Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,2,Mod(59,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.59");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.h (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: | \(0.479102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 59.1 | ||
Root | \(1.58114 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.59 |
Dual form | 60.2.h.a.59.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 1.00000i | ||||||
\(3\) | −1.58114 | − | 0.707107i | −0.912871 | − | 0.408248i | ||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | − | 2.23607i | − | 1.00000i | ||||||
\(6\) | −1.00000 | + | 2.23607i | −0.408248 | + | 0.912871i | ||||
\(7\) | 3.16228 | 1.19523 | 0.597614 | − | 0.801784i | \(-0.296115\pi\) | ||||
0.597614 | + | 0.801784i | \(0.296115\pi\) | |||||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | 2.00000 | + | 2.23607i | 0.666667 | + | 0.745356i | ||||
\(10\) | −3.16228 | −1.00000 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 3.16228 | + | 1.41421i | 0.912871 | + | 0.408248i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | − | 4.47214i | − | 1.19523i | ||||||
\(15\) | −1.58114 | + | 3.53553i | −0.408248 | + | 0.912871i | ||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 3.16228 | − | 2.82843i | 0.745356 | − | 0.666667i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 4.47214i | 1.00000i | ||||||||
\(21\) | −5.00000 | − | 2.23607i | −1.09109 | − | 0.487950i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.41421i | 0.294884i | 0.989071 | + | 0.147442i | \(0.0471040\pi\) | ||||
−0.989071 | + | 0.147442i | \(0.952896\pi\) | |||||||
\(24\) | 2.00000 | − | 4.47214i | 0.408248 | − | 0.912871i | ||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.58114 | − | 4.94975i | −0.304290 | − | 0.952579i | ||||
\(28\) | −6.32456 | −1.19523 | ||||||||
\(29\) | 8.94427i | 1.66091i | 0.557086 | + | 0.830455i | \(0.311919\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 5.00000 | + | 2.23607i | 0.912871 | + | 0.408248i | ||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | − | 5.65685i | − | 1.00000i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 7.07107i | − | 1.19523i | ||||||
\(36\) | −4.00000 | − | 4.47214i | −0.666667 | − | 0.745356i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.32456 | 1.00000 | ||||||||
\(41\) | − | 4.47214i | − | 0.698430i | −0.937043 | − | 0.349215i | \(-0.886448\pi\) | ||
0.937043 | − | 0.349215i | \(-0.113552\pi\) | |||||||
\(42\) | −3.16228 | + | 7.07107i | −0.487950 | + | 1.09109i | ||||
\(43\) | 3.16228 | 0.482243 | 0.241121 | − | 0.970495i | \(-0.422485\pi\) | ||||
0.241121 | + | 0.970495i | \(0.422485\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.00000 | − | 4.47214i | 0.745356 | − | 0.666667i | ||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | 9.89949i | 1.44399i | 0.691898 | + | 0.721995i | \(0.256775\pi\) | ||||
−0.691898 | + | 0.721995i | \(0.743225\pi\) | |||||||
\(48\) | −6.32456 | − | 2.82843i | −0.912871 | − | 0.408248i | ||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 7.07107i | 1.00000i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −7.00000 | + | 2.23607i | −0.952579 | + | 0.304290i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.94427i | 1.19523i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.6491 | 1.66091 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 3.16228 | − | 7.07107i | 0.408248 | − | 0.912871i | ||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.32456 | + | 7.07107i | 0.796819 | + | 0.890871i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.8114 | −1.93167 | −0.965834 | − | 0.259161i | \(-0.916554\pi\) | ||||
−0.965834 | + | 0.259161i | \(0.916554\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | − | 2.23607i | 0.120386 | − | 0.269191i | ||||
\(70\) | −10.0000 | −1.19523 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −6.32456 | + | 5.65685i | −0.745356 | + | 0.666667i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.90569 | + | 3.53553i | 0.912871 | + | 0.408248i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | − | 8.94427i | − | 1.00000i | ||||||
\(81\) | −1.00000 | + | 8.94427i | −0.111111 | + | 0.993808i | ||||
\(82\) | −6.32456 | −0.698430 | ||||||||
\(83\) | − | 15.5563i | − | 1.70753i | −0.520658 | − | 0.853766i | \(-0.674313\pi\) | ||
0.520658 | − | 0.853766i | \(-0.325687\pi\) | |||||||
\(84\) | 10.0000 | + | 4.47214i | 1.09109 | + | 0.487950i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 4.47214i | − | 0.482243i | ||||||
\(87\) | 6.32456 | − | 14.1421i | 0.678064 | − | 1.51620i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 17.8885i | − | 1.89618i | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||
0.317999 | − | 0.948091i | \(-0.396989\pi\) | |||||||
\(90\) | −6.32456 | − | 7.07107i | −0.666667 | − | 0.745356i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 2.82843i | − | 0.294884i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.0000 | 1.44399 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.00000 | + | 8.94427i | −0.408248 | + | 0.912871i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | − | 4.24264i | − | 0.428571i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.0000 | 1.00000 | ||||||||
\(101\) | 8.94427i | 0.889988i | 0.895533 | + | 0.444994i | \(0.146794\pi\) | ||||
−0.895533 | + | 0.444994i | \(0.853206\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.8114 | −1.55794 | −0.778971 | − | 0.627060i | \(-0.784258\pi\) | ||||
−0.778971 | + | 0.627060i | \(0.784258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.00000 | + | 11.1803i | −0.487950 | + | 1.09109i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.3848i | 1.77732i | 0.458563 | + | 0.888662i | \(0.348364\pi\) | ||||
−0.458563 | + | 0.888662i | \(0.651636\pi\) | |||||||
\(108\) | 3.16228 | + | 9.89949i | 0.304290 | + | 0.952579i | ||||
\(109\) | −16.0000 | −1.53252 | −0.766261 | − | 0.642529i | \(-0.777885\pi\) | ||||
−0.766261 | + | 0.642529i | \(0.777885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.6491 | 1.19523 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.16228 | 0.294884 | ||||||||
\(116\) | − | 17.8885i | − | 1.66091i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −10.0000 | − | 4.47214i | −0.912871 | − | 0.408248i | ||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | − | 11.3137i | − | 1.02430i | ||||||
\(123\) | −3.16228 | + | 7.07107i | −0.285133 | + | 0.637577i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 1.00000i | ||||||||
\(126\) | 10.0000 | − | 8.94427i | 0.890871 | − | 0.796819i | ||||
\(127\) | 22.1359 | 1.96425 | 0.982124 | − | 0.188237i | \(-0.0602772\pi\) | ||||
0.982124 | + | 0.188237i | \(0.0602772\pi\) | |||||||
\(128\) | 11.3137i | 1.00000i | ||||||||
\(129\) | −5.00000 | − | 2.23607i | −0.440225 | − | 0.196875i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 22.3607i | 1.93167i | ||||||||
\(135\) | −11.0680 | + | 3.53553i | −0.952579 | + | 0.304290i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | −3.16228 | − | 1.41421i | −0.269191 | − | 0.120386i | ||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 14.1421i | 1.19523i | ||||||||
\(141\) | 7.00000 | − | 15.6525i | 0.589506 | − | 1.31818i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 8.00000 | + | 8.94427i | 0.666667 | + | 0.745356i | ||||
\(145\) | 20.0000 | 1.66091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.74342 | − | 2.12132i | −0.391230 | − | 0.174964i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 4.47214i | − | 0.366372i | −0.983078 | − | 0.183186i | \(-0.941359\pi\) | ||
0.983078 | − | 0.183186i | \(-0.0586410\pi\) | |||||||
\(150\) | 5.00000 | − | 11.1803i | 0.408248 | − | 0.912871i | ||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.6491 | −1.00000 | ||||||||
\(161\) | 4.47214i | 0.352454i | ||||||||
\(162\) | 12.6491 | + | 1.41421i | 0.993808 | + | 0.111111i | ||||
\(163\) | 22.1359 | 1.73382 | 0.866910 | − | 0.498464i | \(-0.166102\pi\) | ||||
0.866910 | + | 0.498464i | \(0.166102\pi\) | |||||||
\(164\) | 8.94427i | 0.698430i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22.0000 | −1.70753 | ||||||||
\(167\) | − | 24.0416i | − | 1.86040i | −0.367057 | − | 0.930199i | \(-0.619634\pi\) | ||
0.367057 | − | 0.930199i | \(-0.380366\pi\) | |||||||
\(168\) | 6.32456 | − | 14.1421i | 0.487950 | − | 1.09109i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.32456 | −0.482243 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | −20.0000 | − | 8.94427i | −1.51620 | − | 0.678064i | ||||
\(175\) | −15.8114 | −1.19523 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −25.2982 | −1.89618 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | −10.0000 | + | 8.94427i | −0.745356 | + | 0.666667i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.6491 | − | 5.65685i | −0.935049 | − | 0.418167i | ||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 19.7990i | − | 1.44399i | ||||||
\(189\) | −5.00000 | − | 15.6525i | −0.363696 | − | 1.13855i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 12.6491 | + | 5.65685i | 0.912871 | + | 0.408248i | ||||
\(193\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.00000 | −0.428571 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | − | 14.1421i | − | 1.00000i | ||||||
\(201\) | 25.0000 | + | 11.1803i | 1.76336 | + | 0.788600i | ||||
\(202\) | 12.6491 | 0.889988 | ||||||||
\(203\) | 28.2843i | 1.98517i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.0000 | −0.698430 | ||||||||
\(206\) | 22.3607i | 1.55794i | ||||||||
\(207\) | −3.16228 | + | 2.82843i | −0.219793 | + | 0.196589i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 15.8114 | + | 7.07107i | 1.09109 | + | 0.487950i | ||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 26.0000 | 1.77732 | ||||||||
\(215\) | − | 7.07107i | − | 0.482243i | ||||||
\(216\) | 14.0000 | − | 4.47214i | 0.952579 | − | 0.304290i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 22.6274i | 1.53252i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.16228 | 0.211762 | 0.105881 | − | 0.994379i | \(-0.466234\pi\) | ||||
0.105881 | + | 0.994379i | \(0.466234\pi\) | |||||||
\(224\) | − | 17.8885i | − | 1.19523i | ||||||
\(225\) | −10.0000 | − | 11.1803i | −0.666667 | − | 0.745356i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.89949i | 0.657053i | 0.944495 | + | 0.328526i | \(0.106552\pi\) | ||||
−0.944495 | + | 0.328526i | \(0.893448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | − | 4.47214i | − | 0.294884i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −25.2982 | −1.66091 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.1359 | 1.44399 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | −6.32456 | + | 14.1421i | −0.408248 | + | 0.912871i | ||||
\(241\) | −28.0000 | −1.80364 | −0.901819 | − | 0.432113i | \(-0.857768\pi\) | ||||
−0.901819 | + | 0.432113i | \(0.857768\pi\) | |||||||
\(242\) | 15.5563i | 1.00000i | ||||||||
\(243\) | 7.90569 | − | 13.4350i | 0.507151 | − | 0.861858i | ||||
\(244\) | −16.0000 | −1.02430 | ||||||||
\(245\) | − | 6.70820i | − | 0.428571i | ||||||
\(246\) | 10.0000 | + | 4.47214i | 0.637577 | + | 0.285133i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.0000 | + | 24.5967i | −0.697097 | + | 1.55876i | ||||
\(250\) | 15.8114 | 1.00000 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −12.6491 | − | 14.1421i | −0.796819 | − | 0.890871i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 31.3050i | − | 1.96425i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | −3.16228 | + | 7.07107i | −0.196875 | + | 0.440225i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.0000 | + | 17.8885i | −1.23797 | + | 1.10727i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 15.5563i | − | 0.959246i | −0.877475 | − | 0.479623i | \(-0.840774\pi\) | ||
0.877475 | − | 0.479623i | \(-0.159226\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.6491 | + | 28.2843i | −0.774113 | + | 1.73097i | ||||
\(268\) | 31.6228 | 1.93167 | ||||||||
\(269\) | 22.3607i | 1.36335i | 0.731653 | + | 0.681677i | \(0.238749\pi\) | ||||
−0.731653 | + | 0.681677i | \(0.761251\pi\) | |||||||
\(270\) | 5.00000 | + | 15.6525i | 0.304290 | + | 0.952579i | ||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.00000 | + | 4.47214i | −0.120386 | + | 0.269191i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 20.0000 | 1.19523 | ||||||||
\(281\) | − | 31.3050i | − | 1.86750i | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||
0.357930 | − | 0.933748i | \(-0.383483\pi\) | |||||||
\(282\) | −22.1359 | − | 9.89949i | −1.31818 | − | 0.589506i | ||||
\(283\) | −15.8114 | −0.939889 | −0.469945 | − | 0.882696i | \(-0.655726\pi\) | ||||
−0.469945 | + | 0.882696i | \(0.655726\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 14.1421i | − | 0.834784i | ||||||
\(288\) | 12.6491 | − | 11.3137i | 0.745356 | − | 0.666667i | ||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | − | 28.2843i | − | 1.66091i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | −3.00000 | + | 6.70820i | −0.174964 | + | 0.391230i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.32456 | −0.366372 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −15.8114 | − | 7.07107i | −0.912871 | − | 0.408248i | ||||
\(301\) | 10.0000 | 0.576390 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.32456 | − | 14.1421i | 0.363336 | − | 0.812444i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 17.8885i | − | 1.02430i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.7851 | −1.98529 | −0.992644 | − | 0.121070i | \(-0.961367\pi\) | ||||
−0.992644 | + | 0.121070i | \(0.961367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.0000 | + | 11.1803i | 1.42220 | + | 0.636027i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 15.8114 | − | 14.1421i | 0.890871 | − | 0.796819i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 17.8885i | 1.00000i | ||||||||
\(321\) | 13.0000 | − | 29.0689i | 0.725589 | − | 1.62247i | ||||
\(322\) | 6.32456 | 0.352454 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.00000 | − | 17.8885i | 0.111111 | − | 0.993808i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 31.3050i | − | 1.73382i | ||||||
\(327\) | 25.2982 | + | 11.3137i | 1.39899 | + | 0.625650i | ||||
\(328\) | 12.6491 | 0.698430 | ||||||||
\(329\) | 31.3050i | 1.72590i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 31.1127i | 1.70753i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −34.0000 | −1.86040 | ||||||||
\(335\) | 35.3553i | 1.93167i | ||||||||
\(336\) | −20.0000 | − | 8.94427i | −1.09109 | − | 0.487950i | ||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | − | 18.3848i | − | 1.00000i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.6491 | −0.682988 | ||||||||
\(344\) | 8.94427i | 0.482243i | ||||||||
\(345\) | −5.00000 | − | 2.23607i | −0.269191 | − | 0.120386i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 24.0416i | − | 1.29062i | −0.763920 | − | 0.645311i | \(-0.776728\pi\) | ||
0.763920 | − | 0.645311i | \(-0.223272\pi\) | |||||||
\(348\) | −12.6491 | + | 28.2843i | −0.678064 | + | 1.51620i | ||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | 22.3607i | 1.19523i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 35.7771i | 1.89618i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 12.6491 | + | 14.1421i | 0.666667 | + | 0.745356i | ||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | − | 2.82843i | − | 0.148659i | ||||||
\(363\) | 17.3925 | + | 7.77817i | 0.912871 | + | 0.408248i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.00000 | + | 17.8885i | −0.418167 | + | 0.935049i | ||||
\(367\) | 3.16228 | 0.165070 | 0.0825348 | − | 0.996588i | \(-0.473698\pi\) | ||||
0.0825348 | + | 0.996588i | \(0.473698\pi\) | |||||||
\(368\) | 5.65685i | 0.294884i | ||||||||
\(369\) | 10.0000 | − | 8.94427i | 0.520579 | − | 0.465620i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.90569 | − | 17.6777i | 0.408248 | − | 0.912871i | ||||
\(376\) | −28.0000 | −1.44399 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −22.1359 | + | 7.07107i | −1.13855 | + | 0.363696i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.0000 | − | 15.6525i | −1.79310 | − | 0.801901i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.8701i | 1.37300i | 0.727132 | + | 0.686498i | \(0.240853\pi\) | ||||
−0.727132 | + | 0.686498i | \(0.759147\pi\) | |||||||
\(384\) | 8.00000 | − | 17.8885i | 0.408248 | − | 0.912871i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.32456 | + | 7.07107i | 0.321495 | + | 0.359443i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 31.3050i | − | 1.58722i | −0.608424 | − | 0.793612i | \(-0.708198\pi\) | ||
0.608424 | − | 0.793612i | \(-0.291802\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 8.48528i | 0.428571i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | −1.00000 | ||||||||
\(401\) | 35.7771i | 1.78662i | 0.449439 | + | 0.893311i | \(0.351624\pi\) | ||||
−0.449439 | + | 0.893311i | \(0.648376\pi\) | |||||||
\(402\) | 15.8114 | − | 35.3553i | 0.788600 | − | 1.76336i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 17.8885i | − | 0.889988i | ||||||
\(405\) | 20.0000 | + | 2.23607i | 0.993808 | + | 0.111111i | ||||
\(406\) | 40.0000 | 1.98517 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.00000 | −0.197787 | −0.0988936 | − | 0.995098i | \(-0.531530\pi\) | ||||
−0.0988936 | + | 0.995098i | \(0.531530\pi\) | |||||||
\(410\) | 14.1421i | 0.698430i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 31.6228 | 1.55794 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.00000 | + | 4.47214i | 0.196589 | + | 0.219793i | ||||
\(415\) | −34.7851 | −1.70753 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 10.0000 | − | 22.3607i | 0.487950 | − | 1.09109i | ||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.1359 | + | 19.7990i | −1.07629 | + | 0.962660i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.2982 | 1.22427 | ||||||||
\(428\) | − | 36.7696i | − | 1.77732i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.0000 | −0.482243 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −6.32456 | − | 19.7990i | −0.304290 | − | 0.952579i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −31.6228 | − | 14.1421i | −1.51620 | − | 0.678064i | ||||
\(436\) | 32.0000 | 1.53252 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.00000 | + | 6.70820i | 0.285714 | + | 0.319438i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 41.0122i | − | 1.94855i | −0.225367 | − | 0.974274i | \(-0.572358\pi\) | ||
0.225367 | − | 0.974274i | \(-0.427642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −40.0000 | −1.89618 | ||||||||
\(446\) | − | 4.47214i | − | 0.211762i | ||||||
\(447\) | −3.16228 | + | 7.07107i | −0.149571 | + | 0.334450i | ||||
\(448\) | −25.2982 | −1.19523 | ||||||||
\(449\) | 22.3607i | 1.05527i | 0.849473 | + | 0.527633i | \(0.176920\pi\) | ||||
−0.849473 | + | 0.527633i | \(0.823080\pi\) | |||||||
\(450\) | −15.8114 | + | 14.1421i | −0.745356 | + | 0.666667i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.0000 | 0.657053 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | − | 19.7990i | − | 0.925146i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.32456 | −0.294884 | ||||||||
\(461\) | 8.94427i | 0.416576i | 0.978068 | + | 0.208288i | \(0.0667892\pi\) | ||||
−0.978068 | + | 0.208288i | \(0.933211\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 41.1096 | 1.91053 | 0.955263 | − | 0.295758i | \(-0.0955723\pi\) | ||||
0.955263 | + | 0.295758i | \(0.0955723\pi\) | |||||||
\(464\) | 35.7771i | 1.66091i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 32.5269i | − | 1.50517i | −0.658497 | − | 0.752583i | \(-0.728808\pi\) | ||
0.658497 | − | 0.752583i | \(-0.271192\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −50.0000 | −2.30879 | ||||||||
\(470\) | − | 31.3050i | − | 1.44399i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 20.0000 | + | 8.94427i | 0.912871 | + | 0.408248i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 39.5980i | 1.80364i | ||||||||
\(483\) | 3.16228 | − | 7.07107i | 0.143889 | − | 0.321745i | ||||
\(484\) | 22.0000 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.0000 | − | 11.1803i | −0.861858 | − | 0.507151i | ||||
\(487\) | 22.1359 | 1.00308 | 0.501538 | − | 0.865136i | \(-0.332768\pi\) | ||||
0.501538 | + | 0.865136i | \(0.332768\pi\) | |||||||
\(488\) | 22.6274i | 1.02430i | ||||||||
\(489\) | −35.0000 | − | 15.6525i | −1.58275 | − | 0.707829i | ||||
\(490\) | −9.48683 | −0.428571 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 6.32456 | − | 14.1421i | 0.285133 | − | 0.637577i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 34.7851 | + | 15.5563i | 1.55876 | + | 0.697097i | ||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | − | 22.3607i | − | 1.00000i | ||||||
\(501\) | −17.0000 | + | 38.0132i | −0.759504 | + | 1.69830i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 43.8406i | 1.95476i | 0.211498 | + | 0.977378i | \(0.432166\pi\) | ||||
−0.211498 | + | 0.977378i | \(0.567834\pi\) | |||||||
\(504\) | −20.0000 | + | 17.8885i | −0.890871 | + | 0.796819i | ||||
\(505\) | 20.0000 | 0.889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.5548 | − | 9.19239i | −0.912871 | − | 0.408248i | ||||
\(508\) | −44.2719 | −1.96425 | ||||||||
\(509\) | − | 44.7214i | − | 1.98224i | −0.132973 | − | 0.991120i | \(-0.542452\pi\) | ||
0.132973 | − | 0.991120i | \(-0.457548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 35.3553i | 1.55794i | ||||||||
\(516\) | 10.0000 | + | 4.47214i | 0.440225 | + | 0.196875i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 17.8885i | − | 0.783711i | −0.920027 | − | 0.391856i | \(-0.871833\pi\) | ||
0.920027 | − | 0.391856i | \(-0.128167\pi\) | |||||||
\(522\) | 25.2982 | + | 28.2843i | 1.10727 | + | 1.23797i | ||||
\(523\) | −34.7851 | −1.52104 | −0.760522 | − | 0.649312i | \(-0.775057\pi\) | ||||
−0.760522 | + | 0.649312i | \(0.775057\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 25.0000 | + | 11.1803i | 1.09109 | + | 0.487950i | ||||
\(526\) | −22.0000 | −0.959246 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.0000 | 0.913043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 40.0000 | + | 17.8885i | 1.73097 | + | 0.774113i | ||||
\(535\) | 41.1096 | 1.77732 | ||||||||
\(536\) | − | 44.7214i | − | 1.93167i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.6228 | 1.36335 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 22.1359 | − | 7.07107i | 0.952579 | − | 0.304290i | ||||
\(541\) | 38.0000 | 1.63375 | 0.816874 | − | 0.576816i | \(-0.195705\pi\) | ||||
0.816874 | + | 0.576816i | \(0.195705\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.16228 | − | 1.41421i | −0.135706 | − | 0.0606897i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 35.7771i | 1.53252i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.16228 | 0.135209 | 0.0676046 | − | 0.997712i | \(-0.478464\pi\) | ||||
0.0676046 | + | 0.997712i | \(0.478464\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.0000 | + | 17.8885i | 0.682863 | + | 0.763464i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 6.32456 | + | 2.82843i | 0.269191 | + | 0.120386i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | − | 28.2843i | − | 1.19523i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −44.2719 | −1.86750 | ||||||||
\(563\) | 1.41421i | 0.0596020i | 0.999556 | + | 0.0298010i | \(0.00948736\pi\) | ||||
−0.999556 | + | 0.0298010i | \(0.990513\pi\) | |||||||
\(564\) | −14.0000 | + | 31.3050i | −0.589506 | + | 1.31818i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.3607i | 0.939889i | ||||||||
\(567\) | −3.16228 | + | 28.2843i | −0.132803 | + | 1.18783i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 31.3050i | − | 1.31237i | −0.754599 | − | 0.656186i | \(-0.772169\pi\) | ||
0.754599 | − | 0.656186i | \(-0.227831\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −20.0000 | −0.834784 | ||||||||
\(575\) | − | 7.07107i | − | 0.294884i | ||||||
\(576\) | −16.0000 | − | 17.8885i | −0.666667 | − | 0.745356i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 24.0416i | 1.00000i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −40.0000 | −1.66091 | ||||||||
\(581\) | − | 49.1935i | − | 2.04089i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.89949i | 0.408596i | 0.978909 | + | 0.204298i | \(0.0654911\pi\) | ||||
−0.978909 | + | 0.204298i | \(0.934509\pi\) | |||||||
\(588\) | 9.48683 | + | 4.24264i | 0.391230 | + | 0.174964i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.94427i | 0.366372i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | −10.0000 | + | 22.3607i | −0.408248 | + | 0.912871i | ||||
\(601\) | −28.0000 | −1.14214 | −0.571072 | − | 0.820900i | \(-0.693472\pi\) | ||||
−0.571072 | + | 0.820900i | \(0.693472\pi\) | |||||||
\(602\) | − | 14.1421i | − | 0.576390i | ||||||
\(603\) | −31.6228 | − | 35.3553i | −1.28778 | − | 1.43978i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.5967i | 1.00000i | ||||||||
\(606\) | −20.0000 | − | 8.94427i | −0.812444 | − | 0.363336i | ||||
\(607\) | −15.8114 | −0.641764 | −0.320882 | − | 0.947119i | \(-0.603979\pi\) | ||||
−0.320882 | + | 0.947119i | \(0.603979\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.0000 | − | 44.7214i | 0.810441 | − | 1.81220i | ||||
\(610\) | −25.2982 | −1.02430 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 49.1935i | 1.98529i | ||||||||
\(615\) | 15.8114 | + | 7.07107i | 0.637577 | + | 0.285133i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 15.8114 | − | 35.3553i | 0.636027 | − | 1.42220i | ||||
\(619\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.00000 | − | 2.23607i | 0.280900 | − | 0.0897303i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 56.5685i | − | 2.26637i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −20.0000 | − | 22.3607i | −0.796819 | − | 0.890871i | ||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 49.4975i | − | 1.96425i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 25.2982 | 1.00000 | ||||||||
\(641\) | 49.1935i | 1.94303i | 0.236986 | + | 0.971513i | \(0.423841\pi\) | ||||
−0.236986 | + | 0.971513i | \(0.576159\pi\) | |||||||
\(642\) | −41.1096 | − | 18.3848i | −1.62247 | − | 0.725589i | ||||
\(643\) | 41.1096 | 1.62120 | 0.810602 | − | 0.585597i | \(-0.199140\pi\) | ||||
0.810602 | + | 0.585597i | \(0.199140\pi\) | |||||||
\(644\) | − | 8.94427i | − | 0.352454i | ||||||
\(645\) | −5.00000 | + | 11.1803i | −0.196875 | + | 0.440225i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.3848i | 0.722780i | 0.932415 | + | 0.361390i | \(0.117698\pi\) | ||||
−0.932415 | + | 0.361390i | \(0.882302\pi\) | |||||||
\(648\) | −25.2982 | − | 2.82843i | −0.993808 | − | 0.111111i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −44.2719 | −1.73382 | ||||||||
\(653\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(654\) | 16.0000 | − | 35.7771i | 0.625650 | − | 1.39899i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 17.8885i | − | 0.698430i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 44.2719 | 1.72590 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.0000 | 1.24466 | 0.622328 | − | 0.782757i | \(-0.286187\pi\) | ||||
0.622328 | + | 0.782757i | \(0.286187\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 44.0000 | 1.70753 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.6491 | −0.489776 | ||||||||
\(668\) | 48.0833i | 1.86040i | ||||||||
\(669\) | −5.00000 | − | 2.23607i | −0.193311 | − | 0.0864514i | ||||
\(670\) | 50.0000 | 1.93167 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −12.6491 | + | 28.2843i | −0.487950 | + | 1.09109i | ||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.90569 | + | 24.7487i | 0.304290 | + | 0.952579i | ||||
\(676\) | −26.0000 | −1.00000 | ||||||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.00000 | − | 15.6525i | 0.268241 | − | 0.599804i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 43.8406i | 1.67751i | 0.544505 | + | 0.838757i | \(0.316717\pi\) | ||||
−0.544505 | + | 0.838757i | \(0.683283\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.8885i | 0.682988i | ||||||||
\(687\) | −22.1359 | − | 9.89949i | −0.844539 | − | 0.377689i | ||||
\(688\) | 12.6491 | 0.482243 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3.16228 | + | 7.07107i | −0.120386 | + | 0.269191i | ||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −34.0000 | −1.29062 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 40.0000 | + | 17.8885i | 1.51620 | + | 0.678064i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − | 36.7696i | − | 1.39175i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 31.6228 | 1.19523 | ||||||||
\(701\) | 22.3607i | 0.844551i | 0.906467 | + | 0.422276i | \(0.138769\pi\) | ||||
−0.906467 | + | 0.422276i | \(0.861231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −35.0000 | − | 15.6525i | −1.31818 | − | 0.589506i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.2843i | 1.06374i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.0000 | −1.72757 | −0.863783 | − | 0.503864i | \(-0.831911\pi\) | ||||
−0.863783 | + | 0.503864i | \(0.831911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 50.5964 | 1.89618 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 20.0000 | − | 17.8885i | 0.745356 | − | 0.666667i | ||||
\(721\) | −50.0000 | −1.86210 | ||||||||
\(722\) | − | 26.8701i | − | 1.00000i | ||||||
\(723\) | 44.2719 | + | 19.7990i | 1.64649 | + | 0.736332i | ||||
\(724\) | −4.00000 | −0.148659 | ||||||||
\(725\) | − | 44.7214i | − | 1.66091i | ||||||
\(726\) | 11.0000 | − | 24.5967i | 0.408248 | − | 0.912871i | ||||
\(727\) | −53.7587 | −1.99380 | −0.996900 | − | 0.0786754i | \(-0.974931\pi\) | ||||
−0.996900 | + | 0.0786754i | \(0.974931\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.0000 | + | 15.6525i | −0.814815 | + | 0.579721i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 25.2982 | + | 11.3137i | 0.935049 | + | 0.418167i | ||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | − | 4.47214i | − | 0.165070i | ||||||
\(735\) | −4.74342 | + | 10.6066i | −0.174964 | + | 0.391230i | ||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12.6491 | − | 14.1421i | −0.465620 | − | 0.520579i | ||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.8701i | 0.985767i | 0.870095 | + | 0.492883i | \(0.164057\pi\) | ||||
−0.870095 | + | 0.492883i | \(0.835943\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.0000 | −0.366372 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.7851 | − | 31.1127i | 1.27272 | − | 1.13835i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 58.1378i | 2.12431i | ||||||||
\(750\) | −25.0000 | − | 11.1803i | −0.912871 | − | 0.408248i | ||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 39.5980i | 1.44399i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 10.0000 | + | 31.3050i | 0.363696 | + | 1.13855i | ||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.7771i | 1.29692i | 0.761249 | + | 0.648459i | \(0.224586\pi\) | ||||
−0.761249 | + | 0.648459i | \(0.775414\pi\) | |||||||
\(762\) | −22.1359 | + | 49.4975i | −0.801901 | + | 1.79310i | ||||
\(763\) | −50.5964 | −1.83171 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 38.0000 | 1.37300 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −25.2982 | − | 11.3137i | −0.912871 | − | 0.408248i | ||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 10.0000 | − | 8.94427i | 0.359443 | − | 0.321495i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −44.2719 | −1.58722 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 44.2719 | − | 14.1421i | 1.58215 | − | 0.505399i | ||||
\(784\) | 12.0000 | 0.428571 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.1096 | 1.46540 | 0.732700 | − | 0.680552i | \(-0.238260\pi\) | ||||
0.732700 | + | 0.680552i | \(0.238260\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.0000 | + | 24.5967i | −0.391610 | + | 0.875667i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 28.2843i | 1.00000i | ||||||||
\(801\) | 40.0000 | − | 35.7771i | 1.41333 | − | 1.26412i | ||||
\(802\) | 50.5964 | 1.78662 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −50.0000 | − | 22.3607i | −1.76336 | − | 0.788600i | ||||
\(805\) | 10.0000 | 0.352454 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.8114 | − | 35.3553i | 0.556587 | − | 1.24457i | ||||
\(808\) | −25.2982 | −0.889988 | ||||||||
\(809\) | − | 17.8885i | − | 0.628928i | −0.949269 | − | 0.314464i | \(-0.898175\pi\) | ||
0.949269 | − | 0.314464i | \(-0.101825\pi\) | |||||||
\(810\) | 3.16228 | − | 28.2843i | 0.111111 | − | 0.993808i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | − | 56.5685i | − | 1.98517i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 49.4975i | − | 1.73382i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 5.65685i | 0.197787i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.0000 | 0.698430 | ||||||||
\(821\) | − | 31.3050i | − | 1.09255i | −0.837606 | − | 0.546275i | \(-0.816045\pi\) | ||
0.837606 | − | 0.546275i | \(-0.183955\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.8114 | −0.551150 | −0.275575 | − | 0.961280i | \(-0.588868\pi\) | ||||
−0.275575 | + | 0.961280i | \(0.588868\pi\) | |||||||
\(824\) | − | 44.7214i | − | 1.55794i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 32.5269i | − | 1.13107i | −0.824724 | − | 0.565536i | \(-0.808669\pi\) | ||
0.824724 | − | 0.565536i | \(-0.191331\pi\) | |||||||
\(828\) | 6.32456 | − | 5.65685i | 0.219793 | − | 0.196589i | ||||
\(829\) | 56.0000 | 1.94496 | 0.972480 | − | 0.232986i | \(-0.0748495\pi\) | ||||
0.972480 | + | 0.232986i | \(0.0748495\pi\) | |||||||
\(830\) | 49.1935i | 1.70753i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −53.7587 | −1.86040 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | −31.6228 | − | 14.1421i | −1.09109 | − | 0.487950i | ||||
\(841\) | −51.0000 | −1.75862 | ||||||||
\(842\) | − | 11.3137i | − | 0.389896i | ||||||
\(843\) | −22.1359 | + | 49.4975i | −0.762402 | + | 1.70478i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 29.0689i | − | 1.00000i | ||||||
\(846\) | 28.0000 | + | 31.3050i | 0.962660 | + | 1.07629i | ||||
\(847\) | −34.7851 | −1.19523 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.0000 | + | 11.1803i | 0.857998 | + | 0.383708i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(854\) | − | 35.7771i | − | 1.22427i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −52.0000 | −1.77732 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 14.1421i | 0.482243i | ||||||||
\(861\) | −10.0000 | + | 22.3607i | −0.340799 | + | 0.762050i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 57.9828i | − | 1.97376i | −0.161468 | − | 0.986878i | \(-0.551623\pi\) | ||
0.161468 | − | 0.986878i | \(-0.448377\pi\) | |||||||
\(864\) | −28.0000 | + | 8.94427i | −0.952579 | + | 0.304290i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.8794 | + | 12.0208i | 0.912871 | + | 0.408248i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −20.0000 | + | 44.7214i | −0.678064 | + | 1.51620i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 45.2548i | − | 1.53252i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 35.3553i | 1.19523i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 58.1378i | − | 1.95871i | −0.202145 | − | 0.979356i | \(-0.564791\pi\) | ||
0.202145 | − | 0.979356i | \(-0.435209\pi\) | |||||||
\(882\) | 9.48683 | − | 8.48528i | 0.319438 | − | 0.285714i | ||||
\(883\) | 22.1359 | 0.744934 | 0.372467 | − | 0.928045i | \(-0.378512\pi\) | ||||
0.372467 | + | 0.928045i | \(0.378512\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −58.0000 | −1.94855 | ||||||||
\(887\) | 52.3259i | 1.75693i | 0.477805 | + | 0.878466i | \(0.341433\pi\) | ||||
−0.477805 | + | 0.878466i | \(0.658567\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 70.0000 | 2.34772 | ||||||||
\(890\) | 56.5685i | 1.89618i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.32456 | −0.211762 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 10.0000 | + | 4.47214i | 0.334450 | + | 0.149571i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 35.7771i | 1.19523i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.6228 | 1.05527 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 20.0000 | + | 22.3607i | 0.666667 | + | 0.745356i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.8114 | − | 7.07107i | −0.526170 | − | 0.235310i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 4.47214i | − | 0.148659i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 60.0833 | 1.99503 | 0.997516 | − | 0.0704373i | \(-0.0224395\pi\) | ||||
0.997516 | + | 0.0704373i | \(0.0224395\pi\) | |||||||
\(908\) | − | 19.7990i | − | 0.657053i | ||||||
\(909\) | −20.0000 | + | 17.8885i | −0.663358 | + | 0.593326i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.6491 | + | 28.2843i | −0.418167 | + | 0.935049i | ||||
\(916\) | −28.0000 | −0.925146 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 8.94427i | 0.294884i | ||||||||
\(921\) | 55.0000 | + | 24.5967i | 1.81231 | + | 0.810490i | ||||
\(922\) | 12.6491 | 0.416576 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 58.1378i | − | 1.91053i | ||||||
\(927\) | −31.6228 | − | 35.3553i | −1.03863 | − | 1.16122i | ||||
\(928\) | 50.5964 | 1.66091 | ||||||||
\(929\) | 49.1935i | 1.61399i | 0.590561 | + | 0.806993i | \(0.298907\pi\) | ||||
−0.590561 | + | 0.806993i | \(0.701093\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −46.0000 | −1.50517 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 70.7107i | 2.30879i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −44.2719 | −1.44399 | ||||||||
\(941\) | − | 44.7214i | − | 1.45787i | −0.684580 | − | 0.728937i | \(-0.740015\pi\) | ||
0.684580 | − | 0.728937i | \(-0.259985\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.32456 | 0.205956 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −35.0000 | + | 11.1803i | −1.13855 | + | 0.363696i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 60.8112i | 1.97610i | 0.154140 | + | 0.988049i | \(0.450739\pi\) | ||||
−0.154140 | + | 0.988049i | \(0.549261\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 12.6491 | − | 28.2843i | 0.408248 | − | 0.912871i | ||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −41.1096 | + | 36.7696i | −1.32474 | + | 1.18488i | ||||
\(964\) | 56.0000 | 1.80364 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −10.0000 | − | 4.47214i | −0.321745 | − | 0.143889i | ||||
\(967\) | 41.1096 | 1.32200 | 0.660998 | − | 0.750388i | \(-0.270133\pi\) | ||||
0.660998 | + | 0.750388i | \(0.270133\pi\) | |||||||
\(968\) | − | 31.1127i | − | 1.00000i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | −15.8114 | + | 26.8701i | −0.507151 | + | 0.861858i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 31.3050i | − | 1.00308i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.0000 | 1.02430 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | −22.1359 | + | 49.4975i | −0.707829 | + | 1.58275i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 13.4164i | 0.428571i | ||||||||
\(981\) | −32.0000 | − | 35.7771i | −1.02168 | − | 1.14227i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 41.0122i | − | 1.30809i | −0.756457 | − | 0.654043i | \(-0.773072\pi\) | ||
0.756457 | − | 0.654043i | \(-0.226928\pi\) | |||||||
\(984\) | −20.0000 | − | 8.94427i | −0.637577 | − | 0.285133i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.1359 | − | 49.4975i | 0.704595 | − | 1.57552i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.47214i | 0.142206i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 22.0000 | − | 49.1935i | 0.697097 | − | 1.55876i | ||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 60.2.h.a.59.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 60.2.h.a.59.3 | yes | 4 | |
4.3 | odd | 2 | inner | 60.2.h.a.59.4 | yes | 4 | |
5.2 | odd | 4 | 300.2.e.b.251.4 | 4 | |||
5.3 | odd | 4 | 300.2.e.b.251.1 | 4 | |||
5.4 | even | 2 | inner | 60.2.h.a.59.4 | yes | 4 | |
8.3 | odd | 2 | 960.2.o.c.959.1 | 4 | |||
8.5 | even | 2 | 960.2.o.c.959.4 | 4 | |||
12.11 | even | 2 | inner | 60.2.h.a.59.2 | yes | 4 | |
15.2 | even | 4 | 300.2.e.b.251.2 | 4 | |||
15.8 | even | 4 | 300.2.e.b.251.3 | 4 | |||
15.14 | odd | 2 | inner | 60.2.h.a.59.2 | yes | 4 | |
20.3 | even | 4 | 300.2.e.b.251.4 | 4 | |||
20.7 | even | 4 | 300.2.e.b.251.1 | 4 | |||
20.19 | odd | 2 | CM | 60.2.h.a.59.1 | ✓ | 4 | |
24.5 | odd | 2 | 960.2.o.c.959.3 | 4 | |||
24.11 | even | 2 | 960.2.o.c.959.2 | 4 | |||
40.19 | odd | 2 | 960.2.o.c.959.4 | 4 | |||
40.29 | even | 2 | 960.2.o.c.959.1 | 4 | |||
60.23 | odd | 4 | 300.2.e.b.251.2 | 4 | |||
60.47 | odd | 4 | 300.2.e.b.251.3 | 4 | |||
60.59 | even | 2 | inner | 60.2.h.a.59.3 | yes | 4 | |
120.29 | odd | 2 | 960.2.o.c.959.2 | 4 | |||
120.59 | even | 2 | 960.2.o.c.959.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.2.h.a.59.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
60.2.h.a.59.1 | ✓ | 4 | 20.19 | odd | 2 | CM | |
60.2.h.a.59.2 | yes | 4 | 12.11 | even | 2 | inner | |
60.2.h.a.59.2 | yes | 4 | 15.14 | odd | 2 | inner | |
60.2.h.a.59.3 | yes | 4 | 3.2 | odd | 2 | inner | |
60.2.h.a.59.3 | yes | 4 | 60.59 | even | 2 | inner | |
60.2.h.a.59.4 | yes | 4 | 4.3 | odd | 2 | inner | |
60.2.h.a.59.4 | yes | 4 | 5.4 | even | 2 | inner | |
300.2.e.b.251.1 | 4 | 5.3 | odd | 4 | |||
300.2.e.b.251.1 | 4 | 20.7 | even | 4 | |||
300.2.e.b.251.2 | 4 | 15.2 | even | 4 | |||
300.2.e.b.251.2 | 4 | 60.23 | odd | 4 | |||
300.2.e.b.251.3 | 4 | 15.8 | even | 4 | |||
300.2.e.b.251.3 | 4 | 60.47 | odd | 4 | |||
300.2.e.b.251.4 | 4 | 5.2 | odd | 4 | |||
300.2.e.b.251.4 | 4 | 20.3 | even | 4 | |||
960.2.o.c.959.1 | 4 | 8.3 | odd | 2 | |||
960.2.o.c.959.1 | 4 | 40.29 | even | 2 | |||
960.2.o.c.959.2 | 4 | 24.11 | even | 2 | |||
960.2.o.c.959.2 | 4 | 120.29 | odd | 2 | |||
960.2.o.c.959.3 | 4 | 24.5 | odd | 2 | |||
960.2.o.c.959.3 | 4 | 120.59 | even | 2 | |||
960.2.o.c.959.4 | 4 | 8.5 | even | 2 | |||
960.2.o.c.959.4 | 4 | 40.19 | odd | 2 |