Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,2,Mod(815,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.815");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.q (of order \(6\), degree \(2\), 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: | \(12.5205430369\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.144054149089536.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1391.2 | ||
Root | \(-2.37165 - 1.78079i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.1391 |
Dual form | 1568.2.q.g.815.2 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.27230 | + | 1.31191i | −1.31191 | + | 0.757434i | −0.982413 | − | 0.186720i | \(-0.940214\pi\) |
−0.329502 | + | 0.944155i | \(0.606881\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.03926 | − | 1.80005i | 0.464771 | − | 0.805007i | −0.534420 | − | 0.845219i | \(-0.679470\pi\) |
0.999191 | + | 0.0402117i | \(0.0128032\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.94224 | − | 3.36406i | 0.647414 | − | 1.12135i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.669938 | + | 1.16037i | 0.201994 | + | 0.349864i | 0.949171 | − | 0.314761i | \(-0.101925\pi\) |
−0.747177 | + | 0.664625i | \(0.768591\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.50406 | −0.694500 | −0.347250 | − | 0.937773i | \(-0.612884\pi\) | ||||
−0.347250 | + | 0.937773i | \(0.612884\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.45368i | 1.40814i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.78212 | − | 1.60626i | 0.674763 | − | 0.389575i | −0.123116 | − | 0.992392i | \(-0.539289\pi\) |
0.797879 | + | 0.602818i | \(0.205955\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.55442 | + | 2.05215i | 0.815440 | + | 0.470795i | 0.848842 | − | 0.528647i | \(-0.177301\pi\) |
−0.0334012 | + | 0.999442i | \(0.510634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.54952 | − | 3.20402i | −1.15716 | − | 0.668084i | −0.206535 | − | 0.978439i | \(-0.566219\pi\) |
−0.950621 | + | 0.310355i | \(0.899552\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.339877 | + | 0.588684i | 0.0679754 | + | 0.117737i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.32073i | 0.446626i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.66151i | 0.865621i | 0.901485 | + | 0.432811i | \(0.142478\pi\) | ||||
−0.901485 | + | 0.432811i | \(0.857522\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.21897 | − | 3.84337i | −0.398539 | − | 0.690290i | 0.595007 | − | 0.803721i | \(-0.297149\pi\) |
−0.993546 | + | 0.113430i | \(0.963816\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.04461 | − | 1.75780i | −0.529998 | − | 0.305994i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.50178 | − | 3.17646i | −0.904488 | − | 0.522206i | −0.0258343 | − | 0.999666i | \(-0.508224\pi\) |
−0.878653 | + | 0.477460i | \(0.841558\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.68997 | − | 3.28511i | 0.911125 | − | 0.526038i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.55076i | − | 0.866882i | −0.901182 | − | 0.433441i | \(-0.857299\pi\) | ||
0.901182 | − | 0.433441i | \(-0.142701\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.03699 | − | 6.99227i | −0.601799 | − | 1.04235i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.565988 | − | 0.980320i | 0.0825579 | − | 0.142994i | −0.821790 | − | 0.569790i | \(-0.807024\pi\) |
0.904348 | + | 0.426796i | \(0.140358\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.21455 | + | 7.29981i | −0.590154 | + | 1.02218i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.43567 | − | 4.29299i | 1.02137 | − | 0.589687i | 0.106868 | − | 0.994273i | \(-0.465918\pi\) |
0.914500 | + | 0.404586i | \(0.132584\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.78496 | 0.375524 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.7690 | −1.42638 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.29193 | − | 3.63265i | 0.819140 | − | 0.472931i | −0.0309798 | − | 0.999520i | \(-0.509863\pi\) |
0.850120 | + | 0.526589i | \(0.176529\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.57219 | − | 4.45517i | 0.329336 | − | 0.570426i | −0.653045 | − | 0.757319i | \(-0.726509\pi\) |
0.982380 | + | 0.186893i | \(0.0598419\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.60236 | + | 4.50743i | −0.322784 | + | 0.559078i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.93243 | − | 6.81116i | −0.480422 | − | 0.832116i | 0.519325 | − | 0.854577i | \(-0.326183\pi\) |
−0.999748 | + | 0.0224607i | \(0.992850\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.8136 | 2.02412 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.29150i | − | 0.627986i | −0.949425 | − | 0.313993i | \(-0.898333\pi\) | ||
0.949425 | − | 0.313993i | \(-0.101667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.480369 | + | 0.277341i | −0.0562230 | + | 0.0324604i | −0.527848 | − | 0.849339i | \(-0.677001\pi\) |
0.471625 | + | 0.881799i | \(0.343668\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.54461 | − | 0.891779i | −0.178356 | − | 0.102974i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.26862 | + | 3.04184i | 0.592766 | + | 0.342233i | 0.766190 | − | 0.642614i | \(-0.222150\pi\) |
−0.173425 | + | 0.984847i | \(0.555483\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.78212 | + | 4.81877i | 0.309124 | + | 0.535419i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 0.503175i | − | 0.0552307i | −0.999619 | − | 0.0276153i | \(-0.991209\pi\) | ||
0.999619 | − | 0.0276153i | \(-0.00879135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 6.67728i | − | 0.724252i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.11551 | − | 10.5924i | −0.655651 | − | 1.13562i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.50000 | − | 0.866025i | −0.159000 | − | 0.0917985i | 0.418389 | − | 0.908268i | \(-0.362595\pi\) |
−0.577389 | + | 0.816469i | \(0.695928\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.0844 | + | 5.82221i | 1.04570 | + | 0.603735i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.38794 | − | 4.26543i | 0.757986 | − | 0.437624i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.2234i | 1.74878i | 0.485228 | + | 0.874388i | \(0.338737\pi\) | ||||
−0.485228 | + | 0.874388i | \(0.661263\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.20473 | 0.523095 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.613725 | − | 1.06300i | −0.0610679 | − | 0.105773i | 0.833875 | − | 0.551953i | \(-0.186117\pi\) |
−0.894943 | + | 0.446180i | \(0.852784\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.62804 | − | 13.2122i | 0.751613 | − | 1.30183i | −0.195427 | − | 0.980718i | \(-0.562609\pi\) |
0.947041 | − | 0.321114i | \(-0.104057\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.55442 | − | 9.62054i | 0.536966 | − | 0.930053i | −0.462099 | − | 0.886828i | \(-0.652904\pi\) |
0.999065 | − | 0.0432246i | \(-0.0137631\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.9109 | − | 6.29938i | 1.04507 | − | 0.603372i | 0.123805 | − | 0.992307i | \(-0.460490\pi\) |
0.921265 | + | 0.388935i | \(0.127157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.6690 | 1.58215 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.0629 | 1.88736 | 0.943680 | − | 0.330860i | \(-0.107339\pi\) | ||||
0.943680 | + | 0.330860i | \(0.107339\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.5348 | + | 6.65961i | −1.07562 | + | 0.621012i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.86348 | + | 8.42380i | −0.449629 | + | 0.778780i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.60236 | − | 7.97153i | 0.418397 | − | 0.724685i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.28212 | + | 12.6130i | 0.656607 | + | 1.13728i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8055 | 1.05591 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.6145i | − | 1.29683i | −0.761287 | − | 0.648415i | \(-0.775432\pi\) | ||
0.761287 | − | 0.648415i | \(-0.224568\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.27230 | − | 3.04397i | −0.460643 | − | 0.265953i | 0.251671 | − | 0.967813i | \(-0.419020\pi\) |
−0.712315 | + | 0.701860i | \(0.752353\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.17744 | + | 2.41185i | 0.359537 | + | 0.207579i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.98685 | − | 12.1016i | −0.596927 | − | 1.03391i | −0.993272 | − | 0.115806i | \(-0.963055\pi\) |
0.396345 | − | 0.918102i | \(-0.370278\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.503175i | 0.0426788i | 0.999772 | + | 0.0213394i | \(0.00679305\pi\) | ||||
−0.999772 | + | 0.0213394i | \(0.993207\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.97011i | 0.250129i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.67756 | − | 2.90562i | −0.140285 | − | 0.242981i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.39096 | + | 4.84452i | 0.696832 | + | 0.402316i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.77077 | − | 2.75440i | −0.390836 | − | 0.225649i | 0.291686 | − | 0.956514i | \(-0.405784\pi\) |
−0.682522 | + | 0.730865i | \(0.739117\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.09511 | − | 3.51901i | 0.496013 | − | 0.286373i | −0.231053 | − | 0.972941i | \(-0.574217\pi\) |
0.727066 | + | 0.686568i | \(0.240884\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 12.4790i | − | 1.00886i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.22436 | −0.740918 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.15477 | − | 12.3924i | −0.571013 | − | 0.989023i | −0.996462 | − | 0.0840409i | \(-0.973217\pi\) |
0.425450 | − | 0.904982i | \(-0.360116\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.2641 | + | 19.5099i | −0.893299 | + | 1.54724i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.15679 | − | 7.19977i | 0.325585 | − | 0.563929i | −0.656046 | − | 0.754721i | \(-0.727772\pi\) |
0.981631 | + | 0.190792i | \(0.0611055\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.32828 | + | 3.65363i | −0.492656 | + | 0.284435i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.50406 | 0.193770 | 0.0968848 | − | 0.995296i | \(-0.469112\pi\) | ||||
0.0968848 | + | 0.995296i | \(0.469112\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.72971 | −0.517670 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.8071 | − | 7.97153i | 1.05585 | − | 0.609598i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.71682 | − | 4.70568i | 0.206556 | − | 0.357766i | −0.744071 | − | 0.668100i | \(-0.767108\pi\) |
0.950627 | + | 0.310334i | \(0.100441\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.53146 | + | 16.5090i | −0.716428 | + | 1.24089i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.75915 | + | 3.04694i | 0.131485 | + | 0.227739i | 0.924249 | − | 0.381790i | \(-0.124692\pi\) |
−0.792764 | + | 0.609529i | \(0.791359\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.1981 | −1.64997 | −0.824985 | − | 0.565154i | \(-0.808817\pi\) | ||||
−0.824985 | + | 0.565154i | \(0.808817\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.4980i | 0.997801i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.4356 | + | 6.60233i | −0.840760 | + | 0.485413i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.72770 | + | 2.15219i | 0.272596 | + | 0.157383i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.13615 | − | 0.655958i | −0.0822091 | − | 0.0474635i | 0.458332 | − | 0.888781i | \(-0.348447\pi\) |
−0.540541 | + | 0.841318i | \(0.681780\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.64697 | + | 9.78084i | 0.406478 | + | 0.704040i | 0.994492 | − | 0.104810i | \(-0.0334235\pi\) |
−0.588014 | + | 0.808851i | \(0.700090\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 13.6563i | − | 0.977950i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.92149i | − | 0.421889i | −0.977498 | − | 0.210944i | \(-0.932346\pi\) | ||
0.977498 | − | 0.210944i | \(-0.0676539\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.30560 | + | 16.1178i | 0.659657 | + | 1.14256i | 0.980704 | + | 0.195496i | \(0.0626317\pi\) |
−0.321048 | + | 0.947063i | \(0.604035\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.8713 | + | 10.3180i | 1.26055 | + | 0.727777i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.99164 | − | 5.76868i | −0.697847 | − | 0.402902i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −21.5570 | + | 12.4460i | −1.49832 | + | 0.865054i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.49925i | 0.380391i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.72971 | −0.394449 | −0.197225 | − | 0.980358i | \(-0.563193\pi\) | ||||
−0.197225 | + | 0.980358i | \(0.563193\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.94200 | + | 12.0239i | 0.475658 | + | 0.823864i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.727697 | − | 1.26041i | 0.0491732 | − | 0.0851704i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.96658 | + | 4.02216i | −0.468623 | + | 0.270560i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.8668 | −1.39734 | −0.698672 | − | 0.715442i | \(-0.746225\pi\) | ||||
−0.698672 | + | 0.715442i | \(0.746225\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.64049 | 0.176033 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.2775 | − | 8.24309i | 0.947628 | − | 0.547113i | 0.0552847 | − | 0.998471i | \(-0.482393\pi\) |
0.892343 | + | 0.451357i | \(0.149060\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.24976 | − | 7.36079i | 0.280832 | − | 0.486415i | −0.690758 | − | 0.723086i | \(-0.742723\pi\) |
0.971590 | + | 0.236671i | \(0.0760564\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.23751 | + | 3.87548i | −0.146584 | + | 0.253891i | −0.929963 | − | 0.367653i | \(-0.880161\pi\) |
0.783379 | + | 0.621545i | \(0.213495\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.17642 | − | 2.03762i | −0.0767410 | − | 0.132919i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.9625 | −1.03688 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.5675i | 1.58914i | 0.607171 | + | 0.794571i | \(0.292304\pi\) | ||||
−0.607171 | + | 0.794571i | \(0.707696\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.02498 | − | 2.90117i | 0.323687 | − | 0.186881i | −0.329348 | − | 0.944209i | \(-0.606829\pi\) |
0.653035 | + | 0.757328i | \(0.273495\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −18.6731 | − | 10.7809i | −1.19788 | − | 0.691596i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.90047 | − | 5.13869i | −0.566323 | − | 0.326967i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.660123 | + | 1.14337i | 0.0418336 | + | 0.0724579i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.8010i | 1.18671i | 0.804942 | + | 0.593353i | \(0.202196\pi\) | ||||
−0.804942 | + | 0.593353i | \(0.797804\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.58598i | − | 0.539796i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.76002 | + | 15.1728i | 0.548574 | + | 0.950157i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.9106 | − | 6.29923i | −0.680584 | − | 0.392935i | 0.119491 | − | 0.992835i | \(-0.461874\pi\) |
−0.800075 | + | 0.599900i | \(0.795207\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.6816 | + | 9.05379i | 0.970668 | + | 0.560415i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.27292 | + | 2.46697i | −0.263479 | + | 0.152120i | −0.625921 | − | 0.779887i | \(-0.715277\pi\) |
0.362441 | + | 0.932007i | \(0.381943\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 17.8461i | − | 1.09628i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.54461 | 0.278125 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1502 | + | 22.7769i | 0.801783 | + | 1.38873i | 0.918441 | + | 0.395558i | \(0.129449\pi\) |
−0.116658 | + | 0.993172i | \(0.537218\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0490 | − | 24.3336i | 0.853418 | − | 1.47816i | −0.0246868 | − | 0.999695i | \(-0.507859\pi\) |
0.878105 | − | 0.478468i | \(-0.158808\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.455393 | + | 0.788764i | −0.0274612 | + | 0.0475643i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.3982 | + | 13.5090i | −1.40586 | + | 0.811675i | −0.994986 | − | 0.100017i | \(-0.968110\pi\) |
−0.410876 | + | 0.911691i | \(0.634777\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.2391 | −1.03208 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0629 | −1.19685 | −0.598426 | − | 0.801178i | \(-0.704207\pi\) | ||||
−0.598426 | + | 0.801178i | \(0.704207\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.75248 | + | 2.74385i | −0.282506 | + | 0.163105i | −0.634557 | − | 0.772876i | \(-0.718817\pi\) |
0.352052 | + | 0.935981i | \(0.385484\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.1918 | + | 19.3847i | −0.662943 | + | 1.14825i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.33988 | + | 5.78484i | −0.196463 | + | 0.340284i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.5957 | − | 39.1369i | −1.32458 | − | 2.29425i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.6931 | −0.799957 | −0.399978 | − | 0.916525i | \(-0.630982\pi\) | ||||
−0.399978 | + | 0.916525i | \(0.630982\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 15.1011i | − | 0.879218i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.69291 | + | 1.55475i | −0.156258 | + | 0.0902157i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.8963 | + | 8.02304i | 0.803644 | + | 0.463984i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.78914 | + | 1.61031i | 0.160232 | + | 0.0925099i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.34636 | − | 9.26016i | −0.306131 | − | 0.530235i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.4197i | − | 1.39371i | −0.717213 | − | 0.696854i | \(-0.754583\pi\) | ||
0.717213 | − | 0.696854i | \(-0.245417\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 40.0294i | 2.27719i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.61539 | + | 14.9223i | 0.488534 | + | 0.846165i | 0.999913 | − | 0.0131898i | \(-0.00419856\pi\) |
−0.511379 | + | 0.859355i | \(0.670865\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.0446 | − | 8.68601i | −0.850371 | − | 0.490962i | 0.0104047 | − | 0.999946i | \(-0.496688\pi\) |
−0.860776 | + | 0.508984i | \(0.830021\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.7863 | − | 9.69155i | −0.942810 | − | 0.544332i | −0.0519701 | − | 0.998649i | \(-0.516550\pi\) |
−0.890840 | + | 0.454317i | \(0.849883\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.40907 | + | 3.12293i | −0.302850 | + | 0.174850i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 29.1477i | 1.62687i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.1851 | 0.733639 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.851071 | − | 1.47410i | −0.0472089 | − | 0.0817682i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.5285 | + | 28.6282i | −0.914029 | + | 1.58314i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.4008 | + | 18.0147i | −0.571678 | + | 0.990176i | 0.424715 | + | 0.905327i | \(0.360374\pi\) |
−0.996394 | + | 0.0848492i | \(0.972959\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.3716 | + | 12.3389i | −1.17116 | + | 0.676167i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.3473 | −0.893146 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.3332 | 0.562886 | 0.281443 | − | 0.959578i | \(-0.409187\pi\) | ||||
0.281443 | + | 0.959578i | \(0.409187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −45.5890 | + | 26.3208i | −2.47606 | + | 1.42955i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.97315 | − | 5.14965i | 0.161005 | − | 0.278869i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.4737 | − | 30.2653i | 0.940752 | − | 1.62943i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.8169 | + | 29.1277i | 0.902779 | + | 1.56366i | 0.823871 | + | 0.566777i | \(0.191810\pi\) |
0.0789080 | + | 0.996882i | \(0.474857\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.3546 | −0.714858 | −0.357429 | − | 0.933940i | \(-0.616347\pi\) | ||||
−0.357429 | + | 0.933940i | \(0.616347\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5.81125i | − | 0.310182i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.80175 | + | 3.92699i | −0.362021 | + | 0.209013i | −0.669967 | − | 0.742391i | \(-0.733692\pi\) |
0.307946 | + | 0.951404i | \(0.400358\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.52498 | − | 5.49925i | −0.505533 | − | 0.291870i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.140453 | − | 0.0810905i | −0.00741282 | − | 0.00427979i | 0.496289 | − | 0.868157i | \(-0.334696\pi\) |
−0.503702 | + | 0.863878i | \(0.668029\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.07739 | − | 1.86609i | −0.0567047 | − | 0.0982154i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.1516i | 1.26763i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.15292i | 0.0603466i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.1321 | − | 17.5493i | −0.528891 | − | 0.916066i | −0.999432 | − | 0.0336883i | \(-0.989275\pi\) |
0.470541 | − | 0.882378i | \(-0.344059\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.6731 | − | 10.7809i | −0.972082 | − | 0.561232i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.78269 | + | 3.33864i | 0.299416 | + | 0.172868i | 0.642181 | − | 0.766553i | \(-0.278030\pi\) |
−0.342764 | + | 0.939421i | \(0.611363\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −26.8256 | + | 15.4878i | −1.38527 | + | 0.799786i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 11.6727i | − | 0.601174i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.60350 | 0.236466 | 0.118233 | − | 0.992986i | \(-0.462277\pi\) | ||||
0.118233 | + | 0.992986i | \(0.462277\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.1730 | + | 33.2086i | 0.982264 | + | 1.70133i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.71038 | + | 9.89066i | −0.291787 | + | 0.505389i | −0.974232 | − | 0.225547i | \(-0.927583\pi\) |
0.682446 | + | 0.730936i | \(0.260916\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.0307 | − | 15.0288i | 1.31981 | − | 0.761991i | 0.336109 | − | 0.941823i | \(-0.390889\pi\) |
0.983697 | + | 0.179832i | \(0.0575555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.5859 | −1.04107 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.9737 | 0.805766 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.9509 | − | 6.32252i | 0.551001 | − | 0.318120i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.17124 | + | 3.76069i | −0.108971 | + | 0.188744i | −0.915354 | − | 0.402651i | \(-0.868089\pi\) |
0.806383 | + | 0.591394i | \(0.201422\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.98685 | − | 17.2977i | 0.498719 | − | 0.863807i | −0.501279 | − | 0.865285i | \(-0.667137\pi\) |
0.999999 | + | 0.00147805i | \(0.000470479\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.55643 | + | 9.62402i | 0.276786 | + | 0.479407i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.5654 | 0.574688 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8.51212i | − | 0.421930i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.4356 | − | 15.2626i | 1.30715 | − | 0.754686i | 0.325534 | − | 0.945530i | \(-0.394456\pi\) |
0.981620 | + | 0.190844i | \(0.0611225\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.7525 | + | 18.3323i | 1.56623 | + | 0.904266i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.905741 | − | 0.522930i | −0.0444611 | − | 0.0256696i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.660123 | − | 1.14337i | −0.0323264 | − | 0.0559909i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 2.08070i | − | 0.101649i | −0.998708 | − | 0.0508245i | \(-0.983815\pi\) | ||
0.998708 | − | 0.0508245i | \(-0.0161849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 30.4039i | − | 1.48180i | −0.671618 | − | 0.740898i | \(-0.734400\pi\) | ||
0.671618 | − | 0.740898i | \(-0.265600\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.19857 | − | 3.80804i | −0.106898 | − | 0.185153i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.89116 | + | 1.09186i | 0.0917345 | + | 0.0529630i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.62386 | + | 4.40164i | 0.368084 | + | 0.212513i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.32280 | − | 1.34107i | 0.111885 | − | 0.0645970i | −0.443013 | − | 0.896515i | \(-0.646090\pi\) |
0.554898 | + | 0.831918i | \(0.312757\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29.4673i | − | 1.41611i | −0.706158 | − | 0.708054i | \(-0.749573\pi\) | ||
0.706158 | − | 0.708054i | \(-0.250427\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −25.4224 | −1.21891 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.1502 | − | 22.7769i | −0.629061 | − | 1.08957i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.77648 | − | 6.54106i | 0.180242 | − | 0.312188i | −0.761721 | − | 0.647905i | \(-0.775645\pi\) |
0.941963 | + | 0.335717i | \(0.108979\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.75915 | + | 6.51104i | −0.178603 | + | 0.309349i | −0.941402 | − | 0.337286i | \(-0.890491\pi\) |
0.762799 | + | 0.646635i | \(0.223824\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.11778 | + | 1.80005i | −0.147797 | + | 0.0853306i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.4542 | 0.683659 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.3332 | −0.676426 | −0.338213 | − | 0.941070i | \(-0.609822\pi\) | ||||
−0.338213 | + | 0.941070i | \(0.609822\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.44092 | − | 3.71866i | 0.303291 | − | 0.175105i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.23329 | + | 15.9925i | −0.433818 | + | 0.751394i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.48037 | + | 11.2243i | −0.303139 | + | 0.525052i | −0.976845 | − | 0.213947i | \(-0.931368\pi\) |
0.673706 | + | 0.738999i | \(0.264701\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.72770 | + | 6.45656i | 0.173994 | + | 0.301366i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.3871 | 1.55499 | 0.777496 | − | 0.628888i | \(-0.216490\pi\) | ||||
0.777496 | + | 0.628888i | \(0.216490\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 29.7739i | − | 1.38371i | −0.722036 | − | 0.691855i | \(-0.756794\pi\) | ||
0.722036 | − | 0.691855i | \(-0.243206\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.9605 | − | 12.1016i | 0.972022 | − | 0.561197i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.5399 | + | 13.5908i | 1.08930 | + | 0.628907i | 0.933390 | − | 0.358865i | \(-0.116836\pi\) |
0.155909 | + | 0.987771i | \(0.450169\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.5156 | + | 18.7729i | 1.49824 | + | 0.865009i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.78991i | 0.128010i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 33.3521i | − | 1.52709i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.2187 | + | 29.8237i | 0.786744 | + | 1.36268i | 0.927952 | + | 0.372700i | \(0.121568\pi\) |
−0.141208 | + | 0.989980i | \(0.545099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.7768 | + | 7.95402i | 0.628167 | + | 0.362672i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 31.0031 | + | 17.8996i | 1.40778 | + | 0.812781i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.82613 | + | 3.94107i | −0.309321 | + | 0.178587i | −0.646623 | − | 0.762810i | \(-0.723819\pi\) |
0.337301 | + | 0.941397i | \(0.390486\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.8134i | 0.986436i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.06291 | 0.363874 | 0.181937 | − | 0.983310i | \(-0.441763\pi\) | ||||
0.181937 | + | 0.983310i | \(0.441763\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.48759 | + | 12.9689i | 0.337224 | + | 0.584089i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.40907 | − | 9.36878i | 0.243120 | − | 0.421095i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0216 | + | 20.8221i | −0.538163 | + | 0.932125i | 0.460841 | + | 0.887483i | \(0.347548\pi\) |
−0.999003 | + | 0.0446419i | \(0.985785\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.68997 | + | 3.28511i | −0.254209 | + | 0.146768i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 40.8993 | 1.82361 | 0.911804 | − | 0.410626i | \(-0.134690\pi\) | ||||
0.911804 | + | 0.410626i | \(0.134690\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.55128 | −0.113530 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.2919 | − | 8.82880i | 0.679139 | − | 0.392101i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.02661 | + | 3.51019i | −0.0898278 | + | 0.155586i | −0.907438 | − | 0.420186i | \(-0.861965\pi\) |
0.817610 | + | 0.575772i | \(0.195298\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.76249 | + | 8.24887i | −0.210269 | + | 0.364197i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.8550 | − | 27.4617i | −0.698656 | − | 1.21011i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.51671 | 0.0667048 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.2570i | 0.625811i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.1927 | + | 15.6997i | −1.19133 | + | 0.687817i | −0.958609 | − | 0.284725i | \(-0.908098\pi\) |
−0.232725 | + | 0.972543i | \(0.574764\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.7132 | − | 6.76263i | −0.512183 | − | 0.295709i | 0.221547 | − | 0.975150i | \(-0.428889\pi\) |
−0.733731 | + | 0.679440i | \(0.762223\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.3469 | − | 7.12848i | −0.537839 | − | 0.310522i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.03146 | + | 15.6429i | 0.392672 | + | 0.680128i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 28.2219i | − | 1.22473i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.8994i | 0.602050i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.5450 | − | 19.9965i | −0.499133 | − | 0.864524i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.99465 | − | 4.61572i | −0.344995 | − | 0.199183i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.1543 | + | 15.6775i | 1.16745 | + | 0.674030i | 0.953079 | − | 0.302722i | \(-0.0978953\pi\) |
0.214375 | + | 0.976751i | \(0.431229\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 50.4408 | − | 29.1220i | 2.16462 | − | 1.24974i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 26.1868i | − | 1.12172i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.7293 | 1.91249 | 0.956244 | − | 0.292571i | \(-0.0945108\pi\) | ||||
0.956244 | + | 0.292571i | \(0.0945108\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.99164 | − | 17.3060i | −0.426433 | − | 0.738604i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.56611 | + | 16.5690i | −0.407530 | + | 0.705863i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.3234 | − | 30.0050i | 0.735337 | − | 1.27364i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.5345 | + | 6.08208i | −0.446360 | + | 0.257706i | −0.706292 | − | 0.707921i | \(-0.749633\pi\) |
0.259932 | + | 0.965627i | \(0.416300\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.2939 | −0.476831 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.4311 | + | 18.1468i | −1.32466 | + | 0.764794i | −0.984469 | − | 0.175561i | \(-0.943826\pi\) |
−0.340194 | + | 0.940355i | \(0.610493\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.8506 | − | 36.1143i | 0.877191 | − | 1.51934i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.01830 | + | 10.4240i | −0.252300 | + | 0.436997i | −0.964159 | − | 0.265326i | \(-0.914520\pi\) |
0.711858 | + | 0.702323i | \(0.247854\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.10570 | + | 7.11128i | 0.171818 | + | 0.297598i | 0.939056 | − | 0.343765i | \(-0.111702\pi\) |
−0.767237 | + | 0.641363i | \(0.778369\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.44225 | 0.143802 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 4.35589i | − | 0.181653i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.5500 | + | 8.40042i | −0.605722 | + | 0.349714i | −0.771289 | − | 0.636485i | \(-0.780388\pi\) |
0.165567 | + | 0.986199i | \(0.447055\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.6633 | − | 14.8167i | −1.06653 | − | 0.615761i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.96289 | + | 5.75208i | 0.412621 | + | 0.238227i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.1088 | + | 17.5090i | 0.417949 | + | 0.723909i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.4261i | 1.04945i | 0.851273 | + | 0.524723i | \(0.175831\pi\) | ||||
−0.851273 | + | 0.524723i | \(0.824169\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 18.2146i | − | 0.750521i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.76849 | + | 13.4554i | 0.319553 | + | 0.553482i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.0694 | + | 11.0097i | 0.783086 | + | 0.452115i | 0.837523 | − | 0.546402i | \(-0.184003\pi\) |
−0.0544368 | + | 0.998517i | \(0.517336\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −42.2903 | − | 24.4163i | −1.73083 | − | 0.999294i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.500607 | + | 0.289026i | −0.0204543 | + | 0.0118093i | −0.510192 | − | 0.860060i | \(-0.670426\pi\) |
0.489738 | + | 0.871870i | \(0.337092\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.3186i | 1.11435i | 0.830395 | + | 0.557175i | \(0.188115\pi\) | ||||
−0.830395 | + | 0.557175i | \(0.811885\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.5509 | −1.24413 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.56611 | − | 16.5690i | −0.388918 | − | 0.673625i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.99963 | + | 10.3917i | −0.243518 | + | 0.421785i | −0.961714 | − | 0.274056i | \(-0.911635\pi\) |
0.718196 | + | 0.695841i | \(0.244968\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.41727 | + | 2.45478i | −0.0573364 | + | 0.0993096i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.96050 | − | 2.28659i | 0.159963 | − | 0.0923547i | −0.417882 | − | 0.908501i | \(-0.637227\pi\) |
0.577845 | + | 0.816147i | \(0.303894\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 30.2721 | 1.22069 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.12621 | 0.206373 | 0.103187 | − | 0.994662i | \(-0.467096\pi\) | ||||
0.103187 | + | 0.994662i | \(0.467096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.5293 | − | 22.8222i | 1.58881 | − | 0.917303i | 0.595312 | − | 0.803495i | \(-0.297028\pi\) |
0.993503 | − | 0.113808i | \(-0.0363049\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.43567 | − | 12.8790i | 0.298383 | − | 0.516815i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.5696 | − | 18.3071i | 0.422783 | − | 0.732282i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.21455 | − | 12.4960i | −0.288121 | − | 0.499041i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.4088 | −0.813753 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.1345i | 0.682113i | 0.940043 | + | 0.341057i | \(0.110785\pi\) | ||||
−0.940043 | + | 0.341057i | \(0.889215\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.0196 | − | 7.51689i | 0.517484 | − | 0.298769i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26.3069 | − | 15.1883i | −1.04396 | − | 0.602729i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.8009 | − | 10.2774i | −0.704194 | − | 0.406567i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.02498 | − | 6.97146i | −0.158977 | − | 0.275356i | 0.775523 | − | 0.631319i | \(-0.217486\pi\) |
−0.934500 | + | 0.355963i | \(0.884153\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.2710i | 0.878283i | 0.898418 | + | 0.439142i | \(0.144717\pi\) | ||||
−0.898418 | + | 0.439142i | \(0.855283\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.9125 | − | 32.7574i | −0.743528 | − | 1.28783i | −0.950879 | − | 0.309561i | \(-0.899818\pi\) |
0.207352 | − | 0.978266i | \(-0.433516\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.43042 | + | 4.86730i | 0.330923 | + | 0.191058i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.6130 | − | 14.7877i | −1.00231 | − | 0.578686i | −0.0933818 | − | 0.995630i | \(-0.529768\pi\) |
−0.908932 | + | 0.416944i | \(0.863101\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.9586 | + | 6.32694i | −0.428188 | + | 0.247214i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.15466i | 0.0840611i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.3961 | −0.716611 | −0.358305 | − | 0.933604i | \(-0.616645\pi\) | ||||
−0.358305 | + | 0.933604i | \(0.616645\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.92732 | + | 10.2664i | 0.230546 | + | 0.399317i | 0.957969 | − | 0.286872i | \(-0.0926154\pi\) |
−0.727423 | + | 0.686189i | \(0.759282\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.5535 | − | 18.2791i | 0.409862 | − | 0.709902i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.9356 | − | 25.8692i | 0.578308 | − | 1.00166i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 47.4157 | − | 27.3755i | 1.83320 | − | 1.05840i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.89285 | 0.266095 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.8738 | 0.419154 | 0.209577 | − | 0.977792i | \(-0.432791\pi\) | ||||
0.209577 | + | 0.977792i | \(0.432791\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.36618 | + | 0.788764i | −0.0525843 | + | 0.0303595i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.7163 | + | 39.3458i | −0.873060 | + | 1.51218i | −0.0142443 | + | 0.999899i | \(0.504534\pi\) |
−0.858815 | + | 0.512285i | \(0.828799\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.6285 | + | 37.4616i | −0.828805 | + | 1.43553i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.3693 | + | 21.4243i | 0.473299 | + | 0.819778i | 0.999533 | − | 0.0305620i | \(-0.00972970\pi\) |
−0.526234 | + | 0.850340i | \(0.676396\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.0446 | −1.10974 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.3013i | 0.850847i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.6193 | + | 10.7499i | −0.709340 | + | 0.409538i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.10457 | − | 2.36977i | −0.156145 | − | 0.0901504i | 0.419892 | − | 0.907574i | \(-0.362068\pi\) |
−0.576037 | + | 0.817424i | \(0.695401\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.905741 | + | 0.522930i | 0.0343567 | + | 0.0198359i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.91594 | − | 15.4429i | −0.337715 | − | 0.584940i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 11.7417i | − | 0.444112i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.8121i | 1.50368i | 0.659345 | + | 0.751840i | \(0.270834\pi\) | ||||
−0.659345 | + | 0.751840i | \(0.729166\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.0371 | − | 22.5809i | −0.491704 | − | 0.851656i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.34636 | + | 3.08672i | 0.201355 | + | 0.116253i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.97242 | − | 2.87083i | −0.186743 | − | 0.107816i | 0.403714 | − | 0.914885i | \(-0.367719\pi\) |
−0.590457 | + | 0.807069i | \(0.701052\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.4659 | − | 11.8160i | 0.767529 | − | 0.443133i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.4385i | 1.06503i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.97370 | −0.260801 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −32.2305 | − | 55.8249i | −1.20367 | − | 2.08482i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.62804 | − | 13.2122i | 0.284478 | − | 0.492730i | −0.688005 | − | 0.725706i | \(-0.741513\pi\) |
0.972482 | + | 0.232976i | \(0.0748464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.61218 | + | 13.1847i | −0.283100 | + | 0.490344i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.74416 | + | 1.58434i | −0.101915 | + | 0.0588409i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.8993 | −1.51687 | −0.758435 | − | 0.651749i | \(-0.774036\pi\) | ||||
−0.758435 | + | 0.651749i | \(0.774036\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 39.8818 | 1.47710 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.2037 | − | 21.1374i | 0.450753 | − | 0.780728i | −0.547680 | − | 0.836688i | \(-0.684489\pi\) |
0.998433 | + | 0.0559605i | \(0.0178221\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.26897 | − | 9.12612i | 0.194085 | − | 0.336165i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.3996 | − | 26.6730i | −0.566485 | − | 0.981181i | −0.996910 | − | 0.0785545i | \(-0.974970\pi\) |
0.430425 | − | 0.902626i | \(-0.358364\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.9661 | 0.990624 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.9376i | 0.878184i | 0.898442 | + | 0.439092i | \(0.144700\pi\) | ||||
−0.898442 | + | 0.439092i | \(0.855300\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.91613 | + | 5.72508i | −0.363299 | + | 0.209751i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.69271 | − | 0.977288i | −0.0619331 | − | 0.0357571i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.9543 | − | 6.90181i | −0.436218 | − | 0.251851i | 0.265774 | − | 0.964035i | \(-0.414373\pi\) |
−0.701992 | + | 0.712185i | \(0.747706\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.6653 | − | 42.7215i | −0.898853 | − | 1.55686i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 14.6287i | − | 0.532392i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.14156i | − | 0.0778362i | −0.999242 | − | 0.0389181i | \(-0.987609\pi\) | ||
0.999242 | − | 0.0389181i | \(-0.0123911\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.2641 | + | 19.5099i | 0.408860 | + | 0.708166i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.8321 | − | 21.2650i | −1.33516 | − | 0.770856i | −0.349076 | − | 0.937094i | \(-0.613504\pi\) |
−0.986086 | + | 0.166239i | \(0.946838\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22.4628 | − | 12.9689i | −0.812143 | − | 0.468891i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.7554 | + | 9.09636i | −0.568893 | + | 0.328450i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 15.6459i | − | 0.564206i | −0.959384 | − | 0.282103i | \(-0.908968\pi\) | ||
0.959384 | − | 0.282103i | \(-0.0910320\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.0562 | 1.19049 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.2125 | + | 26.3489i | 0.547156 | + | 0.947703i | 0.998468 | + | 0.0553362i | \(0.0176230\pi\) |
−0.451311 | + | 0.892367i | \(0.649044\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.50836 | − | 2.61255i | 0.0541817 | − | 0.0938455i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.3910 | − | 19.7297i | 0.408124 | − | 0.706891i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.14009 | − | 3.54498i | 0.219710 | − | 0.126849i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.8181 | −0.386609 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.7427 | −1.06156 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.3722 | + | 16.3807i | −1.01136 | + | 0.583909i | −0.911590 | − | 0.411102i | \(-0.865144\pi\) |
−0.0997704 | + | 0.995010i | \(0.531811\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.47291 | − | 11.2114i | 0.230442 | − | 0.399137i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.44092 | + | 11.1560i | −0.228724 | + | 0.396161i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.4126 | + | 40.5518i | 0.830359 | + | 1.43822i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.3790 | 1.00523 | 0.502617 | − | 0.864509i | \(-0.332370\pi\) | ||||
0.502617 | + | 0.864509i | \(0.332370\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.63649i | − | 0.128650i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.82673 | + | 3.36406i | −0.205877 | + | 0.118863i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.643636 | − | 0.371603i | −0.0227134 | − | 0.0131136i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −59.7626 | − | 34.5040i | −2.10374 | − | 1.21460i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.08387 | + | 7.07347i | 0.143581 | + | 0.248690i | 0.928843 | − | 0.370474i | \(-0.120805\pi\) |
−0.785262 | + | 0.619164i | \(0.787472\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.2710i | − | 0.782041i | −0.920382 | − | 0.391021i | \(-0.872122\pi\) | ||
0.920382 | − | 0.391021i | \(-0.127878\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 73.7246i | 2.58563i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.63997 | − | 14.9649i | −0.302645 | − | 0.524196i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.52231 | + | 2.61096i | 0.157830 | + | 0.0911230i | 0.576835 | − | 0.816861i | \(-0.304288\pi\) |
−0.419005 | + | 0.907984i | \(0.637621\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.29368 | − | 4.78836i | 0.289099 | − | 0.166912i | −0.348436 | − | 0.937333i | \(-0.613287\pi\) |
0.637536 | + | 0.770421i | \(0.279954\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.38975i | − | 0.0832004i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.6664 | −1.41411 | −0.707055 | − | 0.707159i | \(-0.749977\pi\) | ||||
−0.707055 | + | 0.707159i | \(0.749977\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.6171 | − | 28.7816i | −0.577134 | − | 0.999625i | −0.995806 | − | 0.0914880i | \(-0.970838\pi\) |
0.418672 | − | 0.908137i | \(-0.362496\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 35.4452 | − | 61.3929i | 1.22958 | − | 2.12970i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.60236 | − | 4.50743i | 0.0900586 | − | 0.155986i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.91945 | − | 5.14965i | 0.308301 | − | 0.177998i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.0243 | −0.518698 | −0.259349 | − | 0.965784i | \(-0.583508\pi\) | ||||
−0.259349 | + | 0.965784i | \(0.583508\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.27029 | 0.250700 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 45.5890 | − | 26.3208i | 1.57017 | − | 0.906538i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.99392 | + | 12.1138i | −0.240598 | + | 0.416728i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.19938 | − | 12.4697i | 0.247082 | − | 0.427959i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.3548 | + | 35.2556i | 0.697755 | + | 1.20855i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.5203 | 0.428686 | 0.214343 | − | 0.976758i | \(-0.431239\pi\) | ||||
0.214343 | + | 0.976758i | \(0.431239\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 33.1380i | − | 1.13329i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.8265 | − | 27.0353i | 1.59956 | − | 0.923509i | 0.607993 | − | 0.793942i | \(-0.291975\pi\) |
0.991571 | − | 0.129566i | \(-0.0413585\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.0990 | + | 9.87213i | 0.583411 | + | 0.336833i | 0.762488 | − | 0.647002i | \(-0.223978\pi\) |
−0.179077 | + | 0.983835i | \(0.557311\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.3755 | + | 15.2279i | 0.897833 | + | 0.518364i | 0.876497 | − | 0.481408i | \(-0.159874\pi\) |
0.0213367 | + | 0.999772i | \(0.493208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.64697 | − | 9.78084i | −0.192003 | − | 0.332559i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 17.5265i | − | 0.595232i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.15137i | 0.276516i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.84701 | + | 17.0555i | 0.333653 | + | 0.577905i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 57.9407 | + | 33.4521i | 1.96100 | + | 1.13218i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.3275 | + | 10.5814i | 0.618877 | + | 0.357309i | 0.776432 | − | 0.630201i | \(-0.217028\pi\) |
−0.157555 | + | 0.987510i | \(0.550361\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.1148 | − | 17.9641i | 1.04948 | − | 0.605915i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 11.5367i | − | 0.388681i | −0.980934 | − | 0.194340i | \(-0.937743\pi\) | ||
0.980934 | − | 0.194340i | \(-0.0622566\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.8555 | −1.67777 | −0.838886 | − | 0.544307i | \(-0.816793\pi\) | ||||
−0.838886 | + | 0.544307i | \(0.816793\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.8113 | + | 34.3142i | 0.665950 | + | 1.15346i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.56575 | + | 9.64015i | −0.186879 | + | 0.323685i | −0.944208 | − | 0.329349i | \(-0.893171\pi\) |
0.757329 | + | 0.653034i | \(0.226504\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.72770 | + | 6.45656i | −0.124883 | + | 0.216303i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.02352 | − | 2.32298i | 0.134642 | − | 0.0777356i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.31287 | 0.244442 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.1022 | −1.40575 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.9159 | − | 10.3438i | 0.597530 | − | 0.344984i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.7913 | − | 23.8872i | 0.459454 | − | 0.795798i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.0696 | + | 39.9577i | −0.766859 | + | 1.32824i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.20674 | − | 12.4824i | −0.239296 | − | 0.414473i | 0.721217 | − | 0.692710i | \(-0.243583\pi\) |
−0.960512 | + | 0.278237i | \(0.910250\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.76801 | −0.158145 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.1909i | 0.635823i | 0.948120 | + | 0.317911i | \(0.102981\pi\) | ||||
−0.948120 | + | 0.317911i | \(0.897019\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.583868 | − | 0.337096i | 0.0193232 | − | 0.0111563i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.2971 | + | 14.0279i | 0.803237 | + | 0.463749i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.4285 | + | 12.9491i | 0.739848 | + | 0.427151i | 0.822014 | − | 0.569467i | \(-0.192850\pi\) |
−0.0821662 | + | 0.996619i | \(0.526184\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.0366 | + | 55.4890i | 1.05564 | + | 1.82843i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.2502i | 0.436136i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 4.31842i | − | 0.141989i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.6310 | − | 51.3224i | −0.973210 | − | 1.68565i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.7480 | + | 21.2165i | 1.20566 | + | 0.696090i | 0.961809 | − | 0.273722i | \(-0.0882548\pi\) |
0.243854 | + | 0.969812i | \(0.421588\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −39.1536 | − | 22.6053i | −1.28183 | − | 0.740065i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.74809 | − | 4.47336i | 0.253390 | − | 0.146295i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.5547i | 1.52088i | 0.649410 | + | 0.760439i | \(0.275016\pi\) | ||||
−0.649410 | + | 0.760439i | \(0.724984\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 45.5812 | 1.48749 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.48937 | − | 2.57967i | −0.0485522 | − | 0.0840949i | 0.840728 | − | 0.541458i | \(-0.182127\pi\) |
−0.889280 | + | 0.457363i | \(0.848794\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.7847 | + | 30.8040i | −0.579150 | + | 1.00312i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.5270 | + | 23.4294i | −0.439568 | + | 0.761354i | −0.997656 | − | 0.0684276i | \(-0.978202\pi\) |
0.558088 | + | 0.829782i | \(0.311535\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.20287 | − | 0.694478i | 0.0390469 | − | 0.0225437i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 50.8580 | 1.64918 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.7293 | 0.930634 | 0.465317 | − | 0.885144i | \(-0.345940\pi\) | ||||
0.465317 | + | 0.885144i | \(0.345940\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.36152 | + | 1.36342i | −0.0764169 | + | 0.0441193i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.19403 | − | 14.1925i | 0.264875 | − | 0.458778i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.65232 | − | 9.79010i | 0.182333 | − | 0.315810i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.5761 | − | 37.3708i | −0.695279 | − | 1.20426i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.4747 | 0.755677 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 13.3546i | − | 0.429453i | −0.976674 | − | 0.214727i | \(-0.931114\pi\) | ||
0.976674 | − | 0.214727i | \(-0.0688861\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.9605 | + | 17.2977i | −0.962471 | + | 0.555683i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.71876 | − | 0.992325i | −0.0551575 | − | 0.0318452i | 0.472168 | − | 0.881509i | \(-0.343472\pi\) |
−0.527325 | + | 0.849664i | \(0.676805\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.86778 | + | 2.23306i | 0.123868 | + | 0.0715153i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.2242 | + | 54.0818i | 0.998950 | + | 1.73023i | 0.539158 | + | 0.842205i | \(0.318743\pi\) |
0.459792 | + | 0.888027i | \(0.347924\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.32073i | − | 0.0741710i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 48.9397i | − | 1.56252i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.64021 | + | 6.30503i | 0.116105 | + | 0.201099i | 0.918221 | − | 0.396069i | \(-0.129626\pi\) |
−0.802116 | + | 0.597168i | \(0.796293\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.6590 | − | 6.15397i | −0.339624 | − | 0.196082i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.3345 | + | 18.0910i | −0.995373 | + | 0.574679i | −0.906876 | − | 0.421398i | \(-0.861540\pi\) |
−0.0884967 | + | 0.996076i | \(0.528206\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 54.5797i | − | 1.73204i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 38.6838 | 1.22636 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.1218 | − | 29.6559i | −0.542254 | − | 0.939211i | −0.998774 | − | 0.0494984i | \(-0.984238\pi\) |
0.456520 | − | 0.889713i | \(-0.349096\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.37171 | − | 12.7682i | 0.233231 | − | 0.403967i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))