Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.56155 | 0.968176 | 0.484088 | − | 0.875019i | \(-0.339151\pi\) | ||||
0.484088 | + | 0.875019i | \(0.339151\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.56155 | −0.987797 | −0.493899 | − | 0.869520i | \(-0.664429\pi\) | ||||
−0.493899 | + | 0.869520i | \(0.664429\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.56155 | 0.403191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.43845 | 0.348875 | 0.174437 | − | 0.984668i | \(-0.444189\pi\) | ||||
0.174437 | + | 0.984668i | \(0.444189\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.00000 | −0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.12311 | −1.50842 | −0.754211 | − | 0.656632i | \(-0.771981\pi\) | ||||
−0.754211 | + | 0.656632i | \(0.771981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.123106 | −0.0221104 | −0.0110552 | − | 0.999939i | \(-0.503519\pi\) | ||||
−0.0110552 | + | 0.999939i | \(0.503519\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.12311 | −0.543663 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.56155 | −0.432981 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.561553 | 0.0923187 | 0.0461594 | − | 0.998934i | \(-0.485302\pi\) | ||||
0.0461594 | + | 0.998934i | \(0.485302\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.56155 | 0.890561 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.12311 | 0.643921 | 0.321960 | − | 0.946753i | \(-0.395658\pi\) | ||||
0.321960 | + | 0.946753i | \(0.395658\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.24621 | −0.952538 | −0.476269 | − | 0.879300i | \(-0.658011\pi\) | ||||
−0.476269 | + | 0.879300i | \(0.658011\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.561553 | 0.0837114 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.68466 | 1.26679 | 0.633394 | − | 0.773830i | \(-0.281661\pi\) | ||||
0.633394 | + | 0.773830i | \(0.281661\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.438447 | −0.0626353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.24621 | −0.314532 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.56155 | 1.17602 | 0.588010 | − | 0.808854i | \(-0.299912\pi\) | ||||
0.588010 | + | 0.808854i | \(0.299912\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.12311 | −0.413665 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.43845 | 0.187270 | 0.0936349 | − | 0.995607i | \(-0.470151\pi\) | ||||
0.0936349 | + | 0.995607i | \(0.470151\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.876894 | −0.112275 | −0.0561374 | − | 0.998423i | \(-0.517878\pi\) | ||||
−0.0561374 | + | 0.998423i | \(0.517878\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.43845 | −0.181227 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.56155 | 0.441756 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.43845 | 0.908751 | 0.454375 | − | 0.890810i | \(-0.349862\pi\) | ||||
0.454375 | + | 0.890810i | \(0.349862\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.56155 | −0.187989 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.00000 | 0.593391 | 0.296695 | − | 0.954972i | \(-0.404115\pi\) | ||||
0.296695 | + | 0.954972i | \(0.404115\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.56155 | 0.885013 | 0.442506 | − | 0.896765i | \(-0.354089\pi\) | ||||
0.442506 | + | 0.896765i | \(0.354089\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.56155 | −0.180313 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.12311 | 0.583832 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.876894 | 0.0986583 | 0.0493292 | − | 0.998783i | \(-0.484292\pi\) | ||||
0.0493292 | + | 0.998783i | \(0.484292\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.68466 | −0.843501 | −0.421750 | − | 0.906712i | \(-0.638584\pi\) | ||||
−0.421750 | + | 0.906712i | \(0.638584\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.43845 | −0.156022 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.6847 | 1.35994 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.00000 | 0.847998 | 0.423999 | − | 0.905663i | \(-0.360626\pi\) | ||||
0.423999 | + | 0.905663i | \(0.360626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.12311 | −0.956361 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.192236 | 0.0199339 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.00000 | −0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.12311 | 0.520173 | 0.260086 | − | 0.965585i | \(-0.416249\pi\) | ||||
0.260086 | + | 0.965585i | \(0.416249\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.12311 | −0.112876 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.8078 | 1.07541 | 0.537706 | − | 0.843132i | \(-0.319291\pi\) | ||||
0.537706 | + | 0.843132i | \(0.319291\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2462 | 1.40372 | 0.701860 | − | 0.712314i | \(-0.252353\pi\) | ||||
0.701860 | + | 0.712314i | \(0.252353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.00000 | 0.390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.68466 | 0.162862 | 0.0814310 | − | 0.996679i | \(-0.474051\pi\) | ||||
0.0814310 | + | 0.996679i | \(0.474051\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.12311 | −0.107574 | −0.0537870 | − | 0.998552i | \(-0.517129\pi\) | ||||
−0.0537870 | + | 0.998552i | \(0.517129\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.876894 | −0.0832311 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.43845 | 0.511606 | 0.255803 | − | 0.966729i | \(-0.417660\pi\) | ||||
0.255803 | + | 0.966729i | \(0.417660\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.68466 | 0.337772 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.43845 | −0.580535 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.8078 | 1.75765 | 0.878827 | − | 0.477140i | \(-0.158326\pi\) | ||||
0.878827 | + | 0.477140i | \(0.158326\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.75379 | 0.858773 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.9309 | 1.65400 | 0.826999 | − | 0.562204i | \(-0.190046\pi\) | ||||
0.826999 | + | 0.562204i | \(0.190046\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.12311 | 0.444230 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.56155 | −0.478662 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.6155 | 1.84674 | 0.923370 | − | 0.383912i | \(-0.125423\pi\) | ||||
0.923370 | + | 0.383912i | \(0.125423\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.3693 | 0.879514 | 0.439757 | − | 0.898117i | \(-0.355065\pi\) | ||||
0.439757 | + | 0.898117i | \(0.355065\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.5616 | −1.14209 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.12311 | −0.595664 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.12311 | 0.674587 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.684658 | 0.0564697 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.876894 | 0.0718380 | 0.0359190 | − | 0.999355i | \(-0.488564\pi\) | ||||
0.0359190 | + | 0.999355i | \(0.488564\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.56155 | −0.127077 | −0.0635387 | − | 0.997979i | \(-0.520239\pi\) | ||||
−0.0635387 | + | 0.997979i | \(0.520239\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.807764 | −0.0653039 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.123106 | 0.00988808 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.6847 | −1.25177 | −0.625886 | − | 0.779915i | \(-0.715262\pi\) | ||||
−0.625886 | + | 0.779915i | \(0.715262\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.3693 | −1.06026 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.56155 | 0.201879 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.68466 | 0.523583 | 0.261791 | − | 0.965124i | \(-0.415687\pi\) | ||||
0.261791 | + | 0.965124i | \(0.415687\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.12311 | 0.243133 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.315342 | −0.0242570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.12311 | −0.0858860 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.12311 | −0.541560 | −0.270780 | − | 0.962641i | \(-0.587282\pi\) | ||||
−0.270780 | + | 0.962641i | \(0.587282\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.56155 | 0.193635 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.24621 | −0.168836 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.31534 | 0.546774 | 0.273387 | − | 0.961904i | \(-0.411856\pi\) | ||||
0.273387 | + | 0.961904i | \(0.411856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.87689 | −0.659814 | −0.329907 | − | 0.944013i | \(-0.607017\pi\) | ||||
−0.329907 | + | 0.944013i | \(0.607017\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.36932 | 0.101223 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.561553 | −0.0412862 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.87689 | 0.210379 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.2462 | 1.03626 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.12311 | 0.225980 | 0.112990 | − | 0.993596i | \(-0.463957\pi\) | ||||
0.112990 | + | 0.993596i | \(0.463957\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.9309 | 1.36267 | 0.681337 | − | 0.731970i | \(-0.261399\pi\) | ||||
0.681337 | + | 0.731970i | \(0.261399\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.56155 | −0.398271 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.8078 | 1.26875 | 0.634375 | − | 0.773025i | \(-0.281257\pi\) | ||||
0.634375 | + | 0.773025i | \(0.281257\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.0000 | −1.27599 | −0.637993 | − | 0.770042i | \(-0.720235\pi\) | ||||
−0.637993 | + | 0.770042i | \(0.720235\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.6155 | −0.819296 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.8078 | −1.46042 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.12311 | −0.287970 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.561553 | −0.0390306 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.93087 | 0.683669 | 0.341835 | − | 0.939760i | \(-0.388952\pi\) | ||||
0.341835 | + | 0.939760i | \(0.388952\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.80776 | −0.534979 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.24621 | 0.425988 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.315342 | −0.0214068 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.8078 | −0.797895 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.12311 | −0.344617 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.8769 | −1.26409 | −0.632045 | − | 0.774932i | \(-0.717784\pi\) | ||||
−0.632045 | + | 0.774932i | \(0.717784\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.561553 | −0.0374369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.2462 | −1.21104 | −0.605522 | − | 0.795829i | \(-0.707036\pi\) | ||||
−0.605522 | + | 0.795829i | \(0.707036\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.75379 | −0.380221 | −0.190111 | − | 0.981763i | \(-0.560885\pi\) | ||||
−0.190111 | + | 0.981763i | \(0.560885\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.3002 | 1.85401 | 0.927003 | − | 0.375053i | \(-0.122375\pi\) | ||||
0.927003 | + | 0.375053i | \(0.122375\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.68466 | −0.566525 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.36932 | −0.0889467 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.87689 | 0.509514 | 0.254757 | − | 0.967005i | \(-0.418005\pi\) | ||||
0.254757 | + | 0.967005i | \(0.418005\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.4924 | −1.19120 | −0.595601 | − | 0.803281i | \(-0.703086\pi\) | ||||
−0.595601 | + | 0.803281i | \(0.703086\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.438447 | 0.0280114 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.12311 | −0.453232 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.12311 | −0.575845 | −0.287923 | − | 0.957654i | \(-0.592965\pi\) | ||||
−0.287923 | + | 0.957654i | \(0.592965\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.24621 | 0.140663 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.684658 | −0.0427078 | −0.0213539 | − | 0.999772i | \(-0.506798\pi\) | ||||
−0.0213539 | + | 0.999772i | \(0.506798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.43845 | 0.0893808 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.56155 | 0.282353 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.3153 | 0.882722 | 0.441361 | − | 0.897330i | \(-0.354496\pi\) | ||||
0.441361 | + | 0.897330i | \(0.354496\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.56155 | −0.525932 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.4924 | −0.764524 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.4924 | −1.67624 | −0.838121 | − | 0.545484i | \(-0.816346\pi\) | ||||
−0.838121 | + | 0.545484i | \(0.816346\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.1771 | −1.46865 | −0.734327 | − | 0.678796i | \(-0.762502\pi\) | ||||
−0.734327 | + | 0.678796i | \(0.762502\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.2462 | 0.862220 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | 0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.4384 | −1.22803 | −0.614014 | − | 0.789295i | \(-0.710446\pi\) | ||||
−0.614014 | + | 0.789295i | \(0.710446\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.0691303 | 0.00413872 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.12311 | −0.544239 | −0.272119 | − | 0.962263i | \(-0.587725\pi\) | ||||
−0.272119 | + | 0.962263i | \(0.587725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.93087 | −0.233666 | −0.116833 | − | 0.993152i | \(-0.537274\pi\) | ||||
−0.116833 | + | 0.993152i | \(0.537274\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.12311 | 0.184997 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.5616 | 0.623429 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9309 | −0.878286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.00000 | −0.468968 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.5616 | 0.850695 | 0.425347 | − | 0.905030i | \(-0.360152\pi\) | ||||
0.425347 | + | 0.905030i | \(0.360152\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.43845 | −0.0837496 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.1231 | 0.645428 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.56155 | −0.205970 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | −0.922225 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.8769 | −0.969552 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.876894 | 0.0502108 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.3693 | 0.877173 | 0.438587 | − | 0.898689i | \(-0.355479\pi\) | ||||
0.438587 | + | 0.898689i | \(0.355479\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.2462 | −1.26554 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.19224 | 0.237720 | 0.118860 | − | 0.992911i | \(-0.462076\pi\) | ||||
0.118860 | + | 0.992911i | \(0.462076\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.9309 | −0.787419 | −0.393710 | − | 0.919235i | \(-0.628808\pi\) | ||||
−0.393710 | + | 0.919235i | \(0.628808\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.43845 | 0.0810473 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.3693 | 1.42488 | 0.712441 | − | 0.701732i | \(-0.247589\pi\) | ||||
0.712441 | + | 0.701732i | \(0.247589\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.2462 | −0.909613 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.63068 | −0.146830 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.87689 | 0.160075 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.56155 | −0.197559 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.75379 | 0.0969847 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.2462 | 1.22647 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.49242 | 0.191961 | 0.0959805 | − | 0.995383i | \(-0.469401\pi\) | ||||
0.0959805 | + | 0.995383i | \(0.469401\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.315342 | −0.0172806 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.43845 | −0.406406 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.1231 | 0.714861 | 0.357431 | − | 0.933940i | \(-0.383653\pi\) | ||||
0.357431 | + | 0.933940i | \(0.383653\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.49242 | −0.461245 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.246211 | −0.0133331 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.0540 | −1.02882 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.56155 | 0.0840712 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.2462 | 0.764777 | 0.382388 | − | 0.924002i | \(-0.375102\pi\) | ||||
0.382388 | + | 0.924002i | \(0.375102\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.12311 | −0.220705 | −0.110352 | − | 0.993893i | \(-0.535198\pi\) | ||||
−0.110352 | + | 0.993893i | \(0.535198\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.8078 | −1.05726 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.19224 | 0.223130 | 0.111565 | − | 0.993757i | \(-0.464414\pi\) | ||||
0.111565 | + | 0.993757i | \(0.464414\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.00000 | −0.265372 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.75379 | −0.304523 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.1231 | −0.587055 | −0.293528 | − | 0.955951i | \(-0.594829\pi\) | ||||
−0.293528 | + | 0.955951i | \(0.594829\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.9309 | 0.573722 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.56155 | −0.395790 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.1922 | 0.584230 | 0.292115 | − | 0.956383i | \(-0.405641\pi\) | ||||
0.292115 | + | 0.956383i | \(0.405641\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.31534 | −0.120532 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.9309 | 1.13859 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.7386 | 1.28092 | 0.640459 | − | 0.767992i | \(-0.278744\pi\) | ||||
0.640459 | + | 0.767992i | \(0.278744\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.56155 | 0.0806382 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.9309 | 1.49002 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.9848 | 1.69432 | 0.847159 | − | 0.531340i | \(-0.178311\pi\) | ||||
0.847159 | + | 0.531340i | \(0.178311\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −30.9309 | −1.58464 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.9309 | 0.711834 | 0.355917 | − | 0.934518i | \(-0.384169\pi\) | ||||
0.355917 | + | 0.934518i | \(0.384169\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.12311 | −0.261098 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.50758 | 0.178300 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.8769 | −0.957097 | −0.478548 | − | 0.878061i | \(-0.658837\pi\) | ||||
−0.478548 | + | 0.878061i | \(0.658837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.43845 | 0.0727454 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.5616 | −1.49118 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.876894 | −0.0441213 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.1771 | −1.06285 | −0.531424 | − | 0.847106i | \(-0.678343\pi\) | ||||
−0.531424 | + | 0.847106i | \(0.678343\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.7386 | −1.63489 | −0.817445 | − | 0.576007i | \(-0.804610\pi\) | ||||
−0.817445 | + | 0.576007i | \(0.804610\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.438447 | 0.0218406 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.00000 | 0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.12311 | 0.0556703 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | 0.247234 | 0.123617 | − | 0.992330i | \(-0.460551\pi\) | ||||
0.123617 | + | 0.992330i | \(0.460551\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −33.7538 | −1.66495 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.68466 | 0.181310 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.68466 | 0.377225 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.1922 | −0.792937 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.6155 | 1.05599 | 0.527994 | − | 0.849248i | \(-0.322944\pi\) | ||||
0.527994 | + | 0.849248i | \(0.322944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.8769 | −1.50485 | −0.752424 | − | 0.658679i | \(-0.771115\pi\) | ||||
−0.752424 | + | 0.658679i | \(0.771115\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.87689 | −0.237123 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.43845 | 0.0697749 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.24621 | −0.108702 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.1231 | 0.537029 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.2462 | −1.45691 | −0.728454 | − | 0.685094i | \(-0.759761\pi\) | ||||
−0.728454 | + | 0.685094i | \(0.759761\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.6847 | −0.657643 | −0.328821 | − | 0.944392i | \(-0.606651\pi\) | ||||
−0.328821 | + | 0.944392i | \(0.606651\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.6847 | −0.608183 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.00000 | 0.0956730 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.80776 | 0.181735 | 0.0908673 | − | 0.995863i | \(-0.471036\pi\) | ||||
0.0908673 | + | 0.995863i | \(0.471036\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.246211 | 0.0117243 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.0540 | −1.04782 | −0.523908 | − | 0.851775i | \(-0.675526\pi\) | ||||
−0.523908 | + | 0.851775i | \(0.675526\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.00000 | −0.379236 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.36932 | −0.0647665 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.3153 | 0.864354 | 0.432177 | − | 0.901789i | \(-0.357745\pi\) | ||||
0.432177 | + | 0.901789i | \(0.357745\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.24621 | 0.388299 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.43845 | 0.114568 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.12311 | 0.427698 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.9309 | −0.838771 | −0.419385 | − | 0.907808i | \(-0.637754\pi\) | ||||
−0.419385 | + | 0.907808i | \(0.637754\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.00000 | 0.373408 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.1771 | −1.82466 | −0.912329 | − | 0.409457i | \(-0.865718\pi\) | ||||
−0.912329 | + | 0.409457i | \(0.865718\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.1231 | 1.35347 | 0.676733 | − | 0.736229i | \(-0.263395\pi\) | ||||
0.676733 | + | 0.736229i | \(0.263395\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.192236 | −0.00891473 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.68466 | 0.448153 | 0.224076 | − | 0.974572i | \(-0.428064\pi\) | ||||
0.224076 | + | 0.974572i | \(0.428064\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.0540 | 0.879831 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.4924 | 1.12855 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.4924 | −0.574402 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.80776 | −0.220132 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.00000 | 0.182765 | 0.0913823 | − | 0.995816i | \(-0.470871\pi\) | ||||
0.0913823 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | −0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.00000 | −0.182006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.12311 | −0.232628 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.684658 | −0.0310248 | −0.0155124 | − | 0.999880i | \(-0.504938\pi\) | ||||
−0.0155124 | + | 0.999880i | \(0.504938\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.4384 | −0.472043 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.6155 | 0.569331 | 0.284665 | − | 0.958627i | \(-0.408118\pi\) | ||||
0.284665 | + | 0.958627i | \(0.408118\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.6847 | −0.526251 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.12311 | 0.0504798 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.8078 | 0.574507 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.7386 | 1.77895 | 0.889473 | − | 0.456988i | \(-0.151072\pi\) | ||||
0.889473 | + | 0.456988i | \(0.151072\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.4924 | 0.558120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.4384 | −0.688366 | −0.344183 | − | 0.938903i | \(-0.611844\pi\) | ||||
−0.344183 | + | 0.938903i | \(0.611844\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.8078 | −0.480939 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.492423 | 0.0218693 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.4384 | −1.08322 | −0.541608 | − | 0.840631i | \(-0.682184\pi\) | ||||
−0.541608 | + | 0.840631i | \(0.682184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.3693 | 0.856848 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.1231 | 0.491097 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.2462 | −0.627763 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.3693 | 0.763902 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.1231 | 0.488250 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.8617 | 1.04540 | 0.522701 | − | 0.852516i | \(-0.324924\pi\) | ||||
0.522701 | + | 0.852516i | \(0.324924\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.2462 | −0.448036 | −0.224018 | − | 0.974585i | \(-0.571917\pi\) | ||||
−0.224018 | + | 0.974585i | \(0.571917\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.00000 | −0.174574 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.177081 | −0.00771377 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.807764 | −0.0350540 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.6847 | −0.636063 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.68466 | −0.0728341 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.4233 | −0.492951 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.876894 | −0.0377705 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.0540 | 0.690214 | 0.345107 | − | 0.938563i | \(-0.387843\pi\) | ||||
0.345107 | + | 0.938563i | \(0.387843\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.8617 | 0.594864 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.12311 | 0.0481086 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.31534 | 0.312781 | 0.156391 | − | 0.987695i | \(-0.450014\pi\) | ||||
0.156391 | + | 0.987695i | \(0.450014\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.492423 | 0.0210161 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.2462 | −0.692112 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.24621 | 0.0955186 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.876894 | 0.0372221 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.3002 | −0.902518 | −0.451259 | − | 0.892393i | \(-0.649025\pi\) | ||||
−0.451259 | + | 0.892393i | \(0.649025\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.2462 | 0.940914 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.49242 | −0.189670 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.1922 | 0.471697 | 0.235848 | − | 0.971790i | \(-0.424213\pi\) | ||||
0.235848 | + | 0.971790i | \(0.424213\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.43845 | −0.228797 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.9309 | −0.753026 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 44.7386 | 1.87554 | 0.937771 | − | 0.347256i | \(-0.112886\pi\) | ||||
0.937771 | + | 0.347256i | \(0.112886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.7386 | 1.28637 | 0.643186 | − | 0.765710i | \(-0.277612\pi\) | ||||
0.643186 | + | 0.765710i | \(0.277612\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.87689 | −0.203735 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.31534 | −0.304542 | −0.152271 | − | 0.988339i | \(-0.548659\pi\) | ||||
−0.152271 | + | 0.988339i | \(0.548659\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.5616 | −1.22854 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.6847 | −0.816657 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.1231 | 0.709167 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.00000 | −0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.3002 | 0.425134 | 0.212567 | − | 0.977146i | \(-0.431818\pi\) | ||||
0.212567 | + | 0.977146i | \(0.431818\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.246211 | −0.0101450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.8078 | −1.14386 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.3542 | −1.73928 | −0.869638 | − | 0.493689i | \(-0.835648\pi\) | ||||
−0.869638 | + | 0.493689i | \(0.835648\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.68466 | −0.151056 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 28.1080 | 1.15038 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.0000 | 0.653742 | 0.326871 | − | 0.945069i | \(-0.394006\pi\) | ||||
0.326871 | + | 0.945069i | \(0.394006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.8617 | 0.687805 | 0.343902 | − | 0.939005i | \(-0.388251\pi\) | ||||
0.343902 | + | 0.939005i | \(0.388251\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.17708 | −0.170104 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | 0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.0000 | −1.46119 | −0.730597 | − | 0.682808i | \(-0.760758\pi\) | ||||
−0.730597 | + | 0.682808i | \(0.760758\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 32.4924 | 1.31666 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.9309 | −1.25133 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.61553 | −0.388368 | −0.194184 | − | 0.980965i | \(-0.562206\pi\) | ||||
−0.194184 | + | 0.980965i | \(0.562206\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.43845 | 0.259623 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.30019 | −0.293894 | −0.146947 | − | 0.989144i | \(-0.546945\pi\) | ||||
−0.146947 | + | 0.989144i | \(0.546945\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.4924 | −1.78830 | −0.894151 | − | 0.447766i | \(-0.852220\pi\) | ||||
−0.894151 | + | 0.447766i | \(0.852220\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.56155 | 0.223177 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.4924 | 0.821012 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.24621 | −0.249450 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.807764 | 0.0322077 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.7386 | −0.586736 | −0.293368 | − | 0.956000i | \(-0.594776\pi\) | ||||
−0.293368 | + | 0.956000i | \(0.594776\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.5076 | −0.616371 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.8078 | −0.786047 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.56155 | 0.0618710 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.80776 | −0.111073 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.87689 | 0.113630 | 0.0568152 | − | 0.998385i | \(-0.481905\pi\) | ||||
0.0568152 | + | 0.998385i | \(0.481905\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.1771 | 0.874579 | 0.437289 | − | 0.899321i | \(-0.355939\pi\) | ||||
0.437289 | + | 0.899321i | \(0.355939\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.75379 | −0.384055 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.1771 | −0.439416 | −0.219708 | − | 0.975566i | \(-0.570511\pi\) | ||||
−0.219708 | + | 0.975566i | \(0.570511\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.87689 | 0.112928 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.492423 | 0.0192996 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.4233 | 1.15142 | 0.575711 | − | 0.817653i | \(-0.304725\pi\) | ||||
0.575711 | + | 0.817653i | \(0.304725\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.9309 | −0.739690 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.24621 | −0.165660 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.6155 | 1.15366 | 0.576829 | − | 0.816865i | \(-0.304290\pi\) | ||||
0.576829 | + | 0.816865i | \(0.304290\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.7538 | 1.07950 | 0.539749 | − | 0.841826i | \(-0.318519\pi\) | ||||
0.539749 | + | 0.841826i | \(0.318519\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.00000 | 0.310694 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.12311 | −0.198666 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.12311 | −0.314528 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29.4773 | 1.13966 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.75379 | −0.0677043 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.1922 | −0.624165 | −0.312082 | − | 0.950055i | \(-0.601027\pi\) | ||||
−0.312082 | + | 0.950055i | \(0.601027\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.56155 | 0.214064 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.68466 | 0.218479 | 0.109240 | − | 0.994015i | \(-0.465158\pi\) | ||||
0.109240 | + | 0.994015i | \(0.465158\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.1231 | 0.503619 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.4924 | 1.09183 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.93087 | −0.265202 | −0.132601 | − | 0.991169i | \(-0.542333\pi\) | ||||
−0.132601 | + | 0.991169i | \(0.542333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.6155 | −0.825887 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.98485 | 0.342793 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.4924 | −1.16167 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.492423 | 0.0187326 | 0.00936632 | − | 0.999956i | \(-0.497019\pi\) | ||||
0.00936632 | + | 0.999956i | \(0.497019\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.87689 | −0.109284 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.3693 | −0.393331 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.93087 | 0.224648 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −44.1922 | −1.67150 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.75379 | 0.368396 | 0.184198 | − | 0.982889i | \(-0.441031\pi\) | ||||
0.184198 | + | 0.982889i | \(0.441031\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.12311 | 0.0423587 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.5616 | 0.510758 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.6847 | 1.04119 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0000 | −0.600893 | −0.300446 | − | 0.953799i | \(-0.597136\pi\) | ||||
−0.300446 | + | 0.953799i | \(0.597136\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.492423 | −0.0184673 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.123106 | −0.00461034 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.12311 | 0.266389 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.3002 | −0.459359 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.68466 | 0.137415 | 0.0687073 | − | 0.997637i | \(-0.478113\pi\) | ||||
0.0687073 | + | 0.997637i | \(0.478113\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.4924 | 1.35905 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.8769 | 1.07394 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.12311 | −0.301685 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.4384 | −0.424229 | −0.212114 | − | 0.977245i | \(-0.568035\pi\) | ||||
−0.212114 | + | 0.977245i | \(0.568035\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.98485 | −0.332316 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.1771 | 1.48397 | 0.741987 | − | 0.670414i | \(-0.233884\pi\) | ||||
0.741987 | + | 0.670414i | \(0.233884\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.684658 | −0.0252540 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.8769 | 0.547997 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.49242 | −0.0548996 | −0.0274498 | − | 0.999623i | \(-0.508739\pi\) | ||||
−0.0274498 | + | 0.999623i | \(0.508739\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.1231 | 0.408617 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.2462 | 1.69661 | 0.848304 | − | 0.529509i | \(-0.177624\pi\) | ||||
0.848304 | + | 0.529509i | \(0.177624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.876894 | −0.0321269 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.31534 | 0.157890 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.31534 | 0.157679 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.3542 | −1.61851 | −0.809253 | − | 0.587460i | \(-0.800128\pi\) | ||||
−0.809253 | + | 0.587460i | \(0.800128\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.2462 | 0.519161 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.56155 | 0.0568307 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.5464 | −0.928500 | −0.464250 | − | 0.885704i | \(-0.653676\pi\) | ||||
−0.464250 | + | 0.885704i | \(0.653676\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.12311 | −0.113362 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.9848 | 0.796950 | 0.398475 | − | 0.917179i | \(-0.369540\pi\) | ||||
0.398475 | + | 0.917179i | \(0.369540\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.87689 | −0.104151 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.807764 | 0.0292048 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.12311 | −0.184985 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.61553 | −0.274623 | −0.137311 | − | 0.990528i | \(-0.543846\pi\) | ||||
−0.137311 | + | 0.990528i | \(0.543846\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.06913 | 0.0385038 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.1231 | −1.04749 | −0.523743 | − | 0.851877i | \(-0.675465\pi\) | ||||
−0.523743 | + | 0.851877i | \(0.675465\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.123106 | −0.00442208 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.24621 | −0.0805824 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.24621 | 0.295451 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | 0.357828 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −45.1771 | −1.61450 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.6847 | 0.559809 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.3002 | 1.18702 | 0.593512 | − | 0.804825i | \(-0.297741\pi\) | ||||
0.593512 | + | 0.804825i | \(0.297741\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.3542 | −0.795829 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.9309 | 0.495325 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.12311 | 0.110905 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.3693 | 0.474161 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.1922 | 0.892355 | 0.446177 | − | 0.894945i | \(-0.352785\pi\) | ||||
0.446177 | + | 0.894945i | \(0.352785\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.4924 | 0.441950 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.49242 | −0.158732 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.1231 | 0.533683 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.56155 | −0.0902829 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 42.9309 | 1.51124 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.8078 | 1.78631 | 0.893153 | − | 0.449753i | \(-0.148488\pi\) | ||||
0.893153 | + | 0.449753i | \(0.148488\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.3693 | −0.504575 | −0.252287 | − | 0.967652i | \(-0.581183\pi\) | ||||
−0.252287 | + | 0.967652i | \(0.581183\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.7538 | 1.32408 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.68466 | −0.234153 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.4924 | −0.437055 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.12311 | 0.179016 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.4924 | 1.34339 | 0.671697 | − | 0.740826i | \(-0.265566\pi\) | ||||
0.671697 | + | 0.740826i | \(0.265566\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.1771 | 1.15648 | 0.578240 | − | 0.815867i | \(-0.303740\pi\) | ||||
0.578240 | + | 0.815867i | \(0.303740\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.12311 | −0.108733 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.3153 | −0.984621 | −0.492310 | − | 0.870420i | \(-0.663848\pi\) | ||||
−0.492310 | + | 0.870420i | \(0.663848\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.5616 | −0.714132 | −0.357066 | − | 0.934079i | \(-0.616223\pi\) | ||||
−0.357066 | + | 0.934079i | \(0.616223\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.9157 | 1.10714 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.630683 | −0.0218519 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000 | 0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.684658 | −0.0236653 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.6155 | 1.16054 | 0.580268 | − | 0.814425i | \(-0.302948\pi\) | ||||
0.580268 | + | 0.814425i | \(0.302948\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.9848 | 1.27534 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.2462 | 0.490666 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.315342 | 0.0108481 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.9309 | −0.616112 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.13826 | 0.210665 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.561553 | 0.0192498 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.4924 | −0.496211 | −0.248106 | − | 0.968733i | \(-0.579808\pi\) | ||||
−0.248106 | + | 0.968733i | \(0.579808\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.12311 | 0.0384094 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.5464 | −1.38504 | −0.692519 | − | 0.721399i | \(-0.743499\pi\) | ||||
−0.692519 | + | 0.721399i | \(0.743499\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.369317 | 0.0126009 | 0.00630046 | − | 0.999980i | \(-0.497994\pi\) | ||||
0.00630046 | + | 0.999980i | \(0.497994\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.4924 | −0.562060 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.31534 | −0.317098 | −0.158549 | − | 0.987351i | \(-0.550682\pi\) | ||||
−0.158549 | + | 0.987351i | \(0.550682\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.12311 | 0.242193 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.3153 | 0.791831 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.75379 | 0.0594932 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.4924 | −0.897661 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.87689 | −0.0973681 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.56155 | −0.0865963 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.4773 | −1.60319 | −0.801597 | − | 0.597865i | \(-0.796016\pi\) | ||||
−0.801597 | + | 0.597865i | \(0.796016\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.7386 | −0.766955 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.7386 | 0.766084 | 0.383042 | − | 0.923731i | \(-0.374876\pi\) | ||||
0.383042 | + | 0.923731i | \(0.374876\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.9848 | −1.51386 | −0.756930 | − | 0.653496i | \(-0.773302\pi\) | ||||
−0.756930 | + | 0.653496i | \(0.773302\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.24621 | 0.0755056 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.1771 | −1.44974 | −0.724872 | − | 0.688883i | \(-0.758101\pi\) | ||||
−0.724872 | + | 0.688883i | \(0.758101\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 50.7386 | 1.70172 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.0000 | −0.469018 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.3693 | 0.581242 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.31534 | −0.244525 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.56155 | 0.185695 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.00000 | 0.0333519 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.3153 | 0.410284 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.9848 | 0.831444 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.87689 | 0.295078 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.4233 | 0.810962 | 0.405481 | − | 0.914103i | \(-0.367104\pi\) | ||||
0.405481 | + | 0.914103i | \(0.367104\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.06913 | −0.201300 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.1231 | −0.766103 | −0.383051 | − | 0.923727i | \(-0.625127\pi\) | ||||
−0.383051 | + | 0.923727i | \(0.625127\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.3693 | −0.508650 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.36932 | −0.0452682 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 48.4924 | 1.60136 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.4924 | 0.675983 | 0.337991 | − | 0.941149i | \(-0.390253\pi\) | ||||
0.337991 | + | 0.941149i | \(0.390253\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.0000 | −0.790827 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.8078 | −0.586150 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.561553 | 0.0184637 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.00000 | −0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.261366 | 0.00857515 | 0.00428757 | − | 0.999991i | \(-0.498635\pi\) | ||||
0.00428757 | + | 0.999991i | \(0.498635\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.876894 | −0.0287391 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.54640 | −0.214319 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.87689 | −0.0940845 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.7538 | 0.709908 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.4924 | 1.05922 | 0.529611 | − | 0.848240i | \(-0.322338\pi\) | ||||
0.529611 | + | 0.848240i | \(0.322338\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.12311 | 0.134267 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.2462 | −0.463429 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.5616 | −0.570674 | −0.285337 | − | 0.958427i | \(-0.592105\pi\) | ||||
−0.285337 | + | 0.958427i | \(0.592105\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.9309 | −0.874213 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39.6155 | −1.28462 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.2462 | −1.43328 | −0.716638 | − | 0.697446i | \(-0.754320\pi\) | ||||
−0.716638 | + | 0.697446i | \(0.754320\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.12311 | −0.101061 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.3693 | 0.820074 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 55.3693 | 1.78797 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9848 | −0.999511 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.946025 | −0.0304852 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.9309 | −0.609406 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.17708 | −0.295115 | −0.147558 | − | 0.989053i | \(-0.547141\pi\) | ||||
−0.147558 | + | 0.989053i | \(0.547141\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.49242 | −0.144317 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.1080 | 1.28713 | 0.643563 | − | 0.765393i | \(-0.277456\pi\) | ||||
0.643563 | + | 0.765393i | \(0.277456\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.5616 | 0.851524 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.56155 | 0.178112 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.6847 | 1.71752 | 0.858762 | − | 0.512374i | \(-0.171234\pi\) | ||||
0.858762 | + | 0.512374i | \(0.171234\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.0000 | 0.511362 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.630683 | 0.0201362 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −62.0388 | −1.97873 | −0.989366 | − | 0.145450i | \(-0.953537\pi\) | ||||
−0.989366 | + | 0.145450i | \(0.953537\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.8078 | −0.567403 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −34.7386 | −1.10574 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.24621 | −0.198618 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.5616 | −0.716691 | −0.358346 | − | 0.933589i | \(-0.616659\pi\) | ||||
−0.358346 | + | 0.933589i | \(0.616659\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.45360 | −0.173065 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.0000 | 0.570638 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.1080 | 0.890188 | 0.445094 | − | 0.895484i | \(-0.353170\pi\) | ||||
0.445094 | + | 0.895484i | \(0.353170\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.12311 | 0.0988107 |
(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 | 1840.2.a.o.1.1 | 2 | ||
4.3 | odd | 2 | 920.2.a.e.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 9200.2.a.bq.1.2 | 2 | |||
8.3 | odd | 2 | 7360.2.a.bp.1.1 | 2 | |||
8.5 | even | 2 | 7360.2.a.bl.1.2 | 2 | |||
12.11 | even | 2 | 8280.2.a.bf.1.1 | 2 | |||
20.3 | even | 4 | 4600.2.e.n.4049.3 | 4 | |||
20.7 | even | 4 | 4600.2.e.n.4049.2 | 4 | |||
20.19 | odd | 2 | 4600.2.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.e.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
1840.2.a.o.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4600.2.a.t.1.1 | 2 | 20.19 | odd | 2 | |||
4600.2.e.n.4049.2 | 4 | 20.7 | even | 4 | |||
4600.2.e.n.4049.3 | 4 | 20.3 | even | 4 | |||
7360.2.a.bl.1.2 | 2 | 8.5 | even | 2 | |||
7360.2.a.bp.1.1 | 2 | 8.3 | odd | 2 | |||
8280.2.a.bf.1.1 | 2 | 12.11 | even | 2 | |||
9200.2.a.bq.1.2 | 2 | 5.4 | even | 2 |