Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(2431,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4560.2431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.d (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: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 35x^{10} + 202x^{8} + 362x^{6} + 245x^{4} + 63x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.8 | ||
Root | \(-1.19434i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.2431 |
Dual form | 4560.2.d.j.2431.5 |
$q$-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 \(\left(\mathbb{Z}/4560\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(1711\) | \(1921\) | \(2737\) | \(3041\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.25182i | 0.473145i | 0.971614 | + | 0.236573i | \(0.0760241\pi\) | ||||
−0.971614 | + | 0.236573i | \(0.923976\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.630063i | 0.189971i | 0.995479 | + | 0.0949855i | \(0.0302805\pi\) | ||||
−0.995479 | + | 0.0949855i | \(0.969720\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.96496i | 1.09968i | 0.835269 | + | 0.549841i | \(0.185312\pi\) | ||||
−0.835269 | + | 0.549841i | \(0.814688\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.90373 | −1.67440 | −0.837200 | − | 0.546896i | \(-0.815809\pi\) | ||||
−0.837200 | + | 0.546896i | \(0.815809\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.11425 | − | 3.81182i | 0.485041 | − | 0.874491i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.25182i | − | 0.273170i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.49272i | − | 1.35382i | −0.736064 | − | 0.676912i | \(-0.763318\pi\) | ||
0.736064 | − | 0.676912i | \(-0.236682\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.83404i | − | 0.526268i | −0.964759 | − | 0.263134i | \(-0.915244\pi\) | ||
0.964759 | − | 0.263134i | \(-0.0847561\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.48802 | 1.34489 | 0.672444 | − | 0.740148i | \(-0.265245\pi\) | ||||
0.672444 | + | 0.740148i | \(0.265245\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.630063i | − | 0.109680i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.25182i | 0.211597i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.57487i | − | 1.57410i | −0.616890 | − | 0.787049i | \(-0.711608\pi\) | ||
0.616890 | − | 0.787049i | \(-0.288392\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 3.96496i | − | 0.634902i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.74454i | 1.20949i | 0.796418 | + | 0.604747i | \(0.206726\pi\) | ||||
−0.796418 | + | 0.604747i | \(0.793274\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.37089i | − | 1.12405i | −0.827120 | − | 0.562025i | \(-0.810022\pi\) | ||
0.827120 | − | 0.562025i | \(-0.189978\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.33490i | − | 0.486445i | −0.969971 | − | 0.243222i | \(-0.921796\pi\) | ||
0.969971 | − | 0.243222i | \(-0.0782045\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.43294 | 0.776134 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.90373 | 0.966716 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.95682i | 1.36767i | 0.729635 | + | 0.683837i | \(0.239690\pi\) | ||||
−0.729635 | + | 0.683837i | \(0.760310\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.630063i | 0.0849576i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.11425 | + | 3.81182i | −0.280039 | + | 0.504888i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.92095 | 1.29160 | 0.645799 | − | 0.763507i | \(-0.276524\pi\) | ||||
0.645799 | + | 0.763507i | \(0.276524\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4329 | −1.59187 | −0.795937 | − | 0.605379i | \(-0.793021\pi\) | ||||
−0.795937 | + | 0.605379i | \(0.793021\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.25182i | 0.157715i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.96496i | 0.491793i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.82681 | 0.956197 | 0.478098 | − | 0.878306i | \(-0.341326\pi\) | ||||
0.478098 | + | 0.878306i | \(0.341326\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.49272i | 0.781631i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.41571 | −0.168014 | −0.0840072 | − | 0.996465i | \(-0.526772\pi\) | ||||
−0.0840072 | + | 0.996465i | \(0.526772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.64421 | 0.894687 | 0.447343 | − | 0.894362i | \(-0.352370\pi\) | ||||
0.447343 | + | 0.894362i | \(0.352370\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.788728 | −0.0898839 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.8485 | 1.55808 | 0.779040 | − | 0.626974i | \(-0.215707\pi\) | ||||
0.779040 | + | 0.626974i | \(0.215707\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.45397i | 1.03771i | 0.854863 | + | 0.518854i | \(0.173641\pi\) | ||||
−0.854863 | + | 0.518854i | \(0.826359\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.90373 | −0.748815 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.83404i | 0.303841i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.52855i | 0.480026i | 0.970770 | + | 0.240013i | \(0.0771516\pi\) | ||||
−0.970770 | + | 0.240013i | \(0.922848\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.96343 | −0.520309 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.48802 | −0.776471 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.11425 | − | 3.81182i | 0.216917 | − | 0.391084i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.90679i | − | 0.396674i | −0.980134 | − | 0.198337i | \(-0.936446\pi\) | ||
0.980134 | − | 0.198337i | \(-0.0635541\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.630063i | 0.0633237i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.7934 | 1.47200 | 0.736001 | − | 0.676981i | \(-0.236712\pi\) | ||||
0.736001 | + | 0.676981i | \(0.236712\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.82681 | −0.771198 | −0.385599 | − | 0.922666i | \(-0.626005\pi\) | ||||
−0.385599 | + | 0.922666i | \(0.626005\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1.25182i | − | 0.122166i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.24252 | 0.120119 | 0.0600596 | − | 0.998195i | \(-0.480871\pi\) | ||||
0.0600596 | + | 0.998195i | \(0.480871\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.2068i | 1.64811i | 0.566507 | + | 0.824057i | \(0.308294\pi\) | ||||
−0.566507 | + | 0.824057i | \(0.691706\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.57487i | 0.908806i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.29604i | − | 0.874498i | −0.899341 | − | 0.437249i | \(-0.855953\pi\) | ||
0.899341 | − | 0.437249i | \(-0.144047\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 6.49272i | − | 0.605449i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.96496i | 0.366561i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 8.64226i | − | 0.792235i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6030 | 0.963911 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 7.74454i | − | 0.698302i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.4710 | −1.19536 | −0.597680 | − | 0.801735i | \(-0.703911\pi\) | ||||
−0.597680 | + | 0.801735i | \(0.703911\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.37089i | 0.648971i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 8.50842i | − | 0.743385i | −0.928356 | − | 0.371692i | \(-0.878778\pi\) | ||
0.928356 | − | 0.371692i | \(-0.121222\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.77173 | + | 2.64667i | 0.413761 | + | 0.229495i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.608472 | −0.0519853 | −0.0259926 | − | 0.999662i | \(-0.508275\pi\) | ||||
−0.0259926 | + | 0.999662i | \(0.508275\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.1578i | 1.28567i | 0.766006 | + | 0.642834i | \(0.222241\pi\) | ||||
−0.766006 | + | 0.642834i | \(0.777759\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.33490i | 0.280849i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.49817 | −0.208908 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.83404i | − | 0.235354i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.43294 | −0.448101 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.5603 | −1.27475 | −0.637376 | − | 0.770553i | \(-0.719980\pi\) | ||||
−0.637376 | + | 0.770553i | \(0.719980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.31793 | −0.514146 | −0.257073 | − | 0.966392i | \(-0.582758\pi\) | ||||
−0.257073 | + | 0.966392i | \(0.582758\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.90373 | −0.558134 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.48802 | 0.601452 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.9069 | 1.18970 | 0.594851 | − | 0.803836i | \(-0.297211\pi\) | ||||
0.594851 | + | 0.803836i | \(0.297211\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 9.95682i | − | 0.789627i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.12774 | 0.640556 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 11.8536i | − | 0.928447i | −0.885718 | − | 0.464223i | \(-0.846333\pi\) | ||
0.885718 | − | 0.464223i | \(-0.153667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 0.630063i | − | 0.0490503i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.4742 | 1.04267 | 0.521333 | − | 0.853353i | \(-0.325435\pi\) | ||||
0.521333 | + | 0.853353i | \(0.325435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.72091 | −0.209301 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.11425 | − | 3.81182i | 0.161680 | − | 0.291497i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.69008i | 0.660695i | 0.943859 | + | 0.330347i | \(0.107166\pi\) | ||||
−0.943859 | + | 0.330347i | \(0.892834\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.25182i | 0.0946290i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.92095 | −0.745704 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.95895 | −0.295906 | −0.147953 | − | 0.988994i | \(-0.547268\pi\) | ||||
−0.147953 | + | 0.988994i | \(0.547268\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.1264i | 0.827016i | 0.910500 | + | 0.413508i | \(0.135697\pi\) | ||||
−0.910500 | + | 0.413508i | \(0.864303\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.4329 | 0.919069 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 9.57487i | − | 0.703958i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.34978i | − | 0.318088i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.25182i | − | 0.0910568i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.75195i | 0.705626i | 0.935694 | + | 0.352813i | \(0.114775\pi\) | ||||
−0.935694 | + | 0.352813i | \(0.885225\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 17.5048i | − | 1.26002i | −0.776586 | − | 0.630011i | \(-0.783050\pi\) | ||
0.776586 | − | 0.630011i | \(-0.216950\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 3.96496i | − | 0.283937i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.6568 | 1.54298 | 0.771492 | − | 0.636239i | \(-0.219511\pi\) | ||||
0.771492 | + | 0.636239i | \(0.219511\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.70101i | 0.333246i | 0.986021 | + | 0.166623i | \(0.0532863\pi\) | ||||
−0.986021 | + | 0.166623i | \(0.946714\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.82681 | −0.552061 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.54772 | 0.249001 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.74454i | 0.540902i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.49272i | − | 0.451275i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.40168 | + | 1.33211i | 0.166128 | + | 0.0921438i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.4183 | 1.95640 | 0.978198 | − | 0.207674i | \(-0.0665893\pi\) | ||||
0.978198 | + | 0.207674i | \(0.0665893\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.41571 | 0.0970032 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 7.37089i | − | 0.502691i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.37368i | 0.636327i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.64421 | −0.516548 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 27.3730i | − | 1.84131i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.509638 | −0.0341279 | −0.0170639 | − | 0.999854i | \(-0.505432\pi\) | ||||
−0.0170639 | + | 0.999854i | \(0.505432\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.3056 | 1.08224 | 0.541122 | − | 0.840944i | \(-0.318000\pi\) | ||||
0.541122 | + | 0.840944i | \(0.318000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.6375 | 1.29768 | 0.648840 | − | 0.760925i | \(-0.275254\pi\) | ||||
0.648840 | + | 0.760925i | \(0.275254\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.788728 | 0.0518945 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.0910 | −1.11967 | −0.559836 | − | 0.828604i | \(-0.689136\pi\) | ||||
−0.559836 | + | 0.828604i | \(0.689136\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.33490i | − | 0.217545i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.8485 | −0.899558 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.0418i | − | 1.23171i | −0.787860 | − | 0.615855i | \(-0.788811\pi\) | ||
0.787860 | − | 0.615855i | \(-0.211189\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3.56019i | − | 0.229332i | −0.993404 | − | 0.114666i | \(-0.963420\pi\) | ||
0.993404 | − | 0.114666i | \(-0.0365798\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.43294 | 0.347098 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.1137 | + | 8.38290i | 0.961662 | + | 0.533391i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 9.45397i | − | 0.599121i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.5397i | 0.980860i | 0.871481 | + | 0.490430i | \(0.163160\pi\) | ||||
−0.871481 | + | 0.490430i | \(0.836840\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.09082 | 0.257187 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.90373 | 0.432328 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.13092i | 0.0705449i | 0.999378 | + | 0.0352725i | \(0.0112299\pi\) | ||||
−0.999378 | + | 0.0352725i | \(0.988770\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.9861 | 0.744777 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 2.83404i | − | 0.175423i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.33000i | − | 0.266999i | −0.991049 | − | 0.133500i | \(-0.957378\pi\) | ||
0.991049 | − | 0.133500i | \(-0.0426215\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.95682i | 0.611642i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 4.52855i | − | 0.277143i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.64379i | 0.161195i | 0.996747 | + | 0.0805974i | \(0.0256828\pi\) | ||||
−0.996747 | + | 0.0805974i | \(0.974317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 25.2272i | − | 1.53244i | −0.642576 | − | 0.766222i | \(-0.722134\pi\) | ||
0.642576 | − | 0.766222i | \(-0.277866\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.96343 | 0.300401 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.630063i | 0.0379942i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.6753 | 1.42251 | 0.711256 | − | 0.702933i | \(-0.248127\pi\) | ||||
0.711256 | + | 0.702933i | \(0.248127\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.48802 | 0.448296 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.0714i | 1.49563i | 0.663906 | + | 0.747816i | \(0.268897\pi\) | ||||
−0.663906 | + | 0.747816i | \(0.731103\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.4772i | 0.622802i | 0.950279 | + | 0.311401i | \(0.100798\pi\) | ||||
−0.950279 | + | 0.311401i | \(0.899202\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.11425 | + | 3.81182i | −0.125237 | + | 0.225793i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.69480 | −0.572266 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.6615 | 1.80362 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.90679i | 0.229020i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.4541i | 1.72073i | 0.509681 | + | 0.860364i | \(0.329763\pi\) | ||||
−0.509681 | + | 0.860364i | \(0.670237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.92095 | 0.577620 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.630063i | − | 0.0365599i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.7434 | 1.48878 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.22706 | 0.531839 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.7934 | −0.849861 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.4329 | −0.711908 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.3610 | 1.73279 | 0.866396 | − | 0.499358i | \(-0.166431\pi\) | ||||
0.866396 | + | 0.499358i | \(0.166431\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.82681 | 0.445252 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 19.7798i | − | 1.12161i | −0.827948 | − | 0.560805i | \(-0.810492\pi\) | ||
0.827948 | − | 0.560805i | \(-0.189508\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.1152 | −1.19350 | −0.596752 | − | 0.802426i | \(-0.703542\pi\) | ||||
−0.596752 | + | 0.802426i | \(0.703542\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.25182i | 0.0705323i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.7057i | 0.825955i | 0.910741 | + | 0.412977i | \(0.135511\pi\) | ||||
−0.910741 | + | 0.412977i | \(0.864489\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.78562 | 0.0999756 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.24252 | −0.0693509 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.5962 | + | 26.3158i | −0.812154 | + | 1.46425i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.96496i | 0.219936i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 17.2068i | − | 0.951539i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.17471 | 0.230159 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8795 | −0.707924 | −0.353962 | − | 0.935260i | \(-0.615166\pi\) | ||||
−0.353962 | + | 0.935260i | \(0.615166\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 9.57487i | − | 0.524700i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.82681 | 0.427624 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6.25842i | − | 0.340918i | −0.985365 | − | 0.170459i | \(-0.945475\pi\) | ||
0.985365 | − | 0.170459i | \(-0.0545250\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.29604i | 0.504891i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.71792i | 0.255490i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5639i | 0.840369i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.49272i | 0.349556i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.2171i | 1.67582i | 0.545808 | + | 0.837910i | \(0.316223\pi\) | ||||
−0.545808 | + | 0.837910i | \(0.683777\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.8911 | 0.636515 | 0.318257 | − | 0.948004i | \(-0.396902\pi\) | ||||
0.318257 | + | 0.948004i | \(0.396902\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.96496i | − | 0.211634i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.7603 | −1.63720 | −0.818602 | − | 0.574361i | \(-0.805251\pi\) | ||||
−0.818602 | + | 0.574361i | \(0.805251\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.41571 | −0.0751383 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.64226i | 0.457397i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 24.6285i | − | 1.29984i | −0.760002 | − | 0.649920i | \(-0.774802\pi\) | ||
0.760002 | − | 0.649920i | \(-0.225198\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0599 | − | 16.1182i | −0.529470 | − | 0.848329i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.6030 | −0.556514 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.64421 | 0.400116 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.12358i | 0.476247i | 0.971235 | + | 0.238123i | \(0.0765323\pi\) | ||||
−0.971235 | + | 0.238123i | \(0.923468\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.74454i | 0.403165i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.4642 | −0.647108 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.8785i | − | 1.39171i | −0.718180 | − | 0.695857i | \(-0.755025\pi\) | ||
0.718180 | − | 0.695857i | \(-0.244975\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.2369 | 0.578727 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.96192 | −0.460343 | −0.230171 | − | 0.973150i | \(-0.573929\pi\) | ||||
−0.230171 | + | 0.973150i | \(0.573929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.4710 | 0.690141 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.84395 | 0.196416 | 0.0982082 | − | 0.995166i | \(-0.468689\pi\) | ||||
0.0982082 | + | 0.995166i | \(0.468689\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.788728 | −0.0401973 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.37089i | − | 0.374684i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.35048 | −0.169876 | −0.0849380 | − | 0.996386i | \(-0.527069\pi\) | ||||
−0.0849380 | + | 0.996386i | \(0.527069\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.8240i | 2.26685i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.50842i | 0.429193i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.8485 | 0.696794 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.42125 | 0.171708 | 0.0858538 | − | 0.996308i | \(-0.472638\pi\) | ||||
0.0858538 | + | 0.996308i | \(0.472638\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.77173 | − | 2.64667i | −0.238885 | − | 0.132499i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 30.4328i | − | 1.51974i | −0.650073 | − | 0.759872i | \(-0.725262\pi\) | ||
0.650073 | − | 0.759872i | \(-0.274738\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.6897i | 1.47895i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.03277 | 0.299033 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.1192i | − | 0.698151i | −0.937095 | − | 0.349075i | \(-0.886496\pi\) | ||
0.937095 | − | 0.349075i | \(-0.113504\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.608472 | 0.0300137 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.4193i | 0.611113i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.45397i | 0.464077i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 15.1578i | − | 0.742280i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 19.0252i | − | 0.929440i | −0.885458 | − | 0.464720i | \(-0.846155\pi\) | ||
0.885458 | − | 0.464720i | \(-0.153845\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.9451i | − | 0.582168i | −0.956698 | − | 0.291084i | \(-0.905984\pi\) | ||
0.956698 | − | 0.291084i | \(-0.0940159\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3.33490i | − | 0.162148i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.90373 | −0.334880 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 15.5639i | − | 0.753188i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.49817 | 0.120613 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.95197 | −0.142191 | −0.0710957 | − | 0.997470i | \(-0.522650\pi\) | ||||
−0.0710957 | + | 0.997470i | \(0.522650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29.6192i | − | 1.42341i | −0.702478 | − | 0.711705i | \(-0.747923\pi\) | ||
0.702478 | − | 0.711705i | \(-0.252077\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.83404i | 0.135882i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.7491 | − | 13.7272i | −1.18391 | − | 0.656661i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.6919 | 1.79894 | 0.899469 | − | 0.436985i | \(-0.143954\pi\) | ||||
0.899469 | + | 0.436985i | \(0.143954\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.43294 | 0.258711 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 25.8140i | − | 1.22646i | −0.789904 | − | 0.613231i | \(-0.789870\pi\) | ||
0.789904 | − | 0.613231i | \(-0.210130\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.52855i | 0.214674i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.5603 | 0.735978 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.2815i | 0.532408i | 0.963917 | + | 0.266204i | \(0.0857694\pi\) | ||||
−0.963917 | + | 0.266204i | \(0.914231\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.87955 | −0.229769 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.31793 | 0.296842 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.96343 | −0.232689 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.7642 | 1.15842 | 0.579209 | − | 0.815179i | \(-0.303361\pi\) | ||||
0.579209 | + | 0.815179i | \(0.303361\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.90373 | 0.322239 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.7142 | −0.825031 | −0.412515 | − | 0.910951i | \(-0.635350\pi\) | ||||
−0.412515 | + | 0.910951i | \(0.635350\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 0.191937i | − | 0.00892008i | −0.999990 | − | 0.00446004i | \(-0.998580\pi\) | ||
0.999990 | − | 0.00446004i | \(-0.00141968\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.48802 | −0.347248 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 31.4589i | − | 1.45574i | −0.685713 | − | 0.727872i | \(-0.740510\pi\) | ||
0.685713 | − | 0.727872i | \(-0.259490\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.79779i | 0.452420i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.9069 | −0.686875 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.64412 | 0.213537 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.11425 | − | 3.81182i | 0.0970083 | − | 0.174898i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.95682i | 0.455891i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.7854i | 1.08678i | 0.839480 | + | 0.543391i | \(0.182860\pi\) | ||||
−0.839480 | + | 0.543391i | \(0.817140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37.9640 | 1.73101 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.12774 | −0.369825 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 3.90679i | − | 0.177398i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.55349 | −0.206338 | −0.103169 | − | 0.994664i | \(-0.532898\pi\) | ||||
−0.103169 | + | 0.994664i | \(0.532898\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.8536i | 0.536039i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 36.5290i | − | 1.64853i | −0.566204 | − | 0.824265i | \(-0.691588\pi\) | ||
0.566204 | − | 0.824265i | \(-0.308412\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.5654i | 0.881183i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.630063i | 0.0283192i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.77223i | − | 0.0794952i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.0346536i | 0.00155131i | 1.00000 | 0.000775653i | \(0.000246898\pi\) | |||||
−1.00000 | 0.000775653i | \(0.999753\pi\) | ||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.4742 | −0.601983 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 14.6538i | − | 0.653383i | −0.945131 | − | 0.326691i | \(-0.894066\pi\) | ||
0.945131 | − | 0.326691i | \(-0.105934\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.7934 | 0.658299 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.72091 | 0.120840 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.1830i | 1.51513i | 0.652758 | + | 0.757567i | \(0.273612\pi\) | ||||
−0.652758 | + | 0.757567i | \(0.726388\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.56921i | 0.423317i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.11425 | + | 3.81182i | −0.0933463 | + | 0.168296i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.82681 | −0.344890 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.10119 | 0.0924104 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 8.69008i | − | 0.381452i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 21.6319i | − | 0.947712i | −0.880602 | − | 0.473856i | \(-0.842862\pi\) | ||
0.880602 | − | 0.473856i | \(-0.157138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.3171 | 1.15077 | 0.575383 | − | 0.817884i | \(-0.304853\pi\) | ||||
0.575383 | + | 0.817884i | \(0.304853\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.25182i | − | 0.0546341i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −51.6953 | −2.25188 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.1554 | −0.832842 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.92095 | 0.430533 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.7068 | −1.33006 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.24252 | 0.0537190 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.95895 | 0.170841 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.42309i | 0.147443i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.6108 | 0.714155 | 0.357078 | − | 0.934075i | \(-0.383773\pi\) | ||||
0.357078 | + | 0.934075i | \(0.383773\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 11.1264i | − | 0.477478i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.2068i | 0.737059i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.7975 | −1.61611 | −0.808053 | − | 0.589110i | \(-0.799478\pi\) | ||||
−0.808053 | + | 0.589110i | \(0.799478\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.4329 | −0.530625 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.8028 | − | 5.99186i | −0.460217 | − | 0.255262i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.3359i | 0.737198i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.57487i | 0.406431i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.58935 | 0.406314 | 0.203157 | − | 0.979146i | \(-0.434880\pi\) | ||||
0.203157 | + | 0.979146i | \(0.434880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.2253 | 1.23610 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.34978i | 0.183648i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −46.0307 | −1.93996 | −0.969982 | − | 0.243177i | \(-0.921810\pi\) | ||||
−0.969982 | + | 0.243177i | \(0.921810\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 9.29604i | − | 0.391087i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.25182i | 0.0525717i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 23.2020i | − | 0.972679i | −0.873770 | − | 0.486339i | \(-0.838332\pi\) | ||
0.873770 | − | 0.486339i | \(-0.161668\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.4551i | 0.856020i | 0.903774 | + | 0.428010i | \(0.140785\pi\) | ||||
−0.903774 | + | 0.428010i | \(0.859215\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 9.75195i | − | 0.407393i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.49272i | − | 0.270765i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.0188 | −1.33296 | −0.666480 | − | 0.745522i | \(-0.732200\pi\) | ||||
−0.666480 | + | 0.745522i | \(0.732200\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.5048i | 0.727474i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.8347 | −0.490986 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.27342 | −0.259818 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.96496i | 0.163931i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 13.9566i | − | 0.576052i | −0.957623 | − | 0.288026i | \(-0.907001\pi\) | ||
0.957623 | − | 0.288026i | \(-0.0929990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.8315 | − | 28.5430i | 0.652326 | − | 1.17609i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.6568 | −0.890842 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.2855 | 1.24367 | 0.621837 | − | 0.783146i | \(-0.286386\pi\) | ||||
0.621837 | + | 0.783146i | \(0.286386\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 8.64226i | − | 0.354298i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 4.70101i | − | 0.192400i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.4402 | 1.44805 | 0.724024 | − | 0.689775i | \(-0.242290\pi\) | ||||
0.724024 | + | 0.689775i | \(0.242290\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.2505i | − | 0.540497i | −0.962791 | − | 0.270249i | \(-0.912894\pi\) | ||
0.962791 | − | 0.270249i | \(-0.0871059\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.82681 | 0.318732 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.6030 | 0.431074 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.2364 | 1.14608 | 0.573040 | − | 0.819528i | \(-0.305764\pi\) | ||||
0.573040 | + | 0.819528i | \(0.305764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.54772 | −0.143761 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.2227 | 0.534935 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.1176 | 0.610593 | 0.305297 | − | 0.952257i | \(-0.401244\pi\) | ||||
0.305297 | + | 0.952257i | \(0.401244\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 7.74454i | − | 0.312290i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.32628 | −0.214428 | −0.107214 | − | 0.994236i | \(-0.534193\pi\) | ||||
−0.107214 | + | 0.994236i | \(0.534193\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 37.8063i | − | 1.51956i | −0.650178 | − | 0.759782i | \(-0.725306\pi\) | ||
0.650178 | − | 0.759782i | \(-0.274694\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.49272i | 0.260544i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.66895 | −0.227122 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.40168 | − | 1.33211i | −0.0959140 | − | 0.0531993i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 66.1023i | 2.63567i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.40333i | 0.254912i | 0.991844 | + | 0.127456i | \(0.0406812\pi\) | ||||
−0.991844 | + | 0.127456i | \(0.959319\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −28.4183 | −1.12953 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.4710 | −0.534581 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.5414i | 0.853500i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.41571 | −0.0560048 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.4809i | 1.32242i | 0.750203 | + | 0.661208i | \(0.229956\pi\) | ||||
−0.750203 | + | 0.661208i | \(0.770044\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.5225i | 0.967072i | 0.875325 | + | 0.483536i | \(0.160648\pi\) | ||||
−0.875325 | + | 0.483536i | \(0.839352\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.37089i | 0.290229i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.4957i | 1.63136i | 0.578501 | + | 0.815682i | \(0.303638\pi\) | ||||
−0.578501 | + | 0.815682i | \(0.696362\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.25082i | 0.245366i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 9.37368i | − | 0.367384i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.80018 | 0.266112 | 0.133056 | − | 0.991109i | \(-0.457521\pi\) | ||||
0.133056 | + | 0.991109i | \(0.457521\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 8.50842i | − | 0.332452i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.64421 | 0.298229 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.8583 | 1.43580 | 0.717898 | − | 0.696149i | \(-0.245105\pi\) | ||||
0.717898 | + | 0.696149i | \(0.245105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.97211i | − | 0.271183i | −0.990765 | − | 0.135592i | \(-0.956706\pi\) | ||
0.990765 | − | 0.135592i | \(-0.0432936\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27.3730i | 1.06308i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.77173 | + | 2.64667i | 0.185040 | + | 0.102633i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.4006 | −0.712474 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.509638 | 0.0197037 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 7.83353i | − | 0.302410i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.1423i | 0.622239i | 0.950371 | + | 0.311119i | \(0.100704\pi\) | ||||
−0.950371 | + | 0.311119i | \(0.899296\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 34.9941i | − | 1.34493i | −0.740128 | − | 0.672466i | \(-0.765235\pi\) | ||
0.740128 | − | 0.672466i | \(-0.234765\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.89062 | 0.187685 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.3056 | −0.624833 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.5170 | −0.861589 | −0.430795 | − | 0.902450i | \(-0.641767\pi\) | ||||
−0.430795 | + | 0.902450i | \(0.641767\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.608472 | −0.0232485 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.6375 | −0.749216 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39.4784 | −1.50401 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.5236i | 1.50355i | 0.659420 | + | 0.751775i | \(0.270802\pi\) | ||||
−0.659420 | + | 0.751775i | \(0.729198\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.788728 | −0.0299613 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.1578i | 0.574968i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 53.4662i | − | 2.02518i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.0910 | 0.646442 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.7767 | 1.27573 | 0.637864 | − | 0.770149i | \(-0.279818\pi\) | ||||
0.637864 | + | 0.770149i | \(0.279818\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.4977 | − | 20.2436i | −1.37654 | − | 0.763503i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.33490i | 0.125600i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.5188i | 0.696470i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.19262 | 0.0447898 | 0.0223949 | − | 0.999749i | \(-0.492871\pi\) | ||||
0.0223949 | + | 0.999749i | \(0.492871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.8485 | 0.519360 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 48.6176i | − | 1.82074i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.49817 | −0.0934264 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.0418i | 0.711128i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 40.1949i | − | 1.49902i | −0.661994 | − | 0.749509i | \(-0.730290\pi\) | ||
0.661994 | − | 0.749509i | \(-0.269710\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 9.79779i | − | 0.364889i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.56019i | 0.132405i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 2.83404i | − | 0.105254i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.40487i | 0.0891918i | 0.999005 | + | 0.0445959i | \(0.0142000\pi\) | ||||
−0.999005 | + | 0.0445959i | \(0.985800\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.8867i | 1.88211i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.5401 | −0.647859 | −0.323930 | − | 0.946081i | \(-0.605004\pi\) | ||||
−0.323930 | + | 0.946081i | \(0.605004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.43294 | −0.200397 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.93138i | 0.181650i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 16.4628i | − | 0.605592i | −0.953055 | − | 0.302796i | \(-0.902080\pi\) | ||
0.953055 | − | 0.302796i | \(-0.0979201\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.1137 | − | 8.38290i | −0.555216 | − | 0.307954i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.3965 | −1.37195 | −0.685973 | − | 0.727627i | \(-0.740623\pi\) | ||||
−0.685973 | + | 0.727627i | \(0.740623\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.5603 | −0.570086 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.45397i | 0.345903i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.55542i | 0.0568339i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.2116 | −1.21191 | −0.605954 | − | 0.795500i | \(-0.707208\pi\) | ||||
−0.605954 | + | 0.795500i | \(0.707208\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 15.5397i | − | 0.566300i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.31793 | −0.229933 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.3936 | −0.450452 | −0.225226 | − | 0.974307i | \(-0.572312\pi\) | ||||
−0.225226 | + | 0.974307i | \(0.572312\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.09082 | −0.148487 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.0173 | −0.725627 | −0.362813 | − | 0.931862i | \(-0.618184\pi\) | ||||
−0.362813 | + | 0.931862i | \(0.618184\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.5399 | −0.779797 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.90373 | −0.249605 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.3362i | 1.42035i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.6864 | 1.57537 | 0.787686 | − | 0.616077i | \(-0.211279\pi\) | ||||
0.787686 | + | 0.616077i | \(0.211279\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1.13092i | − | 0.0407291i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 32.6219i | − | 1.17333i | −0.809830 | − | 0.586664i | \(-0.800441\pi\) | ||
0.809830 | − | 0.586664i | \(-0.199559\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.48802 | 0.268978 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.9861 | −0.429997 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.5208 | + | 16.3739i | 1.05769 | + | 0.586655i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 0.891989i | − | 0.0319179i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.83404i | 0.101280i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.9069 | 0.532051 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.0146 | −1.56895 | −0.784475 | − | 0.620160i | \(-0.787068\pi\) | ||||
−0.784475 | + | 0.620160i | \(0.787068\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.33000i | 0.154152i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.6370 | 0.413764 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 49.2961i | − | 1.75056i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 9.95682i | − | 0.353132i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.1194i | 1.63363i | 0.576896 | + | 0.816817i | \(0.304264\pi\) | ||||
−0.576896 | + | 0.816817i | \(0.695736\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.0232i | 0.814504i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.52855i | 0.160009i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.81633i | 0.169965i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.12774 | 0.286465 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 2.64379i | − | 0.0930659i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.5769 | −0.547656 | −0.273828 | − | 0.961779i | \(-0.588290\pi\) | ||||
−0.273828 | + | 0.961779i | \(0.588290\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.69944 | 0.235249 | 0.117625 | − | 0.993058i | \(-0.462472\pi\) | ||||
0.117625 | + | 0.993058i | \(0.462472\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.2272i | 0.884757i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 11.8536i | − | 0.415214i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.0965 | − | 15.5839i | −0.982972 | − | 0.545211i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.96343 | −0.173436 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.1444 | −1.75005 | −0.875025 | − | 0.484078i | \(-0.839155\pi\) | ||||
−0.875025 | + | 0.484078i | \(0.839155\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.6443i | 0.789331i | 0.918825 | + | 0.394666i | \(0.129140\pi\) | ||||
−0.918825 | + | 0.394666i | \(0.870860\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 0.630063i | − | 0.0219360i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.28426 | −0.322845 | −0.161423 | − | 0.986885i | \(-0.551608\pi\) | ||||
−0.161423 | + | 0.986885i | \(0.551608\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.47550i | − | 0.190172i | −0.995469 | − | 0.0950859i | \(-0.969687\pi\) | ||
0.995469 | − | 0.0950859i | \(-0.0303126\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.6753 | −0.821288 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37.5075 | −1.29956 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.4742 | 0.466294 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.48802 | −0.258824 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −55.8731 | −1.92896 | −0.964478 | − | 0.264165i | \(-0.914904\pi\) | ||||
−0.964478 | + | 0.264165i | \(0.914904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.9682 | 0.723042 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 25.0714i | − | 0.863503i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.72091 | −0.0936022 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.2731i | 0.456070i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 10.4772i | − | 0.359575i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −62.1669 | −2.13105 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.6753 | 0.810628 | 0.405314 | − | 0.914178i | \(-0.367162\pi\) | ||||
0.405314 | + | 0.914178i | \(0.367162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.11425 | − | 3.81182i | 0.0723057 | − | 0.130361i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 22.8312i | − | 0.779898i | −0.920836 | − | 0.389949i | \(-0.872493\pi\) | ||
0.920836 | − | 0.389949i | \(-0.127507\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 35.8305i | − | 1.22252i | −0.791430 | − | 0.611260i | \(-0.790663\pi\) | ||
0.791430 | − | 0.611260i | \(-0.209337\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.69480 | 0.330398 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.528289 | 0.0179832 | 0.00899159 | − | 0.999960i | \(-0.497138\pi\) | ||||
0.00899159 | + | 0.999960i | \(0.497138\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.69008i | 0.295472i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.6615 | −1.04132 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.72543i | 0.295990i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.0330i | 1.05151i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3.90679i | − | 0.132225i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.25182i | 0.0423194i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.2630i | 1.35959i | 0.733404 | + | 0.679793i | \(0.237930\pi\) | ||||
−0.733404 | + | 0.679793i | \(0.762070\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 29.4541i | − | 0.993462i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.3270 | −0.954359 | −0.477180 | − | 0.878806i | \(-0.658341\pi\) | ||||
−0.477180 | + | 0.878806i | \(0.658341\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.9458i | 1.47890i | 0.673214 | + | 0.739448i | \(0.264913\pi\) | ||||
−0.673214 | + | 0.739448i | \(0.735087\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.92095 | −0.333489 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.8147 | 1.60546 | 0.802730 | − | 0.596343i | \(-0.203380\pi\) | ||||
0.802730 | + | 0.596343i | \(0.203380\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 16.8633i | − | 0.565579i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.630063i | 0.0211079i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.7120 | − | 7.05080i | −0.425392 | − | 0.235946i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.95895 | −0.132333 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25.7434 | −0.859546 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 21.2213i | − | 0.707771i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 68.7392i | − | 2.29003i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.22706 | −0.307057 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.1264i | 0.369853i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.3042 | −1.10585 | −0.552924 | − | 0.833232i | \(-0.686488\pi\) | ||||
−0.552924 | + | 0.833232i | \(0.686488\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.7934 | 0.490667 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.9036 | −0.361252 | −0.180626 | − | 0.983552i | \(-0.557812\pi\) | ||||
−0.180626 | + | 0.983552i | \(0.557812\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.95659 | −0.197134 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.4329 | 0.411020 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.6511 | 0.351729 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27.0384i | − | 0.891914i | −0.895054 | − | 0.445957i | \(-0.852863\pi\) | ||
0.895054 | − | 0.445957i | \(-0.147137\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.3610 | −1.00043 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 5.61325i | − | 0.184762i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 9.57487i | − | 0.314820i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.82681 | −0.257066 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.19877 | 0.203375 | 0.101688 | − | 0.994816i | \(-0.467576\pi\) | ||||
0.101688 | + | 0.994816i | \(0.467576\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.4866 | − | 20.7094i | 0.376457 | − | 0.678722i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.7798i | 0.647562i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 4.34978i | − | 0.142253i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.4565 | −1.51767 | −0.758833 | − | 0.651285i | \(-0.774230\pi\) | ||||
−0.758833 | + | 0.651285i | \(0.774230\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.1152 | 0.689069 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.2829i | 1.76957i | 0.465999 | + | 0.884785i | \(0.345695\pi\) | ||||
−0.465999 | + | 0.884785i | \(0.654305\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50.2831 | 1.63744 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 1.25182i | − | 0.0407219i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.7316i | 0.478711i | 0.970932 | + | 0.239356i | \(0.0769362\pi\) | ||||
−0.970932 | + | 0.239356i | \(0.923064\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.3090i | 0.983871i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 14.7057i | − | 0.476865i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 53.1515i | − | 1.72175i | −0.508820 | − | 0.860873i | \(-0.669918\pi\) | ||
0.508820 | − | 0.860873i | \(-0.330082\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.75195i | 0.315566i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.78562 | −0.0577210 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 0.761700i | − | 0.0245966i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.0704 | 0.808723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.24252 | 0.0400398 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 17.5048i | − | 0.563499i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 14.1838i | − | 0.456119i | −0.973647 | − | 0.228060i | \(-0.926762\pi\) | ||
0.973647 | − | 0.228060i | \(-0.0732381\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.5962 | − | 26.3158i | 0.468897 | − | 0.845384i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.2231 | −1.35500 | −0.677502 | − | 0.735521i | \(-0.736938\pi\) | ||||
−0.677502 | + | 0.735521i | \(0.736938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.9749 | −0.608307 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 3.96496i | − | 0.126980i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 53.1731i | − | 1.70116i | −0.525847 | − | 0.850579i | \(-0.676251\pi\) | ||
0.525847 | − | 0.850579i | \(-0.323749\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.85327 | −0.0911910 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.2068i | 0.549371i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.9449 | −0.891303 | −0.445652 | − | 0.895206i | \(-0.647028\pi\) | ||||
−0.445652 | + | 0.895206i | \(0.647028\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.6568 | 0.690043 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.17471 | −0.132882 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −47.8571 | −1.52177 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.2741 | −0.993454 | −0.496727 | − | 0.867907i | \(-0.665465\pi\) | ||||
−0.496727 | + | 0.867907i | \(0.665465\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.8795 | 0.408720 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.70101i | 0.149032i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.8729 | 0.629380 | 0.314690 | − | 0.949195i | \(-0.398100\pi\) | ||||
0.314690 | + | 0.949195i | \(0.398100\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.57487i | 0.302935i |
(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 | 4560.2.d.j.2431.8 | yes | 12 | |
4.3 | odd | 2 | 4560.2.d.l.2431.5 | yes | 12 | ||
19.18 | odd | 2 | 4560.2.d.l.2431.8 | yes | 12 | ||
76.75 | even | 2 | inner | 4560.2.d.j.2431.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4560.2.d.j.2431.5 | ✓ | 12 | 76.75 | even | 2 | inner | |
4560.2.d.j.2431.8 | yes | 12 | 1.1 | even | 1 | trivial | |
4560.2.d.l.2431.5 | yes | 12 | 4.3 | odd | 2 | ||
4560.2.d.l.2431.8 | yes | 12 | 19.18 | odd | 2 |