Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [275,2,Mod(199,275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(275, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("275.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.19588605559\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(2.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 275.199 |
Dual form | 275.2.b.c.199.1 |
$q$-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 \(\left(\mathbb{Z}/275\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.30278i | 1.62831i | 0.580649 | + | 0.814154i | \(0.302799\pi\) | ||||
−0.580649 | + | 0.814154i | \(0.697201\pi\) | |||||||
\(3\) | 1.30278i | 0.752158i | 0.926588 | + | 0.376079i | \(0.122728\pi\) | ||||
−0.926588 | + | 0.376079i | \(0.877272\pi\) | |||||||
\(4\) | −3.30278 | −1.65139 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.00000 | −1.22474 | ||||||||
\(7\) | 4.30278i | 1.62630i | 0.582057 | + | 0.813148i | \(0.302248\pi\) | ||||
−0.582057 | + | 0.813148i | \(0.697752\pi\) | |||||||
\(8\) | − 3.00000i | − 1.06066i | ||||||||
\(9\) | 1.30278 | 0.434259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | − 4.30278i | − 1.24210i | ||||||||
\(13\) | − 5.00000i | − 1.38675i | −0.720577 | − | 0.693375i | \(-0.756123\pi\) | ||||
0.720577 | − | 0.693375i | \(-0.243877\pi\) | |||||||
\(14\) | −9.90833 | −2.64811 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.302776 | 0.0756939 | ||||||||
\(17\) | − 3.90833i | − 0.947909i | −0.880549 | − | 0.473954i | \(-0.842826\pi\) | ||||
0.880549 | − | 0.473954i | \(-0.157174\pi\) | |||||||
\(18\) | 3.00000i | 0.707107i | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.60555 | −1.22323 | ||||||||
\(22\) | − 2.30278i | − 0.490953i | ||||||||
\(23\) | 3.69722i | 0.770925i | 0.922724 | + | 0.385462i | \(0.125958\pi\) | ||||
−0.922724 | + | 0.385462i | \(0.874042\pi\) | |||||||
\(24\) | 3.90833 | 0.797784 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 11.5139 | 2.25806 | ||||||||
\(27\) | 5.60555i | 1.07879i | ||||||||
\(28\) | − 14.2111i | − 2.68565i | ||||||||
\(29\) | 9.90833 | 1.83993 | 0.919965 | − | 0.392000i | \(-0.128217\pi\) | ||||
0.919965 | + | 0.392000i | \(0.128217\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.21110 | −0.756336 | −0.378168 | − | 0.925737i | \(-0.623446\pi\) | ||||
−0.378168 | + | 0.925737i | \(0.623446\pi\) | |||||||
\(32\) | − 5.30278i | − 0.937407i | ||||||||
\(33\) | − 1.30278i | − 0.226784i | ||||||||
\(34\) | 9.00000 | 1.54349 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.30278 | −0.717129 | ||||||||
\(37\) | 9.60555i | 1.57914i | 0.613659 | + | 0.789571i | \(0.289697\pi\) | ||||
−0.613659 | + | 0.789571i | \(0.710303\pi\) | |||||||
\(38\) | 2.30278i | 0.373560i | ||||||||
\(39\) | 6.51388 | 1.04306 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.60555 | 0.250745 | 0.125372 | − | 0.992110i | \(-0.459987\pi\) | ||||
0.125372 | + | 0.992110i | \(0.459987\pi\) | |||||||
\(42\) | − 12.9083i | − 1.99180i | ||||||||
\(43\) | 7.21110i | 1.09968i | 0.835269 | + | 0.549841i | \(0.185312\pi\) | ||||
−0.835269 | + | 0.549841i | \(0.814688\pi\) | |||||||
\(44\) | 3.30278 | 0.497912 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.51388 | −1.25530 | ||||||||
\(47\) | − 3.00000i | − 0.437595i | −0.975770 | − | 0.218797i | \(-0.929787\pi\) | ||||
0.975770 | − | 0.218797i | \(-0.0702134\pi\) | |||||||
\(48\) | 0.394449i | 0.0569338i | ||||||||
\(49\) | −11.5139 | −1.64484 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.09167 | 0.712977 | ||||||||
\(52\) | 16.5139i | 2.29006i | ||||||||
\(53\) | − 2.30278i | − 0.316311i | −0.987414 | − | 0.158155i | \(-0.949445\pi\) | ||||
0.987414 | − | 0.158155i | \(-0.0505547\pi\) | |||||||
\(54\) | −12.9083 | −1.75660 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.9083 | 1.72495 | ||||||||
\(57\) | 1.30278i | 0.172557i | ||||||||
\(58\) | 22.8167i | 2.99597i | ||||||||
\(59\) | −0.211103 | −0.0274832 | −0.0137416 | − | 0.999906i | \(-0.504374\pi\) | ||||
−0.0137416 | + | 0.999906i | \(0.504374\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.90833 | 0.372373 | 0.186187 | − | 0.982514i | \(-0.440387\pi\) | ||||
0.186187 | + | 0.982514i | \(0.440387\pi\) | |||||||
\(62\) | − 9.69722i | − 1.23155i | ||||||||
\(63\) | 5.60555i | 0.706233i | ||||||||
\(64\) | 12.8167 | 1.60208 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.00000 | 0.369274 | ||||||||
\(67\) | − 4.00000i | − 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | 12.9083i | 1.56536i | ||||||||
\(69\) | −4.81665 | −0.579857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.60555 | 0.546578 | 0.273289 | − | 0.961932i | \(-0.411888\pi\) | ||||
0.273289 | + | 0.961932i | \(0.411888\pi\) | |||||||
\(72\) | − 3.90833i | − 0.460601i | ||||||||
\(73\) | − 2.90833i | − 0.340394i | −0.985410 | − | 0.170197i | \(-0.945560\pi\) | ||||
0.985410 | − | 0.170197i | \(-0.0544404\pi\) | |||||||
\(74\) | −22.1194 | −2.57133 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.30278 | −0.378854 | ||||||||
\(77\) | − 4.30278i | − 0.490347i | ||||||||
\(78\) | 15.0000i | 1.69842i | ||||||||
\(79\) | 0.0916731 | 0.0103140 | 0.00515701 | − | 0.999987i | \(-0.498358\pi\) | ||||
0.00515701 | + | 0.999987i | \(0.498358\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.39445 | −0.377161 | ||||||||
\(82\) | 3.69722i | 0.408290i | ||||||||
\(83\) | − 14.5139i | − 1.59311i | −0.604569 | − | 0.796553i | \(-0.706655\pi\) | ||||
0.604569 | − | 0.796553i | \(-0.293345\pi\) | |||||||
\(84\) | 18.5139 | 2.02003 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −16.6056 | −1.79062 | ||||||||
\(87\) | 12.9083i | 1.38392i | ||||||||
\(88\) | 3.00000i | 0.319801i | ||||||||
\(89\) | −5.30278 | −0.562093 | −0.281047 | − | 0.959694i | \(-0.590682\pi\) | ||||
−0.281047 | + | 0.959694i | \(0.590682\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.5139 | 2.25527 | ||||||||
\(92\) | − 12.2111i | − 1.27310i | ||||||||
\(93\) | − 5.48612i | − 0.568884i | ||||||||
\(94\) | 6.90833 | 0.712540 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.90833 | 0.705078 | ||||||||
\(97\) | 11.6972i | 1.18767i | 0.804586 | + | 0.593837i | \(0.202387\pi\) | ||||
−0.804586 | + | 0.593837i | \(0.797613\pi\) | |||||||
\(98\) | − 26.5139i | − 2.67831i | ||||||||
\(99\) | −1.30278 | −0.130934 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.5139 | 1.74270 | 0.871348 | − | 0.490666i | \(-0.163246\pi\) | ||||
0.871348 | + | 0.490666i | \(0.163246\pi\) | |||||||
\(102\) | 11.7250i | 1.16095i | ||||||||
\(103\) | 7.90833i | 0.779231i | 0.920978 | + | 0.389615i | \(0.127392\pi\) | ||||
−0.920978 | + | 0.389615i | \(0.872608\pi\) | |||||||
\(104\) | −15.0000 | −1.47087 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.30278 | 0.515051 | ||||||||
\(107\) | − 3.00000i | − 0.290021i | −0.989430 | − | 0.145010i | \(-0.953678\pi\) | ||||
0.989430 | − | 0.145010i | \(-0.0463216\pi\) | |||||||
\(108\) | − 18.5139i | − 1.78150i | ||||||||
\(109\) | 6.51388 | 0.623916 | 0.311958 | − | 0.950096i | \(-0.399015\pi\) | ||||
0.311958 | + | 0.950096i | \(0.399015\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.5139 | −1.18776 | ||||||||
\(112\) | 1.30278i | 0.123101i | ||||||||
\(113\) | − 10.8167i | − 1.01755i | −0.860901 | − | 0.508773i | \(-0.830099\pi\) | ||||
0.860901 | − | 0.508773i | \(-0.169901\pi\) | |||||||
\(114\) | −3.00000 | −0.280976 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −32.7250 | −3.03844 | ||||||||
\(117\) | − 6.51388i | − 0.602208i | ||||||||
\(118\) | − 0.486122i | − 0.0447511i | ||||||||
\(119\) | 16.8167 | 1.54158 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.69722i | 0.606338i | ||||||||
\(123\) | 2.09167i | 0.188600i | ||||||||
\(124\) | 13.9083 | 1.24900 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12.9083 | −1.14997 | ||||||||
\(127\) | − 17.1194i | − 1.51910i | −0.650447 | − | 0.759552i | \(-0.725418\pi\) | ||||
0.650447 | − | 0.759552i | \(-0.274582\pi\) | |||||||
\(128\) | 18.9083i | 1.67128i | ||||||||
\(129\) | −9.39445 | −0.827135 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.908327 | 0.0793609 | 0.0396804 | − | 0.999212i | \(-0.487366\pi\) | ||||
0.0396804 | + | 0.999212i | \(0.487366\pi\) | |||||||
\(132\) | 4.30278i | 0.374509i | ||||||||
\(133\) | 4.30278i | 0.373098i | ||||||||
\(134\) | 9.21110 | 0.795718 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.7250 | −1.00541 | ||||||||
\(137\) | − 2.09167i | − 0.178704i | −0.996000 | − | 0.0893518i | \(-0.971520\pi\) | ||||
0.996000 | − | 0.0893518i | \(-0.0284796\pi\) | |||||||
\(138\) | − 11.0917i | − 0.944186i | ||||||||
\(139\) | −8.21110 | −0.696457 | −0.348228 | − | 0.937410i | \(-0.613217\pi\) | ||||
−0.348228 | + | 0.937410i | \(0.613217\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.90833 | 0.329141 | ||||||||
\(142\) | 10.6056i | 0.889998i | ||||||||
\(143\) | 5.00000i | 0.418121i | ||||||||
\(144\) | 0.394449 | 0.0328707 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.69722 | 0.554266 | ||||||||
\(147\) | − 15.0000i | − 1.23718i | ||||||||
\(148\) | − 31.7250i | − 2.60778i | ||||||||
\(149\) | −2.78890 | −0.228475 | −0.114238 | − | 0.993453i | \(-0.536443\pi\) | ||||
−0.114238 | + | 0.993453i | \(0.536443\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.8167 | −1.69404 | −0.847018 | − | 0.531565i | \(-0.821604\pi\) | ||||
−0.847018 | + | 0.531565i | \(0.821604\pi\) | |||||||
\(152\) | − 3.00000i | − 0.243332i | ||||||||
\(153\) | − 5.09167i | − 0.411637i | ||||||||
\(154\) | 9.90833 | 0.798436 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −21.5139 | −1.72249 | ||||||||
\(157\) | 4.78890i | 0.382196i | 0.981571 | + | 0.191098i | \(0.0612048\pi\) | ||||
−0.981571 | + | 0.191098i | \(0.938795\pi\) | |||||||
\(158\) | 0.211103i | 0.0167944i | ||||||||
\(159\) | 3.00000 | 0.237915 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.9083 | −1.25375 | ||||||||
\(162\) | − 7.81665i | − 0.614134i | ||||||||
\(163\) | − 5.69722i | − 0.446241i | −0.974791 | − | 0.223121i | \(-0.928376\pi\) | ||||
0.974791 | − | 0.223121i | \(-0.0716243\pi\) | |||||||
\(164\) | −5.30278 | −0.414077 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 33.4222 | 2.59407 | ||||||||
\(167\) | − 15.4222i | − 1.19341i | −0.802462 | − | 0.596703i | \(-0.796477\pi\) | ||||
0.802462 | − | 0.596703i | \(-0.203523\pi\) | |||||||
\(168\) | 16.8167i | 1.29743i | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.30278 | 0.0996257 | ||||||||
\(172\) | − 23.8167i | − 1.81600i | ||||||||
\(173\) | − 16.8167i | − 1.27855i | −0.768980 | − | 0.639273i | \(-0.779235\pi\) | ||||
0.768980 | − | 0.639273i | \(-0.220765\pi\) | |||||||
\(174\) | −29.7250 | −2.25344 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.302776 | −0.0228226 | ||||||||
\(177\) | − 0.275019i | − 0.0206717i | ||||||||
\(178\) | − 12.2111i | − 0.915261i | ||||||||
\(179\) | 5.51388 | 0.412127 | 0.206063 | − | 0.978539i | \(-0.433935\pi\) | ||||
0.206063 | + | 0.978539i | \(0.433935\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.09167 | −0.675779 | −0.337889 | − | 0.941186i | \(-0.609713\pi\) | ||||
−0.337889 | + | 0.941186i | \(0.609713\pi\) | |||||||
\(182\) | 49.5416i | 3.67227i | ||||||||
\(183\) | 3.78890i | 0.280083i | ||||||||
\(184\) | 11.0917 | 0.817689 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 12.6333 | 0.926319 | ||||||||
\(187\) | 3.90833i | 0.285805i | ||||||||
\(188\) | 9.90833i | 0.722639i | ||||||||
\(189\) | −24.1194 | −1.75443 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.69722 | 0.484594 | 0.242297 | − | 0.970202i | \(-0.422099\pi\) | ||||
0.242297 | + | 0.970202i | \(0.422099\pi\) | |||||||
\(192\) | 16.6972i | 1.20502i | ||||||||
\(193\) | 1.21110i | 0.0871771i | 0.999050 | + | 0.0435885i | \(0.0138791\pi\) | ||||
−0.999050 | + | 0.0435885i | \(0.986121\pi\) | |||||||
\(194\) | −26.9361 | −1.93390 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 38.0278 | 2.71627 | ||||||||
\(197\) | 9.69722i | 0.690899i | 0.938437 | + | 0.345449i | \(0.112273\pi\) | ||||
−0.938437 | + | 0.345449i | \(0.887727\pi\) | |||||||
\(198\) | − 3.00000i | − 0.213201i | ||||||||
\(199\) | 24.5139 | 1.73774 | 0.868871 | − | 0.495038i | \(-0.164846\pi\) | ||||
0.868871 | + | 0.495038i | \(0.164846\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.21110 | 0.367563 | ||||||||
\(202\) | 40.3305i | 2.83765i | ||||||||
\(203\) | 42.6333i | 2.99227i | ||||||||
\(204\) | −16.8167 | −1.17740 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −18.2111 | −1.26883 | ||||||||
\(207\) | 4.81665i | 0.334781i | ||||||||
\(208\) | − 1.51388i | − 0.104969i | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.2389 | 1.73751 | 0.868757 | − | 0.495238i | \(-0.164919\pi\) | ||||
0.868757 | + | 0.495238i | \(0.164919\pi\) | |||||||
\(212\) | 7.60555i | 0.522351i | ||||||||
\(213\) | 6.00000i | 0.411113i | ||||||||
\(214\) | 6.90833 | 0.472244 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 16.8167 | 1.14423 | ||||||||
\(217\) | − 18.1194i | − 1.23003i | ||||||||
\(218\) | 15.0000i | 1.01593i | ||||||||
\(219\) | 3.78890 | 0.256030 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.5416 | −1.31451 | ||||||||
\(222\) | − 28.8167i | − 1.93405i | ||||||||
\(223\) | − 20.6333i | − 1.38171i | −0.722994 | − | 0.690854i | \(-0.757235\pi\) | ||||
0.722994 | − | 0.690854i | \(-0.242765\pi\) | |||||||
\(224\) | 22.8167 | 1.52450 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.9083 | 1.65688 | ||||||||
\(227\) | 5.30278i | 0.351958i | 0.984394 | + | 0.175979i | \(0.0563090\pi\) | ||||
−0.984394 | + | 0.175979i | \(0.943691\pi\) | |||||||
\(228\) | − 4.30278i | − 0.284958i | ||||||||
\(229\) | −13.7250 | −0.906972 | −0.453486 | − | 0.891263i | \(-0.649820\pi\) | ||||
−0.453486 | + | 0.891263i | \(0.649820\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.60555 | 0.368818 | ||||||||
\(232\) | − 29.7250i | − 1.95154i | ||||||||
\(233\) | − 5.09167i | − 0.333567i | −0.985994 | − | 0.166783i | \(-0.946662\pi\) | ||||
0.985994 | − | 0.166783i | \(-0.0533380\pi\) | |||||||
\(234\) | 15.0000 | 0.980581 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.697224 | 0.0453854 | ||||||||
\(237\) | 0.119429i | 0.00775778i | ||||||||
\(238\) | 38.7250i | 2.51017i | ||||||||
\(239\) | 4.11943 | 0.266464 | 0.133232 | − | 0.991085i | \(-0.457465\pi\) | ||||
0.133232 | + | 0.991085i | \(0.457465\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.9361 | −1.60627 | −0.803137 | − | 0.595794i | \(-0.796837\pi\) | ||||
−0.803137 | + | 0.595794i | \(0.796837\pi\) | |||||||
\(242\) | 2.30278i | 0.148028i | ||||||||
\(243\) | 12.3944i | 0.795104i | ||||||||
\(244\) | −9.60555 | −0.614932 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.81665 | −0.307099 | ||||||||
\(247\) | − 5.00000i | − 0.318142i | ||||||||
\(248\) | 12.6333i | 0.802216i | ||||||||
\(249\) | 18.9083 | 1.19827 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.90833 | −0.246691 | −0.123346 | − | 0.992364i | \(-0.539362\pi\) | ||||
−0.123346 | + | 0.992364i | \(0.539362\pi\) | |||||||
\(252\) | − 18.5139i | − 1.16626i | ||||||||
\(253\) | − 3.69722i | − 0.232443i | ||||||||
\(254\) | 39.4222 | 2.47357 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.9083 | −1.11927 | ||||||||
\(257\) | − 18.0000i | − 1.12281i | −0.827541 | − | 0.561405i | \(-0.810261\pi\) | ||||
0.827541 | − | 0.561405i | \(-0.189739\pi\) | |||||||
\(258\) | − 21.6333i | − 1.34683i | ||||||||
\(259\) | −41.3305 | −2.56815 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.9083 | 0.799005 | ||||||||
\(262\) | 2.09167i | 0.129224i | ||||||||
\(263\) | 1.18335i | 0.0729683i | 0.999334 | + | 0.0364841i | \(0.0116158\pi\) | ||||
−0.999334 | + | 0.0364841i | \(0.988384\pi\) | |||||||
\(264\) | −3.90833 | −0.240541 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.90833 | −0.607519 | ||||||||
\(267\) | − 6.90833i | − 0.422783i | ||||||||
\(268\) | 13.2111i | 0.806997i | ||||||||
\(269\) | 23.7250 | 1.44654 | 0.723269 | − | 0.690567i | \(-0.242639\pi\) | ||||
0.723269 | + | 0.690567i | \(0.242639\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.2111 | 0.863263 | 0.431632 | − | 0.902050i | \(-0.357938\pi\) | ||||
0.431632 | + | 0.902050i | \(0.357938\pi\) | |||||||
\(272\) | − 1.18335i | − 0.0717509i | ||||||||
\(273\) | 28.0278i | 1.69632i | ||||||||
\(274\) | 4.81665 | 0.290985 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 15.9083 | 0.957569 | ||||||||
\(277\) | 21.6056i | 1.29815i | 0.760724 | + | 0.649076i | \(0.224844\pi\) | ||||
−0.760724 | + | 0.649076i | \(0.775156\pi\) | |||||||
\(278\) | − 18.9083i | − 1.13405i | ||||||||
\(279\) | −5.48612 | −0.328446 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.8167 | −1.36113 | −0.680564 | − | 0.732689i | \(-0.738265\pi\) | ||||
−0.680564 | + | 0.732689i | \(0.738265\pi\) | |||||||
\(282\) | 9.00000i | 0.535942i | ||||||||
\(283\) | − 2.69722i | − 0.160333i | −0.996781 | − | 0.0801667i | \(-0.974455\pi\) | ||||
0.996781 | − | 0.0801667i | \(-0.0255453\pi\) | |||||||
\(284\) | −15.2111 | −0.902613 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.5139 | −0.680830 | ||||||||
\(287\) | 6.90833i | 0.407786i | ||||||||
\(288\) | − 6.90833i | − 0.407077i | ||||||||
\(289\) | 1.72498 | 0.101469 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.2389 | −0.893318 | ||||||||
\(292\) | 9.60555i | 0.562122i | ||||||||
\(293\) | − 15.2111i | − 0.888642i | −0.895868 | − | 0.444321i | \(-0.853445\pi\) | ||||
0.895868 | − | 0.444321i | \(-0.146555\pi\) | |||||||
\(294\) | 34.5416 | 2.01451 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 28.8167 | 1.67493 | ||||||||
\(297\) | − 5.60555i | − 0.325267i | ||||||||
\(298\) | − 6.42221i | − 0.372028i | ||||||||
\(299\) | 18.4861 | 1.06908 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.0278 | −1.78841 | ||||||||
\(302\) | − 47.9361i | − 2.75841i | ||||||||
\(303\) | 22.8167i | 1.31078i | ||||||||
\(304\) | 0.302776 | 0.0173654 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.7250 | 0.670273 | ||||||||
\(307\) | − 6.09167i | − 0.347670i | −0.984775 | − | 0.173835i | \(-0.944384\pi\) | ||||
0.984775 | − | 0.173835i | \(-0.0556160\pi\) | |||||||
\(308\) | 14.2111i | 0.809753i | ||||||||
\(309\) | −10.3028 | −0.586104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.8167 | −0.953585 | −0.476792 | − | 0.879016i | \(-0.658201\pi\) | ||||
−0.476792 | + | 0.879016i | \(0.658201\pi\) | |||||||
\(312\) | − 19.5416i | − 1.10633i | ||||||||
\(313\) | − 21.8167i | − 1.23315i | −0.787296 | − | 0.616575i | \(-0.788520\pi\) | ||||
0.787296 | − | 0.616575i | \(-0.211480\pi\) | |||||||
\(314\) | −11.0278 | −0.622332 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.302776 | −0.0170325 | ||||||||
\(317\) | 9.90833i | 0.556507i | 0.960508 | + | 0.278254i | \(0.0897555\pi\) | ||||
−0.960508 | + | 0.278254i | \(0.910244\pi\) | |||||||
\(318\) | 6.90833i | 0.387400i | ||||||||
\(319\) | −9.90833 | −0.554760 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.90833 | 0.218142 | ||||||||
\(322\) | − 36.6333i | − 2.04149i | ||||||||
\(323\) | − 3.90833i | − 0.217465i | ||||||||
\(324\) | 11.2111 | 0.622839 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.1194 | 0.726618 | ||||||||
\(327\) | 8.48612i | 0.469284i | ||||||||
\(328\) | − 4.81665i | − 0.265955i | ||||||||
\(329\) | 12.9083 | 0.711659 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.3944 | −0.791190 | −0.395595 | − | 0.918425i | \(-0.629462\pi\) | ||||
−0.395595 | + | 0.918425i | \(0.629462\pi\) | |||||||
\(332\) | 47.9361i | 2.63083i | ||||||||
\(333\) | 12.5139i | 0.685756i | ||||||||
\(334\) | 35.5139 | 1.94323 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.69722 | −0.0925912 | ||||||||
\(337\) | 26.8444i | 1.46231i | 0.682212 | + | 0.731154i | \(0.261018\pi\) | ||||
−0.682212 | + | 0.731154i | \(0.738982\pi\) | |||||||
\(338\) | − 27.6333i | − 1.50305i | ||||||||
\(339\) | 14.0917 | 0.765355 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.21110 | 0.228044 | ||||||||
\(342\) | 3.00000i | 0.162221i | ||||||||
\(343\) | − 19.4222i | − 1.04870i | ||||||||
\(344\) | 21.6333 | 1.16639 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 38.7250 | 2.08187 | ||||||||
\(347\) | 5.51388i | 0.296000i | 0.988987 | + | 0.148000i | \(0.0472836\pi\) | ||||
−0.988987 | + | 0.148000i | \(0.952716\pi\) | |||||||
\(348\) | − 42.6333i | − 2.28539i | ||||||||
\(349\) | 26.8167 | 1.43546 | 0.717731 | − | 0.696320i | \(-0.245181\pi\) | ||||
0.717731 | + | 0.696320i | \(0.245181\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.0278 | 1.49601 | ||||||||
\(352\) | 5.30278i | 0.282639i | ||||||||
\(353\) | 24.6333i | 1.31110i | 0.755152 | + | 0.655549i | \(0.227563\pi\) | ||||
−0.755152 | + | 0.655549i | \(0.772437\pi\) | |||||||
\(354\) | 0.633308 | 0.0336599 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 17.5139 | 0.928234 | ||||||||
\(357\) | 21.9083i | 1.15951i | ||||||||
\(358\) | 12.6972i | 0.671069i | ||||||||
\(359\) | −15.2111 | −0.802811 | −0.401406 | − | 0.915900i | \(-0.631478\pi\) | ||||
−0.401406 | + | 0.915900i | \(0.631478\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | − 20.9361i | − 1.10038i | ||||||||
\(363\) | 1.30278i | 0.0683780i | ||||||||
\(364\) | −71.0555 | −3.72432 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.72498 | −0.456062 | ||||||||
\(367\) | − 24.3028i | − 1.26859i | −0.773089 | − | 0.634297i | \(-0.781290\pi\) | ||||
0.773089 | − | 0.634297i | \(-0.218710\pi\) | |||||||
\(368\) | 1.11943i | 0.0583543i | ||||||||
\(369\) | 2.09167 | 0.108888 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.90833 | 0.514415 | ||||||||
\(372\) | 18.1194i | 0.939449i | ||||||||
\(373\) | 1.42221i | 0.0736390i | 0.999322 | + | 0.0368195i | \(0.0117227\pi\) | ||||
−0.999322 | + | 0.0368195i | \(0.988277\pi\) | |||||||
\(374\) | −9.00000 | −0.465379 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.00000 | −0.464140 | ||||||||
\(377\) | − 49.5416i | − 2.55152i | ||||||||
\(378\) | − 55.5416i | − 2.85675i | ||||||||
\(379\) | −24.8167 | −1.27475 | −0.637373 | − | 0.770555i | \(-0.719979\pi\) | ||||
−0.637373 | + | 0.770555i | \(0.719979\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.3028 | 1.14261 | ||||||||
\(382\) | 15.4222i | 0.789069i | ||||||||
\(383\) | 21.6333i | 1.10541i | 0.833377 | + | 0.552705i | \(0.186404\pi\) | ||||
−0.833377 | + | 0.552705i | \(0.813596\pi\) | |||||||
\(384\) | −24.6333 | −1.25706 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.78890 | −0.141951 | ||||||||
\(387\) | 9.39445i | 0.477547i | ||||||||
\(388\) | − 38.6333i | − 1.96131i | ||||||||
\(389\) | −12.0000 | −0.608424 | −0.304212 | − | 0.952604i | \(-0.598393\pi\) | ||||
−0.304212 | + | 0.952604i | \(0.598393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.4500 | 0.730766 | ||||||||
\(392\) | 34.5416i | 1.74462i | ||||||||
\(393\) | 1.18335i | 0.0596919i | ||||||||
\(394\) | −22.3305 | −1.12500 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.30278 | 0.216223 | ||||||||
\(397\) | 25.3028i | 1.26991i | 0.772549 | + | 0.634955i | \(0.218981\pi\) | ||||
−0.772549 | + | 0.634955i | \(0.781019\pi\) | |||||||
\(398\) | 56.4500i | 2.82958i | ||||||||
\(399\) | −5.60555 | −0.280629 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.2111 | −1.35886 | −0.679429 | − | 0.733741i | \(-0.737772\pi\) | ||||
−0.679429 | + | 0.733741i | \(0.737772\pi\) | |||||||
\(402\) | 12.0000i | 0.598506i | ||||||||
\(403\) | 21.0555i | 1.04885i | ||||||||
\(404\) | −57.8444 | −2.87787 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −98.1749 | −4.87234 | ||||||||
\(407\) | − 9.60555i | − 0.476129i | ||||||||
\(408\) | − 15.2750i | − 0.756226i | ||||||||
\(409\) | −8.21110 | −0.406013 | −0.203006 | − | 0.979177i | \(-0.565071\pi\) | ||||
−0.203006 | + | 0.979177i | \(0.565071\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.72498 | 0.134413 | ||||||||
\(412\) | − 26.1194i | − 1.28681i | ||||||||
\(413\) | − 0.908327i | − 0.0446958i | ||||||||
\(414\) | −11.0917 | −0.545126 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −26.5139 | −1.29995 | ||||||||
\(417\) | − 10.6972i | − 0.523845i | ||||||||
\(418\) | − 2.30278i | − 0.112632i | ||||||||
\(419\) | −13.6056 | −0.664675 | −0.332337 | − | 0.943161i | \(-0.607837\pi\) | ||||
−0.332337 | + | 0.943161i | \(0.607837\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.30278 | 0.209704 | 0.104852 | − | 0.994488i | \(-0.466563\pi\) | ||||
0.104852 | + | 0.994488i | \(0.466563\pi\) | |||||||
\(422\) | 58.1194i | 2.82921i | ||||||||
\(423\) | − 3.90833i | − 0.190029i | ||||||||
\(424\) | −6.90833 | −0.335498 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −13.8167 | −0.669419 | ||||||||
\(427\) | 12.5139i | 0.605589i | ||||||||
\(428\) | 9.90833i | 0.478937i | ||||||||
\(429\) | −6.51388 | −0.314493 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.0000 | 1.58955 | 0.794777 | − | 0.606902i | \(-0.207588\pi\) | ||||
0.794777 | + | 0.606902i | \(0.207588\pi\) | |||||||
\(432\) | 1.69722i | 0.0816577i | ||||||||
\(433\) | − 5.00000i | − 0.240285i | −0.992757 | − | 0.120142i | \(-0.961665\pi\) | ||||
0.992757 | − | 0.120142i | \(-0.0383351\pi\) | |||||||
\(434\) | 41.7250 | 2.00286 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.5139 | −1.03033 | ||||||||
\(437\) | 3.69722i | 0.176862i | ||||||||
\(438\) | 8.72498i | 0.416896i | ||||||||
\(439\) | −20.6972 | −0.987825 | −0.493912 | − | 0.869512i | \(-0.664434\pi\) | ||||
−0.493912 | + | 0.869512i | \(0.664434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | − 45.0000i | − 2.14043i | ||||||||
\(443\) | 1.39445i | 0.0662523i | 0.999451 | + | 0.0331261i | \(0.0105463\pi\) | ||||
−0.999451 | + | 0.0331261i | \(0.989454\pi\) | |||||||
\(444\) | 41.3305 | 1.96146 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 47.5139 | 2.24985 | ||||||||
\(447\) | − 3.63331i | − 0.171850i | ||||||||
\(448\) | 55.1472i | 2.60546i | ||||||||
\(449\) | −41.5139 | −1.95916 | −0.979581 | − | 0.201052i | \(-0.935564\pi\) | ||||
−0.979581 | + | 0.201052i | \(0.935564\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.60555 | −0.0756025 | ||||||||
\(452\) | 35.7250i | 1.68036i | ||||||||
\(453\) | − 27.1194i | − 1.27418i | ||||||||
\(454\) | −12.2111 | −0.573095 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.90833 | 0.183024 | ||||||||
\(457\) | − 24.3028i | − 1.13684i | −0.822740 | − | 0.568418i | \(-0.807556\pi\) | ||||
0.822740 | − | 0.568418i | \(-0.192444\pi\) | |||||||
\(458\) | − 31.6056i | − 1.47683i | ||||||||
\(459\) | 21.9083 | 1.02259 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.7889 | 0.828512 | 0.414256 | − | 0.910161i | \(-0.364042\pi\) | ||||
0.414256 | + | 0.910161i | \(0.364042\pi\) | |||||||
\(462\) | 12.9083i | 0.600550i | ||||||||
\(463\) | − 26.2111i | − 1.21813i | −0.793119 | − | 0.609067i | \(-0.791544\pi\) | ||||
0.793119 | − | 0.609067i | \(-0.208456\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.7250 | 0.543149 | ||||||||
\(467\) | 24.6333i | 1.13989i | 0.821682 | + | 0.569947i | \(0.193036\pi\) | ||||
−0.821682 | + | 0.569947i | \(0.806964\pi\) | |||||||
\(468\) | 21.5139i | 0.994479i | ||||||||
\(469\) | 17.2111 | 0.794735 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.23886 | −0.287471 | ||||||||
\(472\) | 0.633308i | 0.0291503i | ||||||||
\(473\) | − 7.21110i | − 0.331567i | ||||||||
\(474\) | −0.275019 | −0.0126321 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −55.5416 | −2.54575 | ||||||||
\(477\) | − 3.00000i | − 0.137361i | ||||||||
\(478\) | 9.48612i | 0.433885i | ||||||||
\(479\) | 13.1833 | 0.602362 | 0.301181 | − | 0.953567i | \(-0.402619\pi\) | ||||
0.301181 | + | 0.953567i | \(0.402619\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 48.0278 | 2.18988 | ||||||||
\(482\) | − 57.4222i | − 2.61551i | ||||||||
\(483\) | − 20.7250i | − 0.943019i | ||||||||
\(484\) | −3.30278 | −0.150126 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −28.5416 | −1.29467 | ||||||||
\(487\) | − 10.2111i | − 0.462709i | −0.972869 | − | 0.231355i | \(-0.925684\pi\) | ||||
0.972869 | − | 0.231355i | \(-0.0743158\pi\) | |||||||
\(488\) | − 8.72498i | − 0.394961i | ||||||||
\(489\) | 7.42221 | 0.335644 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.2111 | −1.09263 | −0.546316 | − | 0.837579i | \(-0.683970\pi\) | ||||
−0.546316 | + | 0.837579i | \(0.683970\pi\) | |||||||
\(492\) | − 6.90833i | − 0.311451i | ||||||||
\(493\) | − 38.7250i | − 1.74409i | ||||||||
\(494\) | 11.5139 | 0.518034 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.27502 | −0.0572501 | ||||||||
\(497\) | 19.8167i | 0.888898i | ||||||||
\(498\) | 43.5416i | 1.95115i | ||||||||
\(499\) | 21.5139 | 0.963093 | 0.481547 | − | 0.876420i | \(-0.340075\pi\) | ||||
0.481547 | + | 0.876420i | \(0.340075\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.0917 | 0.897630 | ||||||||
\(502\) | − 9.00000i | − 0.401690i | ||||||||
\(503\) | − 16.6056i | − 0.740405i | −0.928951 | − | 0.370202i | \(-0.879288\pi\) | ||||
0.928951 | − | 0.370202i | \(-0.120712\pi\) | |||||||
\(504\) | 16.8167 | 0.749073 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.51388 | 0.378488 | ||||||||
\(507\) | − 15.6333i | − 0.694300i | ||||||||
\(508\) | 56.5416i | 2.50863i | ||||||||
\(509\) | 26.3028 | 1.16585 | 0.582925 | − | 0.812526i | \(-0.301908\pi\) | ||||
0.582925 | + | 0.812526i | \(0.301908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.5139 | 0.553581 | ||||||||
\(512\) | − 3.42221i | − 0.151242i | ||||||||
\(513\) | 5.60555i | 0.247491i | ||||||||
\(514\) | 41.4500 | 1.82828 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 31.0278 | 1.36592 | ||||||||
\(517\) | 3.00000i | 0.131940i | ||||||||
\(518\) | − 95.1749i | − 4.18175i | ||||||||
\(519\) | 21.9083 | 0.961669 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.4500 | 1.02736 | 0.513681 | − | 0.857981i | \(-0.328282\pi\) | ||||
0.513681 | + | 0.857981i | \(0.328282\pi\) | |||||||
\(522\) | 29.7250i | 1.30103i | ||||||||
\(523\) | 3.57779i | 0.156446i | 0.996936 | + | 0.0782230i | \(0.0249246\pi\) | ||||
−0.996936 | + | 0.0782230i | \(0.975075\pi\) | |||||||
\(524\) | −3.00000 | −0.131056 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.72498 | −0.118815 | ||||||||
\(527\) | 16.4584i | 0.716938i | ||||||||
\(528\) | − 0.394449i | − 0.0171662i | ||||||||
\(529\) | 9.33053 | 0.405675 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.275019 | −0.0119348 | ||||||||
\(532\) | − 14.2111i | − 0.616129i | ||||||||
\(533\) | − 8.02776i | − 0.347721i | ||||||||
\(534\) | 15.9083 | 0.688421 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.0000 | −0.518321 | ||||||||
\(537\) | 7.18335i | 0.309984i | ||||||||
\(538\) | 54.6333i | 2.35541i | ||||||||
\(539\) | 11.5139 | 0.495938 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.72498 | −0.289130 | −0.144565 | − | 0.989495i | \(-0.546178\pi\) | ||||
−0.144565 | + | 0.989495i | \(0.546178\pi\) | |||||||
\(542\) | 32.7250i | 1.40566i | ||||||||
\(543\) | − 11.8444i | − 0.508292i | ||||||||
\(544\) | −20.7250 | −0.888576 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −64.5416 | −2.76213 | ||||||||
\(547\) | 18.1194i | 0.774731i | 0.921926 | + | 0.387365i | \(0.126615\pi\) | ||||
−0.921926 | + | 0.387365i | \(0.873385\pi\) | |||||||
\(548\) | 6.90833i | 0.295109i | ||||||||
\(549\) | 3.78890 | 0.161706 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.90833 | 0.422109 | ||||||||
\(552\) | 14.4500i | 0.615031i | ||||||||
\(553\) | 0.394449i | 0.0167737i | ||||||||
\(554\) | −49.7527 | −2.11379 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27.1194 | 1.15012 | ||||||||
\(557\) | − 9.42221i | − 0.399232i | −0.979874 | − | 0.199616i | \(-0.936031\pi\) | ||||
0.979874 | − | 0.199616i | \(-0.0639694\pi\) | |||||||
\(558\) | − 12.6333i | − 0.534811i | ||||||||
\(559\) | 36.0555 | 1.52499 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.09167 | −0.214971 | ||||||||
\(562\) | − 52.5416i | − 2.21634i | ||||||||
\(563\) | − 18.9083i | − 0.796891i | −0.917192 | − | 0.398445i | \(-0.869550\pi\) | ||||
0.917192 | − | 0.398445i | \(-0.130450\pi\) | |||||||
\(564\) | −12.9083 | −0.543539 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.21110 | 0.261072 | ||||||||
\(567\) | − 14.6056i | − 0.613375i | ||||||||
\(568\) | − 13.8167i | − 0.579734i | ||||||||
\(569\) | −15.1472 | −0.635003 | −0.317502 | − | 0.948258i | \(-0.602844\pi\) | ||||
−0.317502 | + | 0.948258i | \(0.602844\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.3305 | −0.725260 | −0.362630 | − | 0.931933i | \(-0.618121\pi\) | ||||
−0.362630 | + | 0.931933i | \(0.618121\pi\) | |||||||
\(572\) | − 16.5139i | − 0.690480i | ||||||||
\(573\) | 8.72498i | 0.364491i | ||||||||
\(574\) | −15.9083 | −0.664001 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 16.6972 | 0.695718 | ||||||||
\(577\) | − 31.3583i | − 1.30546i | −0.757589 | − | 0.652731i | \(-0.773623\pi\) | ||||
0.757589 | − | 0.652731i | \(-0.226377\pi\) | |||||||
\(578\) | 3.97224i | 0.165224i | ||||||||
\(579\) | −1.57779 | −0.0655709 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 62.4500 | 2.59086 | ||||||||
\(582\) | − 35.0917i | − 1.45460i | ||||||||
\(583\) | 2.30278i | 0.0953712i | ||||||||
\(584\) | −8.72498 | −0.361042 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 35.0278 | 1.44698 | ||||||||
\(587\) | − 37.5416i | − 1.54951i | −0.632262 | − | 0.774755i | \(-0.717873\pi\) | ||||
0.632262 | − | 0.774755i | \(-0.282127\pi\) | |||||||
\(588\) | 49.5416i | 2.04306i | ||||||||
\(589\) | −4.21110 | −0.173515 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.6333 | −0.519665 | ||||||||
\(592\) | 2.90833i | 0.119531i | ||||||||
\(593\) | 13.6056i | 0.558713i | 0.960187 | + | 0.279357i | \(0.0901211\pi\) | ||||
−0.960187 | + | 0.279357i | \(0.909879\pi\) | |||||||
\(594\) | 12.9083 | 0.529635 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.21110 | 0.377301 | ||||||||
\(597\) | 31.9361i | 1.30706i | ||||||||
\(598\) | 42.5694i | 1.74079i | ||||||||
\(599\) | 14.0917 | 0.575770 | 0.287885 | − | 0.957665i | \(-0.407048\pi\) | ||||
0.287885 | + | 0.957665i | \(0.407048\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.90833 | 0.363378 | 0.181689 | − | 0.983356i | \(-0.441844\pi\) | ||||
0.181689 | + | 0.983356i | \(0.441844\pi\) | |||||||
\(602\) | − 71.4500i | − 2.91208i | ||||||||
\(603\) | − 5.21110i | − 0.212213i | ||||||||
\(604\) | 68.7527 | 2.79751 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −52.5416 | −2.13436 | ||||||||
\(607\) | − 7.21110i | − 0.292690i | −0.989234 | − | 0.146345i | \(-0.953249\pi\) | ||||
0.989234 | − | 0.146345i | \(-0.0467509\pi\) | |||||||
\(608\) | − 5.30278i | − 0.215056i | ||||||||
\(609\) | −55.5416 | −2.25066 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0000 | −0.606835 | ||||||||
\(612\) | 16.8167i | 0.679773i | ||||||||
\(613\) | 41.1194i | 1.66080i | 0.557169 | + | 0.830399i | \(0.311888\pi\) | ||||
−0.557169 | + | 0.830399i | \(0.688112\pi\) | |||||||
\(614\) | 14.0278 | 0.566114 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.9083 | −0.520091 | ||||||||
\(617\) | 10.6056i | 0.426963i | 0.976947 | + | 0.213482i | \(0.0684804\pi\) | ||||
−0.976947 | + | 0.213482i | \(0.931520\pi\) | |||||||
\(618\) | − 23.7250i | − 0.954359i | ||||||||
\(619\) | −17.4222 | −0.700258 | −0.350129 | − | 0.936702i | \(-0.613862\pi\) | ||||
−0.350129 | + | 0.936702i | \(0.613862\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.7250 | −0.831665 | ||||||||
\(622\) | − 38.7250i | − 1.55273i | ||||||||
\(623\) | − 22.8167i | − 0.914130i | ||||||||
\(624\) | 1.97224 | 0.0789529 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 50.2389 | 2.00795 | ||||||||
\(627\) | − 1.30278i | − 0.0520278i | ||||||||
\(628\) | − 15.8167i | − 0.631153i | ||||||||
\(629\) | 37.5416 | 1.49688 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.9361 | −1.58983 | −0.794915 | − | 0.606721i | \(-0.792485\pi\) | ||||
−0.794915 | + | 0.606721i | \(0.792485\pi\) | |||||||
\(632\) | − 0.275019i | − 0.0109397i | ||||||||
\(633\) | 32.8806i | 1.30689i | ||||||||
\(634\) | −22.8167 | −0.906165 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.90833 | −0.392891 | ||||||||
\(637\) | 57.5694i | 2.28098i | ||||||||
\(638\) | − 22.8167i | − 0.903320i | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.2111 | 1.66724 | 0.833619 | − | 0.552340i | \(-0.186265\pi\) | ||||
0.833619 | + | 0.552340i | \(0.186265\pi\) | |||||||
\(642\) | 9.00000i | 0.355202i | ||||||||
\(643\) | 22.0000i | 0.867595i | 0.901010 | + | 0.433798i | \(0.142827\pi\) | ||||
−0.901010 | + | 0.433798i | \(0.857173\pi\) | |||||||
\(644\) | 52.5416 | 2.07043 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.00000 | 0.354100 | ||||||||
\(647\) | 17.2389i | 0.677729i | 0.940835 | + | 0.338865i | \(0.110043\pi\) | ||||
−0.940835 | + | 0.338865i | \(0.889957\pi\) | |||||||
\(648\) | 10.1833i | 0.400040i | ||||||||
\(649\) | 0.211103 | 0.00828650 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.6056 | 0.925174 | ||||||||
\(652\) | 18.8167i | 0.736917i | ||||||||
\(653\) | 19.1194i | 0.748201i | 0.927388 | + | 0.374101i | \(0.122049\pi\) | ||||
−0.927388 | + | 0.374101i | \(0.877951\pi\) | |||||||
\(654\) | −19.5416 | −0.764138 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.486122 | 0.0189799 | ||||||||
\(657\) | − 3.78890i | − 0.147819i | ||||||||
\(658\) | 29.7250i | 1.15880i | ||||||||
\(659\) | 20.0917 | 0.782660 | 0.391330 | − | 0.920250i | \(-0.372015\pi\) | ||||
0.391330 | + | 0.920250i | \(0.372015\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8167 | 0.498510 | 0.249255 | − | 0.968438i | \(-0.419814\pi\) | ||||
0.249255 | + | 0.968438i | \(0.419814\pi\) | |||||||
\(662\) | − 33.1472i | − 1.28830i | ||||||||
\(663\) | − 25.4584i | − 0.988721i | ||||||||
\(664\) | −43.5416 | −1.68974 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −28.8167 | −1.11662 | ||||||||
\(667\) | 36.6333i | 1.41845i | ||||||||
\(668\) | 50.9361i | 1.97078i | ||||||||
\(669\) | 26.8806 | 1.03926 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.90833 | −0.112275 | ||||||||
\(672\) | 29.7250i | 1.14667i | ||||||||
\(673\) | 6.02776i | 0.232353i | 0.993229 | + | 0.116176i | \(0.0370638\pi\) | ||||
−0.993229 | + | 0.116176i | \(0.962936\pi\) | |||||||
\(674\) | −61.8167 | −2.38109 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 39.6333 | 1.52436 | ||||||||
\(677\) | − 26.2389i | − 1.00844i | −0.863575 | − | 0.504221i | \(-0.831780\pi\) | ||||
0.863575 | − | 0.504221i | \(-0.168220\pi\) | |||||||
\(678\) | 32.4500i | 1.24623i | ||||||||
\(679\) | −50.3305 | −1.93151 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.90833 | −0.264728 | ||||||||
\(682\) | 9.69722i | 0.371326i | ||||||||
\(683\) | 9.84441i | 0.376686i | 0.982103 | + | 0.188343i | \(0.0603116\pi\) | ||||
−0.982103 | + | 0.188343i | \(0.939688\pi\) | |||||||
\(684\) | −4.30278 | −0.164521 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 44.7250 | 1.70761 | ||||||||
\(687\) | − 17.8806i | − 0.682186i | ||||||||
\(688\) | 2.18335i | 0.0832393i | ||||||||
\(689\) | −11.5139 | −0.438644 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.5416 | −1.00969 | −0.504846 | − | 0.863210i | \(-0.668451\pi\) | ||||
−0.504846 | + | 0.863210i | \(0.668451\pi\) | |||||||
\(692\) | 55.5416i | 2.11138i | ||||||||
\(693\) | − 5.60555i | − 0.212937i | ||||||||
\(694\) | −12.6972 | −0.481980 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 38.7250 | 1.46787 | ||||||||
\(697\) | − 6.27502i | − 0.237683i | ||||||||
\(698\) | 61.7527i | 2.33738i | ||||||||
\(699\) | 6.63331 | 0.250895 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.7889 | −1.01180 | −0.505901 | − | 0.862591i | \(-0.668840\pi\) | ||||
−0.505901 | + | 0.862591i | \(0.668840\pi\) | |||||||
\(702\) | 64.5416i | 2.43597i | ||||||||
\(703\) | 9.60555i | 0.362280i | ||||||||
\(704\) | −12.8167 | −0.483046 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −56.7250 | −2.13487 | ||||||||
\(707\) | 75.3583i | 2.83414i | ||||||||
\(708\) | 0.908327i | 0.0341370i | ||||||||
\(709\) | −11.6333 | −0.436898 | −0.218449 | − | 0.975848i | \(-0.570100\pi\) | ||||
−0.218449 | + | 0.975848i | \(0.570100\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.119429 | 0.00447895 | ||||||||
\(712\) | 15.9083i | 0.596190i | ||||||||
\(713\) | − 15.5694i | − 0.583078i | ||||||||
\(714\) | −50.4500 | −1.88804 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.2111 | −0.680581 | ||||||||
\(717\) | 5.36669i | 0.200423i | ||||||||
\(718\) | − 35.0278i | − 1.30722i | ||||||||
\(719\) | −28.8167 | −1.07468 | −0.537340 | − | 0.843366i | \(-0.680571\pi\) | ||||
−0.537340 | + | 0.843366i | \(0.680571\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.0278 | −1.26726 | ||||||||
\(722\) | − 41.4500i | − 1.54261i | ||||||||
\(723\) | − 32.4861i | − 1.20817i | ||||||||
\(724\) | 30.0278 | 1.11597 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.00000 | −0.111340 | ||||||||
\(727\) | 0.330532i | 0.0122588i | 0.999981 | + | 0.00612938i | \(0.00195105\pi\) | ||||
−0.999981 | + | 0.00612938i | \(0.998049\pi\) | |||||||
\(728\) | − 64.5416i | − 2.39207i | ||||||||
\(729\) | −26.3305 | −0.975205 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.1833 | 1.04240 | ||||||||
\(732\) | − 12.5139i | − 0.462526i | ||||||||
\(733\) | − 12.3944i | − 0.457799i | −0.973450 | − | 0.228900i | \(-0.926487\pi\) | ||||
0.973450 | − | 0.228900i | \(-0.0735128\pi\) | |||||||
\(734\) | 55.9638 | 2.06566 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.6056 | 0.722670 | ||||||||
\(737\) | 4.00000i | 0.147342i | ||||||||
\(738\) | 4.81665i | 0.177303i | ||||||||
\(739\) | −9.88057 | −0.363463 | −0.181731 | − | 0.983348i | \(-0.558170\pi\) | ||||
−0.181731 | + | 0.983348i | \(0.558170\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.51388 | 0.239293 | ||||||||
\(742\) | 22.8167i | 0.837626i | ||||||||
\(743\) | − 44.3028i | − 1.62531i | −0.582744 | − | 0.812656i | \(-0.698021\pi\) | ||||
0.582744 | − | 0.812656i | \(-0.301979\pi\) | |||||||
\(744\) | −16.4584 | −0.603393 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.27502 | −0.119907 | ||||||||
\(747\) | − 18.9083i | − 0.691820i | ||||||||
\(748\) | − 12.9083i | − 0.471975i | ||||||||
\(749\) | 12.9083 | 0.471660 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.66947 | −0.206882 | −0.103441 | − | 0.994636i | \(-0.532985\pi\) | ||||
−0.103441 | + | 0.994636i | \(0.532985\pi\) | |||||||
\(752\) | − 0.908327i | − 0.0331233i | ||||||||
\(753\) | − 5.09167i | − 0.185551i | ||||||||
\(754\) | 114.083 | 4.15467 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 79.6611 | 2.89724 | ||||||||
\(757\) | − 23.0555i | − 0.837967i | −0.907994 | − | 0.418983i | \(-0.862387\pi\) | ||||
0.907994 | − | 0.418983i | \(-0.137613\pi\) | |||||||
\(758\) | − 57.1472i | − 2.07568i | ||||||||
\(759\) | 4.81665 | 0.174833 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.4222 | −1.53780 | −0.768902 | − | 0.639367i | \(-0.779197\pi\) | ||||
−0.768902 | + | 0.639367i | \(0.779197\pi\) | |||||||
\(762\) | 51.3583i | 1.86051i | ||||||||
\(763\) | 28.0278i | 1.01467i | ||||||||
\(764\) | −22.1194 | −0.800253 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −49.8167 | −1.79995 | ||||||||
\(767\) | 1.05551i | 0.0381124i | ||||||||
\(768\) | − 23.3305i | − 0.841868i | ||||||||
\(769\) | 26.8167 | 0.967033 | 0.483517 | − | 0.875335i | \(-0.339359\pi\) | ||||
0.483517 | + | 0.875335i | \(0.339359\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.4500 | 0.844530 | ||||||||
\(772\) | − 4.00000i | − 0.143963i | ||||||||
\(773\) | 22.1194i | 0.795581i | 0.917476 | + | 0.397790i | \(0.130223\pi\) | ||||
−0.917476 | + | 0.397790i | \(0.869777\pi\) | |||||||
\(774\) | −21.6333 | −0.777593 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 35.0917 | 1.25972 | ||||||||
\(777\) | − 53.8444i | − 1.93166i | ||||||||
\(778\) | − 27.6333i | − 0.990702i | ||||||||
\(779\) | 1.60555 | 0.0575248 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.60555 | −0.164800 | ||||||||
\(782\) | 33.2750i | 1.18991i | ||||||||
\(783\) | 55.5416i | 1.98490i | ||||||||
\(784\) | −3.48612 | −0.124504 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.72498 | −0.0971968 | ||||||||
\(787\) | − 4.21110i | − 0.150110i | −0.997179 | − | 0.0750548i | \(-0.976087\pi\) | ||||
0.997179 | − | 0.0750548i | \(-0.0239132\pi\) | |||||||
\(788\) | − 32.0278i | − 1.14094i | ||||||||
\(789\) | −1.54163 | −0.0548836 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 46.5416 | 1.65483 | ||||||||
\(792\) | 3.90833i | 0.138876i | ||||||||
\(793\) | − 14.5416i | − 0.516389i | ||||||||
\(794\) | −58.2666 | −2.06780 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −80.9638 | −2.86969 | ||||||||
\(797\) | − 14.5139i | − 0.514108i | −0.966397 | − | 0.257054i | \(-0.917248\pi\) | ||||
0.966397 | − | 0.257054i | \(-0.0827518\pi\) | |||||||
\(798\) | − 12.9083i | − 0.456950i | ||||||||
\(799\) | −11.7250 | −0.414800 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.90833 | −0.244094 | ||||||||
\(802\) | − 62.6611i | − 2.21264i | ||||||||
\(803\) | 2.90833i | 0.102633i | ||||||||
\(804\) | −17.2111 | −0.606989 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −48.4861 | −1.70785 | ||||||||
\(807\) | 30.9083i | 1.08802i | ||||||||
\(808\) | − 52.5416i | − 1.84841i | ||||||||
\(809\) | 3.63331 | 0.127740 | 0.0638701 | − | 0.997958i | \(-0.479656\pi\) | ||||
0.0638701 | + | 0.997958i | \(0.479656\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −54.8722 | −1.92682 | −0.963411 | − | 0.268028i | \(-0.913628\pi\) | ||||
−0.963411 | + | 0.268028i | \(0.913628\pi\) | |||||||
\(812\) | − 140.808i | − 4.94140i | ||||||||
\(813\) | 18.5139i | 0.649310i | ||||||||
\(814\) | 22.1194 | 0.775286 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.54163 | 0.0539680 | ||||||||
\(817\) | 7.21110i | 0.252285i | ||||||||
\(818\) | − 18.9083i | − 0.661114i | ||||||||
\(819\) | 28.0278 | 0.979369 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.0000 | 0.418803 | 0.209401 | − | 0.977830i | \(-0.432848\pi\) | ||||
0.209401 | + | 0.977830i | \(0.432848\pi\) | |||||||
\(822\) | 6.27502i | 0.218866i | ||||||||
\(823\) | 10.4222i | 0.363295i | 0.983364 | + | 0.181648i | \(0.0581430\pi\) | ||||
−0.983364 | + | 0.181648i | \(0.941857\pi\) | |||||||
\(824\) | 23.7250 | 0.826499 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.09167 | 0.0727786 | ||||||||
\(827\) | − 7.81665i | − 0.271812i | −0.990722 | − | 0.135906i | \(-0.956606\pi\) | ||||
0.990722 | − | 0.135906i | \(-0.0433945\pi\) | |||||||
\(828\) | − 15.9083i | − 0.552853i | ||||||||
\(829\) | 38.7527 | 1.34594 | 0.672969 | − | 0.739671i | \(-0.265019\pi\) | ||||
0.672969 | + | 0.739671i | \(0.265019\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.1472 | −0.976415 | ||||||||
\(832\) | − 64.0833i | − 2.22169i | ||||||||
\(833\) | 45.0000i | 1.55916i | ||||||||
\(834\) | 24.6333 | 0.852982 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.30278 | 0.114229 | ||||||||
\(837\) | − 23.6056i | − 0.815927i | ||||||||
\(838\) | − 31.3305i | − 1.08230i | ||||||||
\(839\) | −16.1194 | −0.556505 | −0.278252 | − | 0.960508i | \(-0.589755\pi\) | ||||
−0.278252 | + | 0.960508i | \(0.589755\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 69.1749 | 2.38534 | ||||||||
\(842\) | 9.90833i | 0.341463i | ||||||||
\(843\) | − 29.7250i | − 1.02378i | ||||||||
\(844\) | −83.3583 | −2.86931 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.00000 | 0.309426 | ||||||||
\(847\) | 4.30278i | 0.147845i | ||||||||
\(848\) | − 0.697224i | − 0.0239428i | ||||||||
\(849\) | 3.51388 | 0.120596 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −35.5139 | −1.21740 | ||||||||
\(852\) | − 19.8167i | − 0.678907i | ||||||||
\(853\) | − 19.7250i | − 0.675370i | −0.941259 | − | 0.337685i | \(-0.890356\pi\) | ||||
0.941259 | − | 0.337685i | \(-0.109644\pi\) | |||||||
\(854\) | −28.8167 | −0.986086 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.00000 | −0.307614 | ||||||||
\(857\) | − 3.00000i | − 0.102478i | −0.998686 | − | 0.0512390i | \(-0.983683\pi\) | ||||
0.998686 | − | 0.0512390i | \(-0.0163170\pi\) | |||||||
\(858\) | − 15.0000i | − 0.512092i | ||||||||
\(859\) | −48.6056 | −1.65840 | −0.829200 | − | 0.558952i | \(-0.811204\pi\) | ||||
−0.829200 | + | 0.558952i | \(0.811204\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.00000 | −0.306719 | ||||||||
\(862\) | 75.9916i | 2.58828i | ||||||||
\(863\) | 19.6056i | 0.667381i | 0.942683 | + | 0.333690i | \(0.108294\pi\) | ||||
−0.942683 | + | 0.333690i | \(0.891706\pi\) | |||||||
\(864\) | 29.7250 | 1.01126 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.5139 | 0.391258 | ||||||||
\(867\) | 2.24726i | 0.0763210i | ||||||||
\(868\) | 59.8444i | 2.03125i | ||||||||
\(869\) | −0.0916731 | −0.00310980 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.0000 | −0.677674 | ||||||||
\(872\) | − 19.5416i | − 0.661763i | ||||||||
\(873\) | 15.2389i | 0.515757i | ||||||||
\(874\) | −8.51388 | −0.287986 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.5139 | −0.422805 | ||||||||
\(877\) | 20.0000i | 0.675352i | 0.941262 | + | 0.337676i | \(0.109641\pi\) | ||||
−0.941262 | + | 0.337676i | \(0.890359\pi\) | |||||||
\(878\) | − 47.6611i | − 1.60848i | ||||||||
\(879\) | 19.8167 | 0.668399 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.5416 | −1.16374 | −0.581869 | − | 0.813283i | \(-0.697678\pi\) | ||||
−0.581869 | + | 0.813283i | \(0.697678\pi\) | |||||||
\(882\) | − 34.5416i | − 1.16308i | ||||||||
\(883\) | 12.4500i | 0.418975i | 0.977811 | + | 0.209487i | \(0.0671795\pi\) | ||||
−0.977811 | + | 0.209487i | \(0.932821\pi\) | |||||||
\(884\) | 64.5416 | 2.17077 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.21110 | −0.107879 | ||||||||
\(887\) | 47.2389i | 1.58613i | 0.609140 | + | 0.793063i | \(0.291515\pi\) | ||||
−0.609140 | + | 0.793063i | \(0.708485\pi\) | |||||||
\(888\) | 37.5416i | 1.25981i | ||||||||
\(889\) | 73.6611 | 2.47051 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.39445 | 0.113718 | ||||||||
\(892\) | 68.1472i | 2.28174i | ||||||||
\(893\) | − 3.00000i | − 0.100391i | ||||||||
\(894\) | 8.36669 | 0.279824 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −81.3583 | −2.71799 | ||||||||
\(897\) | 24.0833i | 0.804117i | ||||||||
\(898\) | − 95.5971i | − 3.19012i | ||||||||
\(899\) | −41.7250 | −1.39161 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.00000 | −0.299833 | ||||||||
\(902\) | − 3.69722i | − 0.123104i | ||||||||
\(903\) | − 40.4222i | − 1.34517i | ||||||||
\(904\) | −32.4500 | −1.07927 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 62.4500 | 2.07476 | ||||||||
\(907\) | − 4.00000i | − 0.132818i | −0.997792 | − | 0.0664089i | \(-0.978846\pi\) | ||||
0.997792 | − | 0.0664089i | \(-0.0211542\pi\) | |||||||
\(908\) | − 17.5139i | − 0.581218i | ||||||||
\(909\) | 22.8167 | 0.756781 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.2111 | −1.29912 | −0.649561 | − | 0.760310i | \(-0.725047\pi\) | ||||
−0.649561 | + | 0.760310i | \(0.725047\pi\) | |||||||
\(912\) | 0.394449i | 0.0130615i | ||||||||
\(913\) | 14.5139i | 0.480339i | ||||||||
\(914\) | 55.9638 | 1.85112 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 45.3305 | 1.49776 | ||||||||
\(917\) | 3.90833i | 0.129064i | ||||||||
\(918\) | 50.4500i | 1.66510i | ||||||||
\(919\) | −41.2111 | −1.35943 | −0.679714 | − | 0.733477i | \(-0.737896\pi\) | ||||
−0.679714 | + | 0.733477i | \(0.737896\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.93608 | 0.261503 | ||||||||
\(922\) | 40.9638i | 1.34907i | ||||||||
\(923\) | − 23.0278i | − 0.757968i | ||||||||
\(924\) | −18.5139 | −0.609062 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 60.3583 | 1.98350 | ||||||||
\(927\) | 10.3028i | 0.338388i | ||||||||
\(928\) | − 52.5416i | − 1.72476i | ||||||||
\(929\) | −46.3944 | −1.52215 | −0.761076 | − | 0.648662i | \(-0.775329\pi\) | ||||
−0.761076 | + | 0.648662i | \(0.775329\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.5139 | −0.377352 | ||||||||
\(932\) | 16.8167i | 0.550848i | ||||||||
\(933\) | − 21.9083i | − 0.717246i | ||||||||
\(934\) | −56.7250 | −1.85610 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −19.5416 | −0.638738 | ||||||||
\(937\) | 5.21110i | 0.170239i | 0.996371 | + | 0.0851196i | \(0.0271273\pi\) | ||||
−0.996371 | + | 0.0851196i | \(0.972873\pi\) | |||||||
\(938\) | 39.6333i | 1.29407i | ||||||||
\(939\) | 28.4222 | 0.927524 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.3944 | 1.70801 | 0.854005 | − | 0.520265i | \(-0.174167\pi\) | ||||
0.854005 | + | 0.520265i | \(0.174167\pi\) | |||||||
\(942\) | − 14.3667i | − 0.468092i | ||||||||
\(943\) | 5.93608i | 0.193305i | ||||||||
\(944\) | −0.0639167 | −0.00208031 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.6056 | 0.539893 | ||||||||
\(947\) | − 36.6333i | − 1.19042i | −0.803569 | − | 0.595211i | \(-0.797068\pi\) | ||||
0.803569 | − | 0.595211i | \(-0.202932\pi\) | |||||||
\(948\) | − 0.394449i | − 0.0128111i | ||||||||
\(949\) | −14.5416 | −0.472041 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.9083 | −0.418581 | ||||||||
\(952\) | − 50.4500i | − 1.63509i | ||||||||
\(953\) | 49.2666i | 1.59590i | 0.602722 | + | 0.797951i | \(0.294083\pi\) | ||||
−0.602722 | + | 0.797951i | \(0.705917\pi\) | |||||||
\(954\) | 6.90833 | 0.223665 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.6056 | −0.440035 | ||||||||
\(957\) | − 12.9083i | − 0.417267i | ||||||||
\(958\) | 30.3583i | 0.980832i | ||||||||
\(959\) | 9.00000 | 0.290625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.2666 | −0.427955 | ||||||||
\(962\) | 110.597i | 3.56580i | ||||||||
\(963\) | − 3.90833i | − 0.125944i | ||||||||
\(964\) | 82.3583 | 2.65258 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 47.7250 | 1.53553 | ||||||||
\(967\) | 4.09167i | 0.131579i | 0.997834 | + | 0.0657897i | \(0.0209566\pi\) | ||||
−0.997834 | + | 0.0657897i | \(0.979043\pi\) | |||||||
\(968\) | − 3.00000i | − 0.0964237i | ||||||||
\(969\) | 5.09167 | 0.163568 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.3583 | −0.974244 | −0.487122 | − | 0.873334i | \(-0.661953\pi\) | ||||
−0.487122 | + | 0.873334i | \(0.661953\pi\) | |||||||
\(972\) | − 40.9361i | − 1.31303i | ||||||||
\(973\) | − 35.3305i | − 1.13264i | ||||||||
\(974\) | 23.5139 | 0.753433 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.880571 | 0.0281864 | ||||||||
\(977\) | − 15.9722i | − 0.510997i | −0.966809 | − | 0.255499i | \(-0.917760\pi\) | ||||
0.966809 | − | 0.255499i | \(-0.0822396\pi\) | |||||||
\(978\) | 17.0917i | 0.546531i | ||||||||
\(979\) | 5.30278 | 0.169477 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.48612 | 0.270941 | ||||||||
\(982\) | − 55.7527i | − 1.77914i | ||||||||
\(983\) | 48.8444i | 1.55789i | 0.627089 | + | 0.778947i | \(0.284246\pi\) | ||||
−0.627089 | + | 0.778947i | \(0.715754\pi\) | |||||||
\(984\) | 6.27502 | 0.200040 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 89.1749 | 2.83991 | ||||||||
\(987\) | 16.8167i | 0.535280i | ||||||||
\(988\) | 16.5139i | 0.525376i | ||||||||
\(989\) | −26.6611 | −0.847773 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.09167 | −0.193508 | −0.0967542 | − | 0.995308i | \(-0.530846\pi\) | ||||
−0.0967542 | + | 0.995308i | \(0.530846\pi\) | |||||||
\(992\) | 22.3305i | 0.708995i | ||||||||
\(993\) | − 18.7527i | − 0.595100i | ||||||||
\(994\) | −45.6333 | −1.44740 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −62.4500 | −1.97880 | ||||||||
\(997\) | 14.2750i | 0.452094i | 0.974116 | + | 0.226047i | \(0.0725804\pi\) | ||||
−0.974116 | + | 0.226047i | \(0.927420\pi\) | |||||||
\(998\) | 49.5416i | 1.56821i | ||||||||
\(999\) | −53.8444 | −1.70356 |
(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 | 275.2.b.c.199.4 | 4 | ||
3.2 | odd | 2 | 2475.2.c.k.199.1 | 4 | |||
4.3 | odd | 2 | 4400.2.b.y.4049.2 | 4 | |||
5.2 | odd | 4 | 275.2.a.e.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 275.2.a.f.1.2 | yes | 2 | ||
5.4 | even | 2 | inner | 275.2.b.c.199.1 | 4 | ||
15.2 | even | 4 | 2475.2.a.t.1.2 | 2 | |||
15.8 | even | 4 | 2475.2.a.o.1.1 | 2 | |||
15.14 | odd | 2 | 2475.2.c.k.199.4 | 4 | |||
20.3 | even | 4 | 4400.2.a.bh.1.2 | 2 | |||
20.7 | even | 4 | 4400.2.a.bs.1.1 | 2 | |||
20.19 | odd | 2 | 4400.2.b.y.4049.3 | 4 | |||
55.32 | even | 4 | 3025.2.a.n.1.2 | 2 | |||
55.43 | even | 4 | 3025.2.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
275.2.a.e.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
275.2.a.f.1.2 | yes | 2 | 5.3 | odd | 4 | ||
275.2.b.c.199.1 | 4 | 5.4 | even | 2 | inner | ||
275.2.b.c.199.4 | 4 | 1.1 | even | 1 | trivial | ||
2475.2.a.o.1.1 | 2 | 15.8 | even | 4 | |||
2475.2.a.t.1.2 | 2 | 15.2 | even | 4 | |||
2475.2.c.k.199.1 | 4 | 3.2 | odd | 2 | |||
2475.2.c.k.199.4 | 4 | 15.14 | odd | 2 | |||
3025.2.a.h.1.1 | 2 | 55.43 | even | 4 | |||
3025.2.a.n.1.2 | 2 | 55.32 | even | 4 | |||
4400.2.a.bh.1.2 | 2 | 20.3 | even | 4 | |||
4400.2.a.bs.1.1 | 2 | 20.7 | even | 4 | |||
4400.2.b.y.4049.2 | 4 | 4.3 | odd | 2 | |||
4400.2.b.y.4049.3 | 4 | 20.19 | odd | 2 |