691i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.71769 | − | 0.965858i | −0.408071 | − | 0.0586717i | −0.0647769 | − | 0.997900i | \(-0.520634\pi\) |
−0.343294 | + | 0.939228i | \(0.611543\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 28.6109 | − | 13.0662i | 1.73161 | − | 0.790801i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7331 | − | 5.50053i | −1.12556 | − | 0.330495i | −0.334600 | − | 0.942360i | \(-0.608601\pi\) |
−0.790962 | + | 0.611866i | \(0.790419\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.6935 | + | 16.1600i | 1.35863 | + | 0.967473i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.945001 | − | 0.327068i | \(-0.106061\pi\) | ||||
−0.945001 | + | 0.327068i | \(0.893939\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.8251 | + | 6.40842i | −1.29737 | + | 0.380941i | −0.856274 | − | 0.516522i | \(-0.827227\pi\) |
−0.441091 | + | 0.897462i | \(0.645408\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9230 | + | 1.61595i | −0.995472 | + | 0.0950560i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.04652 | + | 2.39581i | 0.178590 | + | 0.140445i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.9308 | + | 30.4459i | 1.84046 | + | 1.75487i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.0635523 | + | 0.0122487i | −0.00362712 | + | 0.000699071i | −0.191064 | − | 0.981577i | \(-0.561194\pi\) |
0.187437 | + | 0.982277i | \(0.439982\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.0050 | − | 31.0454i | 0.910494 | − | 1.76611i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.1846 | + | 2.90210i | −1.14090 | + | 0.164037i | −0.686753 | − | 0.726891i | \(-0.740965\pi\) |
−0.454146 | + | 0.890927i | \(0.650056\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.64720 | + | 16.6039i | −0.368720 | + | 0.921019i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.6839 | + | 27.3326i | 1.30972 | + | 1.51150i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.9413 | − | 1.33101i | −1.53579 | − | 0.0731589i | −0.737467 | − | 0.675383i | \(-0.763978\pi\) |
−0.798327 | + | 0.602224i | \(0.794281\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.5867 | − | 24.3969i | 1.40214 | − | 1.33694i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.8296 | − | 14.5040i | −0.753344 | − | 0.790085i | 0.229737 | − | 0.973253i | \(-0.426213\pi\) |
−0.983082 | + | 0.183168i | \(0.941365\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 45.1716 | − | 39.1414i | 2.43904 | − | 2.11344i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.189251 | − | 0.981929i | \(-0.439394\pi\) | ||||
−0.189251 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.5438 | + | 16.4160i | 1.36733 | + | 0.878727i | 0.998706 | − | 0.0508535i | \(-0.0161942\pi\) |
0.368620 | + | 0.929580i | \(0.379831\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.5025 | + | 1.76678i | 0.987592 | + | 0.0943036i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.458227 | − | 0.888835i | \(-0.651515\pi\) | ||||
0.458227 | + | 0.888835i | \(0.348485\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.2254 | + | 6.30264i | 0.643443 | + | 0.331718i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.60572 | − | 18.7083i | −0.189251 | − | 0.981929i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.0343 | + | 15.3029i | 0.628185 | + | 0.798803i | 0.991114 | − | 0.133014i | \(-0.0424656\pi\) |
−0.362929 | + | 0.931817i | \(0.618223\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.3674 | − | 10.6044i | 0.951027 | − | 0.549076i | 0.0576272 | − | 0.998338i | \(-0.481647\pi\) |
0.893400 | + | 0.449262i | \(0.148313\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.6349 | + | 17.3382i | −0.700380 | + | 0.890606i | −0.997944 | − | 0.0640964i | \(-0.979583\pi\) |
0.297564 | + | 0.954702i | \(0.403826\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.55714 | + | 37.2521i | 0.182238 | + | 1.90848i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.971812 | − | 0.235759i | \(-0.924242\pi\) | ||||
0.971812 | + | 0.235759i | \(0.0757576\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.34518 | + | 25.0154i | 0.373377 | + | 1.27160i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.5104 | − | 36.1528i | −0.828636 | − | 1.81446i | −0.480387 | − | 0.877057i | \(-0.659504\pi\) |
−0.348249 | − | 0.937402i | \(-0.613224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.86611 | − | 19.9343i | 0.143485 | − | 0.997961i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.2177 | −1.65469 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −39.1856 | + | 9.50631i | −1.93760 | + | 0.470057i | −0.950256 | + | 0.311470i | \(0.899179\pi\) |
−0.987345 | + | 0.158587i | \(0.949306\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −39.0634 | + | 11.4700i | −1.91294 | + | 0.561690i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.63857 | − | 27.3645i | 0.323544 | − | 1.33367i | −0.545159 | − | 0.838333i | \(-0.683531\pi\) |
0.868703 | − | 0.495334i | \(-0.164954\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.08472 | − | 4.71402i | 0.197673 | − | 0.228127i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.1532 | + | 9.39782i | 1.30490 | + | 0.451631i | 0.889053 | − | 0.457804i | \(-0.151364\pi\) |
0.415848 | + | 0.909434i | \(0.363485\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.2369 | + | 28.1232i | −0.774947 | + | 1.34225i | 0.159877 | + | 0.987137i | \(0.448890\pi\) |
−0.934824 | + | 0.355111i | \(0.884443\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 55.3024 | − | 10.6587i | 2.63345 | − | 0.507556i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.458227 | − | 0.888835i | \(-0.348485\pi\) | ||||
−0.458227 | + | 0.888835i | \(0.651515\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.87007 | − | 30.0567i | 0.134848 | − | 1.41219i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −41.9824 | − | 8.09144i | −1.96385 | − | 0.378502i | −0.982291 | − | 0.187363i | \(-0.940006\pi\) |
−0.981563 | − | 0.191139i | \(-0.938782\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.3720 | − | 24.4762i | 1.59740 | − | 1.13751i | 0.684747 | − | 0.728781i | \(-0.259913\pi\) |
0.912657 | − | 0.408726i | \(-0.134027\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.1496 | − | 10.7157i | 1.85394 | − | 0.494806i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.05666 | − | 9.49836i | −0.417309 | − | 0.437661i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.64259 | + | 9.32821i | 0.304783 | + | 0.428008i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.97762 | + | 41.3918i | −0.363748 | + | 1.88730i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0636 | + | 38.9180i | 0.909169 | + | 1.76354i | 0.566429 | + | 0.824110i | \(0.308325\pi\) |
0.342739 | + | 0.939430i | \(0.388645\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.3471 | − | 38.3352i | −0.694020 | − | 1.73358i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.26271 | + | 1.88372i | 0.146059 | + | 0.0843271i | 0.571248 | − | 0.820777i | \(-0.306459\pi\) |
−0.425190 | + | 0.905104i | \(0.639793\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.690079 | − | 0.723734i | \(-0.257576\pi\) | ||||
−0.690079 | + | 0.723734i | \(0.742424\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.307510 | − | 0.177541i | 0.0136570 | − | 0.00788488i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −43.2473 | − | 37.4740i | −1.91315 | − | 1.65775i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.35663 | − | 9.35472i | 0.324803 | − | 0.413021i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.63907 | + | 4.73579i | 0.0716716 | + | 0.207081i | 0.975147 | − | 0.221558i | \(-0.0711142\pi\) |
−0.903476 | + | 0.428640i | \(0.858993\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −25.5028 | + | 35.8136i | −1.11303 | + | 1.56303i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.42246 | + | 22.3517i | 0.235759 | + | 0.971812i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.0955 | − | 19.2244i | 1.80983 | − | 0.826521i | 0.862661 | − | 0.505782i | \(-0.168796\pi\) |
0.947168 | − | 0.320739i | \(-0.103931\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.1919 | − | 6.59669i | 1.16692 | − | 0.283091i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.6063 | + | 22.5067i | 1.35139 | + | 0.962318i | 0.999656 | + | 0.0262168i | \(0.00834602\pi\) |
0.351730 | + | 0.936101i | \(0.385593\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.48322 | − | 1.20555i | 0.148660 | − | 0.0514518i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.455339 | − | 9.55874i | −0.0193630 | − | 0.406479i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.4352 | − | 19.2161i | −1.03350 | − | 0.812753i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 43.1778 | + | 14.9440i | 1.81330 | + | 0.627588i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.8323 | − | 19.5283i | 1.03920 | − | 0.817234i | 0.0557537 | − | 0.998445i | \(-0.482244\pi\) |
0.983444 | + | 0.181210i | \(0.0580014\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.32425 | − | 16.1468i | 0.346543 | − | 0.672200i | −0.649568 | − | 0.760303i | \(-0.725050\pi\) |
0.996111 | + | 0.0881033i | \(0.0280806\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.2635 | + | 29.9746i | 0.800564 | + | 1.24570i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.0950560 | − | 0.995472i | \(-0.469697\pi\) | ||||
−0.0950560 | + | 0.995472i | \(0.530303\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.4989 | + | 17.8926i | −0.473802 | + | 0.737250i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.371662 | − | 0.928368i | \(-0.378788\pi\) | ||||
−0.371662 | + | 0.928368i | \(0.621212\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 37.3529 | − | 26.5989i | 1.52875 | − | 1.08862i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.998867 | − | 0.0475819i | \(-0.984848\pi\) | ||||
0.998867 | + | 0.0475819i | \(0.0151515\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.5916 | − | 12.9596i | 0.554412 | − | 0.528631i | −0.360247 | − | 0.932857i | \(-0.617308\pi\) |
0.914659 | + | 0.404226i | \(0.132459\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.7131 | + | 6.37891i | 0.965671 | + | 0.259769i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.16741 | − | 45.4996i | 0.0879727 | − | 1.84677i | −0.336925 | − | 0.941532i | \(-0.609387\pi\) |
0.424897 | − | 0.905242i | \(-0.360310\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.3793 | − | 4.95591i | −0.499994 | − | 0.200168i | 0.107936 | − | 0.994158i | \(-0.465576\pi\) |
−0.607930 | + | 0.793990i | \(0.708000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −49.3767 | − | 4.71491i | −1.98462 | − | 0.189508i | −0.999880 | − | 0.0154656i | \(-0.995077\pi\) |
−0.984738 | − | 0.174042i | \(-0.944317\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.55787 | − | 24.7455i | −0.142315 | − | 0.989821i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.58920 | + | 39.3765i | 0.302121 | + | 1.56755i | 0.742565 | + | 0.669774i | \(0.233609\pi\) |
−0.440444 | + | 0.897780i | \(0.645179\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.4338 | + | 11.7975i | 0.812172 | + | 0.468908i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −46.3406 | + | 48.6006i | −1.83608 | + | 1.92563i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.97674 | − | 15.2769i | 0.275136 | − | 0.602463i | −0.720738 | − | 0.693207i | \(-0.756197\pi\) |
0.995874 | + | 0.0907437i | \(0.0289244\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.618159 | − | 0.786053i | \(-0.287879\pi\) | ||||
−0.618159 | + | 0.786053i | \(0.712121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −79.3556 | − | 19.2515i | −3.11019 | − | 0.754524i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.998867 | − | 0.0475819i | \(-0.0151515\pi\) | ||||
−0.998867 | + | 0.0475819i | \(0.984848\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.0600 | − | 31.9557i | −0.431491 | − | 1.24671i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.2293 | + | 34.8379i | −0.397875 | + | 1.35504i | 0.480470 | + | 0.877011i | \(0.340466\pi\) |
−0.878345 | + | 0.478027i | \(0.841352\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 49.2484i | 1.90405i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.2699 | − | 6.94017i | −1.86067 | − | 0.267524i | −0.881742 | − | 0.471732i | \(-0.843629\pi\) |
−0.978927 | + | 0.204209i | \(0.934538\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.6329 | + | 10.7928i | −0.909632 | + | 0.415415i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 0.971812 | − | 0.235759i | \(-0.0757576\pi\) | ||||
−0.971812 | + | 0.235759i | \(0.924242\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.8998 | − | 3.20047i | −0.418296 | − | 0.122823i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.945001 | − | 0.327068i | \(-0.106061\pi\) | ||||
−0.945001 | + | 0.327068i | \(0.893939\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.27365 | − | 47.7297i | −0.0867450 | − | 1.82100i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.3072 | + | 4.23083i | −1.68553 | + | 0.160948i | −0.893356 | − | 0.449350i | \(-0.851656\pi\) |
−0.792171 | + | 0.610299i | \(0.791049\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.945001 | − | 0.327068i | \(-0.893939\pi\) | ||||
0.945001 | + | 0.327068i | \(0.106061\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.5340 | + | 18.6256i | 0.736737 | + | 0.702478i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −50.2106 | + | 9.67731i | −1.88570 | + | 0.363439i | −0.995709 | − | 0.0925387i | \(-0.970502\pi\) |
−0.889991 | + | 0.455978i | \(0.849290\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.59124 | − | 5.02631i | 0.0971792 | − | 0.188501i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.73153 | + | 101.913i | −0.362421 | + | 3.79545i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.8113 | − | 44.8313i | 1.07150 | − | 1.66729i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.80575 | − | 7.00842i | 0.104059 | − | 0.259928i | −0.867196 | − | 0.497966i | \(-0.834080\pi\) |
0.971256 | + | 0.238039i | \(0.0765045\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.6812 | + | 20.4052i | 0.654861 | + | 0.755750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.84943 | + | 0.278643i | 0.216053 | + | 0.0102919i | 0.155330 | − | 0.987863i | \(-0.450356\pi\) |
0.0607239 | + | 0.998155i | \(0.480659\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.9309 | − | 38.7320i | −1.35852 | − | 1.42478i | −0.806903 | − | 0.590684i | \(-0.798858\pi\) |
−0.551621 | − | 0.834095i | \(-0.685990\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.675180 | + | 14.1738i | −0.0248033 | + | 0.520686i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.9231 | − | 18.5878i | −1.05542 | − | 0.678278i | −0.106667 | − | 0.994295i | \(-0.534018\pi\) |
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.58391 | + | 6.45428i | 0.0939136 | + | 0.234585i | 0.967885 | − | 0.251392i | \(-0.0808882\pi\) |
−0.873972 | + | 0.485977i | \(0.838464\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −94.2216 | − | 48.5746i | −3.41105 | − | 1.75852i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.8767 | + | 43.0777i | 1.22162 | + | 1.55342i | 0.731643 | + | 0.681688i | \(0.238754\pi\) |
0.489981 | + | 0.871733i | \(0.337004\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.2114 | − | 23.2161i | 1.44444 | − | 0.833946i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −43.0470 | + | 94.2599i | −1.54430 | + | 3.38155i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.5400 | + | 2.12170i | −1.58768 | + | 0.0756305i | −0.822719 | − | 0.568448i | \(-0.807544\pi\) |
−0.764959 | + | 0.644078i | \(0.777241\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.54928 | + | 3.57997i | −0.0905277 | + | 0.127128i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.1251 | + | 11.6750i | −1.68990 | + | 0.409966i | −0.961417 | − | 0.275096i | \(-0.911290\pi\) |
−0.728485 | + | 0.685062i | \(0.759775\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.2789 | + | 3.31178i | 0.395567 | + | 0.116149i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.8093 | + | 6.50997i | −0.658055 | + | 0.227755i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −52.2720 | + | 15.3484i | −1.82653 | + | 0.536318i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.8177 | − | 52.8352i | 0.446796 | − | 1.84172i | −0.0871445 | − | 0.996196i | \(-0.527774\pi\) |
0.533940 | − | 0.845522i | \(-0.320711\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.0927 | + | 27.8044i | −0.836774 | + | 0.965688i | −0.999781 | − | 0.0209367i | \(-0.993335\pi\) |
0.163007 | + | 0.986625i | \(0.447881\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.7605 | + | 14.0479i | 1.06707 | + | 0.487315i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.9229 | − | 33.2989i | −1.20711 | − | 1.15098i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5000 | + | 25.1147i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.1917 | + | 46.9792i | 1.03740 | + | 1.61422i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 38.9970 | − | 5.60692i | 1.33837 | − | 0.192429i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.7863 | − | 26.6977i | 1.77313 | − | 0.914111i | 0.853823 | − | 0.520563i | \(-0.174278\pi\) |
0.919304 | − | 0.393548i | \(-0.128752\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.7756 | + | 9.78620i | 1.73244 | + | 0.333901i | 0.955348 | − | 0.295484i | \(-0.0954809\pi\) |
0.777094 | + | 0.629385i | \(0.216693\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.4115 | + | 1.40104i | 0.998867 | + | 0.0475819i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.4431 | + | 10.2050i | −0.929873 | + | 0.345783i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.63246 | − | 4.85838i | −0.156785 | − | 0.164431i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.9879 | + | 44.9207i | 1.08016 | + | 1.51687i | 0.837254 | + | 0.546814i | \(0.184160\pi\) |
0.242901 | + | 0.970051i | \(0.421901\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.08469 | + | 16.0049i | −0.103808 | + | 0.538608i | 0.892373 | + | 0.451298i | \(0.149039\pi\) |
−0.996181 | + | 0.0873094i | \(0.972173\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50.2605 | − | 97.4918i | −1.68568 | − | 3.26977i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −47.2380 | − | 60.0679i | −1.57198 | − | 1.99894i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.96317 | + | 23.0081i | −0.264413 | + | 0.763971i | 0.732151 | + | 0.681142i | \(0.238517\pi\) |
−0.996564 | + | 0.0828283i | \(0.973605\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.5538 | + | 14.2050i | 1.93151 | + | 0.468580i | 0.992034 | + | 0.125970i | \(0.0402043\pi\) |
0.939478 | + | 0.342610i | \(0.111311\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.111975 | − | 0.00533401i | 0.00368969 | − | 0.000175762i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.2718 | − | 55.6823i | −0.633653 | − | 1.83082i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −35.0920 | + | 49.2798i | −1.15257 | + | 1.61856i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.1370 | + | 41.7851i | 0.332226 | + | 1.36945i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 61.1782i | − | 1.99860i | −0.0373691 | − | 0.999302i | \(-0.511898\pi\) | ||
0.0373691 | − | 0.999302i | \(-0.488102\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.3202 | 1.15263 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.8433 | + | 23.3876i | 1.06614 | + | 0.759194i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.4199 | + | 34.1458i | 1.40064 | + | 1.10148i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3411 | + | 17.9113i | 0.332547 | + | 0.575988i | 0.983010 | − | 0.183550i | \(-0.0587588\pi\) |
−0.650464 | + | 0.759537i | \(0.725425\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 93.8005 | − | 73.7655i | 3.00711 | − | 2.36481i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.4889 | − | 26.8276i | 0.496042 | − | 0.859170i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.8667 | − | 52.6977i | −1.08128 | − | 1.68251i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.5245 | + | 17.9324i | −0.366086 | + | 0.569642i | −0.974614 | − | 0.223891i | \(-0.928124\pi\) |
0.608528 | + | 0.793533i | \(0.291760\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 47.5751 | + | 9.16935i | 1.50975 | + | 0.290980i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.4855 | − | 45.5687i | −1.25052 | − | 1.44317i | −0.849912 | − | 0.526924i | \(-0.823345\pi\) |
−0.400606 | − | 0.916251i | \(-0.631200\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49.8802 | + | 35.5195i | −1.57814 | + | 1.12379i |
(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 | 804.2.ba.a.221.1 | ✓ | 20 | |
3.2 | odd | 2 | CM | 804.2.ba.a.221.1 | ✓ | 20 | |
67.57 | odd | 66 | inner | 804.2.ba.a.593.1 | yes | 20 | |
201.191 | even | 66 | inner | 804.2.ba.a.593.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.ba.a.221.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
804.2.ba.a.221.1 | ✓ | 20 | 3.2 | odd | 2 | CM | |
804.2.ba.a.593.1 | yes | 20 | 67.57 | odd | 66 | inner | |
804.2.ba.a.593.1 | yes | 20 | 201.191 | even | 66 | inner |