Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2400,2,Mod(1199,2400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2400.1199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2400.m (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.1640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} + 4x^{12} + 12x^{10} + 16x^{8} + 48x^{6} + 64x^{4} + 64x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{19} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1199.9 | ||
Root | \(-0.842022 - 1.13622i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2400.1199 |
Dual form | 2400.2.m.d.1199.10 |
$q$-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 \(\left(\mathbb{Z}/2400\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1601\) | \(1951\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.218455 | − | 1.71822i | 0.126125 | − | 0.992014i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.64426 | −1.37740 | −0.688701 | − | 0.725045i | \(-0.741819\pi\) | ||||
−0.688701 | + | 0.725045i | \(0.741819\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.90455 | − | 0.750707i | −0.968185 | − | 0.250236i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.07403i | − | 1.52988i | −0.644103 | − | 0.764938i | \(-0.722769\pi\) | ||
0.644103 | − | 0.764938i | \(-0.277231\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.70594 | 0.473142 | 0.236571 | − | 0.971614i | \(-0.423976\pi\) | ||||
0.236571 | + | 0.971614i | \(0.423976\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.08117 | −0.989830 | −0.494915 | − | 0.868941i | \(-0.664801\pi\) | ||||
−0.494915 | + | 0.868941i | \(0.664801\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.26422 | −0.290033 | −0.145016 | − | 0.989429i | \(-0.546324\pi\) | ||||
−0.145016 | + | 0.989429i | \(0.546324\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.796108 | + | 6.26164i | −0.173725 | + | 1.36640i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.70066i | 0.980156i | 0.871679 | + | 0.490078i | \(0.163032\pi\) | ||||
−0.871679 | + | 0.490078i | \(0.836968\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.92439 | + | 4.82667i | −0.370350 | + | 0.928892i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.06377 | −0.197537 | −0.0987683 | − | 0.995110i | \(-0.531490\pi\) | ||||
−0.0987683 | + | 0.995110i | \(0.531490\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.86950i | − | 0.874588i | −0.899318 | − | 0.437294i | \(-0.855937\pi\) | ||
0.899318 | − | 0.437294i | \(-0.144063\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.71829 | − | 1.10845i | −1.51766 | − | 0.192956i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.56830 | 1.24422 | 0.622110 | − | 0.782930i | \(-0.286276\pi\) | ||||
0.622110 | + | 0.782930i | \(0.286276\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.372671 | − | 2.93118i | 0.0596751 | − | 0.469364i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.50141i | − | 0.234482i | −0.993104 | − | 0.117241i | \(-0.962595\pi\) | ||
0.993104 | − | 0.117241i | \(-0.0374049\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.43644i | 0.524052i | 0.965061 | + | 0.262026i | \(0.0843906\pi\) | ||||
−0.965061 | + | 0.262026i | \(0.915609\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9176i | 1.59249i | 0.604975 | + | 0.796245i | \(0.293183\pi\) | ||||
−0.604975 | + | 0.796245i | \(0.706817\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.28066 | 0.897237 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.891553 | + | 7.01235i | −0.124842 | + | 0.981926i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.87288i | 1.21878i | 0.792869 | + | 0.609392i | \(0.208586\pi\) | ||||
−0.792869 | + | 0.609392i | \(0.791414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.276176 | + | 2.17221i | −0.0365804 | + | 0.287717i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 0.788328i | − | 0.102632i | −0.998682 | − | 0.0513158i | \(-0.983658\pi\) | ||
0.998682 | − | 0.0513158i | \(-0.0163415\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.627594i | 0.0803552i | 0.999193 | + | 0.0401776i | \(0.0127924\pi\) | ||||
−0.999193 | + | 0.0401776i | \(0.987208\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.5850 | + | 2.73578i | 1.33358 | + | 0.344675i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.18178i | − | 0.510886i | −0.966824 | − | 0.255443i | \(-0.917779\pi\) | ||
0.966824 | − | 0.255443i | \(-0.0822213\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.07677 | + | 1.02688i | 0.972329 | + | 0.123622i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.21689 | −0.737810 | −0.368905 | − | 0.929467i | \(-0.620267\pi\) | ||||
−0.368905 | + | 0.929467i | \(0.620267\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.21689i | 0.493550i | 0.969073 | + | 0.246775i | \(0.0793709\pi\) | ||||
−0.969073 | + | 0.246775i | \(0.920629\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.4911i | 2.10726i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 0.992853i | − | 0.111705i | −0.998439 | − | 0.0558524i | \(-0.982212\pi\) | ||
0.998439 | − | 0.0558524i | \(-0.0177876\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.87288 | + | 4.36094i | 0.874764 | + | 0.484549i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.72544 | −0.847977 | −0.423989 | − | 0.905668i | \(-0.639370\pi\) | ||||
−0.423989 | + | 0.905668i | \(0.639370\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.232385 | + | 1.82779i | −0.0249143 | + | 0.195959i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.5742i | 1.22687i | 0.789747 | + | 0.613433i | \(0.210212\pi\) | ||||
−0.789747 | + | 0.613433i | \(0.789788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.21689 | −0.651708 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.36687 | − | 1.06377i | −0.867604 | − | 0.110308i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7.40133i | − | 0.751491i | −0.926723 | − | 0.375745i | \(-0.877387\pi\) | ||
0.926723 | − | 0.375745i | \(-0.122613\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.80911 | + | 14.7378i | −0.382830 | + | 1.48120i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1535 | −1.01031 | −0.505157 | − | 0.863027i | \(-0.668566\pi\) | ||||
−0.505157 | + | 0.863027i | \(0.668566\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.5400 | −1.53120 | −0.765599 | − | 0.643318i | \(-0.777557\pi\) | ||||
−0.765599 | + | 0.643318i | \(0.777557\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.8707 | −1.43760 | −0.718801 | − | 0.695216i | \(-0.755309\pi\) | ||||
−0.718801 | + | 0.695216i | \(0.755309\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.5376i | 1.00932i | 0.863319 | + | 0.504659i | \(0.168382\pi\) | ||||
−0.863319 | + | 0.504659i | \(0.831618\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.65333 | − | 13.0040i | 0.156927 | − | 1.23428i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.94353 | 0.935409 | 0.467704 | − | 0.883885i | \(-0.345081\pi\) | ||||
0.467704 | + | 0.883885i | \(0.345081\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.95499 | − | 1.28066i | −0.458089 | − | 0.118397i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.8729 | 1.36339 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.7458 | −1.34052 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.57976 | − | 0.327992i | −0.232609 | − | 0.0295740i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.62997 | 0.499579 | 0.249790 | − | 0.968300i | \(-0.419639\pi\) | ||||
0.249790 | + | 0.968300i | \(0.419639\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.90455 | + | 0.750707i | 0.519867 | + | 0.0660961i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.66215i | − | 0.145223i | −0.997360 | − | 0.0726113i | \(-0.976867\pi\) | ||
0.997360 | − | 0.0726113i | \(-0.0231333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.60717 | 0.399492 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.3554 | −1.14103 | −0.570515 | − | 0.821287i | \(-0.693256\pi\) | ||||
−0.570515 | + | 0.821287i | \(0.693256\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.3540 | 1.21749 | 0.608745 | − | 0.793366i | \(-0.291673\pi\) | ||||
0.608745 | + | 0.793366i | \(0.291673\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.7588 | + | 2.38500i | 1.57977 | + | 0.200853i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 8.65598i | − | 0.723850i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.37204 | − | 10.7916i | 0.113164 | − | 0.890072i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.2742 | 1.49708 | 0.748540 | − | 0.663089i | \(-0.230755\pi\) | ||||
0.748540 | + | 0.663089i | \(0.230755\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.7652i | 1.36433i | 0.731197 | + | 0.682166i | \(0.238962\pi\) | ||||
−0.731197 | + | 0.682166i | \(0.761038\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.8540 | + | 3.06377i | 0.958339 | + | 0.247691i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.31311 | 0.503841 | 0.251920 | − | 0.967748i | \(-0.418938\pi\) | ||||
0.251920 | + | 0.967748i | \(0.418938\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.2455 | + | 1.93832i | 1.20905 | + | 0.153719i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 17.1305i | − | 1.35007i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.69110i | 0.210783i | 0.994431 | + | 0.105391i | \(0.0336096\pi\) | ||||
−0.994431 | + | 0.105391i | \(0.966390\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.6633i | 1.28945i | 0.764416 | + | 0.644723i | \(0.223027\pi\) | ||||
−0.764416 | + | 0.644723i | \(0.776973\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0898 | −0.776136 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.67201 | + | 0.949062i | 0.280805 | + | 0.0725766i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 11.7458i | − | 0.893013i | −0.894780 | − | 0.446507i | \(-0.852668\pi\) | ||
0.894780 | − | 0.446507i | \(-0.147332\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.35452 | − | 0.172214i | −0.101812 | − | 0.0129444i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.466861i | 0.0348948i | 0.999848 | + | 0.0174474i | \(0.00555396\pi\) | ||||
−0.999848 | + | 0.0174474i | \(0.994446\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.5628i | − | 1.23110i | −0.788098 | − | 0.615550i | \(-0.788934\pi\) | ||
0.788098 | − | 0.615550i | \(-0.211066\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.07834 | + | 0.137101i | 0.0797135 | + | 0.0101348i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.7080i | 1.51432i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.01300 | − | 17.5896i | 0.510121 | − | 1.27946i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.49110 | −0.469679 | −0.234840 | − | 0.972034i | \(-0.575456\pi\) | ||||
−0.234840 | + | 0.972034i | \(0.575456\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 11.4013i | − | 0.820685i | −0.911931 | − | 0.410343i | \(-0.865409\pi\) | ||
0.911931 | − | 0.410343i | \(-0.134591\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.56091i | 0.253704i | 0.991922 | + | 0.126852i | \(0.0404874\pi\) | ||||
−0.991922 | + | 0.126852i | \(0.959513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.40473i | − | 0.312243i | −0.987738 | − | 0.156122i | \(-0.950101\pi\) | ||
0.987738 | − | 0.156122i | \(-0.0498992\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.18522 | − | 0.913531i | −0.506806 | − | 0.0644355i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.87665 | 0.272087 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.52882 | − | 13.6533i | 0.245270 | − | 0.948972i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.41471i | 0.443715i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.1371 | 1.11092 | 0.555462 | − | 0.831542i | \(-0.312541\pi\) | ||||
0.555462 | + | 0.831542i | \(0.312541\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.35811 | + | 10.6820i | −0.0930563 | + | 0.731918i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.7458i | 1.20466i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.24555 | + | 0.921202i | 0.489609 | + | 0.0622490i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.96224 | −0.468331 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.09474 | 0.408134 | 0.204067 | − | 0.978957i | \(-0.434584\pi\) | ||||
0.204067 | + | 0.978957i | \(0.434584\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.4673 | −1.35846 | −0.679230 | − | 0.733925i | \(-0.737686\pi\) | ||||
−0.679230 | + | 0.733925i | \(0.737686\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 26.4728i | − | 1.74937i | −0.484693 | − | 0.874684i | \(-0.661069\pi\) | ||
0.484693 | − | 0.874684i | \(-0.338931\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 31.7718 | + | 4.03947i | 2.09043 | + | 0.265778i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.3773 | −1.59701 | −0.798504 | − | 0.601989i | \(-0.794375\pi\) | ||||
−0.798504 | + | 0.601989i | \(0.794375\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.70594 | − | 0.216894i | −0.110813 | − | 0.0140888i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.47155 | −0.353925 | −0.176963 | − | 0.984218i | \(-0.556627\pi\) | ||||
−0.176963 | + | 0.984218i | \(0.556627\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.6446 | 1.58750 | 0.793750 | − | 0.608244i | \(-0.208126\pi\) | ||||
0.793750 | + | 0.608244i | \(0.208126\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.21292 | − | 12.5747i | 0.591009 | − | 0.806665i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.15669 | −0.137227 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.68766 | + | 13.2740i | −0.106951 | + | 0.841205i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.74973i | 0.110442i | 0.998474 | + | 0.0552210i | \(0.0175863\pi\) | ||||
−0.998474 | + | 0.0552210i | \(0.982414\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.8513 | 1.49952 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.27646 | −0.329137 | −0.164568 | − | 0.986366i | \(-0.552623\pi\) | ||||
−0.164568 | + | 0.986366i | \(0.552623\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.5809 | −1.71379 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.08977 | + | 0.798578i | 0.191252 | + | 0.0494307i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.79043i | − | 0.110403i | −0.998475 | − | 0.0552014i | \(-0.982420\pi\) | ||
0.998475 | − | 0.0552014i | \(-0.0175801\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.8871 | + | 2.52845i | 1.21707 | + | 0.154739i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.7080 | −1.14065 | −0.570323 | − | 0.821420i | \(-0.693182\pi\) | ||||
−0.570323 | + | 0.821420i | \(0.693182\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.8441i | 1.50917i | 0.656200 | + | 0.754587i | \(0.272163\pi\) | ||||
−0.656200 | + | 0.754587i | \(0.727837\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.35811 | + | 10.6820i | −0.0821967 | + | 0.646503i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.2030 | −1.75464 | −0.877319 | − | 0.479908i | \(-0.840670\pi\) | ||||
−0.877319 | + | 0.479908i | \(0.840670\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.65557 | + | 14.1437i | −0.218853 | + | 0.846763i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.9856i | 1.37121i | 0.727975 | + | 0.685604i | \(0.240462\pi\) | ||||
−0.727975 | + | 0.685604i | \(0.759538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.03511i | − | 0.120975i | −0.998169 | − | 0.0604875i | \(-0.980734\pi\) | ||
0.998169 | − | 0.0604875i | \(-0.0192655\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.47155i | 0.322975i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.344017 | −0.0202363 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.7171 | − | 1.61686i | −0.745490 | − | 0.0947818i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.00000i | − | 0.350524i | −0.984522 | − | 0.175262i | \(-0.943923\pi\) | ||
0.984522 | − | 0.175262i | \(-0.0560772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.4906 | + | 9.76443i | 1.42109 | + | 0.566590i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.01905i | 0.463753i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 12.5233i | − | 0.721830i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.21809 | + | 17.4460i | −0.127426 | + | 1.00225i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 19.0547i | − | 1.08751i | −0.839245 | − | 0.543753i | \(-0.817003\pi\) | ||
0.839245 | − | 0.543753i | \(-0.182997\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.39478 | + | 26.7011i | −0.193122 | + | 1.51897i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.0902 | −1.47944 | −0.739719 | − | 0.672916i | \(-0.765042\pi\) | ||||
−0.739719 | + | 0.672916i | \(0.765042\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 20.1795i | − | 1.14062i | −0.821431 | − | 0.570308i | \(-0.806824\pi\) | ||
0.821431 | − | 0.570308i | \(-0.193176\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.81598i | 0.438989i | 0.975614 | + | 0.219495i | \(0.0704408\pi\) | ||||
−0.975614 | + | 0.219495i | \(0.929559\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.39759i | 0.302207i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.24857 | + | 25.5511i | −0.181318 | + | 1.42612i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.15952 | 0.287083 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.1059 | + | 2.30199i | 1.00126 | + | 0.127300i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 39.7865i | − | 2.19350i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0424 | 0.551982 | 0.275991 | − | 0.961160i | \(-0.410994\pi\) | ||||
0.275991 | + | 0.961160i | \(0.410994\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.9825 | − | 5.68157i | −1.20464 | − | 0.311348i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 17.8733i | − | 0.973620i | −0.873508 | − | 0.486810i | \(-0.838160\pi\) | ||
0.873508 | − | 0.486810i | \(-0.161840\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.17221 | − | 17.0852i | 0.117978 | − | 0.927939i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.7080 | −1.33801 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.62146 | 0.141546 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.9886 | 1.87829 | 0.939143 | − | 0.343525i | \(-0.111621\pi\) | ||||
0.939143 | + | 0.343525i | \(0.111621\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.24993i | 0.441609i | 0.975318 | + | 0.220804i | \(0.0708682\pi\) | ||||
−0.975318 | + | 0.220804i | \(0.929132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.28290 | + | 8.23400i | −0.175228 | + | 0.439498i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.935042 | 0.0497673 | 0.0248836 | − | 0.999690i | \(-0.492078\pi\) | ||||
0.0248836 | + | 0.999690i | \(0.492078\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.24906 | − | 25.5549i | 0.171958 | − | 1.35251i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.5813 | −1.71957 | −0.859787 | − | 0.510653i | \(-0.829404\pi\) | ||||
−0.859787 | + | 0.510653i | \(0.829404\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4017 | −0.915881 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.22128 | + | 25.3364i | −0.169074 | + | 1.32982i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.791919 | −0.0413378 | −0.0206689 | − | 0.999786i | \(-0.506580\pi\) | ||||
−0.0206689 | + | 0.999786i | \(0.506580\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.12712 | + | 4.36094i | −0.0586757 | + | 0.227022i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 32.3351i | − | 1.67876i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.7335 | −0.969982 | −0.484991 | − | 0.874519i | \(-0.661177\pi\) | ||||
−0.484991 | + | 0.874519i | \(0.661177\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.81472 | −0.0934630 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.88244 | 0.456260 | 0.228130 | − | 0.973631i | \(-0.426739\pi\) | ||||
0.228130 | + | 0.973631i | \(0.426739\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.22990 | − | 9.67352i | 0.0630095 | − | 0.495590i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.48418i | 0.178033i | 0.996030 | + | 0.0890167i | \(0.0283724\pi\) | ||||
−0.996030 | + | 0.0890167i | \(0.971628\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.57976 | − | 9.98132i | 0.131137 | − | 0.507379i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.8027 | −1.25754 | −0.628772 | − | 0.777590i | \(-0.716442\pi\) | ||||
−0.628772 | + | 0.777590i | \(0.716442\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.1842i | − | 0.970188i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.85594 | − | 0.363105i | −0.144063 | − | 0.0183162i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.5873 | −0.782306 | −0.391153 | − | 0.920326i | \(-0.627924\pi\) | ||||
−0.391153 | + | 0.920326i | \(0.627924\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.00646 | − | 7.91612i | 0.0503860 | − | 0.396302i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 26.3852i | − | 1.31761i | −0.752313 | − | 0.658806i | \(-0.771062\pi\) | ||
0.752313 | − | 0.658806i | \(-0.228938\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8.30708i | − | 0.413805i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 38.4017i | − | 1.90350i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.497143 | 0.0245821 | 0.0122911 | − | 0.999924i | \(-0.496088\pi\) | ||||
0.0122911 | + | 0.999924i | \(0.496088\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.91756 | + | 22.9475i | −0.143912 | + | 1.13192i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.87288i | 0.141365i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.13570 | − | 24.6633i | 0.153556 | − | 1.20777i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 11.0240i | − | 0.538556i | −0.963063 | − | 0.269278i | \(-0.913215\pi\) | ||
0.963063 | − | 0.269278i | \(-0.0867850\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0971i | 0.540840i | 0.962742 | + | 0.270420i | \(0.0871626\pi\) | ||||
−0.962742 | + | 0.270420i | \(0.912837\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.19589 | − | 31.7106i | 0.398498 | − | 1.54182i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2.28712i | − | 0.110681i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.8729 | − | 1.89094i | −0.718069 | − | 0.0912956i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.84000 | 0.329471 | 0.164736 | − | 0.986338i | \(-0.447323\pi\) | ||||
0.164736 | + | 0.986338i | \(0.447323\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.6378i | 1.85681i | 0.371567 | + | 0.928406i | \(0.378821\pi\) | ||||
−0.371567 | + | 0.928406i | \(0.621179\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5.94269i | − | 0.284277i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.07908i | − | 0.194684i | −0.995251 | − | 0.0973420i | \(-0.968966\pi\) | ||
0.995251 | − | 0.0973420i | \(-0.0310341\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.2425 | − | 4.71494i | −0.868692 | − | 0.224521i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.7140 | 0.604059 | 0.302030 | − | 0.953299i | \(-0.402336\pi\) | ||||
0.302030 | + | 0.953299i | \(0.402336\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.99209 | − | 31.3991i | 0.188819 | − | 1.48513i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 31.2985i | − | 1.47707i | −0.674217 | − | 0.738533i | \(-0.735519\pi\) | ||
0.674217 | − | 0.738533i | \(-0.264481\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.61822 | −0.358728 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.8063 | + | 3.66244i | 1.35344 | + | 0.172077i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.1097i | 1.36170i | 0.732425 | + | 0.680848i | \(0.238388\pi\) | ||||
−0.732425 | + | 0.680848i | \(0.761612\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.85379 | − | 19.6985i | 0.366583 | − | 0.919446i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.00687071 | −0.000320001 | −0.000160001 | − | 1.00000i | \(-0.500051\pi\) | ||||
−0.000160001 | 1.00000i | \(0.500051\pi\) | ||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.9904 | −0.836086 | −0.418043 | − | 0.908427i | \(-0.637284\pi\) | ||||
−0.418043 | + | 0.908427i | \(0.637284\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.99927 | −0.185064 | −0.0925321 | − | 0.995710i | \(-0.529496\pi\) | ||||
−0.0925321 | + | 0.995710i | \(0.529496\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.2395i | 0.703695i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.37913 | − | 10.8473i | 0.0635470 | − | 0.499817i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.4366 | 0.801735 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.66093 | − | 25.7718i | 0.304983 | − | 1.18001i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.1467 | −1.56020 | −0.780101 | − | 0.625654i | \(-0.784832\pi\) | ||||
−0.780101 | + | 0.625654i | \(0.784832\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.9111 | 0.588693 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −29.4339 | − | 3.74223i | −1.33929 | − | 0.170278i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.851820 | −0.0385997 | −0.0192998 | − | 0.999814i | \(-0.506144\pi\) | ||||
−0.0192998 | + | 0.999814i | \(0.506144\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.62389 | + | 0.587884i | 0.209100 | + | 0.0265850i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.09115i | 0.274890i | 0.990509 | + | 0.137445i | \(0.0438890\pi\) | ||||
−0.990509 | + | 0.137445i | \(0.956111\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.34142 | 0.195528 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.6560 | 1.01626 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.1375 | 0.588116 | 0.294058 | − | 0.955788i | \(-0.404994\pi\) | ||||
0.294058 | + | 0.955788i | \(0.404994\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.6312 | + | 3.64018i | 1.27915 | + | 0.162631i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.6064i | 1.23091i | 0.788172 | + | 0.615455i | \(0.211028\pi\) | ||||
−0.788172 | + | 0.615455i | \(0.788972\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.20416 | + | 17.3364i | −0.0978902 | + | 0.769938i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.46468 | −0.242218 | −0.121109 | − | 0.992639i | \(-0.538645\pi\) | ||||
−0.121109 | + | 0.992639i | \(0.538645\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 15.3675i | − | 0.679817i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.43287 | − | 6.10199i | 0.107414 | − | 0.269409i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 55.3960 | 2.43631 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.1818 | − | 2.56592i | −0.885882 | − | 0.112631i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 39.1312i | − | 1.71437i | −0.515010 | − | 0.857184i | \(-0.672212\pi\) | ||
0.515010 | − | 0.857184i | \(-0.327788\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 14.3467i | − | 0.627336i | −0.949533 | − | 0.313668i | \(-0.898442\pi\) | ||
0.949533 | − | 0.313668i | \(-0.101558\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.8733i | 0.865694i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.903770 | 0.0392944 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.591804 | + | 2.28974i | −0.0256821 | + | 0.0993664i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.56132i | − | 0.110943i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.802169 | + | 0.101988i | 0.0346161 | + | 0.00440111i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 31.8682i | − | 1.37266i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.8846i | 1.28484i | 0.766352 | + | 0.642420i | \(0.222070\pi\) | ||||
−0.766352 | + | 0.642420i | \(0.777930\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −28.4585 | − | 3.61822i | −1.22127 | − | 0.155273i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.78046i | 0.118884i | 0.998232 | + | 0.0594418i | \(0.0189321\pi\) | ||||
−0.998232 | + | 0.0594418i | \(0.981068\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.471140 | − | 1.82288i | 0.0201078 | − | 0.0777987i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.34484 | 0.0572921 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.61822i | 0.153862i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 39.3640i | − | 1.66791i | −0.551836 | − | 0.833953i | \(-0.686073\pi\) | ||
0.551836 | − | 0.833953i | \(-0.313927\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.86236i | 0.247951i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.5809 | + | 4.52376i | 1.50223 | + | 0.190994i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.1259 | 0.679624 | 0.339812 | − | 0.940493i | \(-0.389637\pi\) | ||||
0.339812 | + | 0.940493i | \(0.389637\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −28.6908 | − | 15.8924i | −1.20490 | − | 0.667419i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.55906i | 0.358814i | 0.983775 | + | 0.179407i | \(0.0574180\pi\) | ||||
−0.983775 | + | 0.179407i | \(0.942582\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.6984 | −1.45208 | −0.726042 | − | 0.687650i | \(-0.758642\pi\) | ||||
−0.726042 | + | 0.687650i | \(0.758642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.41801 | + | 11.1531i | −0.0592383 | + | 0.465929i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 32.8684i | − | 1.36833i | −0.729328 | − | 0.684165i | \(-0.760167\pi\) | ||
0.729328 | − | 0.684165i | \(-0.239833\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.5900 | − | 2.49068i | −0.814132 | − | 0.103509i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.1535 | 1.16801 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.0212 | 1.86459 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.4302 | −0.636872 | −0.318436 | − | 0.947944i | \(-0.603158\pi\) | ||||
−0.318436 | + | 0.947944i | \(0.603158\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.15614i | 0.253659i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.11843 | + | 0.777899i | 0.251678 | + | 0.0319985i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.0511 | 0.577008 | 0.288504 | − | 0.957479i | \(-0.406842\pi\) | ||||
0.288504 | + | 0.957479i | \(0.406842\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.56830 | − | 0.962236i | −0.309750 | − | 0.0393817i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.0200 | 1.22658 | 0.613291 | − | 0.789857i | \(-0.289845\pi\) | ||||
0.613291 | + | 0.789857i | \(0.289845\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.3006 | −1.19520 | −0.597599 | − | 0.801795i | \(-0.703878\pi\) | ||||
−0.597599 | + | 0.801795i | \(0.703878\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.13929 | + | 12.1462i | −0.127842 | + | 0.494632i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.9265 | −1.57998 | −0.789989 | − | 0.613122i | \(-0.789914\pi\) | ||||
−0.789989 | + | 0.613122i | \(0.789914\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.846874 | − | 6.66093i | 0.0343171 | − | 0.269915i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.6247i | 0.753474i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.9092 | −1.16763 | −0.583816 | − | 0.811886i | \(-0.698441\pi\) | ||||
−0.583816 | + | 0.811886i | \(0.698441\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.5340 | 1.06822 | 0.534109 | − | 0.845416i | \(-0.320647\pi\) | ||||
0.534109 | + | 0.845416i | \(0.320647\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.9531 | −0.721595 | −0.360798 | − | 0.932644i | \(-0.617495\pi\) | ||||
−0.360798 | + | 0.932644i | \(0.617495\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.6885 | − | 9.04593i | −0.910459 | − | 0.363001i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 42.1795i | − | 1.68989i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.0219 | + | 1.40133i | 0.440171 | + | 0.0559635i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.8875 | −1.23157 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 33.8875i | − | 1.34904i | −0.738257 | − | 0.674520i | \(-0.764351\pi\) | ||
0.738257 | − | 0.674520i | \(-0.235649\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.52523 | − | 27.7271i | 0.140115 | − | 1.10205i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.7144 | 0.424521 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.0573 | + | 4.66707i | 0.714336 | + | 0.184626i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.1456i | 0.637711i | 0.947803 | + | 0.318856i | \(0.103298\pi\) | ||||
−0.947803 | + | 0.318856i | \(0.896702\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.9604i | 1.65476i | 0.561645 | + | 0.827378i | \(0.310169\pi\) | ||||
−0.561645 | + | 0.827378i | \(0.689831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 9.10158i | − | 0.357820i | −0.983865 | − | 0.178910i | \(-0.942743\pi\) | ||
0.983865 | − | 0.178910i | \(-0.0572571\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.4911 | + | 3.87665i | 1.19504 | + | 0.151938i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0573i | 0.471839i | 0.971773 | + | 0.235919i | \(0.0758102\pi\) | ||||
−0.971773 | + | 0.235919i | \(0.924190\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.16565 | − | 12.2482i | 0.123504 | − | 0.477848i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.1916i | 0.474916i | 0.971398 | + | 0.237458i | \(0.0763142\pi\) | ||||
−0.971398 | + | 0.237458i | \(0.923686\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0284i | 0.856806i | 0.903588 | + | 0.428403i | \(0.140924\pi\) | ||||
−0.903588 | + | 0.428403i | \(0.859076\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.52094 | + | 11.9626i | −0.0590682 | + | 0.464591i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 5.00041i | − | 0.193617i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.33143 | − | 10.4721i | 0.0514759 | − | 0.404875i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.18443 | 0.122934 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 25.3258i | − | 0.976238i | −0.872777 | − | 0.488119i | \(-0.837683\pi\) | ||
0.872777 | − | 0.488119i | \(-0.162317\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.9435i | 0.843358i | 0.906745 | + | 0.421679i | \(0.138559\pi\) | ||||
−0.906745 | + | 0.421679i | \(0.861441\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.9724i | 1.03511i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.47118 | + | 35.1673i | −0.171336 | + | 1.34761i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.0383 | −0.613687 | −0.306844 | − | 0.951760i | \(-0.599273\pi\) | ||||
−0.306844 | + | 0.951760i | \(0.599273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −45.4860 | − | 5.78311i | −1.73540 | − | 0.220639i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.1366i | 0.576658i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.0993 | 0.878740 | 0.439370 | − | 0.898306i | \(-0.355202\pi\) | ||||
0.439370 | + | 0.898306i | \(0.355202\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.8814 | − | 53.7084i | 0.527311 | − | 2.04021i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.12753i | 0.232097i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.32534 | + | 41.8855i | −0.201423 | + | 1.58426i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.254246 | 0.00960274 | 0.00480137 | − | 0.999988i | \(-0.498472\pi\) | ||||
0.00480137 | + | 0.999988i | \(0.498472\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.56802 | −0.360865 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 37.0022 | 1.39161 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 19.9746i | − | 0.750163i | −0.926992 | − | 0.375082i | \(-0.877615\pi\) | ||
0.926992 | − | 0.375082i | \(-0.122385\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.745342 | + | 2.88380i | −0.0279525 | + | 0.108151i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.8899 | 0.857233 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.19529 | + | 9.40133i | −0.0446389 | + | 0.351099i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.7978 | −1.26044 | −0.630222 | − | 0.776415i | \(-0.717036\pi\) | ||||
−0.630222 | + | 0.776415i | \(0.717036\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 56.6317 | 2.10908 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.38374 | − | 42.3449i | 0.200224 | − | 1.57482i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.0308 | 1.00252 | 0.501258 | − | 0.865298i | \(-0.332871\pi\) | ||||
0.501258 | + | 0.865298i | \(0.332871\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.5934 | − | 18.5768i | −0.725682 | − | 0.688030i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 14.0247i | − | 0.518722i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.8811 | −0.586583 | −0.293291 | − | 0.956023i | \(-0.594751\pi\) | ||||
−0.293291 | + | 0.956023i | \(0.594751\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.2185 | −0.781592 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.1753 | −0.521446 | −0.260723 | − | 0.965414i | \(-0.583961\pi\) | ||||
−0.260723 | + | 0.965414i | \(0.583961\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.471140 | + | 3.70567i | −0.0173078 | + | 0.136131i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 29.5744i | − | 1.08498i | −0.840063 | − | 0.542489i | \(-0.817482\pi\) | ||
0.840063 | − | 0.542489i | \(-0.182518\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.4390 | + | 5.79954i | 0.820999 | + | 0.212194i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 54.1926 | 1.98016 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 7.58573i | − | 0.276807i | −0.990376 | − | 0.138404i | \(-0.955803\pi\) | ||
0.990376 | − | 0.138404i | \(-0.0441971\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.00642 | + | 0.382237i | 0.109560 | + | 0.0139295i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.1258 | −1.13129 | −0.565643 | − | 0.824650i | \(-0.691372\pi\) | ||||
−0.565643 | + | 0.824650i | \(0.691372\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.21043 | − | 40.9817i | 0.189127 | − | 1.48754i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.24575i | 0.298908i | 0.988769 | + | 0.149454i | \(0.0477516\pi\) | ||||
−0.988769 | + | 0.149454i | \(0.952248\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 38.4017i | − | 1.39024i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1.34484i | − | 0.0485594i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.3262 | 0.949347 | 0.474674 | − | 0.880162i | \(-0.342566\pi\) | ||||
0.474674 | + | 0.880162i | \(0.342566\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.15267 | + | 9.06612i | −0.0415124 | + | 0.326508i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 27.2417i | − | 0.979817i | −0.871774 | − | 0.489909i | \(-0.837030\pi\) | ||
0.871774 | − | 0.489909i | \(-0.162970\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.02518 | + | 47.3900i | −0.216152 | + | 1.70011i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.89812i | 0.0680074i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.5447i | 1.12876i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.04711 | − | 5.13445i | 0.0731577 | − | 0.183490i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.9324i | 0.960037i | 0.877258 | + | 0.480019i | \(0.159370\pi\) | ||||
−0.877258 | + | 0.480019i | \(0.840630\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.07636 | − | 0.391129i | −0.109521 | − | 0.0139246i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.2369 | −1.28843 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.07064i | 0.0380195i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 13.1279i | − | 0.465016i | −0.972595 | − | 0.232508i | \(-0.925307\pi\) | ||
0.972595 | − | 0.232508i | \(-0.0746931\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 44.5565i | − | 1.57629i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.68886 | − | 33.6180i | 0.307006 | − | 1.18783i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.3966 | 0.755071 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.08685 | + | 32.1444i | −0.143864 | + | 1.13154i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.5632i | 1.03939i | 0.854353 | + | 0.519693i | \(0.173954\pi\) | ||||
−0.854353 | + | 0.519693i | \(0.826046\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.2269 | −1.02629 | −0.513147 | − | 0.858301i | \(-0.671520\pi\) | ||||
−0.513147 | + | 0.858301i | \(0.671520\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 42.6877 | + | 5.42733i | 1.49712 | + | 0.190345i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.34443i | − | 0.151992i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.0573 | + | 4.66707i | 0.630973 | + | 0.163081i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.29201 | −0.184692 | −0.0923462 | − | 0.995727i | \(-0.529437\pi\) | ||||
−0.0923462 | + | 0.995727i | \(0.529437\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0047 | 0.557890 | 0.278945 | − | 0.960307i | \(-0.410015\pi\) | ||||
0.278945 | + | 0.960307i | \(0.410015\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.13539 | −0.143802 | −0.0719009 | − | 0.997412i | \(-0.522907\pi\) | ||||
−0.0719009 | + | 0.997412i | \(0.522907\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.5879i | 0.784512i | 0.919856 | + | 0.392256i | \(0.128305\pi\) | ||||
−0.919856 | + | 0.392256i | \(0.871695\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.37954 | + | 50.1771i | −0.221304 | + | 1.74063i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.6325 | −0.888113 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.5035 | + | 9.37084i | 0.812399 | + | 0.323904i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.0329 | 1.10590 | 0.552949 | − | 0.833215i | \(-0.313502\pi\) | ||||
0.552949 | + | 0.833215i | \(0.313502\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.8684 | −0.960979 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 39.4944 | + | 5.02133i | 1.36026 | + | 0.172944i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 53.7374 | 1.84644 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.49677 | − | 0.444581i | −0.120009 | − | 0.0152580i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.5760i | 1.21953i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.3607 | −0.354745 | −0.177372 | − | 0.984144i | \(-0.556760\pi\) | ||||
−0.177372 | + | 0.984144i | \(0.556760\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.1893 | 0.621334 | 0.310667 | − | 0.950519i | \(-0.399448\pi\) | ||||
0.310667 | + | 0.950519i | \(0.399448\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.2650 | 0.930271 | 0.465136 | − | 0.885239i | \(-0.346006\pi\) | ||||
0.465136 | + | 0.885239i | \(0.346006\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.40133 | + | 1.19529i | 0.320396 | + | 0.0407353i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.4082i | 0.422381i | 0.977445 | + | 0.211191i | \(0.0677341\pi\) | ||||
−0.977445 | + | 0.211191i | \(0.932266\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.0751522 | + | 0.591096i | −0.00255230 | + | 0.0200747i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.03776 | −0.170894 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 7.13386i | − | 0.241722i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.55623 | + | 21.4976i | −0.188050 | + | 0.727582i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.19349 | −0.310442 | −0.155221 | − | 0.987880i | \(-0.549609\pi\) | ||||
−0.155221 | + | 0.987880i | \(0.549609\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.3093 | − | 1.31073i | −0.347725 | − | 0.0442098i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.4479i | 1.29534i | 0.761920 | + | 0.647671i | \(0.224257\pi\) | ||||
−0.761920 | + | 0.647671i | \(0.775743\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.12406i | 0.172438i | 0.996276 | + | 0.0862192i | \(0.0274785\pi\) | ||||
−0.996276 | + | 0.0862192i | \(0.972521\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.79043i | − | 0.0601169i | −0.999548 | − | 0.0300584i | \(-0.990431\pi\) | ||
0.999548 | − | 0.0300584i | \(-0.00956934\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.5171 | −0.688121 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.1275 | − | 39.9472i | 0.741300 | − | 1.33828i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 13.8022i | − | 0.461874i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.7785 | + | 1.75180i | 0.460050 | + | 0.0584909i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.18002i | 0.172763i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 36.2118i | − | 1.20639i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21.5178 | − | 2.73578i | −0.716066 | − | 0.0910409i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 34.5506i | − | 1.14724i | −0.819123 | − | 0.573618i | \(-0.805540\pi\) | ||
0.819123 | − | 0.573618i | \(-0.194460\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.4915 | + | 7.62234i | 0.978172 | + | 0.252817i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.6515 | 1.74442 | 0.872211 | − | 0.489130i | \(-0.162686\pi\) | ||||
0.872211 | + | 0.489130i | \(0.162686\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.1991i | 1.29730i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.05731i | 0.200030i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 13.0595i | − | 0.430794i | −0.976527 | − | 0.215397i | \(-0.930895\pi\) | ||
0.976527 | − | 0.215397i | \(-0.0691046\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.7401 | − | 4.16259i | −1.07882 | − | 0.137162i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.6056 | −0.349089 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 45.1367 | + | 11.6660i | 1.48248 | + | 0.383160i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.9794i | 0.688313i | 0.938912 | + | 0.344156i | \(0.111835\pi\) | ||||
−0.938912 | + | 0.344156i | \(0.888165\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.94016 | −0.260228 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.69953 | + | 44.8287i | −0.186594 | + | 1.46762i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.78393i | 0.188953i | 0.995527 | + | 0.0944764i | \(0.0301177\pi\) | ||||
−0.995527 | + | 0.0944764i | \(0.969882\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34.6729 | − | 4.40832i | −1.13151 | − | 0.143860i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.0131 | −1.36959 | −0.684794 | − | 0.728737i | \(-0.740108\pi\) | ||||
−0.684794 | + | 0.728737i | \(0.740108\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.05764 | 0.229829 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.5854 | −0.766421 | −0.383211 | − | 0.923661i | \(-0.625182\pi\) | ||||
−0.383211 | + | 0.923661i | \(0.625182\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.19377i | 0.233520i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.4296 | + | 1.70744i | 0.435484 | + | 0.0553675i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.8648 | −1.03220 | −0.516102 | − | 0.856527i | \(-0.672617\pi\) | ||||
−0.516102 | + | 0.856527i | \(0.672617\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.27423 | + | 1.17913i | 0.299793 | + | 0.0381159i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 48.6706 | 1.57166 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.28794 | 0.235095 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 43.1927 | + | 11.1635i | 1.39186 | + | 0.359739i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.1038 | −0.357073 | −0.178537 | − | 0.983933i | \(-0.557136\pi\) | ||||
−0.178537 | + | 0.983933i | \(0.557136\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.12712 | − | 8.86519i | 0.0362084 | − | 0.284791i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 47.5500i | − | 1.52595i | −0.646427 | − | 0.762976i | \(-0.723737\pi\) | ||
0.646427 | − | 0.762976i | \(-0.276263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −52.3097 | −1.67697 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.9896 | −1.66329 | −0.831647 | − | 0.555304i | \(-0.812602\pi\) | ||||
−0.831647 | + | 0.555304i | \(0.812602\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.7279 | 1.87695 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.91064 | − | 30.6070i | 0.252567 | − | 0.977206i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.4842i | 0.876609i | 0.898826 | + | 0.438305i | \(0.144421\pi\) | ||||
−0.898826 | + | 0.438305i | \(0.855579\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −68.3619 | − | 8.69155i | −2.17598 | − | 0.276655i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.1535 | −0.513653 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 24.4556i | − | 0.776858i | −0.921479 | − | 0.388429i | \(-0.873018\pi\) | ||
0.921479 | − | 0.388429i | \(-0.126982\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.19382 | − | 17.2551i | 0.0696188 | − | 0.547575i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.1729 | −1.24062 | −0.620309 | − | 0.784358i | \(-0.712993\pi\) | ||||
−0.620309 | + | 0.784358i | \(0.712993\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.5644 | + | 36.5296i | −0.460797 | + | 1.15575i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))