Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [26,3,Mod(5,26)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(26, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("26.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 26 = 2 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 26.d (of order \(4\), degree \(2\), 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: | \(0.708448687337\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 21.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 26.21 |
Dual form | 26.3.d.a.5.1 |
$q$-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 \(\left(\mathbb{Z}/26\mathbb{Z}\right)^\times\).
\(n\) | \(15\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −3.00000 | − | 3.00000i | −0.600000 | − | 0.600000i | 0.340312 | − | 0.940312i | \(-0.389467\pi\) |
−0.940312 | + | 0.340312i | \(0.889467\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 2.00000i | 0.285714 | − | 0.285714i | −0.549669 | − | 0.835383i | \(-0.685246\pi\) |
0.835383 | + | 0.549669i | \(0.185246\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | −9.00000 | −1.00000 | ||||||||
\(10\) | − | 6.00000i | − | 0.600000i | ||||||
\(11\) | 6.00000 | − | 6.00000i | 0.545455 | − | 0.545455i | −0.379668 | − | 0.925123i | \(-0.623962\pi\) |
0.925123 | + | 0.379668i | \(0.123962\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000i | 1.00000i | ||||||||
\(14\) | 4.00000 | 0.285714 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 6.00000i | 0.352941i | 0.984306 | + | 0.176471i | \(0.0564680\pi\) | ||||
−0.984306 | + | 0.176471i | \(0.943532\pi\) | |||||||
\(18\) | −9.00000 | − | 9.00000i | −0.500000 | − | 0.500000i | ||||
\(19\) | 26.0000 | + | 26.0000i | 1.36842 | + | 1.36842i | 0.862693 | + | 0.505728i | \(0.168776\pi\) |
0.505728 | + | 0.862693i | \(0.331224\pi\) | |||||||
\(20\) | 6.00000 | − | 6.00000i | 0.300000 | − | 0.300000i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.0000 | 0.545455 | ||||||||
\(23\) | − | 24.0000i | − | 1.04348i | −0.853105 | − | 0.521739i | \(-0.825283\pi\) | ||
0.853105 | − | 0.521739i | \(-0.174717\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 7.00000i | − | 0.280000i | ||||||
\(26\) | −13.0000 | + | 13.0000i | −0.500000 | + | 0.500000i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.00000 | + | 4.00000i | 0.142857 | + | 0.142857i | ||||
\(29\) | −48.0000 | −1.65517 | −0.827586 | − | 0.561339i | \(-0.810287\pi\) | ||||
−0.827586 | + | 0.561339i | \(0.810287\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.0000 | − | 14.0000i | −0.451613 | − | 0.451613i | 0.444277 | − | 0.895890i | \(-0.353461\pi\) |
−0.895890 | + | 0.444277i | \(0.853461\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.00000 | + | 6.00000i | −0.176471 | + | 0.176471i | ||||
\(35\) | −12.0000 | −0.342857 | ||||||||
\(36\) | − | 18.0000i | − | 0.500000i | ||||||
\(37\) | 37.0000 | − | 37.0000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(38\) | 52.0000i | 1.36842i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.0000 | 0.300000 | ||||||||
\(41\) | −9.00000 | − | 9.00000i | −0.219512 | − | 0.219512i | 0.588781 | − | 0.808293i | \(-0.299608\pi\) |
−0.808293 | + | 0.588781i | \(0.799608\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 36.0000i | 0.837209i | 0.908169 | + | 0.418605i | \(0.137481\pi\) | ||||
−0.908169 | + | 0.418605i | \(0.862519\pi\) | |||||||
\(44\) | 12.0000 | + | 12.0000i | 0.272727 | + | 0.272727i | ||||
\(45\) | 27.0000 | + | 27.0000i | 0.600000 | + | 0.600000i | ||||
\(46\) | 24.0000 | − | 24.0000i | 0.521739 | − | 0.521739i | ||||
\(47\) | 42.0000 | − | 42.0000i | 0.893617 | − | 0.893617i | −0.101245 | − | 0.994862i | \(-0.532282\pi\) |
0.994862 | + | 0.101245i | \(0.0322825\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 41.0000i | 0.836735i | ||||||||
\(50\) | 7.00000 | − | 7.00000i | 0.140000 | − | 0.140000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −26.0000 | −0.500000 | ||||||||
\(53\) | 30.0000 | 0.566038 | 0.283019 | − | 0.959114i | \(-0.408664\pi\) | ||||
0.283019 | + | 0.959114i | \(0.408664\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −36.0000 | −0.654545 | ||||||||
\(56\) | 8.00000i | 0.142857i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −48.0000 | − | 48.0000i | −0.827586 | − | 0.827586i | ||||
\(59\) | −54.0000 | + | 54.0000i | −0.915254 | + | 0.915254i | −0.996679 | − | 0.0814252i | \(-0.974053\pi\) |
0.0814252 | + | 0.996679i | \(0.474053\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −18.0000 | −0.295082 | −0.147541 | − | 0.989056i | \(-0.547136\pi\) | ||||
−0.147541 | + | 0.989056i | \(0.547136\pi\) | |||||||
\(62\) | − | 28.0000i | − | 0.451613i | ||||||
\(63\) | −18.0000 | + | 18.0000i | −0.285714 | + | 0.285714i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 39.0000 | − | 39.0000i | 0.600000 | − | 0.600000i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −22.0000 | − | 22.0000i | −0.328358 | − | 0.328358i | 0.523604 | − | 0.851962i | \(-0.324587\pi\) |
−0.851962 | + | 0.523604i | \(0.824587\pi\) | |||||||
\(68\) | −12.0000 | −0.176471 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.0000 | − | 12.0000i | −0.171429 | − | 0.171429i | ||||
\(71\) | 6.00000 | + | 6.00000i | 0.0845070 | + | 0.0845070i | 0.748097 | − | 0.663590i | \(-0.230968\pi\) |
−0.663590 | + | 0.748097i | \(0.730968\pi\) | |||||||
\(72\) | 18.0000 | − | 18.0000i | 0.250000 | − | 0.250000i | ||||
\(73\) | 17.0000 | − | 17.0000i | 0.232877 | − | 0.232877i | −0.581016 | − | 0.813892i | \(-0.697345\pi\) |
0.813892 | + | 0.581016i | \(0.197345\pi\) | |||||||
\(74\) | 74.0000 | 1.00000 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −52.0000 | + | 52.0000i | −0.684211 | + | 0.684211i | ||||
\(77\) | − | 24.0000i | − | 0.311688i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −108.000 | −1.36709 | −0.683544 | − | 0.729909i | \(-0.739562\pi\) | ||||
−0.683544 | + | 0.729909i | \(0.739562\pi\) | |||||||
\(80\) | 12.0000 | + | 12.0000i | 0.150000 | + | 0.150000i | ||||
\(81\) | 81.0000 | 1.00000 | ||||||||
\(82\) | − | 18.0000i | − | 0.219512i | ||||||
\(83\) | 78.0000 | + | 78.0000i | 0.939759 | + | 0.939759i | 0.998286 | − | 0.0585268i | \(-0.0186403\pi\) |
−0.0585268 | + | 0.998286i | \(0.518640\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.0000 | − | 18.0000i | 0.211765 | − | 0.211765i | ||||
\(86\) | −36.0000 | + | 36.0000i | −0.418605 | + | 0.418605i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 24.0000i | 0.272727i | ||||||||
\(89\) | −9.00000 | + | 9.00000i | −0.101124 | + | 0.101124i | −0.755859 | − | 0.654735i | \(-0.772780\pi\) |
0.654735 | + | 0.755859i | \(0.272780\pi\) | |||||||
\(90\) | 54.0000i | 0.600000i | ||||||||
\(91\) | 26.0000 | + | 26.0000i | 0.285714 | + | 0.285714i | ||||
\(92\) | 48.0000 | 0.521739 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 84.0000 | 0.893617 | ||||||||
\(95\) | − | 156.000i | − | 1.64211i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −47.0000 | − | 47.0000i | −0.484536 | − | 0.484536i | 0.422041 | − | 0.906577i | \(-0.361314\pi\) |
−0.906577 | + | 0.422041i | \(0.861314\pi\) | |||||||
\(98\) | −41.0000 | + | 41.0000i | −0.418367 | + | 0.418367i | ||||
\(99\) | −54.0000 | + | 54.0000i | −0.545455 | + | 0.545455i | ||||
\(100\) | 14.0000 | 0.140000 | ||||||||
\(101\) | 120.000i | 1.18812i | 0.804421 | + | 0.594059i | \(0.202476\pi\) | ||||
−0.804421 | + | 0.594059i | \(0.797524\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 144.000i | − | 1.39806i | −0.715093 | − | 0.699029i | \(-0.753616\pi\) | ||
0.715093 | − | 0.699029i | \(-0.246384\pi\) | |||||||
\(104\) | −26.0000 | − | 26.0000i | −0.250000 | − | 0.250000i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 30.0000 | + | 30.0000i | 0.283019 | + | 0.283019i | ||||
\(107\) | 120.000 | 1.12150 | 0.560748 | − | 0.827987i | \(-0.310514\pi\) | ||||
0.560748 | + | 0.827987i | \(0.310514\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.0000 | − | 19.0000i | −0.174312 | − | 0.174312i | 0.614559 | − | 0.788871i | \(-0.289334\pi\) |
−0.788871 | + | 0.614559i | \(0.789334\pi\) | |||||||
\(110\) | −36.0000 | − | 36.0000i | −0.327273 | − | 0.327273i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.00000 | + | 8.00000i | −0.0714286 | + | 0.0714286i | ||||
\(113\) | −120.000 | −1.06195 | −0.530973 | − | 0.847388i | \(-0.678174\pi\) | ||||
−0.530973 | + | 0.847388i | \(0.678174\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −72.0000 | + | 72.0000i | −0.626087 | + | 0.626087i | ||||
\(116\) | − | 96.0000i | − | 0.827586i | ||||||
\(117\) | − | 117.000i | − | 1.00000i | ||||||
\(118\) | −108.000 | −0.915254 | ||||||||
\(119\) | 12.0000 | + | 12.0000i | 0.100840 | + | 0.100840i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 49.0000i | 0.404959i | ||||||||
\(122\) | −18.0000 | − | 18.0000i | −0.147541 | − | 0.147541i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 28.0000 | − | 28.0000i | 0.225806 | − | 0.225806i | ||||
\(125\) | −96.0000 | + | 96.0000i | −0.768000 | + | 0.768000i | ||||
\(126\) | −36.0000 | −0.285714 | ||||||||
\(127\) | 56.0000i | 0.440945i | 0.975393 | + | 0.220472i | \(0.0707599\pi\) | ||||
−0.975393 | + | 0.220472i | \(0.929240\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 78.0000 | 0.600000 | ||||||||
\(131\) | 72.0000 | 0.549618 | 0.274809 | − | 0.961499i | \(-0.411385\pi\) | ||||
0.274809 | + | 0.961499i | \(0.411385\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 104.000 | 0.781955 | ||||||||
\(134\) | − | 44.0000i | − | 0.328358i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.0000 | − | 12.0000i | −0.0882353 | − | 0.0882353i | ||||
\(137\) | −63.0000 | + | 63.0000i | −0.459854 | + | 0.459854i | −0.898607 | − | 0.438753i | \(-0.855420\pi\) |
0.438753 | + | 0.898607i | \(0.355420\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 152.000 | 1.09353 | 0.546763 | − | 0.837288i | \(-0.315860\pi\) | ||||
0.546763 | + | 0.837288i | \(0.315860\pi\) | |||||||
\(140\) | − | 24.0000i | − | 0.171429i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.0000i | 0.0845070i | ||||||||
\(143\) | 78.0000 | + | 78.0000i | 0.545455 | + | 0.545455i | ||||
\(144\) | 36.0000 | 0.250000 | ||||||||
\(145\) | 144.000 | + | 144.000i | 0.993103 | + | 0.993103i | ||||
\(146\) | 34.0000 | 0.232877 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 74.0000 | + | 74.0000i | 0.500000 | + | 0.500000i | ||||
\(149\) | −99.0000 | − | 99.0000i | −0.664430 | − | 0.664430i | 0.291991 | − | 0.956421i | \(-0.405682\pi\) |
−0.956421 | + | 0.291991i | \(0.905682\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 106.000 | − | 106.000i | 0.701987 | − | 0.701987i | −0.262850 | − | 0.964837i | \(-0.584662\pi\) |
0.964837 | + | 0.262850i | \(0.0846624\pi\) | |||||||
\(152\) | −104.000 | −0.684211 | ||||||||
\(153\) | − | 54.0000i | − | 0.352941i | ||||||
\(154\) | 24.0000 | − | 24.0000i | 0.155844 | − | 0.155844i | ||||
\(155\) | 84.0000i | 0.541935i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −80.0000 | −0.509554 | −0.254777 | − | 0.967000i | \(-0.582002\pi\) | ||||
−0.254777 | + | 0.967000i | \(0.582002\pi\) | |||||||
\(158\) | −108.000 | − | 108.000i | −0.683544 | − | 0.683544i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 24.0000i | 0.150000i | ||||||||
\(161\) | −48.0000 | − | 48.0000i | −0.298137 | − | 0.298137i | ||||
\(162\) | 81.0000 | + | 81.0000i | 0.500000 | + | 0.500000i | ||||
\(163\) | 82.0000 | − | 82.0000i | 0.503067 | − | 0.503067i | −0.409322 | − | 0.912390i | \(-0.634235\pi\) |
0.912390 | + | 0.409322i | \(0.134235\pi\) | |||||||
\(164\) | 18.0000 | − | 18.0000i | 0.109756 | − | 0.109756i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 156.000i | 0.939759i | ||||||||
\(167\) | −138.000 | + | 138.000i | −0.826347 | + | 0.826347i | −0.987009 | − | 0.160662i | \(-0.948637\pi\) |
0.160662 | + | 0.987009i | \(0.448637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −169.000 | −1.00000 | ||||||||
\(170\) | 36.0000 | 0.211765 | ||||||||
\(171\) | −234.000 | − | 234.000i | −1.36842 | − | 1.36842i | ||||
\(172\) | −72.0000 | −0.418605 | ||||||||
\(173\) | − | 24.0000i | − | 0.138728i | −0.997591 | − | 0.0693642i | \(-0.977903\pi\) | ||
0.997591 | − | 0.0693642i | \(-0.0220970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.0000 | − | 14.0000i | −0.0800000 | − | 0.0800000i | ||||
\(176\) | −24.0000 | + | 24.0000i | −0.136364 | + | 0.136364i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −18.0000 | −0.101124 | ||||||||
\(179\) | − | 300.000i | − | 1.67598i | −0.545687 | − | 0.837989i | \(-0.683731\pi\) | ||
0.545687 | − | 0.837989i | \(-0.316269\pi\) | |||||||
\(180\) | −54.0000 | + | 54.0000i | −0.300000 | + | 0.300000i | ||||
\(181\) | 90.0000i | 0.497238i | 0.968601 | + | 0.248619i | \(0.0799766\pi\) | ||||
−0.968601 | + | 0.248619i | \(0.920023\pi\) | |||||||
\(182\) | 52.0000i | 0.285714i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 48.0000 | + | 48.0000i | 0.260870 | + | 0.260870i | ||||
\(185\) | −222.000 | −1.20000 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 36.0000 | + | 36.0000i | 0.192513 | + | 0.192513i | ||||
\(188\) | 84.0000 | + | 84.0000i | 0.446809 | + | 0.446809i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 156.000 | − | 156.000i | 0.821053 | − | 0.821053i | ||||
\(191\) | 252.000 | 1.31937 | 0.659686 | − | 0.751541i | \(-0.270689\pi\) | ||||
0.659686 | + | 0.751541i | \(0.270689\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 257.000 | − | 257.000i | 1.33161 | − | 1.33161i | 0.427672 | − | 0.903934i | \(-0.359334\pi\) |
0.903934 | − | 0.427672i | \(-0.140666\pi\) | |||||||
\(194\) | − | 94.0000i | − | 0.484536i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −82.0000 | −0.418367 | ||||||||
\(197\) | 123.000 | + | 123.000i | 0.624365 | + | 0.624365i | 0.946645 | − | 0.322279i | \(-0.104449\pi\) |
−0.322279 | + | 0.946645i | \(0.604449\pi\) | |||||||
\(198\) | −108.000 | −0.545455 | ||||||||
\(199\) | 200.000i | 1.00503i | 0.864570 | + | 0.502513i | \(0.167591\pi\) | ||||
−0.864570 | + | 0.502513i | \(0.832409\pi\) | |||||||
\(200\) | 14.0000 | + | 14.0000i | 0.0700000 | + | 0.0700000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −120.000 | + | 120.000i | −0.594059 | + | 0.594059i | ||||
\(203\) | −96.0000 | + | 96.0000i | −0.472906 | + | 0.472906i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 54.0000i | 0.263415i | ||||||||
\(206\) | 144.000 | − | 144.000i | 0.699029 | − | 0.699029i | ||||
\(207\) | 216.000i | 1.04348i | ||||||||
\(208\) | − | 52.0000i | − | 0.250000i | ||||||
\(209\) | 312.000 | 1.49282 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −288.000 | −1.36493 | −0.682464 | − | 0.730919i | \(-0.739092\pi\) | ||||
−0.682464 | + | 0.730919i | \(0.739092\pi\) | |||||||
\(212\) | 60.0000i | 0.283019i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 120.000 | + | 120.000i | 0.560748 | + | 0.560748i | ||||
\(215\) | 108.000 | − | 108.000i | 0.502326 | − | 0.502326i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −56.0000 | −0.258065 | ||||||||
\(218\) | − | 38.0000i | − | 0.174312i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 72.0000i | − | 0.327273i | ||||||
\(221\) | −78.0000 | −0.352941 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 38.0000 | + | 38.0000i | 0.170404 | + | 0.170404i | 0.787157 | − | 0.616753i | \(-0.211552\pi\) |
−0.616753 | + | 0.787157i | \(0.711552\pi\) | |||||||
\(224\) | −16.0000 | −0.0714286 | ||||||||
\(225\) | 63.0000i | 0.280000i | ||||||||
\(226\) | −120.000 | − | 120.000i | −0.530973 | − | 0.530973i | ||||
\(227\) | 138.000 | + | 138.000i | 0.607930 | + | 0.607930i | 0.942405 | − | 0.334475i | \(-0.108559\pi\) |
−0.334475 | + | 0.942405i | \(0.608559\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 131.000 | − | 131.000i | 0.572052 | − | 0.572052i | −0.360649 | − | 0.932702i | \(-0.617445\pi\) |
0.932702 | + | 0.360649i | \(0.117445\pi\) | |||||||
\(230\) | −144.000 | −0.626087 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 96.0000 | − | 96.0000i | 0.413793 | − | 0.413793i | ||||
\(233\) | 336.000i | 1.44206i | 0.692904 | + | 0.721030i | \(0.256331\pi\) | ||||
−0.692904 | + | 0.721030i | \(0.743669\pi\) | |||||||
\(234\) | 117.000 | − | 117.000i | 0.500000 | − | 0.500000i | ||||
\(235\) | −252.000 | −1.07234 | ||||||||
\(236\) | −108.000 | − | 108.000i | −0.457627 | − | 0.457627i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 24.0000i | 0.100840i | ||||||||
\(239\) | −114.000 | − | 114.000i | −0.476987 | − | 0.476987i | 0.427179 | − | 0.904167i | \(-0.359507\pi\) |
−0.904167 | + | 0.427179i | \(0.859507\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 151.000 | − | 151.000i | 0.626556 | − | 0.626556i | −0.320644 | − | 0.947200i | \(-0.603899\pi\) |
0.947200 | + | 0.320644i | \(0.103899\pi\) | |||||||
\(242\) | −49.0000 | + | 49.0000i | −0.202479 | + | 0.202479i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 36.0000i | − | 0.147541i | ||||||
\(245\) | 123.000 | − | 123.000i | 0.502041 | − | 0.502041i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −338.000 | + | 338.000i | −1.36842 | + | 1.36842i | ||||
\(248\) | 56.0000 | 0.225806 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −192.000 | −0.768000 | ||||||||
\(251\) | − | 180.000i | − | 0.717131i | −0.933504 | − | 0.358566i | \(-0.883266\pi\) | ||
0.933504 | − | 0.358566i | \(-0.116734\pi\) | |||||||
\(252\) | −36.0000 | − | 36.0000i | −0.142857 | − | 0.142857i | ||||
\(253\) | −144.000 | − | 144.000i | −0.569170 | − | 0.569170i | ||||
\(254\) | −56.0000 | + | 56.0000i | −0.220472 | + | 0.220472i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 144.000i | − | 0.560311i | −0.959955 | − | 0.280156i | \(-0.909614\pi\) | ||
0.959955 | − | 0.280156i | \(-0.0903861\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 148.000i | − | 0.571429i | ||||||
\(260\) | 78.0000 | + | 78.0000i | 0.300000 | + | 0.300000i | ||||
\(261\) | 432.000 | 1.65517 | ||||||||
\(262\) | 72.0000 | + | 72.0000i | 0.274809 | + | 0.274809i | ||||
\(263\) | −60.0000 | −0.228137 | −0.114068 | − | 0.993473i | \(-0.536388\pi\) | ||||
−0.114068 | + | 0.993473i | \(0.536388\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −90.0000 | − | 90.0000i | −0.339623 | − | 0.339623i | ||||
\(266\) | 104.000 | + | 104.000i | 0.390977 | + | 0.390977i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 44.0000 | − | 44.0000i | 0.164179 | − | 0.164179i | ||||
\(269\) | −288.000 | −1.07063 | −0.535316 | − | 0.844652i | \(-0.679807\pi\) | ||||
−0.535316 | + | 0.844652i | \(0.679807\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −134.000 | + | 134.000i | −0.494465 | + | 0.494465i | −0.909710 | − | 0.415245i | \(-0.863696\pi\) |
0.415245 | + | 0.909710i | \(0.363696\pi\) | |||||||
\(272\) | − | 24.0000i | − | 0.0882353i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −126.000 | −0.459854 | ||||||||
\(275\) | −42.0000 | − | 42.0000i | −0.152727 | − | 0.152727i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 216.000i | 0.779783i | 0.920861 | + | 0.389892i | \(0.127488\pi\) | ||||
−0.920861 | + | 0.389892i | \(0.872512\pi\) | |||||||
\(278\) | 152.000 | + | 152.000i | 0.546763 | + | 0.546763i | ||||
\(279\) | 126.000 | + | 126.000i | 0.451613 | + | 0.451613i | ||||
\(280\) | 24.0000 | − | 24.0000i | 0.0857143 | − | 0.0857143i | ||||
\(281\) | −159.000 | + | 159.000i | −0.565836 | + | 0.565836i | −0.930959 | − | 0.365123i | \(-0.881027\pi\) |
0.365123 | + | 0.930959i | \(0.381027\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 404.000i | − | 1.42756i | −0.700369 | − | 0.713781i | \(-0.746981\pi\) | ||
0.700369 | − | 0.713781i | \(-0.253019\pi\) | |||||||
\(284\) | −12.0000 | + | 12.0000i | −0.0422535 | + | 0.0422535i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 156.000i | 0.545455i | ||||||||
\(287\) | −36.0000 | −0.125436 | ||||||||
\(288\) | 36.0000 | + | 36.0000i | 0.125000 | + | 0.125000i | ||||
\(289\) | 253.000 | 0.875433 | ||||||||
\(290\) | 288.000i | 0.993103i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 34.0000 | + | 34.0000i | 0.116438 | + | 0.116438i | ||||
\(293\) | 147.000 | − | 147.000i | 0.501706 | − | 0.501706i | −0.410261 | − | 0.911968i | \(-0.634563\pi\) |
0.911968 | + | 0.410261i | \(0.134563\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 324.000 | 1.09831 | ||||||||
\(296\) | 148.000i | 0.500000i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 198.000i | − | 0.664430i | ||||||
\(299\) | 312.000 | 1.04348 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 72.0000 | + | 72.0000i | 0.239203 | + | 0.239203i | ||||
\(302\) | 212.000 | 0.701987 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −104.000 | − | 104.000i | −0.342105 | − | 0.342105i | ||||
\(305\) | 54.0000 | + | 54.0000i | 0.177049 | + | 0.177049i | ||||
\(306\) | 54.0000 | − | 54.0000i | 0.176471 | − | 0.176471i | ||||
\(307\) | 82.0000 | − | 82.0000i | 0.267101 | − | 0.267101i | −0.560830 | − | 0.827931i | \(-0.689518\pi\) |
0.827931 | + | 0.560830i | \(0.189518\pi\) | |||||||
\(308\) | 48.0000 | 0.155844 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −84.0000 | + | 84.0000i | −0.270968 | + | 0.270968i | ||||
\(311\) | − | 120.000i | − | 0.385852i | −0.981213 | − | 0.192926i | \(-0.938202\pi\) | ||
0.981213 | − | 0.192926i | \(-0.0617977\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −360.000 | −1.15016 | −0.575080 | − | 0.818097i | \(-0.695029\pi\) | ||||
−0.575080 | + | 0.818097i | \(0.695029\pi\) | |||||||
\(314\) | −80.0000 | − | 80.0000i | −0.254777 | − | 0.254777i | ||||
\(315\) | 108.000 | 0.342857 | ||||||||
\(316\) | − | 216.000i | − | 0.683544i | ||||||
\(317\) | −147.000 | − | 147.000i | −0.463722 | − | 0.463722i | 0.436151 | − | 0.899873i | \(-0.356341\pi\) |
−0.899873 | + | 0.436151i | \(0.856341\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −288.000 | + | 288.000i | −0.902821 | + | 0.902821i | ||||
\(320\) | −24.0000 | + | 24.0000i | −0.0750000 | + | 0.0750000i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 96.0000i | − | 0.298137i | ||||||
\(323\) | −156.000 | + | 156.000i | −0.482972 | + | 0.482972i | ||||
\(324\) | 162.000i | 0.500000i | ||||||||
\(325\) | 91.0000 | 0.280000 | ||||||||
\(326\) | 164.000 | 0.503067 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 36.0000 | 0.109756 | ||||||||
\(329\) | − | 168.000i | − | 0.510638i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −214.000 | − | 214.000i | −0.646526 | − | 0.646526i | 0.305626 | − | 0.952152i | \(-0.401134\pi\) |
−0.952152 | + | 0.305626i | \(0.901134\pi\) | |||||||
\(332\) | −156.000 | + | 156.000i | −0.469880 | + | 0.469880i | ||||
\(333\) | −333.000 | + | 333.000i | −1.00000 | + | 1.00000i | ||||
\(334\) | −276.000 | −0.826347 | ||||||||
\(335\) | 132.000i | 0.394030i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 314.000i | − | 0.931751i | −0.884850 | − | 0.465875i | \(-0.845740\pi\) | ||
0.884850 | − | 0.465875i | \(-0.154260\pi\) | |||||||
\(338\) | −169.000 | − | 169.000i | −0.500000 | − | 0.500000i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 36.0000 | + | 36.0000i | 0.105882 | + | 0.105882i | ||||
\(341\) | −168.000 | −0.492669 | ||||||||
\(342\) | − | 468.000i | − | 1.36842i | ||||||
\(343\) | 180.000 | + | 180.000i | 0.524781 | + | 0.524781i | ||||
\(344\) | −72.0000 | − | 72.0000i | −0.209302 | − | 0.209302i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.0000 | − | 24.0000i | 0.0693642 | − | 0.0693642i | ||||
\(347\) | −120.000 | −0.345821 | −0.172911 | − | 0.984938i | \(-0.555317\pi\) | ||||
−0.172911 | + | 0.984938i | \(0.555317\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 101.000 | − | 101.000i | 0.289398 | − | 0.289398i | −0.547444 | − | 0.836842i | \(-0.684399\pi\) |
0.836842 | + | 0.547444i | \(0.184399\pi\) | |||||||
\(350\) | − | 28.0000i | − | 0.0800000i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −48.0000 | −0.136364 | ||||||||
\(353\) | 33.0000 | + | 33.0000i | 0.0934844 | + | 0.0934844i | 0.752302 | − | 0.658818i | \(-0.228943\pi\) |
−0.658818 | + | 0.752302i | \(0.728943\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 36.0000i | − | 0.101408i | ||||||
\(356\) | −18.0000 | − | 18.0000i | −0.0505618 | − | 0.0505618i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 300.000 | − | 300.000i | 0.837989 | − | 0.837989i | ||||
\(359\) | 186.000 | − | 186.000i | 0.518106 | − | 0.518106i | −0.398892 | − | 0.916998i | \(-0.630605\pi\) |
0.916998 | + | 0.398892i | \(0.130605\pi\) | |||||||
\(360\) | −108.000 | −0.300000 | ||||||||
\(361\) | 991.000i | 2.74515i | ||||||||
\(362\) | −90.0000 | + | 90.0000i | −0.248619 | + | 0.248619i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −52.0000 | + | 52.0000i | −0.142857 | + | 0.142857i | ||||
\(365\) | −102.000 | −0.279452 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 580.000 | 1.58038 | 0.790191 | − | 0.612861i | \(-0.209981\pi\) | ||||
0.790191 | + | 0.612861i | \(0.209981\pi\) | |||||||
\(368\) | 96.0000i | 0.260870i | ||||||||
\(369\) | 81.0000 | + | 81.0000i | 0.219512 | + | 0.219512i | ||||
\(370\) | −222.000 | − | 222.000i | −0.600000 | − | 0.600000i | ||||
\(371\) | 60.0000 | − | 60.0000i | 0.161725 | − | 0.161725i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | 72.0000i | 0.192513i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 168.000i | 0.446809i | ||||||||
\(377\) | − | 624.000i | − | 1.65517i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 226.000 | + | 226.000i | 0.596306 | + | 0.596306i | 0.939328 | − | 0.343021i | \(-0.111450\pi\) |
−0.343021 | + | 0.939328i | \(0.611450\pi\) | |||||||
\(380\) | 312.000 | 0.821053 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 252.000 | + | 252.000i | 0.659686 | + | 0.659686i | ||||
\(383\) | 78.0000 | + | 78.0000i | 0.203655 | + | 0.203655i | 0.801564 | − | 0.597909i | \(-0.204002\pi\) |
−0.597909 | + | 0.801564i | \(0.704002\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −72.0000 | + | 72.0000i | −0.187013 | + | 0.187013i | ||||
\(386\) | 514.000 | 1.33161 | ||||||||
\(387\) | − | 324.000i | − | 0.837209i | ||||||
\(388\) | 94.0000 | − | 94.0000i | 0.242268 | − | 0.242268i | ||||
\(389\) | 150.000i | 0.385604i | 0.981238 | + | 0.192802i | \(0.0617575\pi\) | ||||
−0.981238 | + | 0.192802i | \(0.938242\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 144.000 | 0.368286 | ||||||||
\(392\) | −82.0000 | − | 82.0000i | −0.209184 | − | 0.209184i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 246.000i | 0.624365i | ||||||||
\(395\) | 324.000 | + | 324.000i | 0.820253 | + | 0.820253i | ||||
\(396\) | −108.000 | − | 108.000i | −0.272727 | − | 0.272727i | ||||
\(397\) | −253.000 | + | 253.000i | −0.637280 | + | 0.637280i | −0.949884 | − | 0.312604i | \(-0.898799\pi\) |
0.312604 | + | 0.949884i | \(0.398799\pi\) | |||||||
\(398\) | −200.000 | + | 200.000i | −0.502513 | + | 0.502513i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 28.0000i | 0.0700000i | ||||||||
\(401\) | −249.000 | + | 249.000i | −0.620948 | + | 0.620948i | −0.945774 | − | 0.324826i | \(-0.894694\pi\) |
0.324826 | + | 0.945774i | \(0.394694\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 182.000 | − | 182.000i | 0.451613 | − | 0.451613i | ||||
\(404\) | −240.000 | −0.594059 | ||||||||
\(405\) | −243.000 | − | 243.000i | −0.600000 | − | 0.600000i | ||||
\(406\) | −192.000 | −0.472906 | ||||||||
\(407\) | − | 444.000i | − | 1.09091i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −319.000 | − | 319.000i | −0.779951 | − | 0.779951i | 0.199871 | − | 0.979822i | \(-0.435948\pi\) |
−0.979822 | + | 0.199871i | \(0.935948\pi\) | |||||||
\(410\) | −54.0000 | + | 54.0000i | −0.131707 | + | 0.131707i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 288.000 | 0.699029 | ||||||||
\(413\) | 216.000i | 0.523002i | ||||||||
\(414\) | −216.000 | + | 216.000i | −0.521739 | + | 0.521739i | ||||
\(415\) | − | 468.000i | − | 1.12771i | ||||||
\(416\) | 52.0000 | − | 52.0000i | 0.125000 | − | 0.125000i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 312.000 | + | 312.000i | 0.746411 | + | 0.746411i | ||||
\(419\) | −48.0000 | −0.114558 | −0.0572792 | − | 0.998358i | \(-0.518243\pi\) | ||||
−0.0572792 | + | 0.998358i | \(0.518243\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | + | 11.0000i | 0.0261283 | + | 0.0261283i | 0.720050 | − | 0.693922i | \(-0.244119\pi\) |
−0.693922 | + | 0.720050i | \(0.744119\pi\) | |||||||
\(422\) | −288.000 | − | 288.000i | −0.682464 | − | 0.682464i | ||||
\(423\) | −378.000 | + | 378.000i | −0.893617 | + | 0.893617i | ||||
\(424\) | −60.0000 | + | 60.0000i | −0.141509 | + | 0.141509i | ||||
\(425\) | 42.0000 | 0.0988235 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −36.0000 | + | 36.0000i | −0.0843091 | + | 0.0843091i | ||||
\(428\) | 240.000i | 0.560748i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 216.000 | 0.502326 | ||||||||
\(431\) | −414.000 | − | 414.000i | −0.960557 | − | 0.960557i | 0.0386943 | − | 0.999251i | \(-0.487680\pi\) |
−0.999251 | + | 0.0386943i | \(0.987680\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.0000i | 0.0369515i | 0.999829 | + | 0.0184758i | \(0.00588135\pi\) | ||||
−0.999829 | + | 0.0184758i | \(0.994119\pi\) | |||||||
\(434\) | −56.0000 | − | 56.0000i | −0.129032 | − | 0.129032i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 38.0000 | − | 38.0000i | 0.0871560 | − | 0.0871560i | ||||
\(437\) | 624.000 | − | 624.000i | 1.42792 | − | 1.42792i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 360.000i | 0.820046i | 0.912075 | + | 0.410023i | \(0.134479\pi\) | ||||
−0.912075 | + | 0.410023i | \(0.865521\pi\) | |||||||
\(440\) | 72.0000 | − | 72.0000i | 0.163636 | − | 0.163636i | ||||
\(441\) | − | 369.000i | − | 0.836735i | ||||||
\(442\) | −78.0000 | − | 78.0000i | −0.176471 | − | 0.176471i | ||||
\(443\) | −600.000 | −1.35440 | −0.677201 | − | 0.735798i | \(-0.736807\pi\) | ||||
−0.677201 | + | 0.735798i | \(0.736807\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 54.0000 | 0.121348 | ||||||||
\(446\) | 76.0000i | 0.170404i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −16.0000 | − | 16.0000i | −0.0357143 | − | 0.0357143i | ||||
\(449\) | −9.00000 | + | 9.00000i | −0.0200445 | + | 0.0200445i | −0.717058 | − | 0.697013i | \(-0.754512\pi\) |
0.697013 | + | 0.717058i | \(0.254512\pi\) | |||||||
\(450\) | −63.0000 | + | 63.0000i | −0.140000 | + | 0.140000i | ||||
\(451\) | −108.000 | −0.239468 | ||||||||
\(452\) | − | 240.000i | − | 0.530973i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 276.000i | 0.607930i | ||||||||
\(455\) | − | 156.000i | − | 0.342857i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −47.0000 | − | 47.0000i | −0.102845 | − | 0.102845i | 0.653812 | − | 0.756657i | \(-0.273169\pi\) |
−0.756657 | + | 0.653812i | \(0.773169\pi\) | |||||||
\(458\) | 262.000 | 0.572052 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −144.000 | − | 144.000i | −0.313043 | − | 0.313043i | ||||
\(461\) | 171.000 | + | 171.000i | 0.370933 | + | 0.370933i | 0.867817 | − | 0.496884i | \(-0.165523\pi\) |
−0.496884 | + | 0.867817i | \(0.665523\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 202.000 | − | 202.000i | 0.436285 | − | 0.436285i | −0.454475 | − | 0.890760i | \(-0.650173\pi\) |
0.890760 | + | 0.454475i | \(0.150173\pi\) | |||||||
\(464\) | 192.000 | 0.413793 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −336.000 | + | 336.000i | −0.721030 | + | 0.721030i | ||||
\(467\) | 516.000i | 1.10493i | 0.833538 | + | 0.552463i | \(0.186312\pi\) | ||||
−0.833538 | + | 0.552463i | \(0.813688\pi\) | |||||||
\(468\) | 234.000 | 0.500000 | ||||||||
\(469\) | −88.0000 | −0.187633 | ||||||||
\(470\) | −252.000 | − | 252.000i | −0.536170 | − | 0.536170i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 216.000i | − | 0.457627i | ||||||
\(473\) | 216.000 | + | 216.000i | 0.456660 | + | 0.456660i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 182.000 | − | 182.000i | 0.383158 | − | 0.383158i | ||||
\(476\) | −24.0000 | + | 24.0000i | −0.0504202 | + | 0.0504202i | ||||
\(477\) | −270.000 | −0.566038 | ||||||||
\(478\) | − | 228.000i | − | 0.476987i | ||||||
\(479\) | −234.000 | + | 234.000i | −0.488518 | + | 0.488518i | −0.907838 | − | 0.419321i | \(-0.862268\pi\) |
0.419321 | + | 0.907838i | \(0.362268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 481.000 | + | 481.000i | 1.00000 | + | 1.00000i | ||||
\(482\) | 302.000 | 0.626556 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −98.0000 | −0.202479 | ||||||||
\(485\) | 282.000i | 0.581443i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 298.000 | + | 298.000i | 0.611910 | + | 0.611910i | 0.943443 | − | 0.331534i | \(-0.107566\pi\) |
−0.331534 | + | 0.943443i | \(0.607566\pi\) | |||||||
\(488\) | 36.0000 | − | 36.0000i | 0.0737705 | − | 0.0737705i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 246.000 | 0.502041 | ||||||||
\(491\) | 420.000i | 0.855397i | 0.903921 | + | 0.427699i | \(0.140676\pi\) | ||||
−0.903921 | + | 0.427699i | \(0.859324\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 288.000i | − | 0.584178i | ||||||
\(494\) | −676.000 | −1.36842 | ||||||||
\(495\) | 324.000 | 0.654545 | ||||||||
\(496\) | 56.0000 | + | 56.0000i | 0.112903 | + | 0.112903i | ||||
\(497\) | 24.0000 | 0.0482897 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 346.000 | + | 346.000i | 0.693387 | + | 0.693387i | 0.962976 | − | 0.269589i | \(-0.0868878\pi\) |
−0.269589 | + | 0.962976i | \(0.586888\pi\) | |||||||
\(500\) | −192.000 | − | 192.000i | −0.384000 | − | 0.384000i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 180.000 | − | 180.000i | 0.358566 | − | 0.358566i | ||||
\(503\) | −420.000 | −0.834990 | −0.417495 | − | 0.908679i | \(-0.637092\pi\) | ||||
−0.417495 | + | 0.908679i | \(0.637092\pi\) | |||||||
\(504\) | − | 72.0000i | − | 0.142857i | ||||||
\(505\) | 360.000 | − | 360.000i | 0.712871 | − | 0.712871i | ||||
\(506\) | − | 288.000i | − | 0.569170i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −112.000 | −0.220472 | ||||||||
\(509\) | 381.000 | + | 381.000i | 0.748527 | + | 0.748527i | 0.974202 | − | 0.225676i | \(-0.0724590\pi\) |
−0.225676 | + | 0.974202i | \(0.572459\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 68.0000i | − | 0.133072i | ||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 144.000 | − | 144.000i | 0.280156 | − | 0.280156i | ||||
\(515\) | −432.000 | + | 432.000i | −0.838835 | + | 0.838835i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 504.000i | − | 0.974855i | ||||||
\(518\) | 148.000 | − | 148.000i | 0.285714 | − | 0.285714i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 156.000i | 0.300000i | ||||||||
\(521\) | 312.000 | 0.598848 | 0.299424 | − | 0.954120i | \(-0.403205\pi\) | ||||
0.299424 | + | 0.954120i | \(0.403205\pi\) | |||||||
\(522\) | 432.000 | + | 432.000i | 0.827586 | + | 0.827586i | ||||
\(523\) | −560.000 | −1.07075 | −0.535373 | − | 0.844616i | \(-0.679829\pi\) | ||||
−0.535373 | + | 0.844616i | \(0.679829\pi\) | |||||||
\(524\) | 144.000i | 0.274809i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −60.0000 | − | 60.0000i | −0.114068 | − | 0.114068i | ||||
\(527\) | 84.0000 | − | 84.0000i | 0.159393 | − | 0.159393i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −47.0000 | −0.0888469 | ||||||||
\(530\) | − | 180.000i | − | 0.339623i | ||||||
\(531\) | 486.000 | − | 486.000i | 0.915254 | − | 0.915254i | ||||
\(532\) | 208.000i | 0.390977i | ||||||||
\(533\) | 117.000 | − | 117.000i | 0.219512 | − | 0.219512i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −360.000 | − | 360.000i | −0.672897 | − | 0.672897i | ||||
\(536\) | 88.0000 | 0.164179 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −288.000 | − | 288.000i | −0.535316 | − | 0.535316i | ||||
\(539\) | 246.000 | + | 246.000i | 0.456401 | + | 0.456401i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −379.000 | + | 379.000i | −0.700555 | + | 0.700555i | −0.964530 | − | 0.263975i | \(-0.914966\pi\) |
0.263975 | + | 0.964530i | \(0.414966\pi\) | |||||||
\(542\) | −268.000 | −0.494465 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 24.0000 | − | 24.0000i | 0.0441176 | − | 0.0441176i | ||||
\(545\) | 114.000i | 0.209174i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −400.000 | −0.731261 | −0.365631 | − | 0.930760i | \(-0.619147\pi\) | ||||
−0.365631 | + | 0.930760i | \(0.619147\pi\) | |||||||
\(548\) | −126.000 | − | 126.000i | −0.229927 | − | 0.229927i | ||||
\(549\) | 162.000 | 0.295082 | ||||||||
\(550\) | − | 84.0000i | − | 0.152727i | ||||||
\(551\) | −1248.00 | − | 1248.00i | −2.26497 | − | 2.26497i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −216.000 | + | 216.000i | −0.390597 | + | 0.390597i | ||||
\(554\) | −216.000 | + | 216.000i | −0.389892 | + | 0.389892i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 304.000i | 0.546763i | ||||||||
\(557\) | 117.000 | − | 117.000i | 0.210054 | − | 0.210054i | −0.594236 | − | 0.804290i | \(-0.702546\pi\) |
0.804290 | + | 0.594236i | \(0.202546\pi\) | |||||||
\(558\) | 252.000i | 0.451613i | ||||||||
\(559\) | −468.000 | −0.837209 | ||||||||
\(560\) | 48.0000 | 0.0857143 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −318.000 | −0.565836 | ||||||||
\(563\) | 876.000i | 1.55595i | 0.628295 | + | 0.777975i | \(0.283753\pi\) | ||||
−0.628295 | + | 0.777975i | \(0.716247\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 360.000 | + | 360.000i | 0.637168 | + | 0.637168i | ||||
\(566\) | 404.000 | − | 404.000i | 0.713781 | − | 0.713781i | ||||
\(567\) | 162.000 | − | 162.000i | 0.285714 | − | 0.285714i | ||||
\(568\) | −24.0000 | −0.0422535 | ||||||||
\(569\) | − | 720.000i | − | 1.26538i | −0.774406 | − | 0.632689i | \(-0.781951\pi\) | ||
0.774406 | − | 0.632689i | \(-0.218049\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 460.000i | − | 0.805604i | −0.915287 | − | 0.402802i | \(-0.868036\pi\) | ||
0.915287 | − | 0.402802i | \(-0.131964\pi\) | |||||||
\(572\) | −156.000 | + | 156.000i | −0.272727 | + | 0.272727i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −36.0000 | − | 36.0000i | −0.0627178 | − | 0.0627178i | ||||
\(575\) | −168.000 | −0.292174 | ||||||||
\(576\) | 72.0000i | 0.125000i | ||||||||
\(577\) | −377.000 | − | 377.000i | −0.653380 | − | 0.653380i | 0.300426 | − | 0.953805i | \(-0.402871\pi\) |
−0.953805 | + | 0.300426i | \(0.902871\pi\) | |||||||
\(578\) | 253.000 | + | 253.000i | 0.437716 | + | 0.437716i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −288.000 | + | 288.000i | −0.496552 | + | 0.496552i | ||||
\(581\) | 312.000 | 0.537005 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 180.000 | − | 180.000i | 0.308748 | − | 0.308748i | ||||
\(584\) | 68.0000i | 0.116438i | ||||||||
\(585\) | −351.000 | + | 351.000i | −0.600000 | + | 0.600000i | ||||
\(586\) | 294.000 | 0.501706 | ||||||||
\(587\) | 738.000 | + | 738.000i | 1.25724 | + | 1.25724i | 0.952405 | + | 0.304835i | \(0.0986013\pi\) |
0.304835 | + | 0.952405i | \(0.401399\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 728.000i | − | 1.23599i | ||||||
\(590\) | 324.000 | + | 324.000i | 0.549153 | + | 0.549153i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −148.000 | + | 148.000i | −0.250000 | + | 0.250000i | ||||
\(593\) | 327.000 | − | 327.000i | 0.551433 | − | 0.551433i | −0.375421 | − | 0.926854i | \(-0.622502\pi\) |
0.926854 | + | 0.375421i | \(0.122502\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 72.0000i | − | 0.121008i | ||||||
\(596\) | 198.000 | − | 198.000i | 0.332215 | − | 0.332215i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 312.000 | + | 312.000i | 0.521739 | + | 0.521739i | ||||
\(599\) | 372.000 | 0.621035 | 0.310518 | − | 0.950568i | \(-0.399498\pi\) | ||||
0.310518 | + | 0.950568i | \(0.399498\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −648.000 | −1.07820 | −0.539101 | − | 0.842241i | \(-0.681236\pi\) | ||||
−0.539101 | + | 0.842241i | \(0.681236\pi\) | |||||||
\(602\) | 144.000i | 0.239203i | ||||||||
\(603\) | 198.000 | + | 198.000i | 0.328358 | + | 0.328358i | ||||
\(604\) | 212.000 | + | 212.000i | 0.350993 | + | 0.350993i | ||||
\(605\) | 147.000 | − | 147.000i | 0.242975 | − | 0.242975i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −260.000 | −0.428336 | −0.214168 | − | 0.976797i | \(-0.568704\pi\) | ||||
−0.214168 | + | 0.976797i | \(0.568704\pi\) | |||||||
\(608\) | − | 208.000i | − | 0.342105i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 108.000i | 0.177049i | ||||||||
\(611\) | 546.000 | + | 546.000i | 0.893617 | + | 0.893617i | ||||
\(612\) | 108.000 | 0.176471 | ||||||||
\(613\) | −197.000 | − | 197.000i | −0.321370 | − | 0.321370i | 0.527922 | − | 0.849293i | \(-0.322971\pi\) |
−0.849293 | + | 0.527922i | \(0.822971\pi\) | |||||||
\(614\) | 164.000 | 0.267101 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 48.0000 | + | 48.0000i | 0.0779221 | + | 0.0779221i | ||||
\(617\) | 753.000 | + | 753.000i | 1.22042 | + | 1.22042i | 0.967482 | + | 0.252939i | \(0.0813973\pi\) |
0.252939 | + | 0.967482i | \(0.418603\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.0000 | + | 34.0000i | −0.0549273 | + | 0.0549273i | −0.734037 | − | 0.679110i | \(-0.762366\pi\) |
0.679110 | + | 0.734037i | \(0.262366\pi\) | |||||||
\(620\) | −168.000 | −0.270968 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 120.000 | − | 120.000i | 0.192926 | − | 0.192926i | ||||
\(623\) | 36.0000i | 0.0577849i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 401.000 | 0.641600 | ||||||||
\(626\) | −360.000 | − | 360.000i | −0.575080 | − | 0.575080i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 160.000i | − | 0.254777i | ||||||
\(629\) | 222.000 | + | 222.000i | 0.352941 | + | 0.352941i | ||||
\(630\) | 108.000 | + | 108.000i | 0.171429 | + | 0.171429i | ||||
\(631\) | 386.000 | − | 386.000i | 0.611727 | − | 0.611727i | −0.331669 | − | 0.943396i | \(-0.607612\pi\) |
0.943396 | + | 0.331669i | \(0.107612\pi\) | |||||||
\(632\) | 216.000 | − | 216.000i | 0.341772 | − | 0.341772i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 294.000i | − | 0.463722i | ||||||
\(635\) | 168.000 | − | 168.000i | 0.264567 | − | 0.264567i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −533.000 | −0.836735 | ||||||||
\(638\) | −576.000 | −0.902821 | ||||||||
\(639\) | −54.0000 | − | 54.0000i | −0.0845070 | − | 0.0845070i | ||||
\(640\) | −48.0000 | −0.0750000 | ||||||||
\(641\) | 90.0000i | 0.140406i | 0.997533 | + | 0.0702028i | \(0.0223646\pi\) | ||||
−0.997533 | + | 0.0702028i | \(0.977635\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −202.000 | − | 202.000i | −0.314152 | − | 0.314152i | 0.532363 | − | 0.846516i | \(-0.321304\pi\) |
−0.846516 | + | 0.532363i | \(0.821304\pi\) | |||||||
\(644\) | 96.0000 | − | 96.0000i | 0.149068 | − | 0.149068i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −312.000 | −0.482972 | ||||||||
\(647\) | − | 144.000i | − | 0.222566i | −0.993789 | − | 0.111283i | \(-0.964504\pi\) | ||
0.993789 | − | 0.111283i | \(-0.0354960\pi\) | |||||||
\(648\) | −162.000 | + | 162.000i | −0.250000 | + | 0.250000i | ||||
\(649\) | 648.000i | 0.998459i | ||||||||
\(650\) | 91.0000 | + | 91.0000i | 0.140000 | + | 0.140000i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 164.000 | + | 164.000i | 0.251534 | + | 0.251534i | ||||
\(653\) | −240.000 | −0.367534 | −0.183767 | − | 0.982970i | \(-0.558829\pi\) | ||||
−0.183767 | + | 0.982970i | \(0.558829\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −216.000 | − | 216.000i | −0.329771 | − | 0.329771i | ||||
\(656\) | 36.0000 | + | 36.0000i | 0.0548780 | + | 0.0548780i | ||||
\(657\) | −153.000 | + | 153.000i | −0.232877 | + | 0.232877i | ||||
\(658\) | 168.000 | − | 168.000i | 0.255319 | − | 0.255319i | ||||
\(659\) | −168.000 | −0.254932 | −0.127466 | − | 0.991843i | \(-0.540684\pi\) | ||||
−0.127466 | + | 0.991843i | \(0.540684\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −509.000 | + | 509.000i | −0.770045 | + | 0.770045i | −0.978114 | − | 0.208069i | \(-0.933282\pi\) |
0.208069 | + | 0.978114i | \(0.433282\pi\) | |||||||
\(662\) | − | 428.000i | − | 0.646526i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −312.000 | −0.469880 | ||||||||
\(665\) | −312.000 | − | 312.000i | −0.469173 | − | 0.469173i | ||||
\(666\) | −666.000 | −1.00000 | ||||||||
\(667\) | 1152.00i | 1.72714i | ||||||||
\(668\) | −276.000 | − | 276.000i | −0.413174 | − | 0.413174i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −132.000 | + | 132.000i | −0.197015 | + | 0.197015i | ||||
\(671\) | −108.000 | + | 108.000i | −0.160954 | + | 0.160954i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 954.000i | − | 1.41753i | −0.705443 | − | 0.708767i | \(-0.749252\pi\) | ||
0.705443 | − | 0.708767i | \(-0.250748\pi\) | |||||||
\(674\) | 314.000 | − | 314.000i | 0.465875 | − | 0.465875i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | − | 338.000i | − | 0.500000i | ||||||
\(677\) | −930.000 | −1.37371 | −0.686854 | − | 0.726796i | \(-0.741009\pi\) | ||||
−0.686854 | + | 0.726796i | \(0.741009\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −188.000 | −0.276878 | ||||||||
\(680\) | 72.0000i | 0.105882i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −168.000 | − | 168.000i | −0.246334 | − | 0.246334i | ||||
\(683\) | 342.000 | − | 342.000i | 0.500732 | − | 0.500732i | −0.410933 | − | 0.911665i | \(-0.634797\pi\) |
0.911665 | + | 0.410933i | \(0.134797\pi\) | |||||||
\(684\) | 468.000 | − | 468.000i | 0.684211 | − | 0.684211i | ||||
\(685\) | 378.000 | 0.551825 | ||||||||
\(686\) | 360.000i | 0.524781i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 144.000i | − | 0.209302i | ||||||
\(689\) | 390.000i | 0.566038i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −254.000 | − | 254.000i | −0.367583 | − | 0.367583i | 0.499012 | − | 0.866595i | \(-0.333696\pi\) |
−0.866595 | + | 0.499012i | \(0.833696\pi\) | |||||||
\(692\) | 48.0000 | 0.0693642 | ||||||||
\(693\) | 216.000i | 0.311688i | ||||||||
\(694\) | −120.000 | − | 120.000i | −0.172911 | − | 0.172911i | ||||
\(695\) | −456.000 | − | 456.000i | −0.656115 | − | 0.656115i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.0000 | − | 54.0000i | 0.0774749 | − | 0.0774749i | ||||
\(698\) | 202.000 | 0.289398 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 28.0000 | − | 28.0000i | 0.0400000 | − | 0.0400000i | ||||
\(701\) | 150.000i | 0.213980i | 0.994260 | + | 0.106990i | \(0.0341213\pi\) | ||||
−0.994260 | + | 0.106990i | \(0.965879\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1924.00 | 2.73684 | ||||||||
\(704\) | −48.0000 | − | 48.0000i | −0.0681818 | − | 0.0681818i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 66.0000i | 0.0934844i | ||||||||
\(707\) | 240.000 | + | 240.000i | 0.339463 | + | 0.339463i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −299.000 | + | 299.000i | −0.421721 | + | 0.421721i | −0.885796 | − | 0.464075i | \(-0.846387\pi\) |
0.464075 | + | 0.885796i | \(0.346387\pi\) | |||||||
\(710\) | 36.0000 | − | 36.0000i | 0.0507042 | − | 0.0507042i | ||||
\(711\) | 972.000 | 1.36709 | ||||||||
\(712\) | − | 36.0000i | − | 0.0505618i | ||||||
\(713\) | −336.000 | + | 336.000i | −0.471248 | + | 0.471248i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 468.000i | − | 0.654545i | ||||||
\(716\) | 600.000 | 0.837989 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 372.000 | 0.518106 | ||||||||
\(719\) | − | 1200.00i | − | 1.66898i | −0.551020 | − | 0.834492i | \(-0.685761\pi\) | ||
0.551020 | − | 0.834492i | \(-0.314239\pi\) | |||||||
\(720\) | −108.000 | − | 108.000i | −0.150000 | − | 0.150000i | ||||
\(721\) | −288.000 | − | 288.000i | −0.399445 | − | 0.399445i | ||||
\(722\) | −991.000 | + | 991.000i | −1.37258 | + | 1.37258i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −180.000 | −0.248619 | ||||||||
\(725\) | 336.000i | 0.463448i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1336.00i | 1.83769i | 0.394620 | + | 0.918845i | \(0.370876\pi\) | ||||
−0.394620 | + | 0.918845i | \(0.629124\pi\) | |||||||
\(728\) | −104.000 | −0.142857 | ||||||||
\(729\) | −729.000 | −1.00000 | ||||||||
\(730\) | −102.000 | − | 102.000i | −0.139726 | − | 0.139726i | ||||
\(731\) | −216.000 | −0.295486 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 283.000 | + | 283.000i | 0.386085 | + | 0.386085i | 0.873288 | − | 0.487204i | \(-0.161983\pi\) |
−0.487204 | + | 0.873288i | \(0.661983\pi\) | |||||||
\(734\) | 580.000 | + | 580.000i | 0.790191 | + | 0.790191i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −96.0000 | + | 96.0000i | −0.130435 | + | 0.130435i | ||||
\(737\) | −264.000 | −0.358209 | ||||||||
\(738\) | 162.000i | 0.219512i | ||||||||
\(739\) | 926.000 | − | 926.000i | 1.25304 | − | 1.25304i | 0.298696 | − | 0.954348i | \(-0.403448\pi\) |
0.954348 | − | 0.298696i | \(-0.0965518\pi\) | |||||||
\(740\) | − | 444.000i | − | 0.600000i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 120.000 | 0.161725 | ||||||||
\(743\) | 798.000 | + | 798.000i | 1.07402 | + | 1.07402i | 0.997032 | + | 0.0769926i | \(0.0245318\pi\) |
0.0769926 | + | 0.997032i | \(0.475468\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 594.000i | 0.797315i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −702.000 | − | 702.000i | −0.939759 | − | 0.939759i | ||||
\(748\) | −72.0000 | + | 72.0000i | −0.0962567 | + | 0.0962567i | ||||
\(749\) | 240.000 | − | 240.000i | 0.320427 | − | 0.320427i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1080.00i | 1.43808i | 0.694967 | + | 0.719041i | \(0.255419\pi\) | ||||
−0.694967 | + | 0.719041i | \(0.744581\pi\) | |||||||
\(752\) | −168.000 | + | 168.000i | −0.223404 | + | 0.223404i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 624.000 | − | 624.000i | 0.827586 | − | 0.827586i | ||||
\(755\) | −636.000 | −0.842384 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 990.000 | 1.30779 | 0.653897 | − | 0.756584i | \(-0.273133\pi\) | ||||
0.653897 | + | 0.756584i | \(0.273133\pi\) | |||||||
\(758\) | 452.000i | 0.596306i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 312.000 | + | 312.000i | 0.410526 | + | 0.410526i | ||||
\(761\) | 801.000 | − | 801.000i | 1.05256 | − | 1.05256i | 0.0540227 | − | 0.998540i | \(-0.482796\pi\) |
0.998540 | − | 0.0540227i | \(-0.0172043\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −76.0000 | −0.0996068 | ||||||||
\(764\) | 504.000i | 0.659686i | ||||||||
\(765\) | −162.000 | + | 162.000i | −0.211765 | + | 0.211765i | ||||
\(766\) | 156.000i | 0.203655i | ||||||||
\(767\) | −702.000 | − | 702.000i | −0.915254 | − | 0.915254i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −329.000 | − | 329.000i | −0.427828 | − | 0.427828i | 0.460060 | − | 0.887888i | \(-0.347828\pi\) |
−0.887888 | + | 0.460060i | \(0.847828\pi\) | |||||||
\(770\) | −144.000 | −0.187013 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 514.000 | + | 514.000i | 0.665803 | + | 0.665803i | ||||
\(773\) | −867.000 | − | 867.000i | −1.12160 | − | 1.12160i | −0.991500 | − | 0.130104i | \(-0.958469\pi\) |
−0.130104 | − | 0.991500i | \(-0.541531\pi\) | |||||||
\(774\) | 324.000 | − | 324.000i | 0.418605 | − | 0.418605i | ||||
\(775\) | −98.0000 | + | 98.0000i | −0.126452 | + | 0.126452i | ||||
\(776\) | 188.000 | 0.242268 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −150.000 | + | 150.000i | −0.192802 | + | 0.192802i | ||||
\(779\) | − | 468.000i | − | 0.600770i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 72.0000 | 0.0921895 | ||||||||
\(782\) | 144.000 | + | 144.000i | 0.184143 | + | 0.184143i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 164.000i | − | 0.209184i | ||||||
\(785\) | 240.000 | + | 240.000i | 0.305732 | + | 0.305732i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −158.000 | + | 158.000i | −0.200762 | + | 0.200762i | −0.800327 | − | 0.599564i | \(-0.795341\pi\) |
0.599564 | + | 0.800327i | \(0.295341\pi\) | |||||||
\(788\) | −246.000 | + | 246.000i | −0.312183 | + | 0.312183i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 648.000i | 0.820253i | ||||||||
\(791\) | −240.000 | + | 240.000i | −0.303413 | + | 0.303413i | ||||
\(792\) | − | 216.000i | − | 0.272727i | ||||||
\(793\) | − | 234.000i | − | 0.295082i | ||||||
\(794\) | −506.000 | −0.637280 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −400.000 | −0.502513 | ||||||||
\(797\) | − | 954.000i | − | 1.19699i | −0.801127 | − | 0.598494i | \(-0.795766\pi\) | ||
0.801127 | − | 0.598494i | \(-0.204234\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 252.000 | + | 252.000i | 0.315394 | + | 0.315394i | ||||
\(800\) | −28.0000 | + | 28.0000i | −0.0350000 | + | 0.0350000i | ||||
\(801\) | 81.0000 | − | 81.0000i | 0.101124 | − | 0.101124i | ||||
\(802\) | −498.000 | −0.620948 | ||||||||
\(803\) | − | 204.000i | − | 0.254047i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 288.000i | 0.357764i | ||||||||
\(806\) | 364.000 | 0.451613 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −240.000 | − | 240.000i | −0.297030 | − | 0.297030i | ||||
\(809\) | 312.000 | 0.385661 | 0.192831 | − | 0.981232i | \(-0.438233\pi\) | ||||
0.192831 | + | 0.981232i | \(0.438233\pi\) | |||||||
\(810\) | − | 486.000i | − | 0.600000i | ||||||
\(811\) | 566.000 | + | 566.000i | 0.697904 | + | 0.697904i | 0.963958 | − | 0.266054i | \(-0.0857200\pi\) |
−0.266054 | + | 0.963958i | \(0.585720\pi\) | |||||||
\(812\) | −192.000 | − | 192.000i | −0.236453 | − | 0.236453i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 444.000 | − | 444.000i | 0.545455 | − | 0.545455i | ||||
\(815\) | −492.000 | −0.603681 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −936.000 | + | 936.000i | −1.14565 | + | 1.14565i | ||||
\(818\) | − | 638.000i | − | 0.779951i | ||||||
\(819\) | −234.000 | − | 234.000i | −0.285714 | − | 0.285714i | ||||
\(820\) | −108.000 | −0.131707 | ||||||||
\(821\) | −339.000 | − | 339.000i | −0.412911 | − | 0.412911i | 0.469840 | − | 0.882751i | \(-0.344311\pi\) |
−0.882751 | + | 0.469840i | \(0.844311\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1224.00i | − | 1.48724i | −0.668601 | − | 0.743621i | \(-0.733107\pi\) | ||
0.668601 | − | 0.743621i | \(-0.266893\pi\) | |||||||
\(824\) | 288.000 | + | 288.000i | 0.349515 | + | 0.349515i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −216.000 | + | 216.000i | −0.261501 | + | 0.261501i | ||||
\(827\) | −678.000 | + | 678.000i | −0.819831 | + | 0.819831i | −0.986083 | − | 0.166253i | \(-0.946833\pi\) |
0.166253 | + | 0.986083i | \(0.446833\pi\) | |||||||
\(828\) | −432.000 | −0.521739 | ||||||||
\(829\) | − | 920.000i | − | 1.10977i | −0.831927 | − | 0.554885i | \(-0.812762\pi\) | ||
0.831927 | − | 0.554885i | \(-0.187238\pi\) | |||||||
\(830\) | 468.000 | − | 468.000i | 0.563855 | − | 0.563855i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 104.000 | 0.125000 | ||||||||
\(833\) | −246.000 | −0.295318 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 828.000 | 0.991617 | ||||||||
\(836\) | 624.000i | 0.746411i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −48.0000 | − | 48.0000i | −0.0572792 | − | 0.0572792i | ||||
\(839\) | −774.000 | + | 774.000i | −0.922527 | + | 0.922527i | −0.997207 | − | 0.0746807i | \(-0.976206\pi\) |
0.0746807 | + | 0.997207i | \(0.476206\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1463.00 | 1.73960 | ||||||||
\(842\) | 22.0000i | 0.0261283i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 576.000i | − | 0.682464i | ||||||
\(845\) | 507.000 | + | 507.000i | 0.600000 | + | 0.600000i | ||||
\(846\) | −756.000 | −0.893617 | ||||||||
\(847\) | 98.0000 | + | 98.0000i | 0.115702 | + | 0.115702i | ||||
\(848\) | −120.000 | −0.141509 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 42.0000 | + | 42.0000i | 0.0494118 | + | 0.0494118i | ||||
\(851\) | −888.000 | − | 888.000i | −1.04348 | − | 1.04348i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −443.000 | + | 443.000i | −0.519343 | + | 0.519343i | −0.917373 | − | 0.398029i | \(-0.869694\pi\) |
0.398029 | + | 0.917373i | \(0.369694\pi\) | |||||||
\(854\) | −72.0000 | −0.0843091 | ||||||||
\(855\) | 1404.00i | 1.64211i | ||||||||
\(856\) | −240.000 | + | 240.000i | −0.280374 | + | 0.280374i | ||||
\(857\) | − | 384.000i | − | 0.448075i | −0.974581 | − | 0.224037i | \(-0.928076\pi\) | ||
0.974581 | − | 0.224037i | \(-0.0719238\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 72.0000 | 0.0838184 | 0.0419092 | − | 0.999121i | \(-0.486656\pi\) | ||||
0.0419092 | + | 0.999121i | \(0.486656\pi\) | |||||||
\(860\) | 216.000 | + | 216.000i | 0.251163 | + | 0.251163i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 828.000i | − | 0.960557i | ||||||
\(863\) | −702.000 | − | 702.000i | −0.813441 | − | 0.813441i | 0.171707 | − | 0.985148i | \(-0.445072\pi\) |
−0.985148 | + | 0.171707i | \(0.945072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −72.0000 | + | 72.0000i | −0.0832370 | + | 0.0832370i | ||||
\(866\) | −16.0000 | + | 16.0000i | −0.0184758 | + | 0.0184758i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 112.000i | − | 0.129032i | ||||||
\(869\) | −648.000 | + | 648.000i | −0.745685 | + | 0.745685i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 286.000 | − | 286.000i | 0.328358 | − | 0.328358i | ||||
\(872\) | 76.0000 | 0.0871560 | ||||||||
\(873\) | 423.000 | + | 423.000i | 0.484536 | + | 0.484536i | ||||
\(874\) | 1248.00 | 1.42792 | ||||||||
\(875\) | 384.000i | 0.438857i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 733.000 | + | 733.000i | 0.835804 | + | 0.835804i | 0.988304 | − | 0.152500i | \(-0.0487323\pi\) |
−0.152500 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(878\) | −360.000 | + | 360.000i | −0.410023 | + | 0.410023i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 144.000 | 0.163636 | ||||||||
\(881\) | 960.000i | 1.08967i | 0.838543 | + | 0.544835i | \(0.183408\pi\) | ||||
−0.838543 | + | 0.544835i | \(0.816592\pi\) | |||||||
\(882\) | 369.000 | − | 369.000i | 0.418367 | − | 0.418367i | ||||
\(883\) | 236.000i | 0.267271i | 0.991031 | + | 0.133635i | \(0.0426651\pi\) | ||||
−0.991031 | + | 0.133635i | \(0.957335\pi\) | |||||||
\(884\) | − | 156.000i | − | 0.176471i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −600.000 | − | 600.000i | −0.677201 | − | 0.677201i | ||||
\(887\) | 1380.00 | 1.55581 | 0.777903 | − | 0.628384i | \(-0.216283\pi\) | ||||
0.777903 | + | 0.628384i | \(0.216283\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 112.000 | + | 112.000i | 0.125984 | + | 0.125984i | ||||
\(890\) | 54.0000 | + | 54.0000i | 0.0606742 | + | 0.0606742i | ||||
\(891\) | 486.000 | − | 486.000i | 0.545455 | − | 0.545455i | ||||
\(892\) | −76.0000 | + | 76.0000i | −0.0852018 | + | 0.0852018i | ||||
\(893\) | 2184.00 | 2.44569 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −900.000 | + | 900.000i | −1.00559 | + | 1.00559i | ||||
\(896\) | − | 32.0000i | − | 0.0357143i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.0000 | −0.0200445 | ||||||||
\(899\) | 672.000 | + | 672.000i | 0.747497 | + | 0.747497i | ||||
\(900\) | −126.000 | −0.140000 | ||||||||
\(901\) | 180.000i | 0.199778i | ||||||||
\(902\) | −108.000 | − | 108.000i | −0.119734 | − | 0.119734i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 240.000 | − | 240.000i | 0.265487 | − | 0.265487i | ||||
\(905\) | 270.000 | − | 270.000i | 0.298343 | − | 0.298343i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1444.00i | − | 1.59206i | −0.605256 | − | 0.796031i | \(-0.706929\pi\) | ||
0.605256 | − | 0.796031i | \(-0.293071\pi\) | |||||||
\(908\) | −276.000 | + | 276.000i | −0.303965 | + | 0.303965i | ||||
\(909\) | − | 1080.00i | − | 1.18812i | ||||||
\(910\) | 156.000 | − | 156.000i | 0.171429 | − | 0.171429i | ||||
\(911\) | 612.000 | 0.671789 | 0.335895 | − | 0.941900i | \(-0.390961\pi\) | ||||
0.335895 | + | 0.941900i | \(0.390961\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 936.000 | 1.02519 | ||||||||
\(914\) | − | 94.0000i | − | 0.102845i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 262.000 | + | 262.000i | 0.286026 | + | 0.286026i | ||||
\(917\) | 144.000 | − | 144.000i | 0.157034 | − | 0.157034i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1548.00 | −1.68444 | −0.842220 | − | 0.539134i | \(-0.818752\pi\) | ||||
−0.842220 | + | 0.539134i | \(0.818752\pi\) | |||||||
\(920\) | − | 288.000i | − | 0.313043i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 342.000i | 0.370933i | ||||||||
\(923\) | −78.0000 | + | 78.0000i | −0.0845070 | + | 0.0845070i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −259.000 | − | 259.000i | −0.280000 | − | 0.280000i | ||||
\(926\) | 404.000 | 0.436285 | ||||||||
\(927\) | 1296.00i | 1.39806i | ||||||||
\(928\) | 192.000 | + | 192.000i | 0.206897 | + | 0.206897i | ||||
\(929\) | −969.000 | − | 969.000i | −1.04306 | − | 1.04306i | −0.999030 | − | 0.0440267i | \(-0.985981\pi\) |
−0.0440267 | − | 0.999030i | \(-0.514019\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1066.00 | + | 1066.00i | −1.14501 | + | 1.14501i | ||||
\(932\) | −672.000 | −0.721030 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −516.000 | + | 516.000i | −0.552463 | + | 0.552463i | ||||
\(935\) | − | 216.000i | − | 0.231016i | ||||||
\(936\) | 234.000 | + | 234.000i | 0.250000 | + | 0.250000i | ||||
\(937\) | −450.000 | −0.480256 | −0.240128 | − | 0.970741i | \(-0.577189\pi\) | ||||
−0.240128 | + | 0.970741i | \(0.577189\pi\) | |||||||
\(938\) | −88.0000 | − | 88.0000i | −0.0938166 | − | 0.0938166i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 504.000i | − | 0.536170i | ||||||
\(941\) | 411.000 | + | 411.000i | 0.436769 | + | 0.436769i | 0.890923 | − | 0.454154i | \(-0.150058\pi\) |
−0.454154 | + | 0.890923i | \(0.650058\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −216.000 | + | 216.000i | −0.229056 | + | 0.229056i | ||||
\(944\) | 216.000 | − | 216.000i | 0.228814 | − | 0.228814i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 432.000i | 0.456660i | ||||||||
\(947\) | 582.000 | − | 582.000i | 0.614572 | − | 0.614572i | −0.329562 | − | 0.944134i | \(-0.606901\pi\) |
0.944134 | + | 0.329562i | \(0.106901\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 221.000 | + | 221.000i | 0.232877 | + | 0.232877i | ||||
\(950\) | 364.000 | 0.383158 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −48.0000 | −0.0504202 | ||||||||
\(953\) | − | 1344.00i | − | 1.41028i | −0.709066 | − | 0.705142i | \(-0.750883\pi\) | ||
0.709066 | − | 0.705142i | \(-0.249117\pi\) | |||||||
\(954\) | −270.000 | − | 270.000i | −0.283019 | − | 0.283019i | ||||
\(955\) | −756.000 | − | 756.000i | −0.791623 | − | 0.791623i | ||||
\(956\) | 228.000 | − | 228.000i | 0.238494 | − | 0.238494i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −468.000 | −0.488518 | ||||||||
\(959\) | 252.000i | 0.262774i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 569.000i | − | 0.592092i | ||||||
\(962\) | 962.000i | 1.00000i | ||||||||
\(963\) | −1080.00 | −1.12150 | ||||||||
\(964\) | 302.000 | + | 302.000i | 0.313278 | + | 0.313278i | ||||
\(965\) | −1542.00 | −1.59793 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −562.000 | − | 562.000i | −0.581179 | − | 0.581179i | 0.354048 | − | 0.935227i | \(-0.384805\pi\) |
−0.935227 | + | 0.354048i | \(0.884805\pi\) | |||||||
\(968\) | −98.0000 | − | 98.0000i | −0.101240 | − | 0.101240i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −282.000 | + | 282.000i | −0.290722 | + | 0.290722i | ||||
\(971\) | −1248.00 | −1.28527 | −0.642636 | − | 0.766171i | \(-0.722159\pi\) | ||||
−0.642636 | + | 0.766171i | \(0.722159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 304.000 | − | 304.000i | 0.312436 | − | 0.312436i | ||||
\(974\) | 596.000i | 0.611910i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 72.0000 | 0.0737705 | ||||||||
\(977\) | 33.0000 | + | 33.0000i | 0.0337769 | + | 0.0337769i | 0.723794 | − | 0.690017i | \(-0.242397\pi\) |
−0.690017 | + | 0.723794i | \(0.742397\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 108.000i | 0.110317i | ||||||||
\(980\) | 246.000 | + | 246.000i | 0.251020 | + | 0.251020i | ||||
\(981\) | 171.000 | + | 171.000i | 0.174312 | + | 0.174312i | ||||
\(982\) | −420.000 | + | 420.000i | −0.427699 | + | 0.427699i | ||||
\(983\) | 702.000 | − | 702.000i | 0.714140 | − | 0.714140i | −0.253258 | − | 0.967399i | \(-0.581502\pi\) |
0.967399 | + | 0.253258i | \(0.0815023\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 738.000i | − | 0.749239i | ||||||
\(986\) | 288.000 | − | 288.000i | 0.292089 | − | 0.292089i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −676.000 | − | 676.000i | −0.684211 | − | 0.684211i | ||||
\(989\) | 864.000 | 0.873610 | ||||||||
\(990\) | 324.000 | + | 324.000i | 0.327273 | + | 0.327273i | ||||
\(991\) | −268.000 | −0.270434 | −0.135217 | − | 0.990816i | \(-0.543173\pi\) | ||||
−0.135217 | + | 0.990816i | \(0.543173\pi\) | |||||||
\(992\) | 112.000i | 0.112903i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 24.0000 | + | 24.0000i | 0.0241449 | + | 0.0241449i | ||||
\(995\) | 600.000 | − | 600.000i | 0.603015 | − | 0.603015i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1310.00 | −1.31394 | −0.656971 | − | 0.753916i | \(-0.728163\pi\) | ||||
−0.656971 | + | 0.753916i | \(0.728163\pi\) | |||||||
\(998\) | 692.000i | 0.693387i | ||||||||
\(999\) | 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 | 26.3.d.a.21.1 | yes | 2 | |
3.2 | odd | 2 | 234.3.i.a.73.1 | 2 | |||
4.3 | odd | 2 | 208.3.t.b.177.1 | 2 | |||
5.2 | odd | 4 | 650.3.f.b.99.1 | 2 | |||
5.3 | odd | 4 | 650.3.f.e.99.1 | 2 | |||
5.4 | even | 2 | 650.3.k.b.151.1 | 2 | |||
13.2 | odd | 12 | 338.3.f.b.19.1 | 4 | |||
13.3 | even | 3 | 338.3.f.b.319.1 | 4 | |||
13.4 | even | 6 | 338.3.f.g.89.1 | 4 | |||
13.5 | odd | 4 | inner | 26.3.d.a.5.1 | ✓ | 2 | |
13.6 | odd | 12 | 338.3.f.b.249.1 | 4 | |||
13.7 | odd | 12 | 338.3.f.g.249.1 | 4 | |||
13.8 | odd | 4 | 338.3.d.a.239.1 | 2 | |||
13.9 | even | 3 | 338.3.f.b.89.1 | 4 | |||
13.10 | even | 6 | 338.3.f.g.319.1 | 4 | |||
13.11 | odd | 12 | 338.3.f.g.19.1 | 4 | |||
13.12 | even | 2 | 338.3.d.a.99.1 | 2 | |||
39.5 | even | 4 | 234.3.i.a.109.1 | 2 | |||
52.31 | even | 4 | 208.3.t.b.161.1 | 2 | |||
65.18 | even | 4 | 650.3.f.b.499.1 | 2 | |||
65.44 | odd | 4 | 650.3.k.b.551.1 | 2 | |||
65.57 | even | 4 | 650.3.f.e.499.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
26.3.d.a.5.1 | ✓ | 2 | 13.5 | odd | 4 | inner | |
26.3.d.a.21.1 | yes | 2 | 1.1 | even | 1 | trivial | |
208.3.t.b.161.1 | 2 | 52.31 | even | 4 | |||
208.3.t.b.177.1 | 2 | 4.3 | odd | 2 | |||
234.3.i.a.73.1 | 2 | 3.2 | odd | 2 | |||
234.3.i.a.109.1 | 2 | 39.5 | even | 4 | |||
338.3.d.a.99.1 | 2 | 13.12 | even | 2 | |||
338.3.d.a.239.1 | 2 | 13.8 | odd | 4 | |||
338.3.f.b.19.1 | 4 | 13.2 | odd | 12 | |||
338.3.f.b.89.1 | 4 | 13.9 | even | 3 | |||
338.3.f.b.249.1 | 4 | 13.6 | odd | 12 | |||
338.3.f.b.319.1 | 4 | 13.3 | even | 3 | |||
338.3.f.g.19.1 | 4 | 13.11 | odd | 12 | |||
338.3.f.g.89.1 | 4 | 13.4 | even | 6 | |||
338.3.f.g.249.1 | 4 | 13.7 | odd | 12 | |||
338.3.f.g.319.1 | 4 | 13.10 | even | 6 | |||
650.3.f.b.99.1 | 2 | 5.2 | odd | 4 | |||
650.3.f.b.499.1 | 2 | 65.18 | even | 4 | |||
650.3.f.e.99.1 | 2 | 5.3 | odd | 4 | |||
650.3.f.e.499.1 | 2 | 65.57 | even | 4 | |||
650.3.k.b.151.1 | 2 | 5.4 | even | 2 | |||
650.3.k.b.551.1 | 2 | 65.44 | odd | 4 |