Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(1,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.a (trivial) |
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: | yes |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.37228 | 1.27460 | 0.637301 | − | 0.770615i | \(-0.280051\pi\) | ||||
0.637301 | + | 0.770615i | \(0.280051\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0.627719 | 0.189264 | 0.0946322 | − | 0.995512i | \(-0.469833\pi\) | ||||
0.0946322 | + | 0.995512i | \(0.469833\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 3.37228 | 0.901280 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.74456 | −1.15073 | −0.575363 | − | 0.817898i | \(-0.695139\pi\) | ||||
−0.575363 | + | 0.817898i | \(0.695139\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −0.627719 | −0.144009 | −0.0720043 | − | 0.997404i | \(-0.522940\pi\) | ||||
−0.0720043 | + | 0.997404i | \(0.522940\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 3.37228 | 0.735892 | ||||||||
\(22\) | 0.627719 | 0.133830 | ||||||||
\(23\) | 3.37228 | 0.703169 | 0.351585 | − | 0.936156i | \(-0.385643\pi\) | ||||
0.351585 | + | 0.936156i | \(0.385643\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.37228 | 0.637301 | ||||||||
\(29\) | −8.74456 | −1.62382 | −0.811912 | − | 0.583779i | \(-0.801573\pi\) | ||||
−0.811912 | + | 0.583779i | \(0.801573\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.627719 | 0.109272 | ||||||||
\(34\) | −4.74456 | −0.813686 | ||||||||
\(35\) | 3.37228 | 0.570020 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.744563 | −0.122405 | −0.0612027 | − | 0.998125i | \(-0.519494\pi\) | ||||
−0.0612027 | + | 0.998125i | \(0.519494\pi\) | |||||||
\(38\) | −0.627719 | −0.101829 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 0.744563 | 0.116281 | 0.0581406 | − | 0.998308i | \(-0.481483\pi\) | ||||
0.0581406 | + | 0.998308i | \(0.481483\pi\) | |||||||
\(42\) | 3.37228 | 0.520354 | ||||||||
\(43\) | 0.627719 | 0.0957262 | 0.0478631 | − | 0.998854i | \(-0.484759\pi\) | ||||
0.0478631 | + | 0.998854i | \(0.484759\pi\) | |||||||
\(44\) | 0.627719 | 0.0946322 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 3.37228 | 0.497216 | ||||||||
\(47\) | −6.74456 | −0.983796 | −0.491898 | − | 0.870653i | \(-0.663697\pi\) | ||||
−0.491898 | + | 0.870653i | \(0.663697\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 4.37228 | 0.624612 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −4.74456 | −0.664372 | ||||||||
\(52\) | −2.00000 | −0.277350 | ||||||||
\(53\) | 1.37228 | 0.188497 | 0.0942487 | − | 0.995549i | \(-0.469955\pi\) | ||||
0.0942487 | + | 0.995549i | \(0.469955\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.627719 | 0.0846416 | ||||||||
\(56\) | 3.37228 | 0.450640 | ||||||||
\(57\) | −0.627719 | −0.0831434 | ||||||||
\(58\) | −8.74456 | −1.14822 | ||||||||
\(59\) | 2.74456 | 0.357312 | 0.178656 | − | 0.983912i | \(-0.442825\pi\) | ||||
0.178656 | + | 0.983912i | \(0.442825\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 11.4891 | 1.47103 | 0.735516 | − | 0.677507i | \(-0.236940\pi\) | ||||
0.735516 | + | 0.677507i | \(0.236940\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | 3.37228 | 0.424868 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0.627719 | 0.0772668 | ||||||||
\(67\) | 10.7446 | 1.31266 | 0.656329 | − | 0.754475i | \(-0.272108\pi\) | ||||
0.656329 | + | 0.754475i | \(0.272108\pi\) | |||||||
\(68\) | −4.74456 | −0.575363 | ||||||||
\(69\) | 3.37228 | 0.405975 | ||||||||
\(70\) | 3.37228 | 0.403065 | ||||||||
\(71\) | 3.37228 | 0.400216 | 0.200108 | − | 0.979774i | \(-0.435871\pi\) | ||||
0.200108 | + | 0.979774i | \(0.435871\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −8.11684 | −0.950005 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(74\) | −0.744563 | −0.0865536 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −0.627719 | −0.0720043 | ||||||||
\(77\) | 2.11684 | 0.241237 | ||||||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | −4.62772 | −0.520659 | −0.260330 | − | 0.965520i | \(-0.583831\pi\) | ||||
−0.260330 | + | 0.965520i | \(0.583831\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.744563 | 0.0822232 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 3.37228 | 0.367946 | ||||||||
\(85\) | −4.74456 | −0.514620 | ||||||||
\(86\) | 0.627719 | 0.0676886 | ||||||||
\(87\) | −8.74456 | −0.937516 | ||||||||
\(88\) | 0.627719 | 0.0669150 | ||||||||
\(89\) | −1.37228 | −0.145462 | −0.0727308 | − | 0.997352i | \(-0.523171\pi\) | ||||
−0.0727308 | + | 0.997352i | \(0.523171\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −6.74456 | −0.707022 | ||||||||
\(92\) | 3.37228 | 0.351585 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | −6.74456 | −0.695649 | ||||||||
\(95\) | −0.627719 | −0.0644026 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 4.37228 | 0.441667 | ||||||||
\(99\) | 0.627719 | 0.0630881 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 8.11684 | 0.807656 | 0.403828 | − | 0.914835i | \(-0.367679\pi\) | ||||
0.403828 | + | 0.914835i | \(0.367679\pi\) | |||||||
\(102\) | −4.74456 | −0.469782 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 3.37228 | 0.329101 | ||||||||
\(106\) | 1.37228 | 0.133288 | ||||||||
\(107\) | 0.627719 | 0.0606839 | 0.0303419 | − | 0.999540i | \(-0.490340\pi\) | ||||
0.0303419 | + | 0.999540i | \(0.490340\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 4.74456 | 0.454447 | 0.227223 | − | 0.973843i | \(-0.427035\pi\) | ||||
0.227223 | + | 0.973843i | \(0.427035\pi\) | |||||||
\(110\) | 0.627719 | 0.0598506 | ||||||||
\(111\) | −0.744563 | −0.0706708 | ||||||||
\(112\) | 3.37228 | 0.318651 | ||||||||
\(113\) | −2.62772 | −0.247195 | −0.123597 | − | 0.992332i | \(-0.539443\pi\) | ||||
−0.123597 | + | 0.992332i | \(0.539443\pi\) | |||||||
\(114\) | −0.627719 | −0.0587912 | ||||||||
\(115\) | 3.37228 | 0.314467 | ||||||||
\(116\) | −8.74456 | −0.811912 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 2.74456 | 0.252657 | ||||||||
\(119\) | −16.0000 | −1.46672 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −10.6060 | −0.964179 | ||||||||
\(122\) | 11.4891 | 1.04018 | ||||||||
\(123\) | 0.744563 | 0.0671350 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 3.37228 | 0.300427 | ||||||||
\(127\) | 13.4891 | 1.19697 | 0.598483 | − | 0.801135i | \(-0.295770\pi\) | ||||
0.598483 | + | 0.801135i | \(0.295770\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.627719 | 0.0552675 | ||||||||
\(130\) | −2.00000 | −0.175412 | ||||||||
\(131\) | −16.2337 | −1.41834 | −0.709172 | − | 0.705036i | \(-0.750931\pi\) | ||||
−0.709172 | + | 0.705036i | \(0.750931\pi\) | |||||||
\(132\) | 0.627719 | 0.0546359 | ||||||||
\(133\) | −2.11684 | −0.183554 | ||||||||
\(134\) | 10.7446 | 0.928189 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −4.74456 | −0.406843 | ||||||||
\(137\) | −3.48913 | −0.298096 | −0.149048 | − | 0.988830i | \(-0.547621\pi\) | ||||
−0.149048 | + | 0.988830i | \(0.547621\pi\) | |||||||
\(138\) | 3.37228 | 0.287068 | ||||||||
\(139\) | −10.7446 | −0.911342 | −0.455671 | − | 0.890148i | \(-0.650601\pi\) | ||||
−0.455671 | + | 0.890148i | \(0.650601\pi\) | |||||||
\(140\) | 3.37228 | 0.285010 | ||||||||
\(141\) | −6.74456 | −0.567995 | ||||||||
\(142\) | 3.37228 | 0.282996 | ||||||||
\(143\) | −1.25544 | −0.104985 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −8.74456 | −0.726196 | ||||||||
\(146\) | −8.11684 | −0.671755 | ||||||||
\(147\) | 4.37228 | 0.360620 | ||||||||
\(148\) | −0.744563 | −0.0612027 | ||||||||
\(149\) | −12.1168 | −0.992651 | −0.496325 | − | 0.868137i | \(-0.665318\pi\) | ||||
−0.496325 | + | 0.868137i | \(0.665318\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | −0.627719 | −0.0509147 | ||||||||
\(153\) | −4.74456 | −0.383575 | ||||||||
\(154\) | 2.11684 | 0.170580 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | 9.37228 | 0.747989 | 0.373995 | − | 0.927431i | \(-0.377988\pi\) | ||||
0.373995 | + | 0.927431i | \(0.377988\pi\) | |||||||
\(158\) | −4.62772 | −0.368162 | ||||||||
\(159\) | 1.37228 | 0.108829 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 11.3723 | 0.896261 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 24.2337 | 1.89813 | 0.949064 | − | 0.315082i | \(-0.102032\pi\) | ||||
0.949064 | + | 0.315082i | \(0.102032\pi\) | |||||||
\(164\) | 0.744563 | 0.0581406 | ||||||||
\(165\) | 0.627719 | 0.0488678 | ||||||||
\(166\) | −12.0000 | −0.931381 | ||||||||
\(167\) | −12.6277 | −0.977162 | −0.488581 | − | 0.872518i | \(-0.662485\pi\) | ||||
−0.488581 | + | 0.872518i | \(0.662485\pi\) | |||||||
\(168\) | 3.37228 | 0.260177 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −4.74456 | −0.363891 | ||||||||
\(171\) | −0.627719 | −0.0480028 | ||||||||
\(172\) | 0.627719 | 0.0478631 | ||||||||
\(173\) | −18.0000 | −1.36851 | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||||
−0.684257 | + | 0.729241i | \(0.739873\pi\) | |||||||
\(174\) | −8.74456 | −0.662924 | ||||||||
\(175\) | 3.37228 | 0.254921 | ||||||||
\(176\) | 0.627719 | 0.0473161 | ||||||||
\(177\) | 2.74456 | 0.206294 | ||||||||
\(178\) | −1.37228 | −0.102857 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 14.8614 | 1.10464 | 0.552320 | − | 0.833632i | \(-0.313743\pi\) | ||||
0.552320 | + | 0.833632i | \(0.313743\pi\) | |||||||
\(182\) | −6.74456 | −0.499940 | ||||||||
\(183\) | 11.4891 | 0.849301 | ||||||||
\(184\) | 3.37228 | 0.248608 | ||||||||
\(185\) | −0.744563 | −0.0547413 | ||||||||
\(186\) | −1.00000 | −0.0733236 | ||||||||
\(187\) | −2.97825 | −0.217791 | ||||||||
\(188\) | −6.74456 | −0.491898 | ||||||||
\(189\) | 3.37228 | 0.245297 | ||||||||
\(190\) | −0.627719 | −0.0455395 | ||||||||
\(191\) | 16.0000 | 1.15772 | 0.578860 | − | 0.815427i | \(-0.303498\pi\) | ||||
0.578860 | + | 0.815427i | \(0.303498\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 15.4891 | 1.11493 | 0.557466 | − | 0.830200i | \(-0.311774\pi\) | ||||
0.557466 | + | 0.830200i | \(0.311774\pi\) | |||||||
\(194\) | 2.00000 | 0.143592 | ||||||||
\(195\) | −2.00000 | −0.143223 | ||||||||
\(196\) | 4.37228 | 0.312306 | ||||||||
\(197\) | 19.4891 | 1.38854 | 0.694271 | − | 0.719713i | \(-0.255727\pi\) | ||||
0.694271 | + | 0.719713i | \(0.255727\pi\) | |||||||
\(198\) | 0.627719 | 0.0446100 | ||||||||
\(199\) | −12.6277 | −0.895155 | −0.447578 | − | 0.894245i | \(-0.647713\pi\) | ||||
−0.447578 | + | 0.894245i | \(0.647713\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 10.7446 | 0.757863 | ||||||||
\(202\) | 8.11684 | 0.571099 | ||||||||
\(203\) | −29.4891 | −2.06973 | ||||||||
\(204\) | −4.74456 | −0.332186 | ||||||||
\(205\) | 0.744563 | 0.0520025 | ||||||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | 3.37228 | 0.234390 | ||||||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | −0.394031 | −0.0272557 | ||||||||
\(210\) | 3.37228 | 0.232710 | ||||||||
\(211\) | −0.627719 | −0.0432139 | −0.0216070 | − | 0.999767i | \(-0.506878\pi\) | ||||
−0.0216070 | + | 0.999767i | \(0.506878\pi\) | |||||||
\(212\) | 1.37228 | 0.0942487 | ||||||||
\(213\) | 3.37228 | 0.231065 | ||||||||
\(214\) | 0.627719 | 0.0429100 | ||||||||
\(215\) | 0.627719 | 0.0428101 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −3.37228 | −0.228925 | ||||||||
\(218\) | 4.74456 | 0.321342 | ||||||||
\(219\) | −8.11684 | −0.548485 | ||||||||
\(220\) | 0.627719 | 0.0423208 | ||||||||
\(221\) | 9.48913 | 0.638308 | ||||||||
\(222\) | −0.744563 | −0.0499718 | ||||||||
\(223\) | 9.25544 | 0.619790 | 0.309895 | − | 0.950771i | \(-0.399706\pi\) | ||||
0.309895 | + | 0.950771i | \(0.399706\pi\) | |||||||
\(224\) | 3.37228 | 0.225320 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −2.62772 | −0.174793 | ||||||||
\(227\) | 6.11684 | 0.405989 | 0.202995 | − | 0.979180i | \(-0.434933\pi\) | ||||
0.202995 | + | 0.979180i | \(0.434933\pi\) | |||||||
\(228\) | −0.627719 | −0.0415717 | ||||||||
\(229\) | 3.88316 | 0.256606 | 0.128303 | − | 0.991735i | \(-0.459047\pi\) | ||||
0.128303 | + | 0.991735i | \(0.459047\pi\) | |||||||
\(230\) | 3.37228 | 0.222362 | ||||||||
\(231\) | 2.11684 | 0.139278 | ||||||||
\(232\) | −8.74456 | −0.574109 | ||||||||
\(233\) | −14.8614 | −0.973603 | −0.486802 | − | 0.873513i | \(-0.661837\pi\) | ||||
−0.486802 | + | 0.873513i | \(0.661837\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | −6.74456 | −0.439967 | ||||||||
\(236\) | 2.74456 | 0.178656 | ||||||||
\(237\) | −4.62772 | −0.300603 | ||||||||
\(238\) | −16.0000 | −1.03713 | ||||||||
\(239\) | −29.4891 | −1.90749 | −0.953746 | − | 0.300612i | \(-0.902809\pi\) | ||||
−0.953746 | + | 0.300612i | \(0.902809\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 4.51087 | 0.290571 | 0.145285 | − | 0.989390i | \(-0.453590\pi\) | ||||
0.145285 | + | 0.989390i | \(0.453590\pi\) | |||||||
\(242\) | −10.6060 | −0.681778 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 11.4891 | 0.735516 | ||||||||
\(245\) | 4.37228 | 0.279335 | ||||||||
\(246\) | 0.744563 | 0.0474716 | ||||||||
\(247\) | 1.25544 | 0.0798816 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −4.00000 | −0.252478 | −0.126239 | − | 0.992000i | \(-0.540291\pi\) | ||||
−0.126239 | + | 0.992000i | \(0.540291\pi\) | |||||||
\(252\) | 3.37228 | 0.212434 | ||||||||
\(253\) | 2.11684 | 0.133085 | ||||||||
\(254\) | 13.4891 | 0.846383 | ||||||||
\(255\) | −4.74456 | −0.297116 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.3723 | 0.834140 | 0.417070 | − | 0.908874i | \(-0.363057\pi\) | ||||
0.417070 | + | 0.908874i | \(0.363057\pi\) | |||||||
\(258\) | 0.627719 | 0.0390801 | ||||||||
\(259\) | −2.51087 | −0.156018 | ||||||||
\(260\) | −2.00000 | −0.124035 | ||||||||
\(261\) | −8.74456 | −0.541275 | ||||||||
\(262\) | −16.2337 | −1.00292 | ||||||||
\(263\) | −18.9783 | −1.17025 | −0.585125 | − | 0.810943i | \(-0.698954\pi\) | ||||
−0.585125 | + | 0.810943i | \(0.698954\pi\) | |||||||
\(264\) | 0.627719 | 0.0386334 | ||||||||
\(265\) | 1.37228 | 0.0842986 | ||||||||
\(266\) | −2.11684 | −0.129792 | ||||||||
\(267\) | −1.37228 | −0.0839823 | ||||||||
\(268\) | 10.7446 | 0.656329 | ||||||||
\(269\) | −2.00000 | −0.121942 | −0.0609711 | − | 0.998140i | \(-0.519420\pi\) | ||||
−0.0609711 | + | 0.998140i | \(0.519420\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −13.8832 | −0.843342 | −0.421671 | − | 0.906749i | \(-0.638556\pi\) | ||||
−0.421671 | + | 0.906749i | \(0.638556\pi\) | |||||||
\(272\) | −4.74456 | −0.287681 | ||||||||
\(273\) | −6.74456 | −0.408200 | ||||||||
\(274\) | −3.48913 | −0.210786 | ||||||||
\(275\) | 0.627719 | 0.0378529 | ||||||||
\(276\) | 3.37228 | 0.202987 | ||||||||
\(277\) | 15.2554 | 0.916610 | 0.458305 | − | 0.888795i | \(-0.348457\pi\) | ||||
0.458305 | + | 0.888795i | \(0.348457\pi\) | |||||||
\(278\) | −10.7446 | −0.644416 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 3.37228 | 0.201532 | ||||||||
\(281\) | 16.7446 | 0.998897 | 0.499448 | − | 0.866344i | \(-0.333536\pi\) | ||||
0.499448 | + | 0.866344i | \(0.333536\pi\) | |||||||
\(282\) | −6.74456 | −0.401633 | ||||||||
\(283\) | 12.0000 | 0.713326 | 0.356663 | − | 0.934233i | \(-0.383914\pi\) | ||||
0.356663 | + | 0.934233i | \(0.383914\pi\) | |||||||
\(284\) | 3.37228 | 0.200108 | ||||||||
\(285\) | −0.627719 | −0.0371828 | ||||||||
\(286\) | −1.25544 | −0.0742356 | ||||||||
\(287\) | 2.51087 | 0.148212 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 5.51087 | 0.324169 | ||||||||
\(290\) | −8.74456 | −0.513498 | ||||||||
\(291\) | 2.00000 | 0.117242 | ||||||||
\(292\) | −8.11684 | −0.475002 | ||||||||
\(293\) | −7.48913 | −0.437519 | −0.218760 | − | 0.975779i | \(-0.570201\pi\) | ||||
−0.218760 | + | 0.975779i | \(0.570201\pi\) | |||||||
\(294\) | 4.37228 | 0.254997 | ||||||||
\(295\) | 2.74456 | 0.159795 | ||||||||
\(296\) | −0.744563 | −0.0432768 | ||||||||
\(297\) | 0.627719 | 0.0364239 | ||||||||
\(298\) | −12.1168 | −0.701910 | ||||||||
\(299\) | −6.74456 | −0.390048 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 2.11684 | 0.122013 | ||||||||
\(302\) | −8.00000 | −0.460348 | ||||||||
\(303\) | 8.11684 | 0.466301 | ||||||||
\(304\) | −0.627719 | −0.0360021 | ||||||||
\(305\) | 11.4891 | 0.657865 | ||||||||
\(306\) | −4.74456 | −0.271229 | ||||||||
\(307\) | 30.9783 | 1.76802 | 0.884011 | − | 0.467466i | \(-0.154833\pi\) | ||||
0.884011 | + | 0.467466i | \(0.154833\pi\) | |||||||
\(308\) | 2.11684 | 0.120618 | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | −1.00000 | −0.0567962 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | −2.00000 | −0.113228 | ||||||||
\(313\) | 10.0000 | 0.565233 | 0.282617 | − | 0.959233i | \(-0.408798\pi\) | ||||
0.282617 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(314\) | 9.37228 | 0.528908 | ||||||||
\(315\) | 3.37228 | 0.190007 | ||||||||
\(316\) | −4.62772 | −0.260330 | ||||||||
\(317\) | −24.7446 | −1.38979 | −0.694897 | − | 0.719110i | \(-0.744550\pi\) | ||||
−0.694897 | + | 0.719110i | \(0.744550\pi\) | |||||||
\(318\) | 1.37228 | 0.0769537 | ||||||||
\(319\) | −5.48913 | −0.307332 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0.627719 | 0.0350358 | ||||||||
\(322\) | 11.3723 | 0.633752 | ||||||||
\(323\) | 2.97825 | 0.165714 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | 24.2337 | 1.34218 | ||||||||
\(327\) | 4.74456 | 0.262375 | ||||||||
\(328\) | 0.744563 | 0.0411116 | ||||||||
\(329\) | −22.7446 | −1.25395 | ||||||||
\(330\) | 0.627719 | 0.0345548 | ||||||||
\(331\) | −1.48913 | −0.0818497 | −0.0409249 | − | 0.999162i | \(-0.513030\pi\) | ||||
−0.0409249 | + | 0.999162i | \(0.513030\pi\) | |||||||
\(332\) | −12.0000 | −0.658586 | ||||||||
\(333\) | −0.744563 | −0.0408018 | ||||||||
\(334\) | −12.6277 | −0.690958 | ||||||||
\(335\) | 10.7446 | 0.587038 | ||||||||
\(336\) | 3.37228 | 0.183973 | ||||||||
\(337\) | 28.9783 | 1.57855 | 0.789273 | − | 0.614043i | \(-0.210458\pi\) | ||||
0.789273 | + | 0.614043i | \(0.210458\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | −2.62772 | −0.142718 | ||||||||
\(340\) | −4.74456 | −0.257310 | ||||||||
\(341\) | −0.627719 | −0.0339929 | ||||||||
\(342\) | −0.627719 | −0.0339431 | ||||||||
\(343\) | −8.86141 | −0.478471 | ||||||||
\(344\) | 0.627719 | 0.0338443 | ||||||||
\(345\) | 3.37228 | 0.181558 | ||||||||
\(346\) | −18.0000 | −0.967686 | ||||||||
\(347\) | 36.4674 | 1.95767 | 0.978836 | − | 0.204648i | \(-0.0656049\pi\) | ||||
0.978836 | + | 0.204648i | \(0.0656049\pi\) | |||||||
\(348\) | −8.74456 | −0.468758 | ||||||||
\(349\) | 7.25544 | 0.388375 | 0.194187 | − | 0.980964i | \(-0.437793\pi\) | ||||
0.194187 | + | 0.980964i | \(0.437793\pi\) | |||||||
\(350\) | 3.37228 | 0.180256 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0.627719 | 0.0334575 | ||||||||
\(353\) | 15.4891 | 0.824403 | 0.412201 | − | 0.911093i | \(-0.364760\pi\) | ||||
0.412201 | + | 0.911093i | \(0.364760\pi\) | |||||||
\(354\) | 2.74456 | 0.145872 | ||||||||
\(355\) | 3.37228 | 0.178982 | ||||||||
\(356\) | −1.37228 | −0.0727308 | ||||||||
\(357\) | −16.0000 | −0.846810 | ||||||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | 3.37228 | 0.177982 | 0.0889911 | − | 0.996032i | \(-0.471636\pi\) | ||||
0.0889911 | + | 0.996032i | \(0.471636\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −18.6060 | −0.979262 | ||||||||
\(362\) | 14.8614 | 0.781098 | ||||||||
\(363\) | −10.6060 | −0.556669 | ||||||||
\(364\) | −6.74456 | −0.353511 | ||||||||
\(365\) | −8.11684 | −0.424855 | ||||||||
\(366\) | 11.4891 | 0.600546 | ||||||||
\(367\) | −20.2337 | −1.05619 | −0.528095 | − | 0.849185i | \(-0.677093\pi\) | ||||
−0.528095 | + | 0.849185i | \(0.677093\pi\) | |||||||
\(368\) | 3.37228 | 0.175792 | ||||||||
\(369\) | 0.744563 | 0.0387604 | ||||||||
\(370\) | −0.744563 | −0.0387080 | ||||||||
\(371\) | 4.62772 | 0.240259 | ||||||||
\(372\) | −1.00000 | −0.0518476 | ||||||||
\(373\) | 14.8614 | 0.769494 | 0.384747 | − | 0.923022i | \(-0.374289\pi\) | ||||
0.384747 | + | 0.923022i | \(0.374289\pi\) | |||||||
\(374\) | −2.97825 | −0.154002 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −6.74456 | −0.347824 | ||||||||
\(377\) | 17.4891 | 0.900736 | ||||||||
\(378\) | 3.37228 | 0.173451 | ||||||||
\(379\) | −28.8614 | −1.48251 | −0.741255 | − | 0.671223i | \(-0.765769\pi\) | ||||
−0.741255 | + | 0.671223i | \(0.765769\pi\) | |||||||
\(380\) | −0.627719 | −0.0322013 | ||||||||
\(381\) | 13.4891 | 0.691069 | ||||||||
\(382\) | 16.0000 | 0.818631 | ||||||||
\(383\) | 13.4891 | 0.689262 | 0.344631 | − | 0.938738i | \(-0.388004\pi\) | ||||
0.344631 | + | 0.938738i | \(0.388004\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 2.11684 | 0.107884 | ||||||||
\(386\) | 15.4891 | 0.788376 | ||||||||
\(387\) | 0.627719 | 0.0319087 | ||||||||
\(388\) | 2.00000 | 0.101535 | ||||||||
\(389\) | 16.9783 | 0.860831 | 0.430416 | − | 0.902631i | \(-0.358367\pi\) | ||||
0.430416 | + | 0.902631i | \(0.358367\pi\) | |||||||
\(390\) | −2.00000 | −0.101274 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 4.37228 | 0.220834 | ||||||||
\(393\) | −16.2337 | −0.818881 | ||||||||
\(394\) | 19.4891 | 0.981848 | ||||||||
\(395\) | −4.62772 | −0.232846 | ||||||||
\(396\) | 0.627719 | 0.0315441 | ||||||||
\(397\) | −1.60597 | −0.0806013 | −0.0403006 | − | 0.999188i | \(-0.512832\pi\) | ||||
−0.0403006 | + | 0.999188i | \(0.512832\pi\) | |||||||
\(398\) | −12.6277 | −0.632970 | ||||||||
\(399\) | −2.11684 | −0.105975 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 22.6277 | 1.12997 | 0.564987 | − | 0.825100i | \(-0.308881\pi\) | ||||
0.564987 | + | 0.825100i | \(0.308881\pi\) | |||||||
\(402\) | 10.7446 | 0.535890 | ||||||||
\(403\) | 2.00000 | 0.0996271 | ||||||||
\(404\) | 8.11684 | 0.403828 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −29.4891 | −1.46352 | ||||||||
\(407\) | −0.467376 | −0.0231670 | ||||||||
\(408\) | −4.74456 | −0.234891 | ||||||||
\(409\) | −10.2337 | −0.506023 | −0.253012 | − | 0.967463i | \(-0.581421\pi\) | ||||
−0.253012 | + | 0.967463i | \(0.581421\pi\) | |||||||
\(410\) | 0.744563 | 0.0367713 | ||||||||
\(411\) | −3.48913 | −0.172106 | ||||||||
\(412\) | −8.00000 | −0.394132 | ||||||||
\(413\) | 9.25544 | 0.455430 | ||||||||
\(414\) | 3.37228 | 0.165739 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | −2.00000 | −0.0980581 | ||||||||
\(417\) | −10.7446 | −0.526163 | ||||||||
\(418\) | −0.394031 | −0.0192727 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 3.37228 | 0.164550 | ||||||||
\(421\) | 19.4891 | 0.949842 | 0.474921 | − | 0.880028i | \(-0.342477\pi\) | ||||
0.474921 | + | 0.880028i | \(0.342477\pi\) | |||||||
\(422\) | −0.627719 | −0.0305569 | ||||||||
\(423\) | −6.74456 | −0.327932 | ||||||||
\(424\) | 1.37228 | 0.0666439 | ||||||||
\(425\) | −4.74456 | −0.230145 | ||||||||
\(426\) | 3.37228 | 0.163388 | ||||||||
\(427\) | 38.7446 | 1.87498 | ||||||||
\(428\) | 0.627719 | 0.0303419 | ||||||||
\(429\) | −1.25544 | −0.0606131 | ||||||||
\(430\) | 0.627719 | 0.0302713 | ||||||||
\(431\) | −26.9783 | −1.29950 | −0.649748 | − | 0.760149i | \(-0.725126\pi\) | ||||
−0.649748 | + | 0.760149i | \(0.725126\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 36.1168 | 1.73566 | 0.867832 | − | 0.496857i | \(-0.165513\pi\) | ||||
0.867832 | + | 0.496857i | \(0.165513\pi\) | |||||||
\(434\) | −3.37228 | −0.161875 | ||||||||
\(435\) | −8.74456 | −0.419270 | ||||||||
\(436\) | 4.74456 | 0.227223 | ||||||||
\(437\) | −2.11684 | −0.101262 | ||||||||
\(438\) | −8.11684 | −0.387838 | ||||||||
\(439\) | 14.7446 | 0.703720 | 0.351860 | − | 0.936053i | \(-0.385549\pi\) | ||||
0.351860 | + | 0.936053i | \(0.385549\pi\) | |||||||
\(440\) | 0.627719 | 0.0299253 | ||||||||
\(441\) | 4.37228 | 0.208204 | ||||||||
\(442\) | 9.48913 | 0.451352 | ||||||||
\(443\) | 34.3505 | 1.63204 | 0.816022 | − | 0.578022i | \(-0.196175\pi\) | ||||
0.816022 | + | 0.578022i | \(0.196175\pi\) | |||||||
\(444\) | −0.744563 | −0.0353354 | ||||||||
\(445\) | −1.37228 | −0.0650524 | ||||||||
\(446\) | 9.25544 | 0.438258 | ||||||||
\(447\) | −12.1168 | −0.573107 | ||||||||
\(448\) | 3.37228 | 0.159325 | ||||||||
\(449\) | −8.97825 | −0.423710 | −0.211855 | − | 0.977301i | \(-0.567950\pi\) | ||||
−0.211855 | + | 0.977301i | \(0.567950\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 0.467376 | 0.0220079 | ||||||||
\(452\) | −2.62772 | −0.123597 | ||||||||
\(453\) | −8.00000 | −0.375873 | ||||||||
\(454\) | 6.11684 | 0.287078 | ||||||||
\(455\) | −6.74456 | −0.316190 | ||||||||
\(456\) | −0.627719 | −0.0293956 | ||||||||
\(457\) | 34.4674 | 1.61232 | 0.806158 | − | 0.591700i | \(-0.201543\pi\) | ||||
0.806158 | + | 0.591700i | \(0.201543\pi\) | |||||||
\(458\) | 3.88316 | 0.181448 | ||||||||
\(459\) | −4.74456 | −0.221457 | ||||||||
\(460\) | 3.37228 | 0.157233 | ||||||||
\(461\) | −19.7228 | −0.918583 | −0.459291 | − | 0.888286i | \(-0.651897\pi\) | ||||
−0.459291 | + | 0.888286i | \(0.651897\pi\) | |||||||
\(462\) | 2.11684 | 0.0984845 | ||||||||
\(463\) | 2.51087 | 0.116690 | 0.0583451 | − | 0.998296i | \(-0.481418\pi\) | ||||
0.0583451 | + | 0.998296i | \(0.481418\pi\) | |||||||
\(464\) | −8.74456 | −0.405956 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | −14.8614 | −0.688441 | ||||||||
\(467\) | 6.51087 | 0.301287 | 0.150644 | − | 0.988588i | \(-0.451865\pi\) | ||||
0.150644 | + | 0.988588i | \(0.451865\pi\) | |||||||
\(468\) | −2.00000 | −0.0924500 | ||||||||
\(469\) | 36.2337 | 1.67312 | ||||||||
\(470\) | −6.74456 | −0.311103 | ||||||||
\(471\) | 9.37228 | 0.431852 | ||||||||
\(472\) | 2.74456 | 0.126329 | ||||||||
\(473\) | 0.394031 | 0.0181176 | ||||||||
\(474\) | −4.62772 | −0.212558 | ||||||||
\(475\) | −0.627719 | −0.0288017 | ||||||||
\(476\) | −16.0000 | −0.733359 | ||||||||
\(477\) | 1.37228 | 0.0628324 | ||||||||
\(478\) | −29.4891 | −1.34880 | ||||||||
\(479\) | 8.86141 | 0.404888 | 0.202444 | − | 0.979294i | \(-0.435112\pi\) | ||||
0.202444 | + | 0.979294i | \(0.435112\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 1.48913 | 0.0678983 | ||||||||
\(482\) | 4.51087 | 0.205465 | ||||||||
\(483\) | 11.3723 | 0.517457 | ||||||||
\(484\) | −10.6060 | −0.482090 | ||||||||
\(485\) | 2.00000 | 0.0908153 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −37.4891 | −1.69879 | −0.849397 | − | 0.527754i | \(-0.823034\pi\) | ||||
−0.849397 | + | 0.527754i | \(0.823034\pi\) | |||||||
\(488\) | 11.4891 | 0.520088 | ||||||||
\(489\) | 24.2337 | 1.09589 | ||||||||
\(490\) | 4.37228 | 0.197520 | ||||||||
\(491\) | 27.6060 | 1.24584 | 0.622920 | − | 0.782286i | \(-0.285946\pi\) | ||||
0.622920 | + | 0.782286i | \(0.285946\pi\) | |||||||
\(492\) | 0.744563 | 0.0335675 | ||||||||
\(493\) | 41.4891 | 1.86858 | ||||||||
\(494\) | 1.25544 | 0.0564848 | ||||||||
\(495\) | 0.627719 | 0.0282139 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | 11.3723 | 0.510117 | ||||||||
\(498\) | −12.0000 | −0.537733 | ||||||||
\(499\) | 33.4891 | 1.49918 | 0.749590 | − | 0.661903i | \(-0.230251\pi\) | ||||
0.749590 | + | 0.661903i | \(0.230251\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −12.6277 | −0.564165 | ||||||||
\(502\) | −4.00000 | −0.178529 | ||||||||
\(503\) | 5.48913 | 0.244748 | 0.122374 | − | 0.992484i | \(-0.460949\pi\) | ||||
0.122374 | + | 0.992484i | \(0.460949\pi\) | |||||||
\(504\) | 3.37228 | 0.150213 | ||||||||
\(505\) | 8.11684 | 0.361195 | ||||||||
\(506\) | 2.11684 | 0.0941052 | ||||||||
\(507\) | −9.00000 | −0.399704 | ||||||||
\(508\) | 13.4891 | 0.598483 | ||||||||
\(509\) | −27.2554 | −1.20808 | −0.604038 | − | 0.796956i | \(-0.706442\pi\) | ||||
−0.604038 | + | 0.796956i | \(0.706442\pi\) | |||||||
\(510\) | −4.74456 | −0.210093 | ||||||||
\(511\) | −27.3723 | −1.21088 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.627719 | −0.0277145 | ||||||||
\(514\) | 13.3723 | 0.589826 | ||||||||
\(515\) | −8.00000 | −0.352522 | ||||||||
\(516\) | 0.627719 | 0.0276338 | ||||||||
\(517\) | −4.23369 | −0.186197 | ||||||||
\(518\) | −2.51087 | −0.110322 | ||||||||
\(519\) | −18.0000 | −0.790112 | ||||||||
\(520\) | −2.00000 | −0.0877058 | ||||||||
\(521\) | 36.9783 | 1.62005 | 0.810023 | − | 0.586398i | \(-0.199454\pi\) | ||||
0.810023 | + | 0.586398i | \(0.199454\pi\) | |||||||
\(522\) | −8.74456 | −0.382739 | ||||||||
\(523\) | −12.8614 | −0.562390 | −0.281195 | − | 0.959651i | \(-0.590731\pi\) | ||||
−0.281195 | + | 0.959651i | \(0.590731\pi\) | |||||||
\(524\) | −16.2337 | −0.709172 | ||||||||
\(525\) | 3.37228 | 0.147178 | ||||||||
\(526\) | −18.9783 | −0.827491 | ||||||||
\(527\) | 4.74456 | 0.206676 | ||||||||
\(528\) | 0.627719 | 0.0273179 | ||||||||
\(529\) | −11.6277 | −0.505553 | ||||||||
\(530\) | 1.37228 | 0.0596081 | ||||||||
\(531\) | 2.74456 | 0.119104 | ||||||||
\(532\) | −2.11684 | −0.0917768 | ||||||||
\(533\) | −1.48913 | −0.0645012 | ||||||||
\(534\) | −1.37228 | −0.0593844 | ||||||||
\(535\) | 0.627719 | 0.0271386 | ||||||||
\(536\) | 10.7446 | 0.464094 | ||||||||
\(537\) | −12.0000 | −0.517838 | ||||||||
\(538\) | −2.00000 | −0.0862261 | ||||||||
\(539\) | 2.74456 | 0.118217 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −15.4891 | −0.665930 | −0.332965 | − | 0.942939i | \(-0.608049\pi\) | ||||
−0.332965 | + | 0.942939i | \(0.608049\pi\) | |||||||
\(542\) | −13.8832 | −0.596333 | ||||||||
\(543\) | 14.8614 | 0.637764 | ||||||||
\(544\) | −4.74456 | −0.203421 | ||||||||
\(545\) | 4.74456 | 0.203235 | ||||||||
\(546\) | −6.74456 | −0.288641 | ||||||||
\(547\) | −2.74456 | −0.117349 | −0.0586745 | − | 0.998277i | \(-0.518687\pi\) | ||||
−0.0586745 | + | 0.998277i | \(0.518687\pi\) | |||||||
\(548\) | −3.48913 | −0.149048 | ||||||||
\(549\) | 11.4891 | 0.490344 | ||||||||
\(550\) | 0.627719 | 0.0267660 | ||||||||
\(551\) | 5.48913 | 0.233845 | ||||||||
\(552\) | 3.37228 | 0.143534 | ||||||||
\(553\) | −15.6060 | −0.663633 | ||||||||
\(554\) | 15.2554 | 0.648141 | ||||||||
\(555\) | −0.744563 | −0.0316049 | ||||||||
\(556\) | −10.7446 | −0.455671 | ||||||||
\(557\) | 11.8832 | 0.503505 | 0.251753 | − | 0.967792i | \(-0.418993\pi\) | ||||
0.251753 | + | 0.967792i | \(0.418993\pi\) | |||||||
\(558\) | −1.00000 | −0.0423334 | ||||||||
\(559\) | −1.25544 | −0.0530993 | ||||||||
\(560\) | 3.37228 | 0.142505 | ||||||||
\(561\) | −2.97825 | −0.125742 | ||||||||
\(562\) | 16.7446 | 0.706327 | ||||||||
\(563\) | −6.97825 | −0.294098 | −0.147049 | − | 0.989129i | \(-0.546978\pi\) | ||||
−0.147049 | + | 0.989129i | \(0.546978\pi\) | |||||||
\(564\) | −6.74456 | −0.283997 | ||||||||
\(565\) | −2.62772 | −0.110549 | ||||||||
\(566\) | 12.0000 | 0.504398 | ||||||||
\(567\) | 3.37228 | 0.141623 | ||||||||
\(568\) | 3.37228 | 0.141498 | ||||||||
\(569\) | −1.37228 | −0.0575290 | −0.0287645 | − | 0.999586i | \(-0.509157\pi\) | ||||
−0.0287645 | + | 0.999586i | \(0.509157\pi\) | |||||||
\(570\) | −0.627719 | −0.0262922 | ||||||||
\(571\) | −26.7446 | −1.11923 | −0.559613 | − | 0.828754i | \(-0.689050\pi\) | ||||
−0.559613 | + | 0.828754i | \(0.689050\pi\) | |||||||
\(572\) | −1.25544 | −0.0524925 | ||||||||
\(573\) | 16.0000 | 0.668410 | ||||||||
\(574\) | 2.51087 | 0.104802 | ||||||||
\(575\) | 3.37228 | 0.140634 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −2.23369 | −0.0929896 | −0.0464948 | − | 0.998919i | \(-0.514805\pi\) | ||||
−0.0464948 | + | 0.998919i | \(0.514805\pi\) | |||||||
\(578\) | 5.51087 | 0.229222 | ||||||||
\(579\) | 15.4891 | 0.643706 | ||||||||
\(580\) | −8.74456 | −0.363098 | ||||||||
\(581\) | −40.4674 | −1.67887 | ||||||||
\(582\) | 2.00000 | 0.0829027 | ||||||||
\(583\) | 0.861407 | 0.0356758 | ||||||||
\(584\) | −8.11684 | −0.335877 | ||||||||
\(585\) | −2.00000 | −0.0826898 | ||||||||
\(586\) | −7.48913 | −0.309373 | ||||||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | 4.37228 | 0.180310 | ||||||||
\(589\) | 0.627719 | 0.0258647 | ||||||||
\(590\) | 2.74456 | 0.112992 | ||||||||
\(591\) | 19.4891 | 0.801675 | ||||||||
\(592\) | −0.744563 | −0.0306013 | ||||||||
\(593\) | 44.9783 | 1.84704 | 0.923518 | − | 0.383556i | \(-0.125301\pi\) | ||||
0.923518 | + | 0.383556i | \(0.125301\pi\) | |||||||
\(594\) | 0.627719 | 0.0257556 | ||||||||
\(595\) | −16.0000 | −0.655936 | ||||||||
\(596\) | −12.1168 | −0.496325 | ||||||||
\(597\) | −12.6277 | −0.516818 | ||||||||
\(598\) | −6.74456 | −0.275806 | ||||||||
\(599\) | 10.1168 | 0.413363 | 0.206682 | − | 0.978408i | \(-0.433734\pi\) | ||||
0.206682 | + | 0.978408i | \(0.433734\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 12.5109 | 0.510329 | 0.255165 | − | 0.966898i | \(-0.417870\pi\) | ||||
0.255165 | + | 0.966898i | \(0.417870\pi\) | |||||||
\(602\) | 2.11684 | 0.0862761 | ||||||||
\(603\) | 10.7446 | 0.437552 | ||||||||
\(604\) | −8.00000 | −0.325515 | ||||||||
\(605\) | −10.6060 | −0.431194 | ||||||||
\(606\) | 8.11684 | 0.329724 | ||||||||
\(607\) | −4.62772 | −0.187833 | −0.0939167 | − | 0.995580i | \(-0.529939\pi\) | ||||
−0.0939167 | + | 0.995580i | \(0.529939\pi\) | |||||||
\(608\) | −0.627719 | −0.0254574 | ||||||||
\(609\) | −29.4891 | −1.19496 | ||||||||
\(610\) | 11.4891 | 0.465181 | ||||||||
\(611\) | 13.4891 | 0.545712 | ||||||||
\(612\) | −4.74456 | −0.191788 | ||||||||
\(613\) | 35.4891 | 1.43339 | 0.716696 | − | 0.697386i | \(-0.245653\pi\) | ||||
0.716696 | + | 0.697386i | \(0.245653\pi\) | |||||||
\(614\) | 30.9783 | 1.25018 | ||||||||
\(615\) | 0.744563 | 0.0300237 | ||||||||
\(616\) | 2.11684 | 0.0852901 | ||||||||
\(617\) | 7.88316 | 0.317364 | 0.158682 | − | 0.987330i | \(-0.449276\pi\) | ||||
0.158682 | + | 0.987330i | \(0.449276\pi\) | |||||||
\(618\) | −8.00000 | −0.321807 | ||||||||
\(619\) | 16.2337 | 0.652487 | 0.326244 | − | 0.945286i | \(-0.394217\pi\) | ||||
0.326244 | + | 0.945286i | \(0.394217\pi\) | |||||||
\(620\) | −1.00000 | −0.0401610 | ||||||||
\(621\) | 3.37228 | 0.135325 | ||||||||
\(622\) | 8.00000 | 0.320771 | ||||||||
\(623\) | −4.62772 | −0.185406 | ||||||||
\(624\) | −2.00000 | −0.0800641 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 10.0000 | 0.399680 | ||||||||
\(627\) | −0.394031 | −0.0157361 | ||||||||
\(628\) | 9.37228 | 0.373995 | ||||||||
\(629\) | 3.53262 | 0.140855 | ||||||||
\(630\) | 3.37228 | 0.134355 | ||||||||
\(631\) | −46.3505 | −1.84519 | −0.922593 | − | 0.385775i | \(-0.873934\pi\) | ||||
−0.922593 | + | 0.385775i | \(0.873934\pi\) | |||||||
\(632\) | −4.62772 | −0.184081 | ||||||||
\(633\) | −0.627719 | −0.0249496 | ||||||||
\(634\) | −24.7446 | −0.982732 | ||||||||
\(635\) | 13.4891 | 0.535300 | ||||||||
\(636\) | 1.37228 | 0.0544145 | ||||||||
\(637\) | −8.74456 | −0.346472 | ||||||||
\(638\) | −5.48913 | −0.217317 | ||||||||
\(639\) | 3.37228 | 0.133405 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | 0.627719 | 0.0247741 | ||||||||
\(643\) | −25.0951 | −0.989654 | −0.494827 | − | 0.868992i | \(-0.664769\pi\) | ||||
−0.494827 | + | 0.868992i | \(0.664769\pi\) | |||||||
\(644\) | 11.3723 | 0.448131 | ||||||||
\(645\) | 0.627719 | 0.0247164 | ||||||||
\(646\) | 2.97825 | 0.117178 | ||||||||
\(647\) | 50.5842 | 1.98867 | 0.994335 | − | 0.106287i | \(-0.0338964\pi\) | ||||
0.994335 | + | 0.106287i | \(0.0338964\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 1.72281 | 0.0676263 | ||||||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | −3.37228 | −0.132170 | ||||||||
\(652\) | 24.2337 | 0.949064 | ||||||||
\(653\) | 40.9783 | 1.60360 | 0.801801 | − | 0.597591i | \(-0.203875\pi\) | ||||
0.801801 | + | 0.597591i | \(0.203875\pi\) | |||||||
\(654\) | 4.74456 | 0.185527 | ||||||||
\(655\) | −16.2337 | −0.634303 | ||||||||
\(656\) | 0.744563 | 0.0290703 | ||||||||
\(657\) | −8.11684 | −0.316668 | ||||||||
\(658\) | −22.7446 | −0.886675 | ||||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 0.627719 | 0.0244339 | ||||||||
\(661\) | −4.97825 | −0.193632 | −0.0968158 | − | 0.995302i | \(-0.530866\pi\) | ||||
−0.0968158 | + | 0.995302i | \(0.530866\pi\) | |||||||
\(662\) | −1.48913 | −0.0578765 | ||||||||
\(663\) | 9.48913 | 0.368527 | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | −2.11684 | −0.0820877 | ||||||||
\(666\) | −0.744563 | −0.0288512 | ||||||||
\(667\) | −29.4891 | −1.14182 | ||||||||
\(668\) | −12.6277 | −0.488581 | ||||||||
\(669\) | 9.25544 | 0.357836 | ||||||||
\(670\) | 10.7446 | 0.415099 | ||||||||
\(671\) | 7.21194 | 0.278414 | ||||||||
\(672\) | 3.37228 | 0.130089 | ||||||||
\(673\) | −0.510875 | −0.0196928 | −0.00984639 | − | 0.999952i | \(-0.503134\pi\) | ||||
−0.00984639 | + | 0.999952i | \(0.503134\pi\) | |||||||
\(674\) | 28.9783 | 1.11620 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −41.6060 | −1.59905 | −0.799524 | − | 0.600635i | \(-0.794915\pi\) | ||||
−0.799524 | + | 0.600635i | \(0.794915\pi\) | |||||||
\(678\) | −2.62772 | −0.100917 | ||||||||
\(679\) | 6.74456 | 0.258833 | ||||||||
\(680\) | −4.74456 | −0.181946 | ||||||||
\(681\) | 6.11684 | 0.234398 | ||||||||
\(682\) | −0.627719 | −0.0240366 | ||||||||
\(683\) | −12.8614 | −0.492128 | −0.246064 | − | 0.969254i | \(-0.579137\pi\) | ||||
−0.246064 | + | 0.969254i | \(0.579137\pi\) | |||||||
\(684\) | −0.627719 | −0.0240014 | ||||||||
\(685\) | −3.48913 | −0.133313 | ||||||||
\(686\) | −8.86141 | −0.338330 | ||||||||
\(687\) | 3.88316 | 0.148152 | ||||||||
\(688\) | 0.627719 | 0.0239316 | ||||||||
\(689\) | −2.74456 | −0.104560 | ||||||||
\(690\) | 3.37228 | 0.128381 | ||||||||
\(691\) | −19.1386 | −0.728066 | −0.364033 | − | 0.931386i | \(-0.618601\pi\) | ||||
−0.364033 | + | 0.931386i | \(0.618601\pi\) | |||||||
\(692\) | −18.0000 | −0.684257 | ||||||||
\(693\) | 2.11684 | 0.0804123 | ||||||||
\(694\) | 36.4674 | 1.38428 | ||||||||
\(695\) | −10.7446 | −0.407564 | ||||||||
\(696\) | −8.74456 | −0.331462 | ||||||||
\(697\) | −3.53262 | −0.133808 | ||||||||
\(698\) | 7.25544 | 0.274622 | ||||||||
\(699\) | −14.8614 | −0.562110 | ||||||||
\(700\) | 3.37228 | 0.127460 | ||||||||
\(701\) | 45.6060 | 1.72251 | 0.861257 | − | 0.508170i | \(-0.169678\pi\) | ||||
0.861257 | + | 0.508170i | \(0.169678\pi\) | |||||||
\(702\) | −2.00000 | −0.0754851 | ||||||||
\(703\) | 0.467376 | 0.0176274 | ||||||||
\(704\) | 0.627719 | 0.0236580 | ||||||||
\(705\) | −6.74456 | −0.254015 | ||||||||
\(706\) | 15.4891 | 0.582941 | ||||||||
\(707\) | 27.3723 | 1.02944 | ||||||||
\(708\) | 2.74456 | 0.103147 | ||||||||
\(709\) | 40.1168 | 1.50662 | 0.753310 | − | 0.657666i | \(-0.228456\pi\) | ||||
0.753310 | + | 0.657666i | \(0.228456\pi\) | |||||||
\(710\) | 3.37228 | 0.126559 | ||||||||
\(711\) | −4.62772 | −0.173553 | ||||||||
\(712\) | −1.37228 | −0.0514284 | ||||||||
\(713\) | −3.37228 | −0.126293 | ||||||||
\(714\) | −16.0000 | −0.598785 | ||||||||
\(715\) | −1.25544 | −0.0469507 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | −29.4891 | −1.10129 | ||||||||
\(718\) | 3.37228 | 0.125852 | ||||||||
\(719\) | 38.7446 | 1.44493 | 0.722464 | − | 0.691408i | \(-0.243009\pi\) | ||||
0.722464 | + | 0.691408i | \(0.243009\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −26.9783 | −1.00472 | ||||||||
\(722\) | −18.6060 | −0.692442 | ||||||||
\(723\) | 4.51087 | 0.167761 | ||||||||
\(724\) | 14.8614 | 0.552320 | ||||||||
\(725\) | −8.74456 | −0.324765 | ||||||||
\(726\) | −10.6060 | −0.393624 | ||||||||
\(727\) | 19.3723 | 0.718478 | 0.359239 | − | 0.933246i | \(-0.383036\pi\) | ||||
0.359239 | + | 0.933246i | \(0.383036\pi\) | |||||||
\(728\) | −6.74456 | −0.249970 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.11684 | −0.300418 | ||||||||
\(731\) | −2.97825 | −0.110155 | ||||||||
\(732\) | 11.4891 | 0.424650 | ||||||||
\(733\) | −34.0000 | −1.25582 | −0.627909 | − | 0.778287i | \(-0.716089\pi\) | ||||
−0.627909 | + | 0.778287i | \(0.716089\pi\) | |||||||
\(734\) | −20.2337 | −0.746839 | ||||||||
\(735\) | 4.37228 | 0.161274 | ||||||||
\(736\) | 3.37228 | 0.124304 | ||||||||
\(737\) | 6.74456 | 0.248439 | ||||||||
\(738\) | 0.744563 | 0.0274077 | ||||||||
\(739\) | −22.9783 | −0.845269 | −0.422634 | − | 0.906300i | \(-0.638895\pi\) | ||||
−0.422634 | + | 0.906300i | \(0.638895\pi\) | |||||||
\(740\) | −0.744563 | −0.0273707 | ||||||||
\(741\) | 1.25544 | 0.0461196 | ||||||||
\(742\) | 4.62772 | 0.169889 | ||||||||
\(743\) | −35.3723 | −1.29768 | −0.648842 | − | 0.760924i | \(-0.724746\pi\) | ||||
−0.648842 | + | 0.760924i | \(0.724746\pi\) | |||||||
\(744\) | −1.00000 | −0.0366618 | ||||||||
\(745\) | −12.1168 | −0.443927 | ||||||||
\(746\) | 14.8614 | 0.544115 | ||||||||
\(747\) | −12.0000 | −0.439057 | ||||||||
\(748\) | −2.97825 | −0.108896 | ||||||||
\(749\) | 2.11684 | 0.0773478 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −38.7446 | −1.41381 | −0.706905 | − | 0.707309i | \(-0.749909\pi\) | ||||
−0.706905 | + | 0.707309i | \(0.749909\pi\) | |||||||
\(752\) | −6.74456 | −0.245949 | ||||||||
\(753\) | −4.00000 | −0.145768 | ||||||||
\(754\) | 17.4891 | 0.636916 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 3.37228 | 0.122649 | ||||||||
\(757\) | −26.0000 | −0.944986 | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||||
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | −28.8614 | −1.04829 | ||||||||
\(759\) | 2.11684 | 0.0768366 | ||||||||
\(760\) | −0.627719 | −0.0227697 | ||||||||
\(761\) | −46.8614 | −1.69872 | −0.849362 | − | 0.527810i | \(-0.823013\pi\) | ||||
−0.849362 | + | 0.527810i | \(0.823013\pi\) | |||||||
\(762\) | 13.4891 | 0.488659 | ||||||||
\(763\) | 16.0000 | 0.579239 | ||||||||
\(764\) | 16.0000 | 0.578860 | ||||||||
\(765\) | −4.74456 | −0.171540 | ||||||||
\(766\) | 13.4891 | 0.487382 | ||||||||
\(767\) | −5.48913 | −0.198201 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −9.37228 | −0.337973 | −0.168987 | − | 0.985618i | \(-0.554049\pi\) | ||||
−0.168987 | + | 0.985618i | \(0.554049\pi\) | |||||||
\(770\) | 2.11684 | 0.0762858 | ||||||||
\(771\) | 13.3723 | 0.481591 | ||||||||
\(772\) | 15.4891 | 0.557466 | ||||||||
\(773\) | 21.6060 | 0.777113 | 0.388556 | − | 0.921425i | \(-0.372974\pi\) | ||||
0.388556 | + | 0.921425i | \(0.372974\pi\) | |||||||
\(774\) | 0.627719 | 0.0225629 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 2.00000 | 0.0717958 | ||||||||
\(777\) | −2.51087 | −0.0900771 | ||||||||
\(778\) | 16.9783 | 0.608700 | ||||||||
\(779\) | −0.467376 | −0.0167455 | ||||||||
\(780\) | −2.00000 | −0.0716115 | ||||||||
\(781\) | 2.11684 | 0.0757466 | ||||||||
\(782\) | −16.0000 | −0.572159 | ||||||||
\(783\) | −8.74456 | −0.312505 | ||||||||
\(784\) | 4.37228 | 0.156153 | ||||||||
\(785\) | 9.37228 | 0.334511 | ||||||||
\(786\) | −16.2337 | −0.579036 | ||||||||
\(787\) | −9.88316 | −0.352296 | −0.176148 | − | 0.984364i | \(-0.556364\pi\) | ||||
−0.176148 | + | 0.984364i | \(0.556364\pi\) | |||||||
\(788\) | 19.4891 | 0.694271 | ||||||||
\(789\) | −18.9783 | −0.675644 | ||||||||
\(790\) | −4.62772 | −0.164647 | ||||||||
\(791\) | −8.86141 | −0.315075 | ||||||||
\(792\) | 0.627719 | 0.0223050 | ||||||||
\(793\) | −22.9783 | −0.815982 | ||||||||
\(794\) | −1.60597 | −0.0569937 | ||||||||
\(795\) | 1.37228 | 0.0486698 | ||||||||
\(796\) | −12.6277 | −0.447578 | ||||||||
\(797\) | −20.5109 | −0.726532 | −0.363266 | − | 0.931685i | \(-0.618338\pi\) | ||||
−0.363266 | + | 0.931685i | \(0.618338\pi\) | |||||||
\(798\) | −2.11684 | −0.0749355 | ||||||||
\(799\) | 32.0000 | 1.13208 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −1.37228 | −0.0484872 | ||||||||
\(802\) | 22.6277 | 0.799013 | ||||||||
\(803\) | −5.09509 | −0.179802 | ||||||||
\(804\) | 10.7446 | 0.378932 | ||||||||
\(805\) | 11.3723 | 0.400820 | ||||||||
\(806\) | 2.00000 | 0.0704470 | ||||||||
\(807\) | −2.00000 | −0.0704033 | ||||||||
\(808\) | 8.11684 | 0.285550 | ||||||||
\(809\) | 9.60597 | 0.337728 | 0.168864 | − | 0.985639i | \(-0.445990\pi\) | ||||
0.168864 | + | 0.985639i | \(0.445990\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −40.6277 | −1.42663 | −0.713316 | − | 0.700842i | \(-0.752808\pi\) | ||||
−0.713316 | + | 0.700842i | \(0.752808\pi\) | |||||||
\(812\) | −29.4891 | −1.03487 | ||||||||
\(813\) | −13.8832 | −0.486904 | ||||||||
\(814\) | −0.467376 | −0.0163815 | ||||||||
\(815\) | 24.2337 | 0.848869 | ||||||||
\(816\) | −4.74456 | −0.166093 | ||||||||
\(817\) | −0.394031 | −0.0137854 | ||||||||
\(818\) | −10.2337 | −0.357813 | ||||||||
\(819\) | −6.74456 | −0.235674 | ||||||||
\(820\) | 0.744563 | 0.0260013 | ||||||||
\(821\) | 15.2554 | 0.532418 | 0.266209 | − | 0.963915i | \(-0.414229\pi\) | ||||
0.266209 | + | 0.963915i | \(0.414229\pi\) | |||||||
\(822\) | −3.48913 | −0.121697 | ||||||||
\(823\) | −17.2554 | −0.601487 | −0.300743 | − | 0.953705i | \(-0.597235\pi\) | ||||
−0.300743 | + | 0.953705i | \(0.597235\pi\) | |||||||
\(824\) | −8.00000 | −0.278693 | ||||||||
\(825\) | 0.627719 | 0.0218544 | ||||||||
\(826\) | 9.25544 | 0.322038 | ||||||||
\(827\) | −17.4891 | −0.608156 | −0.304078 | − | 0.952647i | \(-0.598348\pi\) | ||||
−0.304078 | + | 0.952647i | \(0.598348\pi\) | |||||||
\(828\) | 3.37228 | 0.117195 | ||||||||
\(829\) | −31.0951 | −1.07998 | −0.539989 | − | 0.841672i | \(-0.681571\pi\) | ||||
−0.539989 | + | 0.841672i | \(0.681571\pi\) | |||||||
\(830\) | −12.0000 | −0.416526 | ||||||||
\(831\) | 15.2554 | 0.529205 | ||||||||
\(832\) | −2.00000 | −0.0693375 | ||||||||
\(833\) | −20.7446 | −0.718756 | ||||||||
\(834\) | −10.7446 | −0.372054 | ||||||||
\(835\) | −12.6277 | −0.437000 | ||||||||
\(836\) | −0.394031 | −0.0136278 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | −12.0000 | −0.414533 | ||||||||
\(839\) | 16.8614 | 0.582120 | 0.291060 | − | 0.956705i | \(-0.405992\pi\) | ||||
0.291060 | + | 0.956705i | \(0.405992\pi\) | |||||||
\(840\) | 3.37228 | 0.116355 | ||||||||
\(841\) | 47.4674 | 1.63681 | ||||||||
\(842\) | 19.4891 | 0.671640 | ||||||||
\(843\) | 16.7446 | 0.576713 | ||||||||
\(844\) | −0.627719 | −0.0216070 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | −6.74456 | −0.231883 | ||||||||
\(847\) | −35.7663 | −1.22895 | ||||||||
\(848\) | 1.37228 | 0.0471243 | ||||||||
\(849\) | 12.0000 | 0.411839 | ||||||||
\(850\) | −4.74456 | −0.162737 | ||||||||
\(851\) | −2.51087 | −0.0860717 | ||||||||
\(852\) | 3.37228 | 0.115532 | ||||||||
\(853\) | −39.0951 | −1.33859 | −0.669295 | − | 0.742997i | \(-0.733404\pi\) | ||||
−0.669295 | + | 0.742997i | \(0.733404\pi\) | |||||||
\(854\) | 38.7446 | 1.32581 | ||||||||
\(855\) | −0.627719 | −0.0214675 | ||||||||
\(856\) | 0.627719 | 0.0214550 | ||||||||
\(857\) | 7.48913 | 0.255824 | 0.127912 | − | 0.991786i | \(-0.459173\pi\) | ||||
0.127912 | + | 0.991786i | \(0.459173\pi\) | |||||||
\(858\) | −1.25544 | −0.0428599 | ||||||||
\(859\) | −17.4891 | −0.596721 | −0.298361 | − | 0.954453i | \(-0.596440\pi\) | ||||
−0.298361 | + | 0.954453i | \(0.596440\pi\) | |||||||
\(860\) | 0.627719 | 0.0214050 | ||||||||
\(861\) | 2.51087 | 0.0855704 | ||||||||
\(862\) | −26.9783 | −0.918883 | ||||||||
\(863\) | −6.35053 | −0.216175 | −0.108087 | − | 0.994141i | \(-0.534473\pi\) | ||||
−0.108087 | + | 0.994141i | \(0.534473\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −18.0000 | −0.612018 | ||||||||
\(866\) | 36.1168 | 1.22730 | ||||||||
\(867\) | 5.51087 | 0.187159 | ||||||||
\(868\) | −3.37228 | −0.114463 | ||||||||
\(869\) | −2.90491 | −0.0985422 | ||||||||
\(870\) | −8.74456 | −0.296468 | ||||||||
\(871\) | −21.4891 | −0.728131 | ||||||||
\(872\) | 4.74456 | 0.160671 | ||||||||
\(873\) | 2.00000 | 0.0676897 | ||||||||
\(874\) | −2.11684 | −0.0716033 | ||||||||
\(875\) | 3.37228 | 0.114004 | ||||||||
\(876\) | −8.11684 | −0.274243 | ||||||||
\(877\) | −44.9783 | −1.51881 | −0.759404 | − | 0.650620i | \(-0.774509\pi\) | ||||
−0.759404 | + | 0.650620i | \(0.774509\pi\) | |||||||
\(878\) | 14.7446 | 0.497605 | ||||||||
\(879\) | −7.48913 | −0.252602 | ||||||||
\(880\) | 0.627719 | 0.0211604 | ||||||||
\(881\) | −3.02175 | −0.101805 | −0.0509027 | − | 0.998704i | \(-0.516210\pi\) | ||||
−0.0509027 | + | 0.998704i | \(0.516210\pi\) | |||||||
\(882\) | 4.37228 | 0.147222 | ||||||||
\(883\) | 44.8614 | 1.50971 | 0.754853 | − | 0.655894i | \(-0.227708\pi\) | ||||
0.754853 | + | 0.655894i | \(0.227708\pi\) | |||||||
\(884\) | 9.48913 | 0.319154 | ||||||||
\(885\) | 2.74456 | 0.0922575 | ||||||||
\(886\) | 34.3505 | 1.15403 | ||||||||
\(887\) | −30.7446 | −1.03230 | −0.516151 | − | 0.856498i | \(-0.672636\pi\) | ||||
−0.516151 | + | 0.856498i | \(0.672636\pi\) | |||||||
\(888\) | −0.744563 | −0.0249859 | ||||||||
\(889\) | 45.4891 | 1.52566 | ||||||||
\(890\) | −1.37228 | −0.0459990 | ||||||||
\(891\) | 0.627719 | 0.0210294 | ||||||||
\(892\) | 9.25544 | 0.309895 | ||||||||
\(893\) | 4.23369 | 0.141675 | ||||||||
\(894\) | −12.1168 | −0.405248 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 3.37228 | 0.112660 | ||||||||
\(897\) | −6.74456 | −0.225194 | ||||||||
\(898\) | −8.97825 | −0.299608 | ||||||||
\(899\) | 8.74456 | 0.291647 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −6.51087 | −0.216909 | ||||||||
\(902\) | 0.467376 | 0.0155619 | ||||||||
\(903\) | 2.11684 | 0.0704442 | ||||||||
\(904\) | −2.62772 | −0.0873966 | ||||||||
\(905\) | 14.8614 | 0.494010 | ||||||||
\(906\) | −8.00000 | −0.265782 | ||||||||
\(907\) | −17.4891 | −0.580717 | −0.290358 | − | 0.956918i | \(-0.593775\pi\) | ||||
−0.290358 | + | 0.956918i | \(0.593775\pi\) | |||||||
\(908\) | 6.11684 | 0.202995 | ||||||||
\(909\) | 8.11684 | 0.269219 | ||||||||
\(910\) | −6.74456 | −0.223580 | ||||||||
\(911\) | −2.51087 | −0.0831890 | −0.0415945 | − | 0.999135i | \(-0.513244\pi\) | ||||
−0.0415945 | + | 0.999135i | \(0.513244\pi\) | |||||||
\(912\) | −0.627719 | −0.0207858 | ||||||||
\(913\) | −7.53262 | −0.249293 | ||||||||
\(914\) | 34.4674 | 1.14008 | ||||||||
\(915\) | 11.4891 | 0.379819 | ||||||||
\(916\) | 3.88316 | 0.128303 | ||||||||
\(917\) | −54.7446 | −1.80782 | ||||||||
\(918\) | −4.74456 | −0.156594 | ||||||||
\(919\) | −12.2337 | −0.403552 | −0.201776 | − | 0.979432i | \(-0.564671\pi\) | ||||
−0.201776 | + | 0.979432i | \(0.564671\pi\) | |||||||
\(920\) | 3.37228 | 0.111181 | ||||||||
\(921\) | 30.9783 | 1.02077 | ||||||||
\(922\) | −19.7228 | −0.649536 | ||||||||
\(923\) | −6.74456 | −0.222000 | ||||||||
\(924\) | 2.11684 | 0.0696391 | ||||||||
\(925\) | −0.744563 | −0.0244811 | ||||||||
\(926\) | 2.51087 | 0.0825125 | ||||||||
\(927\) | −8.00000 | −0.262754 | ||||||||
\(928\) | −8.74456 | −0.287054 | ||||||||
\(929\) | −16.1168 | −0.528776 | −0.264388 | − | 0.964416i | \(-0.585170\pi\) | ||||
−0.264388 | + | 0.964416i | \(0.585170\pi\) | |||||||
\(930\) | −1.00000 | −0.0327913 | ||||||||
\(931\) | −2.74456 | −0.0899494 | ||||||||
\(932\) | −14.8614 | −0.486802 | ||||||||
\(933\) | 8.00000 | 0.261908 | ||||||||
\(934\) | 6.51087 | 0.213042 | ||||||||
\(935\) | −2.97825 | −0.0973992 | ||||||||
\(936\) | −2.00000 | −0.0653720 | ||||||||
\(937\) | −31.2554 | −1.02107 | −0.510535 | − | 0.859857i | \(-0.670553\pi\) | ||||
−0.510535 | + | 0.859857i | \(0.670553\pi\) | |||||||
\(938\) | 36.2337 | 1.18307 | ||||||||
\(939\) | 10.0000 | 0.326338 | ||||||||
\(940\) | −6.74456 | −0.219983 | ||||||||
\(941\) | −19.7228 | −0.642945 | −0.321473 | − | 0.946919i | \(-0.604178\pi\) | ||||
−0.321473 | + | 0.946919i | \(0.604178\pi\) | |||||||
\(942\) | 9.37228 | 0.305365 | ||||||||
\(943\) | 2.51087 | 0.0817653 | ||||||||
\(944\) | 2.74456 | 0.0893279 | ||||||||
\(945\) | 3.37228 | 0.109700 | ||||||||
\(946\) | 0.394031 | 0.0128110 | ||||||||
\(947\) | −2.74456 | −0.0891863 | −0.0445932 | − | 0.999005i | \(-0.514199\pi\) | ||||
−0.0445932 | + | 0.999005i | \(0.514199\pi\) | |||||||
\(948\) | −4.62772 | −0.150301 | ||||||||
\(949\) | 16.2337 | 0.526968 | ||||||||
\(950\) | −0.627719 | −0.0203659 | ||||||||
\(951\) | −24.7446 | −0.802397 | ||||||||
\(952\) | −16.0000 | −0.518563 | ||||||||
\(953\) | 11.7228 | 0.379739 | 0.189870 | − | 0.981809i | \(-0.439193\pi\) | ||||
0.189870 | + | 0.981809i | \(0.439193\pi\) | |||||||
\(954\) | 1.37228 | 0.0444292 | ||||||||
\(955\) | 16.0000 | 0.517748 | ||||||||
\(956\) | −29.4891 | −0.953746 | ||||||||
\(957\) | −5.48913 | −0.177438 | ||||||||
\(958\) | 8.86141 | 0.286299 | ||||||||
\(959\) | −11.7663 | −0.379954 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 1.48913 | 0.0480113 | ||||||||
\(963\) | 0.627719 | 0.0202280 | ||||||||
\(964\) | 4.51087 | 0.145285 | ||||||||
\(965\) | 15.4891 | 0.498613 | ||||||||
\(966\) | 11.3723 | 0.365897 | ||||||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | −10.6060 | −0.340889 | ||||||||
\(969\) | 2.97825 | 0.0956752 | ||||||||
\(970\) | 2.00000 | 0.0642161 | ||||||||
\(971\) | −48.7011 | −1.56289 | −0.781446 | − | 0.623973i | \(-0.785517\pi\) | ||||
−0.781446 | + | 0.623973i | \(0.785517\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −36.2337 | −1.16160 | ||||||||
\(974\) | −37.4891 | −1.20123 | ||||||||
\(975\) | −2.00000 | −0.0640513 | ||||||||
\(976\) | 11.4891 | 0.367758 | ||||||||
\(977\) | −46.0000 | −1.47167 | −0.735835 | − | 0.677161i | \(-0.763210\pi\) | ||||
−0.735835 | + | 0.677161i | \(0.763210\pi\) | |||||||
\(978\) | 24.2337 | 0.774908 | ||||||||
\(979\) | −0.861407 | −0.0275307 | ||||||||
\(980\) | 4.37228 | 0.139667 | ||||||||
\(981\) | 4.74456 | 0.151482 | ||||||||
\(982\) | 27.6060 | 0.880942 | ||||||||
\(983\) | −2.97825 | −0.0949914 | −0.0474957 | − | 0.998871i | \(-0.515124\pi\) | ||||
−0.0474957 | + | 0.998871i | \(0.515124\pi\) | |||||||
\(984\) | 0.744563 | 0.0237358 | ||||||||
\(985\) | 19.4891 | 0.620975 | ||||||||
\(986\) | 41.4891 | 1.32128 | ||||||||
\(987\) | −22.7446 | −0.723967 | ||||||||
\(988\) | 1.25544 | 0.0399408 | ||||||||
\(989\) | 2.11684 | 0.0673117 | ||||||||
\(990\) | 0.627719 | 0.0199502 | ||||||||
\(991\) | −47.6060 | −1.51225 | −0.756127 | − | 0.654425i | \(-0.772911\pi\) | ||||
−0.756127 | + | 0.654425i | \(0.772911\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | −1.48913 | −0.0472560 | ||||||||
\(994\) | 11.3723 | 0.360707 | ||||||||
\(995\) | −12.6277 | −0.400326 | ||||||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | 6.00000 | 0.190022 | 0.0950110 | − | 0.995476i | \(-0.469711\pi\) | ||||
0.0950110 | + | 0.995476i | \(0.469711\pi\) | |||||||
\(998\) | 33.4891 | 1.06008 | ||||||||
\(999\) | −0.744563 | −0.0235569 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 930.2.a.r.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2790.2.a.bd.1.2 | 2 | |||
4.3 | odd | 2 | 7440.2.a.bg.1.1 | 2 | |||
5.2 | odd | 4 | 4650.2.d.bh.3349.4 | 4 | |||
5.3 | odd | 4 | 4650.2.d.bh.3349.1 | 4 | |||
5.4 | even | 2 | 4650.2.a.by.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.a.r.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2790.2.a.bd.1.2 | 2 | 3.2 | odd | 2 | |||
4650.2.a.by.1.1 | 2 | 5.4 | even | 2 | |||
4650.2.d.bh.3349.1 | 4 | 5.3 | odd | 4 | |||
4650.2.d.bh.3349.4 | 4 | 5.2 | odd | 4 | |||
7440.2.a.bg.1.1 | 2 | 4.3 | odd | 2 |