Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(1709,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("2394.1709");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.b (of order \(2\), degree \(1\), 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: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1709.1 | ||
Root | \(-1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2394.1709 |
Dual form | 2394.2.b.b.1709.2 |
$q$-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 \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | − | 2.82843i | − | 1.26491i | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||
0.774597 | − | 0.632456i | \(-0.217953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.82843i | 0.894427i | ||||||||
\(11\) | 5.65685i | 1.70561i | 0.522233 | + | 0.852803i | \(0.325099\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.24264i | − | 1.17670i | −0.808608 | − | 0.588348i | \(-0.799778\pi\) | ||
0.808608 | − | 0.588348i | \(-0.200222\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.65685i | 1.37199i | 0.727607 | + | 0.685994i | \(0.240633\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | − | 4.24264i | 0.229416 | − | 0.973329i | ||||
\(20\) | − | 2.82843i | − | 0.632456i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 5.65685i | − | 1.20605i | ||||||
\(23\) | 5.65685i | 1.17954i | 0.807573 | + | 0.589768i | \(0.200781\pi\) | ||||
−0.807573 | + | 0.589768i | \(0.799219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 4.24264i | 0.832050i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.48528i | 1.52400i | 0.647576 | + | 0.762001i | \(0.275783\pi\) | ||||
−0.647576 | + | 0.762001i | \(0.724217\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 5.65685i | − | 0.970143i | ||||||
\(35\) | − | 2.82843i | − | 0.478091i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | −1.00000 | + | 4.24264i | −0.162221 | + | 0.688247i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.82843i | 0.447214i | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 5.65685i | 0.852803i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 5.65685i | − | 0.834058i | ||||||
\(47\) | 9.89949i | 1.44399i | 0.691898 | + | 0.721995i | \(0.256775\pi\) | ||||
−0.691898 | + | 0.721995i | \(0.743225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.00000 | 0.424264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4.24264i | − | 0.588348i | ||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.0000 | 2.15744 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | − | 8.48528i | − | 1.07763i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.0000 | −1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.7279i | 1.55496i | 0.628906 | + | 0.777482i | \(0.283503\pi\) | ||||
−0.628906 | + | 0.777482i | \(0.716497\pi\) | |||||||
\(68\) | 5.65685i | 0.685994i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.82843i | 0.338062i | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0000 | 1.63858 | 0.819288 | − | 0.573382i | \(-0.194369\pi\) | ||||
0.819288 | + | 0.573382i | \(0.194369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | − | 4.24264i | 0.114708 | − | 0.486664i | ||||
\(77\) | 5.65685i | 0.644658i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.7279i | 1.43200i | 0.698099 | + | 0.716002i | \(0.254030\pi\) | ||||
−0.698099 | + | 0.716002i | \(0.745970\pi\) | |||||||
\(80\) | − | 2.82843i | − | 0.316228i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 15.5563i | − | 1.70753i | −0.520658 | − | 0.853766i | \(-0.674313\pi\) | ||
0.520658 | − | 0.853766i | \(-0.325687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.0000 | 1.73544 | ||||||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 5.65685i | − | 0.603023i | ||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4.24264i | − | 0.444750i | ||||||
\(92\) | 5.65685i | 0.589768i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 9.89949i | − | 1.02105i | ||||||
\(95\) | −12.0000 | − | 2.82843i | −1.23117 | − | 0.290191i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.24264i | − | 0.430775i | −0.976529 | − | 0.215387i | \(-0.930899\pi\) | ||
0.976529 | − | 0.215387i | \(-0.0691014\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | −0.300000 | ||||||||
\(101\) | − | 11.3137i | − | 1.12576i | −0.826540 | − | 0.562878i | \(-0.809694\pi\) | ||
0.826540 | − | 0.562878i | \(-0.190306\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.9706i | − | 1.67216i | −0.548608 | − | 0.836080i | \(-0.684842\pi\) | ||
0.548608 | − | 0.836080i | \(-0.315158\pi\) | |||||||
\(104\) | 4.24264i | 0.416025i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 18.0000 | 1.74013 | 0.870063 | − | 0.492941i | \(-0.164078\pi\) | ||||
0.870063 | + | 0.492941i | \(0.164078\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.48528i | − | 0.812743i | −0.913708 | − | 0.406371i | \(-0.866794\pi\) | ||
0.913708 | − | 0.406371i | \(-0.133206\pi\) | |||||||
\(110\) | −16.0000 | −1.52554 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.0000 | 1.49201 | ||||||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | 5.65685i | 0.518563i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.0000 | −1.90909 | ||||||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.48528i | 0.762001i | ||||||||
\(125\) | − | 5.65685i | − | 0.505964i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7279i | 1.12942i | 0.825289 | + | 0.564710i | \(0.191012\pi\) | ||||
−0.825289 | + | 0.564710i | \(0.808988\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.0000 | 1.05247 | ||||||||
\(131\) | 1.41421i | 0.123560i | 0.998090 | + | 0.0617802i | \(0.0196778\pi\) | ||||
−0.998090 | + | 0.0617802i | \(0.980322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | − | 4.24264i | 0.0867110 | − | 0.367884i | ||||
\(134\) | − | 12.7279i | − | 1.09952i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 5.65685i | − | 0.485071i | ||||||
\(137\) | 9.89949i | 0.845771i | 0.906183 | + | 0.422885i | \(0.138983\pi\) | ||||
−0.906183 | + | 0.422885i | \(0.861017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | 0.169638 | 0.0848189 | − | 0.996396i | \(-0.472969\pi\) | ||||
0.0848189 | + | 0.996396i | \(0.472969\pi\) | |||||||
\(140\) | − | 2.82843i | − | 0.239046i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 24.0000 | 2.00698 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 16.9706i | − | 1.40933i | ||||||
\(146\) | −14.0000 | −1.15865 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 7.07107i | − | 0.579284i | −0.957135 | − | 0.289642i | \(-0.906464\pi\) | ||
0.957135 | − | 0.289642i | \(-0.0935363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.7279i | 1.03578i | 0.855446 | + | 0.517892i | \(0.173283\pi\) | ||||
−0.855446 | + | 0.517892i | \(0.826717\pi\) | |||||||
\(152\) | −1.00000 | + | 4.24264i | −0.0811107 | + | 0.344124i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 5.65685i | − | 0.455842i | ||||||
\(155\) | 24.0000 | 1.92773 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | − | 12.7279i | − | 1.01258i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.82843i | 0.223607i | ||||||||
\(161\) | 5.65685i | 0.445823i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | 0.626608 | 0.313304 | − | 0.949653i | \(-0.398564\pi\) | ||||
0.313304 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.5563i | 1.20741i | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | −16.0000 | −1.22714 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.00000 | −0.304997 | ||||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.00000 | −0.226779 | ||||||||
\(176\) | 5.65685i | 0.426401i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.00000 | −0.449719 | ||||||||
\(179\) | −18.0000 | −1.34538 | −0.672692 | − | 0.739923i | \(-0.734862\pi\) | ||||
−0.672692 | + | 0.739923i | \(0.734862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.24264i | 0.315353i | 0.987491 | + | 0.157676i | \(0.0504003\pi\) | ||||
−0.987491 | + | 0.157676i | \(0.949600\pi\) | |||||||
\(182\) | 4.24264i | 0.314485i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 5.65685i | − | 0.417029i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −32.0000 | −2.34007 | ||||||||
\(188\) | 9.89949i | 0.721995i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.0000 | + | 2.82843i | 0.870572 | + | 0.205196i | ||||
\(191\) | 14.1421i | 1.02329i | 0.859197 | + | 0.511645i | \(0.170964\pi\) | ||||
−0.859197 | + | 0.511645i | \(0.829036\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 16.9706i | − | 1.22157i | −0.791797 | − | 0.610784i | \(-0.790854\pi\) | ||
0.791797 | − | 0.610784i | \(-0.209146\pi\) | |||||||
\(194\) | 4.24264i | 0.304604i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 18.3848i | 1.30986i | 0.755689 | + | 0.654931i | \(0.227302\pi\) | ||||
−0.755689 | + | 0.654931i | \(0.772698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 3.00000 | 0.212132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.3137i | 0.796030i | ||||||||
\(203\) | 6.00000 | 0.421117 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.9706i | 1.18240i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 4.24264i | − | 0.294174i | ||||||
\(209\) | 24.0000 | + | 5.65685i | 1.66011 | + | 0.391293i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.24264i | 0.292075i | 0.989279 | + | 0.146038i | \(0.0466521\pi\) | ||||
−0.989279 | + | 0.146038i | \(0.953348\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.0000 | −1.23045 | ||||||||
\(215\) | 11.3137i | 0.771589i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.48528i | 0.576018i | ||||||||
\(218\) | 8.48528i | 0.574696i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 16.0000 | 1.07872 | ||||||||
\(221\) | 24.0000 | 1.61441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.4558i | 1.70465i | 0.523013 | + | 0.852325i | \(0.324808\pi\) | ||||
−0.523013 | + | 0.852325i | \(0.675192\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 12.0000 | 0.796468 | 0.398234 | − | 0.917284i | \(-0.369623\pi\) | ||||
0.398234 | + | 0.917284i | \(0.369623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | −16.0000 | −1.05501 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | − | 7.07107i | − | 0.463241i | −0.972806 | − | 0.231621i | \(-0.925597\pi\) | ||
0.972806 | − | 0.231621i | \(-0.0744028\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.0000 | 1.82652 | ||||||||
\(236\) | −12.0000 | −0.781133 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 5.65685i | − | 0.366679i | ||||||
\(239\) | 14.1421i | 0.914779i | 0.889267 | + | 0.457389i | \(0.151215\pi\) | ||||
−0.889267 | + | 0.457389i | \(0.848785\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.7279i | 0.819878i | 0.912113 | + | 0.409939i | \(0.134450\pi\) | ||||
−0.912113 | + | 0.409939i | \(0.865550\pi\) | |||||||
\(242\) | 21.0000 | 1.34993 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | − | 2.82843i | − | 0.180702i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.0000 | − | 4.24264i | −1.14531 | − | 0.269953i | ||||
\(248\) | − | 8.48528i | − | 0.538816i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.65685i | 0.357771i | ||||||||
\(251\) | 1.41421i | 0.0892644i | 0.999003 | + | 0.0446322i | \(0.0142116\pi\) | ||||
−0.999003 | + | 0.0446322i | \(0.985788\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.0000 | −2.01182 | ||||||||
\(254\) | − | 12.7279i | − | 0.798621i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −12.0000 | −0.744208 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 1.41421i | − | 0.0873704i | ||||||
\(263\) | − | 28.2843i | − | 1.74408i | −0.489432 | − | 0.872041i | \(-0.662796\pi\) | ||
0.489432 | − | 0.872041i | \(-0.337204\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 16.9706i | − | 1.04249i | ||||||
\(266\) | −1.00000 | + | 4.24264i | −0.0613139 | + | 0.260133i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.7279i | 0.777482i | ||||||||
\(269\) | −12.0000 | −0.731653 | −0.365826 | − | 0.930683i | \(-0.619214\pi\) | ||||
−0.365826 | + | 0.930683i | \(0.619214\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.0000 | 1.57939 | 0.789694 | − | 0.613501i | \(-0.210239\pi\) | ||||
0.789694 | + | 0.613501i | \(0.210239\pi\) | |||||||
\(272\) | 5.65685i | 0.342997i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 9.89949i | − | 0.598050i | ||||||
\(275\) | − | 16.9706i | − | 1.02336i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.00000 | 0.480673 | 0.240337 | − | 0.970690i | \(-0.422742\pi\) | ||||
0.240337 | + | 0.970690i | \(0.422742\pi\) | |||||||
\(278\) | −2.00000 | −0.119952 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.82843i | 0.169031i | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.0000 | −1.41915 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0000 | −0.882353 | ||||||||
\(290\) | 16.9706i | 0.996546i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.0000 | 0.819288 | ||||||||
\(293\) | −24.0000 | −1.40209 | −0.701047 | − | 0.713115i | \(-0.747284\pi\) | ||||
−0.701047 | + | 0.713115i | \(0.747284\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.9411i | 1.97613i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.07107i | 0.409616i | ||||||||
\(299\) | 24.0000 | 1.38796 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | −0.230556 | ||||||||
\(302\) | − | 12.7279i | − | 0.732410i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | − | 4.24264i | 0.0573539 | − | 0.243332i | ||||
\(305\) | − | 5.65685i | − | 0.323911i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 25.4558i | − | 1.45284i | −0.687250 | − | 0.726421i | \(-0.741182\pi\) | ||
0.687250 | − | 0.726421i | \(-0.258818\pi\) | |||||||
\(308\) | 5.65685i | 0.322329i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −24.0000 | −1.36311 | ||||||||
\(311\) | 1.41421i | 0.0801927i | 0.999196 | + | 0.0400963i | \(0.0127665\pi\) | ||||
−0.999196 | + | 0.0400963i | \(0.987234\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | −14.0000 | −0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.7279i | 0.716002i | ||||||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 33.9411i | 1.90034i | ||||||||
\(320\) | − | 2.82843i | − | 0.158114i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 5.65685i | − | 0.315244i | ||||||
\(323\) | 24.0000 | + | 5.65685i | 1.33540 | + | 0.314756i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.7279i | 0.706018i | ||||||||
\(326\) | −8.00000 | −0.443079 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.89949i | 0.545777i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 29.6985i | − | 1.63238i | −0.577786 | − | 0.816188i | \(-0.696083\pi\) | ||
0.577786 | − | 0.816188i | \(-0.303917\pi\) | |||||||
\(332\) | − | 15.5563i | − | 0.853766i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | 36.0000 | 1.96689 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 5.00000 | 0.271964 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.0000 | 0.867722 | ||||||||
\(341\) | −48.0000 | −2.59935 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.00000 | −0.322562 | ||||||||
\(347\) | − | 2.82843i | − | 0.151838i | −0.997114 | − | 0.0759190i | \(-0.975811\pi\) | ||
0.997114 | − | 0.0759190i | \(-0.0241890\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0000 | −0.535288 | −0.267644 | − | 0.963518i | \(-0.586245\pi\) | ||||
−0.267644 | + | 0.963518i | \(0.586245\pi\) | |||||||
\(350\) | 3.00000 | 0.160357 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 5.65685i | − | 0.301511i | ||||||
\(353\) | 22.6274i | 1.20434i | 0.798369 | + | 0.602168i | \(0.205696\pi\) | ||||
−0.798369 | + | 0.602168i | \(0.794304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.9706i | 0.900704i | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.0000 | 0.951330 | ||||||||
\(359\) | − | 28.2843i | − | 1.49279i | −0.665505 | − | 0.746393i | \(-0.731784\pi\) | ||
0.665505 | − | 0.746393i | \(-0.268216\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | − | 8.48528i | −0.894737 | − | 0.446594i | ||||
\(362\) | − | 4.24264i | − | 0.222988i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 4.24264i | − | 0.222375i | ||||||
\(365\) | − | 39.5980i | − | 2.07265i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0000 | −0.521996 | −0.260998 | − | 0.965339i | \(-0.584052\pi\) | ||||
−0.260998 | + | 0.965339i | \(0.584052\pi\) | |||||||
\(368\) | 5.65685i | 0.294884i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | 0.311504 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.4558i | 1.31805i | 0.752119 | + | 0.659027i | \(0.229032\pi\) | ||||
−0.752119 | + | 0.659027i | \(0.770968\pi\) | |||||||
\(374\) | 32.0000 | 1.65468 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 9.89949i | − | 0.510527i | ||||||
\(377\) | − | 25.4558i | − | 1.31104i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.24264i | − | 0.217930i | −0.994046 | − | 0.108965i | \(-0.965246\pi\) | ||
0.994046 | − | 0.108965i | \(-0.0347536\pi\) | |||||||
\(380\) | −12.0000 | − | 2.82843i | −0.615587 | − | 0.145095i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 14.1421i | − | 0.723575i | ||||||
\(383\) | −24.0000 | −1.22634 | −0.613171 | − | 0.789950i | \(-0.710106\pi\) | ||||
−0.613171 | + | 0.789950i | \(0.710106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | 16.9706i | 0.863779i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 4.24264i | − | 0.215387i | ||||||
\(389\) | 9.89949i | 0.501924i | 0.967997 | + | 0.250962i | \(0.0807470\pi\) | ||||
−0.967997 | + | 0.250962i | \(0.919253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.0000 | −1.61831 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 18.3848i | − | 0.926212i | ||||||
\(395\) | 36.0000 | 1.81136 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | −8.00000 | −0.401004 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | 6.00000 | 0.299626 | 0.149813 | − | 0.988714i | \(-0.452133\pi\) | ||||
0.149813 | + | 0.988714i | \(0.452133\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.0000 | 1.79329 | ||||||||
\(404\) | − | 11.3137i | − | 0.562878i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.7279i | − | 0.629355i | −0.949199 | − | 0.314678i | \(-0.898104\pi\) | ||
0.949199 | − | 0.314678i | \(-0.101896\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 16.9706i | − | 0.836080i | ||||||
\(413\) | −12.0000 | −0.590481 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −44.0000 | −2.15988 | ||||||||
\(416\) | 4.24264i | 0.208013i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −24.0000 | − | 5.65685i | −1.17388 | − | 0.276686i | ||||
\(419\) | − | 15.5563i | − | 0.759977i | −0.924991 | − | 0.379989i | \(-0.875928\pi\) | ||
0.924991 | − | 0.379989i | \(-0.124072\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.9706i | 0.827095i | 0.910483 | + | 0.413547i | \(0.135710\pi\) | ||||
−0.910483 | + | 0.413547i | \(0.864290\pi\) | |||||||
\(422\) | − | 4.24264i | − | 0.206529i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | − | 16.9706i | − | 0.823193i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.00000 | 0.0967868 | ||||||||
\(428\) | 18.0000 | 0.870063 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 11.3137i | − | 0.545595i | ||||||
\(431\) | −6.00000 | −0.289010 | −0.144505 | − | 0.989504i | \(-0.546159\pi\) | ||||
−0.144505 | + | 0.989504i | \(0.546159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.24264i | 0.203888i | 0.994790 | + | 0.101944i | \(0.0325063\pi\) | ||||
−0.994790 | + | 0.101944i | \(0.967494\pi\) | |||||||
\(434\) | − | 8.48528i | − | 0.407307i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 8.48528i | − | 0.406371i | ||||||
\(437\) | 24.0000 | + | 5.65685i | 1.14808 | + | 0.270604i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | −16.0000 | −0.762770 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.0000 | −1.14156 | ||||||||
\(443\) | − | 28.2843i | − | 1.34383i | −0.740630 | − | 0.671913i | \(-0.765473\pi\) | ||
0.740630 | − | 0.671913i | \(-0.234527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 16.9706i | − | 0.804482i | ||||||
\(446\) | − | 25.4558i | − | 1.20537i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.0000 | −0.563188 | ||||||||
\(455\) | −12.0000 | −0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.0000 | 1.49690 | 0.748448 | − | 0.663193i | \(-0.230799\pi\) | ||||
0.748448 | + | 0.663193i | \(0.230799\pi\) | |||||||
\(458\) | −14.0000 | −0.654177 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.0000 | 0.746004 | ||||||||
\(461\) | 22.6274i | 1.05386i | 0.849907 | + | 0.526932i | \(0.176658\pi\) | ||||
−0.849907 | + | 0.526932i | \(0.823342\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.0000 | 1.48717 | 0.743583 | − | 0.668644i | \(-0.233125\pi\) | ||||
0.743583 | + | 0.668644i | \(0.233125\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.07107i | 0.327561i | ||||||||
\(467\) | 18.3848i | 0.850746i | 0.905018 | + | 0.425373i | \(0.139857\pi\) | ||||
−0.905018 | + | 0.425373i | \(0.860143\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.7279i | 0.587721i | ||||||||
\(470\) | −28.0000 | −1.29154 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.0000 | 0.552345 | ||||||||
\(473\) | − | 22.6274i | − | 1.04041i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.00000 | + | 12.7279i | −0.137649 | + | 0.583997i | ||||
\(476\) | 5.65685i | 0.259281i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 14.1421i | − | 0.646846i | ||||||
\(479\) | 18.3848i | 0.840022i | 0.907519 | + | 0.420011i | \(0.137974\pi\) | ||||
−0.907519 | + | 0.420011i | \(0.862026\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 12.7279i | − | 0.579741i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.0000 | −0.954545 | ||||||||
\(485\) | −12.0000 | −0.544892 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.7279i | − | 0.576757i | −0.957516 | − | 0.288379i | \(-0.906884\pi\) | ||
0.957516 | − | 0.288379i | \(-0.0931162\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.82843i | 0.127775i | ||||||||
\(491\) | − | 36.7696i | − | 1.65939i | −0.558219 | − | 0.829693i | \(-0.688515\pi\) | ||
0.558219 | − | 0.829693i | \(-0.311485\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.9411i | 1.52863i | ||||||||
\(494\) | 18.0000 | + | 4.24264i | 0.809858 | + | 0.190885i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.48528i | 0.381000i | ||||||||
\(497\) | −6.00000 | −0.269137 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.0000 | −0.716258 | −0.358129 | − | 0.933672i | \(-0.616585\pi\) | ||||
−0.358129 | + | 0.933672i | \(0.616585\pi\) | |||||||
\(500\) | − | 5.65685i | − | 0.252982i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 1.41421i | − | 0.0631194i | ||||||
\(503\) | 9.89949i | 0.441397i | 0.975342 | + | 0.220698i | \(0.0708336\pi\) | ||||
−0.975342 | + | 0.220698i | \(0.929166\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.0000 | −1.42398 | ||||||||
\(506\) | 32.0000 | 1.42257 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.7279i | 0.564710i | ||||||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0000 | 0.619324 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.0000 | −0.793946 | ||||||||
\(515\) | −48.0000 | −2.11513 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −56.0000 | −2.46288 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.0000 | 0.526235 | ||||||||
\(521\) | 12.0000 | 0.525730 | 0.262865 | − | 0.964833i | \(-0.415333\pi\) | ||||
0.262865 | + | 0.964833i | \(0.415333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.9706i | 0.742071i | 0.928619 | + | 0.371035i | \(0.120997\pi\) | ||||
−0.928619 | + | 0.371035i | \(0.879003\pi\) | |||||||
\(524\) | 1.41421i | 0.0617802i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.2843i | 1.23325i | ||||||||
\(527\) | −48.0000 | −2.09091 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.00000 | −0.391304 | ||||||||
\(530\) | 16.9706i | 0.737154i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.00000 | − | 4.24264i | 0.0433555 | − | 0.183942i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 50.9117i | − | 2.20110i | ||||||
\(536\) | − | 12.7279i | − | 0.549762i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.0000 | 0.517357 | ||||||||
\(539\) | 5.65685i | 0.243658i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.0000 | −1.71973 | −0.859867 | − | 0.510518i | \(-0.829454\pi\) | ||||
−0.859867 | + | 0.510518i | \(0.829454\pi\) | |||||||
\(542\) | −26.0000 | −1.11680 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 5.65685i | − | 0.242536i | ||||||
\(545\) | −24.0000 | −1.02805 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.7279i | 0.544207i | 0.962268 | + | 0.272103i | \(0.0877193\pi\) | ||||
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(548\) | 9.89949i | 0.422885i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 16.9706i | 0.723627i | ||||||||
\(551\) | 6.00000 | − | 25.4558i | 0.255609 | − | 1.08446i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.7279i | 0.541246i | ||||||||
\(554\) | −8.00000 | −0.339887 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | 0.0848189 | ||||||||
\(557\) | 35.3553i | 1.49805i | 0.662540 | + | 0.749027i | \(0.269479\pi\) | ||||
−0.662540 | + | 0.749027i | \(0.730521\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.9706i | 0.717778i | ||||||||
\(560\) | − | 2.82843i | − | 0.119523i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.0000 | −0.759284 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 16.9706i | − | 0.713957i | ||||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | −42.0000 | −1.76073 | −0.880366 | − | 0.474295i | \(-0.842703\pi\) | ||||
−0.880366 | + | 0.474295i | \(0.842703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.0000 | −1.17176 | −0.585882 | − | 0.810397i | \(-0.699252\pi\) | ||||
−0.585882 | + | 0.810397i | \(0.699252\pi\) | |||||||
\(572\) | 24.0000 | 1.00349 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 16.9706i | − | 0.707721i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 15.0000 | 0.623918 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 16.9706i | − | 0.704664i | ||||||
\(581\) | − | 15.5563i | − | 0.645386i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.9411i | 1.40570i | ||||||||
\(584\) | −14.0000 | −0.579324 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.0000 | 0.991431 | ||||||||
\(587\) | − | 15.5563i | − | 0.642079i | −0.947066 | − | 0.321040i | \(-0.895968\pi\) | ||
0.947066 | − | 0.321040i | \(-0.104032\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.0000 | + | 8.48528i | 1.48335 | + | 0.349630i | ||||
\(590\) | − | 33.9411i | − | 1.39733i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.5980i | 1.62609i | 0.582198 | + | 0.813047i | \(0.302193\pi\) | ||||
−0.582198 | + | 0.813047i | \(0.697807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.0000 | 0.655936 | ||||||||
\(596\) | − | 7.07107i | − | 0.289642i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −24.0000 | −0.981433 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.24264i | 0.173061i | 0.996249 | + | 0.0865305i | \(0.0275780\pi\) | ||||
−0.996249 | + | 0.0865305i | \(0.972422\pi\) | |||||||
\(602\) | 4.00000 | 0.163028 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.7279i | 0.517892i | ||||||||
\(605\) | 59.3970i | 2.41483i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 33.9411i | − | 1.37763i | −0.724938 | − | 0.688814i | \(-0.758132\pi\) | ||
0.724938 | − | 0.688814i | \(-0.241868\pi\) | |||||||
\(608\) | −1.00000 | + | 4.24264i | −0.0405554 | + | 0.172062i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.65685i | 0.229039i | ||||||||
\(611\) | 42.0000 | 1.69914 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.0000 | −0.646234 | −0.323117 | − | 0.946359i | \(-0.604731\pi\) | ||||
−0.323117 | + | 0.946359i | \(0.604731\pi\) | |||||||
\(614\) | 25.4558i | 1.02731i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 5.65685i | − | 0.227921i | ||||||
\(617\) | − | 32.5269i | − | 1.30948i | −0.755852 | − | 0.654742i | \(-0.772777\pi\) | ||
0.755852 | − | 0.654742i | \(-0.227223\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 24.0000 | 0.963863 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 1.41421i | − | 0.0567048i | ||||||
\(623\) | 6.00000 | 0.240385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | −14.0000 | −0.559553 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.0000 | −1.11466 | −0.557331 | − | 0.830290i | \(-0.688175\pi\) | ||||
−0.557331 | + | 0.830290i | \(0.688175\pi\) | |||||||
\(632\) | − | 12.7279i | − | 0.506290i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.0000 | 0.714871 | ||||||||
\(635\) | 36.0000 | 1.42862 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.24264i | − | 0.168100i | ||||||
\(638\) | − | 33.9411i | − | 1.34374i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.82843i | 0.111803i | ||||||||
\(641\) | −18.0000 | −0.710957 | −0.355479 | − | 0.934684i | \(-0.615682\pi\) | ||||
−0.355479 | + | 0.934684i | \(0.615682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.0000 | −0.867595 | −0.433798 | − | 0.901010i | \(-0.642827\pi\) | ||||
−0.433798 | + | 0.901010i | \(0.642827\pi\) | |||||||
\(644\) | 5.65685i | 0.222911i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.0000 | − | 5.65685i | −0.944267 | − | 0.222566i | ||||
\(647\) | − | 15.5563i | − | 0.611583i | −0.952098 | − | 0.305792i | \(-0.901079\pi\) | ||
0.952098 | − | 0.305792i | \(-0.0989211\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 67.8823i | − | 2.66461i | ||||||
\(650\) | − | 12.7279i | − | 0.499230i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.00000 | 0.313304 | ||||||||
\(653\) | − | 24.0416i | − | 0.940822i | −0.882448 | − | 0.470411i | \(-0.844106\pi\) | ||
0.882448 | − | 0.470411i | \(-0.155894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000 | 0.156293 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 9.89949i | − | 0.385922i | ||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.1838i | 1.48518i | 0.669748 | + | 0.742588i | \(0.266402\pi\) | ||||
−0.669748 | + | 0.742588i | \(0.733598\pi\) | |||||||
\(662\) | 29.6985i | 1.15426i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.5563i | 0.603703i | ||||||||
\(665\) | −12.0000 | − | 2.82843i | −0.465340 | − | 0.109682i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.9411i | 1.31421i | ||||||||
\(668\) | −12.0000 | −0.464294 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −36.0000 | −1.39080 | ||||||||
\(671\) | 11.3137i | 0.436761i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 42.4264i | − | 1.63542i | −0.575632 | − | 0.817709i | \(-0.695244\pi\) | ||
0.575632 | − | 0.817709i | \(-0.304756\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.00000 | −0.192308 | ||||||||
\(677\) | −30.0000 | −1.15299 | −0.576497 | − | 0.817099i | \(-0.695581\pi\) | ||||
−0.576497 | + | 0.817099i | \(0.695581\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4.24264i | − | 0.162818i | ||||||
\(680\) | −16.0000 | −0.613572 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 48.0000 | 1.83801 | ||||||||
\(683\) | 12.0000 | 0.459167 | 0.229584 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.0000 | 1.06983 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.00000 | −0.152499 | ||||||||
\(689\) | − | 25.4558i | − | 0.969790i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.0000 | −1.06517 | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||||
−0.532585 | + | 0.846376i | \(0.678779\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.82843i | 0.107366i | ||||||||
\(695\) | − | 5.65685i | − | 0.214577i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 10.0000 | 0.378506 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.00000 | −0.113389 | ||||||||
\(701\) | − | 7.07107i | − | 0.267071i | −0.991044 | − | 0.133535i | \(-0.957367\pi\) | ||
0.991044 | − | 0.133535i | \(-0.0426329\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 5.65685i | 0.213201i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 22.6274i | − | 0.851594i | ||||||
\(707\) | − | 11.3137i | − | 0.425496i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.00000 | −0.150223 | −0.0751116 | − | 0.997175i | \(-0.523931\pi\) | ||||
−0.0751116 | + | 0.997175i | \(0.523931\pi\) | |||||||
\(710\) | − | 16.9706i | − | 0.636894i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.00000 | −0.224860 | ||||||||
\(713\) | −48.0000 | −1.79761 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 67.8823i | − | 2.53865i | ||||||
\(716\) | −18.0000 | −0.672692 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.2843i | 1.05556i | ||||||||
\(719\) | − | 7.07107i | − | 0.263706i | −0.991269 | − | 0.131853i | \(-0.957907\pi\) | ||
0.991269 | − | 0.131853i | \(-0.0420927\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 16.9706i | − | 0.632017i | ||||||
\(722\) | 17.0000 | + | 8.48528i | 0.632674 | + | 0.315789i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.24264i | 0.157676i | ||||||||
\(725\) | −18.0000 | −0.668503 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.00000 | 0.0741759 | 0.0370879 | − | 0.999312i | \(-0.488192\pi\) | ||||
0.0370879 | + | 0.999312i | \(0.488192\pi\) | |||||||
\(728\) | 4.24264i | 0.157243i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 39.5980i | 1.46559i | ||||||||
\(731\) | − | 22.6274i | − | 0.836905i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0000 | 0.517102 | 0.258551 | − | 0.965998i | \(-0.416755\pi\) | ||||
0.258551 | + | 0.965998i | \(0.416755\pi\) | |||||||
\(734\) | 10.0000 | 0.369107 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 5.65685i | − | 0.208514i | ||||||
\(737\) | −72.0000 | −2.65215 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0000 | −0.588570 | −0.294285 | − | 0.955718i | \(-0.595081\pi\) | ||||
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.00000 | −0.220267 | ||||||||
\(743\) | 48.0000 | 1.76095 | 0.880475 | − | 0.474093i | \(-0.157224\pi\) | ||||
0.880475 | + | 0.474093i | \(0.157224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.0000 | −0.732743 | ||||||||
\(746\) | − | 25.4558i | − | 0.932005i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −32.0000 | −1.17004 | ||||||||
\(749\) | 18.0000 | 0.657706 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 12.7279i | − | 0.464448i | −0.972662 | − | 0.232224i | \(-0.925400\pi\) | ||
0.972662 | − | 0.232224i | \(-0.0746003\pi\) | |||||||
\(752\) | 9.89949i | 0.360997i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 25.4558i | 0.927047i | ||||||||
\(755\) | 36.0000 | 1.31017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.0000 | 1.59921 | 0.799604 | − | 0.600528i | \(-0.205043\pi\) | ||||
0.799604 | + | 0.600528i | \(0.205043\pi\) | |||||||
\(758\) | 4.24264i | 0.154100i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.0000 | + | 2.82843i | 0.435286 | + | 0.102598i | ||||
\(761\) | − | 2.82843i | − | 0.102530i | −0.998685 | − | 0.0512652i | \(-0.983675\pi\) | ||
0.998685 | − | 0.0512652i | \(-0.0163254\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 8.48528i | − | 0.307188i | ||||||
\(764\) | 14.1421i | 0.511645i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | 50.9117i | 1.83831i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | −16.0000 | −0.576600 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 16.9706i | − | 0.610784i | ||||||
\(773\) | −6.00000 | −0.215805 | −0.107903 | − | 0.994161i | \(-0.534413\pi\) | ||||
−0.107903 | + | 0.994161i | \(0.534413\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 25.4558i | − | 0.914401i | ||||||
\(776\) | 4.24264i | 0.152302i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 9.89949i | − | 0.354914i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 33.9411i | − | 1.21451i | ||||||
\(782\) | 32.0000 | 1.14432 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | − | 39.5980i | − | 1.41331i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.9411i | 1.20987i | 0.796275 | + | 0.604935i | \(0.206801\pi\) | ||||
−0.796275 | + | 0.604935i | \(0.793199\pi\) | |||||||
\(788\) | 18.3848i | 0.654931i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −36.0000 | −1.28082 | ||||||||
\(791\) | 6.00000 | 0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 8.48528i | − | 0.301321i | ||||||
\(794\) | −2.00000 | −0.0709773 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00000 | 0.283552 | ||||||||
\(797\) | 48.0000 | 1.70025 | 0.850124 | − | 0.526583i | \(-0.176527\pi\) | ||||
0.850124 | + | 0.526583i | \(0.176527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −56.0000 | −1.98114 | ||||||||
\(800\) | 3.00000 | 0.106066 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.00000 | −0.211867 | ||||||||
\(803\) | 79.1960i | 2.79476i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0000 | 0.563926 | ||||||||
\(806\) | −36.0000 | −1.26805 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.3137i | 0.398015i | ||||||||
\(809\) | 52.3259i | 1.83968i | 0.392293 | + | 0.919840i | \(0.371682\pi\) | ||||
−0.392293 | + | 0.919840i | \(0.628318\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 25.4558i | − | 0.893876i | −0.894565 | − | 0.446938i | \(-0.852515\pi\) | ||
0.894565 | − | 0.446938i | \(-0.147485\pi\) | |||||||
\(812\) | 6.00000 | 0.210559 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 22.6274i | − | 0.792604i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.00000 | + | 16.9706i | −0.139942 | + | 0.593725i | ||||
\(818\) | 12.7279i | 0.445021i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.3848i | 0.641633i | 0.947141 | + | 0.320817i | \(0.103957\pi\) | ||||
−0.947141 | + | 0.320817i | \(0.896043\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0000 | 0.697156 | 0.348578 | − | 0.937280i | \(-0.386665\pi\) | ||||
0.348578 | + | 0.937280i | \(0.386665\pi\) | |||||||
\(824\) | 16.9706i | 0.591198i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.0000 | 0.417533 | ||||||||
\(827\) | 30.0000 | 1.04320 | 0.521601 | − | 0.853189i | \(-0.325335\pi\) | ||||
0.521601 | + | 0.853189i | \(0.325335\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 46.6690i | − | 1.62088i | −0.585820 | − | 0.810442i | \(-0.699227\pi\) | ||
0.585820 | − | 0.810442i | \(-0.300773\pi\) | |||||||
\(830\) | 44.0000 | 1.52726 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 4.24264i | − | 0.147087i | ||||||
\(833\) | 5.65685i | 0.195998i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.9411i | 1.17458i | ||||||||
\(836\) | 24.0000 | + | 5.65685i | 0.830057 | + | 0.195646i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.5563i | 0.537385i | ||||||||
\(839\) | −48.0000 | −1.65714 | −0.828572 | − | 0.559883i | \(-0.810846\pi\) | ||||
−0.828572 | + | 0.559883i | \(0.810846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | − | 16.9706i | − | 0.584844i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.24264i | 0.146038i | ||||||||
\(845\) | 14.1421i | 0.486504i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.0000 | −0.721569 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16.9706i | 0.582086i | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.0000 | −1.16414 | −0.582069 | − | 0.813139i | \(-0.697757\pi\) | ||||
−0.582069 | + | 0.813139i | \(0.697757\pi\) | |||||||
\(854\) | −2.00000 | −0.0684386 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.0000 | −0.615227 | ||||||||
\(857\) | −6.00000 | −0.204956 | −0.102478 | − | 0.994735i | \(-0.532677\pi\) | ||||
−0.102478 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | 0.682391 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(860\) | 11.3137i | 0.385794i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.00000 | 0.204361 | ||||||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 16.9706i | − | 0.577016i | ||||||
\(866\) | − | 4.24264i | − | 0.144171i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.48528i | 0.288009i | ||||||||
\(869\) | −72.0000 | −2.44243 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.0000 | 1.82972 | ||||||||
\(872\) | 8.48528i | 0.287348i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.0000 | − | 5.65685i | −0.811812 | − | 0.191346i | ||||
\(875\) | − | 5.65685i | − | 0.191237i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.9706i | 0.573055i | 0.958072 | + | 0.286528i | \(0.0925010\pi\) | ||||
−0.958072 | + | 0.286528i | \(0.907499\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 16.0000 | 0.539360 | ||||||||
\(881\) | 5.65685i | 0.190584i | 0.995449 | + | 0.0952921i | \(0.0303785\pi\) | ||||
−0.995449 | + | 0.0952921i | \(0.969621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.0000 | −1.74994 | −0.874970 | − | 0.484178i | \(-0.839119\pi\) | ||||
−0.874970 | + | 0.484178i | \(0.839119\pi\) | |||||||
\(884\) | 24.0000 | 0.807207 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.2843i | 0.950229i | ||||||||
\(887\) | −12.0000 | −0.402921 | −0.201460 | − | 0.979497i | \(-0.564569\pi\) | ||||
−0.201460 | + | 0.979497i | \(0.564569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.7279i | 0.426881i | ||||||||
\(890\) | 16.9706i | 0.568855i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 25.4558i | 0.852325i | ||||||||
\(893\) | 42.0000 | + | 9.89949i | 1.40548 | + | 0.331274i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.9117i | 1.70179i | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30.0000 | 1.00111 | ||||||||
\(899\) | 50.9117i | 1.69800i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.9411i | 1.13074i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 12.0000 | 0.398893 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.1838i | 1.26787i | 0.773386 | + | 0.633936i | \(0.218562\pi\) | ||||
−0.773386 | + | 0.633936i | \(0.781438\pi\) | |||||||
\(908\) | 12.0000 | 0.398234 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.0000 | 0.397796 | ||||||||
\(911\) | 24.0000 | 0.795155 | 0.397578 | − | 0.917568i | \(-0.369851\pi\) | ||||
0.397578 | + | 0.917568i | \(0.369851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 88.0000 | 2.91237 | ||||||||
\(914\) | −32.0000 | −1.05847 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | 1.41421i | 0.0467014i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.00000 | −0.131948 | −0.0659739 | − | 0.997821i | \(-0.521015\pi\) | ||||
−0.0659739 | + | 0.997821i | \(0.521015\pi\) | |||||||
\(920\) | −16.0000 | −0.527504 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 22.6274i | − | 0.745194i | ||||||
\(923\) | 25.4558i | 0.837889i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −32.0000 | −1.05159 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.00000 | −0.196960 | ||||||||
\(929\) | − | 36.7696i | − | 1.20637i | −0.797601 | − | 0.603185i | \(-0.793898\pi\) | ||
0.797601 | − | 0.603185i | \(-0.206102\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | − | 4.24264i | 0.0327737 | − | 0.139047i | ||||
\(932\) | − | 7.07107i | − | 0.231621i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 18.3848i | − | 0.601568i | ||||||
\(935\) | 90.5097i | 2.95998i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.0000 | 0.457360 | 0.228680 | − | 0.973502i | \(-0.426559\pi\) | ||||
0.228680 | + | 0.973502i | \(0.426559\pi\) | |||||||
\(938\) | − | 12.7279i | − | 0.415581i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 28.0000 | 0.913259 | ||||||||
\(941\) | −30.0000 | −0.977972 | −0.488986 | − | 0.872292i | \(-0.662633\pi\) | ||||
−0.488986 | + | 0.872292i | \(0.662633\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.6274i | 0.735681i | ||||||||
\(947\) | − | 53.7401i | − | 1.74632i | −0.487435 | − | 0.873160i | \(-0.662067\pi\) | ||
0.487435 | − | 0.873160i | \(-0.337933\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 59.3970i | − | 1.92811i | ||||||
\(950\) | 3.00000 | − | 12.7279i | 0.0973329 | − | 0.412948i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 5.65685i | − | 0.183340i | ||||||
\(953\) | 18.0000 | 0.583077 | 0.291539 | − | 0.956559i | \(-0.405833\pi\) | ||||
0.291539 | + | 0.956559i | \(0.405833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.0000 | 1.29437 | ||||||||
\(956\) | 14.1421i | 0.457389i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 18.3848i | − | 0.593985i | ||||||
\(959\) | 9.89949i | 0.319671i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −41.0000 | −1.32258 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.7279i | 0.409939i | ||||||||
\(965\) | −48.0000 | −1.54517 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | 21.0000 | 0.674966 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.0000 | 0.385297 | ||||||||
\(971\) | −36.0000 | −1.15529 | −0.577647 | − | 0.816286i | \(-0.696029\pi\) | ||||
−0.577647 | + | 0.816286i | \(0.696029\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.00000 | 0.0641171 | ||||||||
\(974\) | 12.7279i | 0.407829i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 6.00000 | 0.191957 | 0.0959785 | − | 0.995383i | \(-0.469402\pi\) | ||||
0.0959785 | + | 0.995383i | \(0.469402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.9411i | 1.08476i | ||||||||
\(980\) | − | 2.82843i | − | 0.0903508i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.7696i | 1.17336i | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.0000 | 1.65686 | ||||||||
\(986\) | − | 33.9411i | − | 1.08091i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.0000 | − | 4.24264i | −0.572656 | − | 0.134976i | ||||
\(989\) | − | 22.6274i | − | 0.719510i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 38.1838i | − | 1.21295i | −0.795104 | − | 0.606474i | \(-0.792584\pi\) | ||
0.795104 | − | 0.606474i | \(-0.207416\pi\) | |||||||
\(992\) | − | 8.48528i | − | 0.269408i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.00000 | 0.190308 | ||||||||
\(995\) | − | 22.6274i | − | 0.717337i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.0000 | −0.316703 | −0.158352 | − | 0.987383i | \(-0.550618\pi\) | ||||
−0.158352 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(998\) | 16.0000 | 0.506471 | ||||||||
\(999\) | 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 | 2394.2.b.b.1709.1 | ✓ | 2 | |
3.2 | odd | 2 | 2394.2.b.e.1709.2 | yes | 2 | ||
19.18 | odd | 2 | 2394.2.b.e.1709.1 | yes | 2 | ||
57.56 | even | 2 | inner | 2394.2.b.b.1709.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2394.2.b.b.1709.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2394.2.b.b.1709.2 | yes | 2 | 57.56 | even | 2 | inner | |
2394.2.b.e.1709.1 | yes | 2 | 19.18 | odd | 2 | ||
2394.2.b.e.1709.2 | yes | 2 | 3.2 | odd | 2 |