Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6080,2,Mod(1,6080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, 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("6080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6080 = 2^{6} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6080.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: | \(48.5490444289\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3040) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6080.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843 | 1.06904 | 0.534522 | − | 0.845154i | \(-0.320491\pi\) | ||||
0.534522 | + | 0.845154i | \(0.320491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.82843 | −1.33916 | −0.669582 | − | 0.742738i | \(-0.733527\pi\) | ||||
−0.669582 | + | 0.742738i | \(0.733527\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.65685 | 1.85706 | 0.928530 | − | 0.371257i | \(-0.121073\pi\) | ||||
0.928530 | + | 0.371257i | \(0.121073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.65685 | 0.679061 | 0.339530 | − | 0.940595i | \(-0.389732\pi\) | ||||
0.339530 | + | 0.940595i | \(0.389732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.65685 | −1.01600 | −0.508001 | − | 0.861357i | \(-0.669615\pi\) | ||||
−0.508001 | + | 0.861357i | \(0.669615\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.82843 | −0.478091 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.48528 | 1.06617 | 0.533087 | − | 0.846061i | \(-0.321032\pi\) | ||||
0.533087 | + | 0.846061i | \(0.321032\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.65685 | −0.571105 | −0.285552 | − | 0.958363i | \(-0.592177\pi\) | ||||
−0.285552 | + | 0.958363i | \(0.592177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.48528 | −1.29399 | −0.646997 | − | 0.762493i | \(-0.723975\pi\) | ||||
−0.646997 | + | 0.762493i | \(0.723975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | 0.447214 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.17157 | −0.754351 | −0.377176 | − | 0.926142i | \(-0.623105\pi\) | ||||
−0.377176 | + | 0.926142i | \(0.623105\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.17157 | −0.985091 | −0.492546 | − | 0.870287i | \(-0.663934\pi\) | ||||
−0.492546 | + | 0.870287i | \(0.663934\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.65685 | 1.25722 | 0.628608 | − | 0.777723i | \(-0.283625\pi\) | ||||
0.628608 | + | 0.777723i | \(0.283625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.48528 | −1.06904 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.82843 | 0.598893 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3137 | 1.38219 | 0.691095 | − | 0.722764i | \(-0.257129\pi\) | ||||
0.691095 | + | 0.722764i | \(0.257129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.6569 | 1.83250 | 0.916248 | − | 0.400611i | \(-0.131202\pi\) | ||||
0.916248 | + | 0.400611i | \(0.131202\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.3137 | −1.28932 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.65685 | 0.636446 | 0.318223 | − | 0.948016i | \(-0.396914\pi\) | ||||
0.318223 | + | 0.948016i | \(0.396914\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.17157 | 0.567654 | 0.283827 | − | 0.958876i | \(-0.408396\pi\) | ||||
0.283827 | + | 0.958876i | \(0.408396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.65685 | −0.830502 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.6569 | −1.23562 | −0.617812 | − | 0.786326i | \(-0.711981\pi\) | ||||
−0.617812 | + | 0.786326i | \(0.711981\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.6569 | −1.43163 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.17157 | 0.728163 | 0.364081 | − | 0.931367i | \(-0.381383\pi\) | ||||
0.364081 | + | 0.931367i | \(0.381383\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.0000 | 1.20605 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.0000 | −1.39305 | −0.696526 | − | 0.717532i | \(-0.745272\pi\) | ||||
−0.696526 | + | 0.717532i | \(0.745272\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.6569 | 1.73978 | 0.869891 | − | 0.493244i | \(-0.164189\pi\) | ||||
0.869891 | + | 0.493244i | \(0.164189\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.6569 | 1.32026 | 0.660129 | − | 0.751152i | \(-0.270502\pi\) | ||||
0.660129 | + | 0.751152i | \(0.270502\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.31371 | −0.508961 | −0.254480 | − | 0.967078i | \(-0.581904\pi\) | ||||
−0.254480 | + | 0.967078i | \(0.581904\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.4853 | 0.986372 | 0.493186 | − | 0.869924i | \(-0.335832\pi\) | ||||
0.493186 | + | 0.869924i | \(0.335832\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.82843 | −0.263752 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.4853 | 1.33916 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 21.6569 | 1.98528 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9706 | −1.15095 | −0.575476 | − | 0.817819i | \(-0.695183\pi\) | ||||
−0.575476 | + | 0.817819i | \(0.695183\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.65685 | 0.843723 | 0.421862 | − | 0.906660i | \(-0.361377\pi\) | ||||
0.421862 | + | 0.906660i | \(0.361377\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.82843 | 0.245256 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.6569 | 1.33766 | 0.668828 | − | 0.743417i | \(-0.266796\pi\) | ||||
0.668828 | + | 0.743417i | \(0.266796\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.9706 | 1.10015 | 0.550074 | − | 0.835116i | \(-0.314599\pi\) | ||||
0.550074 | + | 0.835116i | \(0.314599\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.3137 | 1.61509 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.65685 | −0.303685 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.31371 | −0.269666 | −0.134833 | − | 0.990868i | \(-0.543050\pi\) | ||||
−0.134833 | + | 0.990868i | \(0.543050\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −22.9706 | −1.85706 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.65685 | 0.454369 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.6569 | 1.24955 | 0.624777 | − | 0.780804i | \(-0.285190\pi\) | ||||
0.624777 | + | 0.780804i | \(0.285190\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.8284 | 1.47476 | 0.737378 | − | 0.675480i | \(-0.236064\pi\) | ||||
0.737378 | + | 0.675480i | \(0.236064\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.3137 | 1.80407 | 0.902034 | − | 0.431664i | \(-0.142073\pi\) | ||||
0.902034 | + | 0.431664i | \(0.142073\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3137 | 0.793362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | −0.229416 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.1421 | 0.923149 | 0.461575 | − | 0.887101i | \(-0.347285\pi\) | ||||
0.461575 | + | 0.887101i | \(0.347285\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.82843 | 0.213809 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.9706 | −0.969465 | −0.484733 | − | 0.874662i | \(-0.661083\pi\) | ||||
−0.484733 | + | 0.874662i | \(0.661083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.3137 | −0.989600 | −0.494800 | − | 0.869007i | \(-0.664759\pi\) | ||||
−0.494800 | + | 0.869007i | \(0.664759\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.48528 | −0.476807 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −30.6274 | −2.23970 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.9706 | 0.938517 | 0.469258 | − | 0.883061i | \(-0.344521\pi\) | ||||
0.469258 | + | 0.883061i | \(0.344521\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.82843 | −0.635484 | −0.317742 | − | 0.948177i | \(-0.602925\pi\) | ||||
−0.317742 | + | 0.948177i | \(0.602925\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.31371 | −0.0935979 | −0.0467989 | − | 0.998904i | \(-0.514902\pi\) | ||||
−0.0467989 | + | 0.998904i | \(0.514902\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.31371 | −0.518455 | −0.259228 | − | 0.965816i | \(-0.583468\pi\) | ||||
−0.259228 | + | 0.965816i | \(0.583468\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.3431 | 0.725947 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.65685 | 0.255406 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.48528 | −0.589768 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.48528 | 0.578691 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | −1.08615 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −36.9706 | −2.48691 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.6569 | 1.18239 | 0.591195 | − | 0.806529i | \(-0.298656\pi\) | ||||
0.591195 | + | 0.806529i | \(0.298656\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.65685 | −0.375459 | −0.187729 | − | 0.982221i | \(-0.560113\pi\) | ||||
−0.187729 | + | 0.982221i | \(0.560113\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.68629 | −0.177515 | −0.0887576 | − | 0.996053i | \(-0.528290\pi\) | ||||
−0.0887576 | + | 0.996053i | \(0.528290\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.31371 | −0.0860639 | −0.0430320 | − | 0.999074i | \(-0.513702\pi\) | ||||
−0.0430320 | + | 0.999074i | \(0.513702\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.17157 | 0.337356 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.97056 | −0.449013 | −0.224507 | − | 0.974473i | \(-0.572077\pi\) | ||||
−0.224507 | + | 0.974473i | \(0.572077\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.82843 | −0.307225 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.9706 | 1.32365 | 0.661825 | − | 0.749658i | \(-0.269782\pi\) | ||||
0.661825 | + | 0.749658i | \(0.269782\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.3137 | −0.711287 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.1716 | −0.696864 | −0.348432 | − | 0.937334i | \(-0.613286\pi\) | ||||
−0.348432 | + | 0.937334i | \(0.613286\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.3431 | 1.13979 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.9706 | −0.679061 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.48528 | −0.523225 | −0.261612 | − | 0.965173i | \(-0.584254\pi\) | ||||
−0.261612 | + | 0.965173i | \(0.584254\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.17157 | 0.440546 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0000 | −0.609711 | −0.304855 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304855 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.00000 | 0.242983 | 0.121491 | − | 0.992592i | \(-0.461232\pi\) | ||||
0.121491 | + | 0.992592i | \(0.461232\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.00000 | −0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.9706 | 1.13983 | 0.569915 | − | 0.821703i | \(-0.306976\pi\) | ||||
0.569915 | + | 0.821703i | \(0.306976\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.9706 | 1.01600 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.6569 | 0.934010 | 0.467005 | − | 0.884255i | \(-0.345333\pi\) | ||||
0.467005 | + | 0.884255i | \(0.345333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.51472 | −0.446704 | −0.223352 | − | 0.974738i | \(-0.571700\pi\) | ||||
−0.223352 | + | 0.974738i | \(0.571700\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.3431 | −0.610537 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.4853 | −0.612557 | −0.306278 | − | 0.951942i | \(-0.599084\pi\) | ||||
−0.306278 | + | 0.951942i | \(0.599084\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.65685 | −0.562244 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.6569 | −0.789796 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.0000 | −1.38334 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.65685 | −0.322854 | −0.161427 | − | 0.986885i | \(-0.551610\pi\) | ||||
−0.161427 | + | 0.986885i | \(0.551610\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.0000 | −1.13410 | −0.567048 | − | 0.823685i | \(-0.691915\pi\) | ||||
−0.567048 | + | 0.823685i | \(0.691915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.6274 | 0.939837 | 0.469919 | − | 0.882710i | \(-0.344283\pi\) | ||||
0.469919 | + | 0.882710i | \(0.344283\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.48528 | 0.478091 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.8284 | −0.720516 | −0.360258 | − | 0.932853i | \(-0.617311\pi\) | ||||
−0.360258 | + | 0.932853i | \(0.617311\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.6274 | −0.818978 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.65685 | 0.426039 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.82843 | −0.267833 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.6274 | −0.806436 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.68629 | 0.477442 | 0.238721 | − | 0.971088i | \(-0.423272\pi\) | ||||
0.238721 | + | 0.971088i | \(0.423272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.4558 | −1.06617 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.3137 | −0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.8284 | −0.916703 | −0.458351 | − | 0.888771i | \(-0.651560\pi\) | ||||
−0.458351 | + | 0.888771i | \(0.651560\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.6274 | 1.22534 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.1716 | −1.56601 | −0.783006 | − | 0.622014i | \(-0.786315\pi\) | ||||
−0.783006 | + | 0.622014i | \(0.786315\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.9411 | 1.92388 | 0.961942 | − | 0.273253i | \(-0.0880997\pi\) | ||||
0.961942 | + | 0.273253i | \(0.0880997\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.6569 | −1.04623 | −0.523114 | − | 0.852262i | \(-0.675230\pi\) | ||||
−0.523114 | + | 0.852262i | \(0.675230\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.65685 | 0.300235 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.6569 | 1.35412 | 0.677058 | − | 0.735929i | \(-0.263254\pi\) | ||||
0.677058 | + | 0.735929i | \(0.263254\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.6569 | −0.819517 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.4558 | 1.74638 | 0.873190 | − | 0.487379i | \(-0.162047\pi\) | ||||
0.873190 | + | 0.487379i | \(0.162047\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.9706 | 0.571105 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.2843 | −1.05311 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.1421 | 0.628696 | 0.314348 | − | 0.949308i | \(-0.398214\pi\) | ||||
0.314348 | + | 0.949308i | \(0.398214\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.6569 | −0.909374 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00000 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.00000 | 0.204390 | 0.102195 | − | 0.994764i | \(-0.467413\pi\) | ||||
0.102195 | + | 0.994764i | \(0.467413\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.3137 | 0.576600 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 25.4558 | 1.29399 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.6274 | −0.640235 | −0.320118 | − | 0.947378i | \(-0.603722\pi\) | ||||
−0.320118 | + | 0.947378i | \(0.603722\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.6569 | 1.09523 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.65685 | −0.284627 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.9706 | 1.35361 | 0.676807 | − | 0.736161i | \(-0.263363\pi\) | ||||
0.676807 | + | 0.736161i | \(0.263363\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.0000 | 1.29838 | 0.649189 | − | 0.760627i | \(-0.275108\pi\) | ||||
0.649189 | + | 0.760627i | \(0.275108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.3137 | 1.36059 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.00000 | −0.447214 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.9411 | −1.28585 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.3137 | 0.658321 | 0.329160 | − | 0.944274i | \(-0.393234\pi\) | ||||
0.329160 | + | 0.944274i | \(0.393234\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.3137 | 1.34402 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.17157 | −0.253863 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.686292 | 0.0335275 | 0.0167638 | − | 0.999859i | \(-0.494664\pi\) | ||||
0.0167638 | + | 0.999859i | \(0.494664\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.9706 | 1.11952 | 0.559758 | − | 0.828656i | \(-0.310894\pi\) | ||||
0.559758 | + | 0.828656i | \(0.310894\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.5147 | 0.754351 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.65685 | 0.371412 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.9706 | −0.821263 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.3137 | 1.70100 | 0.850501 | − | 0.525974i | \(-0.176299\pi\) | ||||
0.850501 | + | 0.525974i | \(0.176299\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.82843 | −0.424267 | −0.212134 | − | 0.977241i | \(-0.568041\pi\) | ||||
−0.212134 | + | 0.977241i | \(0.568041\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.82843 | 0.135302 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.9706 | −1.19178 | −0.595890 | − | 0.803066i | \(-0.703201\pi\) | ||||
−0.595890 | + | 0.803066i | \(0.703201\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.485281 | 0.0230564 | 0.0115282 | − | 0.999934i | \(-0.496330\pi\) | ||||
0.0115282 | + | 0.999934i | \(0.496330\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.6569 | 0.552588 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.3137 | −1.57217 | −0.786086 | − | 0.618118i | \(-0.787896\pi\) | ||||
−0.786086 | + | 0.618118i | \(0.787896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.6274 | 0.688778 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.6569 | 0.640243 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.0000 | −1.02912 | −0.514558 | − | 0.857455i | \(-0.672044\pi\) | ||||
−0.514558 | + | 0.857455i | \(0.672044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.00000 | 0.0931493 | 0.0465746 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465746 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.14214 | 0.285449 | 0.142725 | − | 0.989762i | \(-0.454414\pi\) | ||||
0.142725 | + | 0.989762i | \(0.454414\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.1421 | 0.654420 | 0.327210 | − | 0.944952i | \(-0.393892\pi\) | ||||
0.327210 | + | 0.944952i | \(0.393892\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.0000 | 1.47762 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.9411 | 1.56061 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.5147 | 0.985091 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.9706 | −0.958169 | −0.479085 | − | 0.877769i | \(-0.659031\pi\) | ||||
−0.479085 | + | 0.877769i | \(0.659031\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.3137 | −1.42778 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.17157 | −0.325644 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.6274 | 0.844089 | 0.422044 | − | 0.906575i | \(-0.361313\pi\) | ||||
0.422044 | + | 0.906575i | \(0.361313\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.9706 | 1.30742 | 0.653712 | − | 0.756744i | \(-0.273211\pi\) | ||||
0.653712 | + | 0.756744i | \(0.273211\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.0000 | 1.26106 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.0000 | −0.539360 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0000 | −0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.2843 | 1.80337 | 0.901686 | − | 0.432392i | \(-0.142330\pi\) | ||||
0.901686 | + | 0.432392i | \(0.142330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.4853 | −0.735042 | −0.367521 | − | 0.930015i | \(-0.619793\pi\) | ||||
−0.367521 | + | 0.930015i | \(0.619793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.0000 | 0.622992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.9706 | −0.486262 | −0.243131 | − | 0.969994i | \(-0.578174\pi\) | ||||
−0.243131 | + | 0.969994i | \(0.578174\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 44.2843 | 1.95902 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.6569 | −0.778054 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.6863 | 0.909782 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.68629 | 0.292932 | 0.146466 | − | 0.989216i | \(-0.453210\pi\) | ||||
0.146466 | + | 0.989216i | \(0.453210\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.9706 | 1.79152 | 0.895759 | − | 0.444540i | \(-0.146633\pi\) | ||||
0.895759 | + | 0.444540i | \(0.146633\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −43.3137 | −1.88677 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.9706 | −1.25722 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.6569 | 0.764803 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.6569 | −0.590437 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.00000 | −0.172292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.31371 | 0.227614 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.2843 | −1.55140 | −0.775702 | − | 0.631100i | \(-0.782604\pi\) | ||||
−0.775702 | + | 0.631100i | \(0.782604\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.0000 | 0.768221 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.65685 | 0.155787 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000 | 0.680389 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.9706 | 0.464838 | 0.232419 | − | 0.972616i | \(-0.425336\pi\) | ||||
0.232419 | + | 0.972616i | \(0.425336\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.9706 | 1.73287 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.6569 | 0.912728 | 0.456364 | − | 0.889793i | \(-0.349152\pi\) | ||||
0.456364 | + | 0.889793i | \(0.349152\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.4853 | −0.441119 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 25.4558 | 1.06904 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.9411 | −1.33904 | −0.669521 | − | 0.742793i | \(-0.733501\pi\) | ||||
−0.669521 | + | 0.742793i | \(0.733501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.82843 | 0.117954 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.62742 | 0.359164 | 0.179582 | − | 0.983743i | \(-0.442525\pi\) | ||||
0.179582 | + | 0.983743i | \(0.442525\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.6274 | 0.606848 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.6863 | 1.18806 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.4853 | −0.598893 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.14214 | 0.253513 | 0.126757 | − | 0.991934i | \(-0.459543\pi\) | ||||
0.126757 | + | 0.991934i | \(0.459543\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.65685 | −0.233087 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.6274 | −1.50411 | −0.752054 | − | 0.659102i | \(-0.770937\pi\) | ||||
−0.752054 | + | 0.659102i | \(0.770937\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.6569 | −0.887844 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.65685 | 0.231133 | 0.115566 | − | 0.993300i | \(-0.463132\pi\) | ||||
0.115566 | + | 0.993300i | \(0.463132\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.02944 | −0.205155 | −0.102578 | − | 0.994725i | \(-0.532709\pi\) | ||||
−0.102578 | + | 0.994725i | \(0.532709\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.9411 | −1.38219 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.00000 | −0.203279 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.0000 | −1.46119 | −0.730597 | − | 0.682808i | \(-0.760758\pi\) | ||||
−0.730597 | + | 0.682808i | \(0.760758\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.9706 | 1.01020 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.02944 | 0.0415786 | 0.0207893 | − | 0.999784i | \(-0.493382\pi\) | ||||
0.0207893 | + | 0.999784i | \(0.493382\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.5980 | 1.35260 | 0.676302 | − | 0.736625i | \(-0.263582\pi\) | ||||
0.676302 | + | 0.736625i | \(0.263582\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.5980 | −1.43080 | −0.715402 | − | 0.698713i | \(-0.753756\pi\) | ||||
−0.715402 | + | 0.698713i | \(0.753756\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.9706 | −1.32094 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 49.6569 | 1.97995 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.6274 | 0.741546 | 0.370773 | − | 0.928724i | \(-0.379093\pi\) | ||||
0.370773 | + | 0.928724i | \(0.379093\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.9706 | 0.514721 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.82843 | −0.191309 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.9706 | 0.671345 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.6569 | 1.25037 | 0.625185 | − | 0.780476i | \(-0.285023\pi\) | ||||
0.625185 | + | 0.780476i | \(0.285023\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 47.1127 | 1.85794 | 0.928972 | − | 0.370151i | \(-0.120694\pi\) | ||||
0.928972 | + | 0.370151i | \(0.120694\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.1421 | −0.870497 | −0.435249 | − | 0.900310i | \(-0.643340\pi\) | ||||
−0.435249 | + | 0.900310i | \(0.643340\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −38.6274 | −1.51626 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.343146 | −0.0134283 | −0.00671417 | − | 0.999977i | \(-0.502137\pi\) | ||||
−0.00671417 | + | 0.999977i | \(0.502137\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.65685 | −0.377325 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −46.9706 | −1.83250 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.65685 | −0.0645419 | −0.0322709 | − | 0.999479i | \(-0.510274\pi\) | ||||
−0.0322709 | + | 0.999479i | \(0.510274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.6569 | −0.920145 | −0.460072 | − | 0.887881i | \(-0.652177\pi\) | ||||
−0.460072 | + | 0.887881i | \(0.652177\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.82843 | −0.109682 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.3431 | 0.400488 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.1127 | −1.43059 | −0.715295 | − | 0.698823i | \(-0.753708\pi\) | ||||
−0.715295 | + | 0.698823i | \(0.753708\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.4264 | −1.70745 | −0.853723 | − | 0.520728i | \(-0.825661\pi\) | ||||
−0.853723 | + | 0.520728i | \(0.825661\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.2843 | 0.778439 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −44.2843 | −1.69449 | −0.847245 | − | 0.531202i | \(-0.821741\pi\) | ||||
−0.847245 | + | 0.531202i | \(0.821741\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.6569 | −0.598218 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.6274 | 1.31920 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.6863 | 0.634776 | 0.317388 | − | 0.948296i | \(-0.397194\pi\) | ||||
0.317388 | + | 0.948296i | \(0.397194\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 33.9411 | 1.28932 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.9706 | −0.492001 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.0000 | −1.06058 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.3137 | −1.56040 | −0.780199 | − | 0.625532i | \(-0.784882\pi\) | ||||
−0.780199 | + | 0.625532i | \(0.784882\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.48528 | 0.244597 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −39.5980 | −1.48924 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.9411 | −0.899128 | −0.449564 | − | 0.893248i | \(-0.648421\pi\) | ||||
−0.449564 | + | 0.893248i | \(0.648421\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.9706 | −0.636446 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.0000 | −0.599205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.3137 | −0.722292 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.2843 | −1.50235 | −0.751175 | − | 0.660103i | \(-0.770513\pi\) | ||||
−0.751175 | + | 0.660103i | \(0.770513\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.9411 | 1.85990 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.65685 | 0.135812 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.5147 | 0.575409 | 0.287705 | − | 0.957719i | \(-0.407108\pi\) | ||||
0.287705 | + | 0.957719i | \(0.407108\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −64.9706 | −2.40302 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.68629 | 0.246964 | 0.123482 | − | 0.992347i | \(-0.460594\pi\) | ||||
0.123482 | + | 0.992347i | \(0.460594\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −45.2548 | −1.66698 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.68629 | 0.319530 | 0.159765 | − | 0.987155i | \(-0.448926\pi\) | ||||
0.159765 | + | 0.987155i | \(0.448926\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.37258 | −0.197101 | −0.0985505 | − | 0.995132i | \(-0.531421\pi\) | ||||
−0.0985505 | + | 0.995132i | \(0.531421\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | 0.219823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.5147 | −0.567654 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38.6274 | 1.41142 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.6274 | −0.825686 | −0.412843 | − | 0.910802i | \(-0.635464\pi\) | ||||
−0.412843 | + | 0.910802i | \(0.635464\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.31371 | 0.120598 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.31371 | −0.0477475 | −0.0238738 | − | 0.999715i | \(-0.507600\pi\) | ||||
−0.0238738 | + | 0.999715i | \(0.507600\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.6274 | 0.892743 | 0.446372 | − | 0.894848i | \(-0.352716\pi\) | ||||
0.446372 | + | 0.894848i | \(0.352716\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.0294 | −0.544102 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22.9706 | 0.830502 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −46.6274 | −1.68362 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −51.2548 | −1.84830 | −0.924148 | − | 0.382034i | \(-0.875224\pi\) | ||||
−0.924148 | + | 0.382034i | \(0.875224\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.5147 | −0.917701 | −0.458850 | − | 0.888514i | \(-0.651739\pi\) | ||||
−0.458850 | + | 0.888514i | \(0.651739\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.65685 | −0.203200 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.65685 | −0.131020 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.6274 | 0.809673 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.6569 | −0.558817 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.2843 | 1.57856 | 0.789282 | − | 0.614031i | \(-0.210453\pi\) | ||||
0.789282 | + | 0.614031i | \(0.210453\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.6569 | 1.05448 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.9706 | 1.02877 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.8284 | 0.596093 | 0.298047 | − | 0.954551i | \(-0.403665\pi\) | ||||
0.298047 | + | 0.954551i | \(0.403665\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.5980 | −1.40088 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.9706 | 1.23562 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −62.6274 | −2.21007 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | −0.281963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.6274 | 1.70965 | 0.854824 | − | 0.518917i | \(-0.173665\pi\) | ||||
0.854824 | + | 0.518917i | \(0.173665\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.3431 | −0.784574 | −0.392287 | − | 0.919843i | \(-0.628316\pi\) | ||||
−0.392287 | + | 0.919843i | \(0.628316\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.8284 | −0.659531 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.48528 | −0.296862 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 40.9706 | 1.43163 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.31371 | −0.325051 | −0.162525 | − | 0.986704i | \(-0.551964\pi\) | ||||
−0.162525 | + | 0.986704i | \(0.551964\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.7990 | 1.24787 | 0.623937 | − | 0.781475i | \(-0.285532\pi\) | ||||
0.623937 | + | 0.781475i | \(0.285532\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.0000 | −0.556375 | −0.278187 | − | 0.960527i | \(-0.589734\pi\) | ||||
−0.278187 | + | 0.960527i | \(0.589734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.2548 | 1.78015 | 0.890077 | − | 0.455810i | \(-0.150650\pi\) | ||||
0.890077 | + | 0.455810i | \(0.150650\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.65685 | 0.265294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.3137 | −0.806804 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.6569 | 1.30006 | 0.650029 | − | 0.759909i | \(-0.274757\pi\) | ||||
0.650029 | + | 0.759909i | \(0.274757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6274 | −0.538876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.3137 | −0.354802 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.1421 | 0.485930 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.3431 | 0.628795 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.6274 | −1.52801 | −0.764007 | − | 0.645208i | \(-0.776771\pi\) | ||||
−0.764007 | + | 0.645208i | \(0.776771\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.00000 | 0.102598 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.7990 | −0.608002 | −0.304001 | − | 0.952672i | \(-0.598323\pi\) | ||||
−0.304001 | + | 0.952672i | \(0.598323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.3137 | 0.795453 | 0.397727 | − | 0.917504i | \(-0.369799\pi\) | ||||
0.397727 | + | 0.917504i | \(0.369799\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −52.0000 | −1.77010 | −0.885050 | − | 0.465495i | \(-0.845876\pi\) | ||||
−0.885050 | + | 0.465495i | \(0.845876\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.1421 | −0.412845 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.6274 | −0.767583 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −54.6274 | −1.85098 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.5147 | −0.728163 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.82843 | −0.0956183 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.7990 | −1.00624 | −0.503120 | − | 0.864216i | \(-0.667815\pi\) | ||||
−0.503120 | + | 0.864216i | \(0.667815\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.68629 | 0.225267 | 0.112633 | − | 0.993637i | \(-0.464071\pi\) | ||||
0.112633 | + | 0.993637i | \(0.464071\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.17157 | −0.174037 | −0.0870186 | − | 0.996207i | \(-0.527734\pi\) | ||||
−0.0870186 | + | 0.996207i | \(0.527734\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.3431 | −0.481596 | −0.240798 | − | 0.970575i | \(-0.577409\pi\) | ||||
−0.240798 | + | 0.970575i | \(0.577409\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.6863 | −1.23042 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −36.0000 | −1.20605 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.17157 | −0.173060 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.9706 | 0.433558 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.6863 | −0.689926 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −54.9117 | −1.82937 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.3137 | 0.442563 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.2843 | 1.47044 | 0.735218 | − | 0.677831i | \(-0.237080\pi\) | ||||
0.735218 | + | 0.677831i | \(0.237080\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 42.0000 | 1.39305 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.2548 | −1.49936 | −0.749680 | − | 0.661801i | \(-0.769792\pi\) | ||||
−0.749680 | + | 0.661801i | \(0.769792\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.6863 | −0.684616 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.3137 | 0.901978 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.6274 | 1.93394 | 0.966970 | − | 0.254890i | \(-0.0820393\pi\) | ||||
0.966970 | + | 0.254890i | \(0.0820393\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.3137 | 0.899042 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.48528 | 0.213235 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −52.9706 | −1.73978 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.0000 | −1.24674 | −0.623370 | − | 0.781927i | \(-0.714237\pi\) | ||||
−0.623370 | + | 0.781927i | \(0.714237\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.6274 | 1.00162 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.3431 | −1.05660 | −0.528302 | − | 0.849056i | \(-0.677171\pi\) | ||||
−0.528302 | + | 0.849056i | \(0.677171\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.0000 | −0.586783 | −0.293392 | − | 0.955992i | \(-0.594784\pi\) | ||||
−0.293392 | + | 0.955992i | \(0.594784\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.3431 | −0.336819 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.1716 | −1.20791 | −0.603957 | − | 0.797017i | \(-0.706410\pi\) | ||||
−0.603957 | + | 0.797017i | \(0.706410\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −75.5980 | −2.45401 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.79899 | −0.0582750 | −0.0291375 | − | 0.999575i | \(-0.509276\pi\) | ||||
−0.0291375 | + | 0.999575i | \(0.509276\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.9706 | −0.419718 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 44.2843 | 1.43001 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −40.9706 | −1.32026 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.82843 | 0.284197 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.1127 | 1.25778 | 0.628890 | − | 0.777494i | \(-0.283510\pi\) | ||||
0.628890 | + | 0.777494i | \(0.283510\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.9706 | 0.929710 | 0.464855 | − | 0.885387i | \(-0.346107\pi\) | ||||
0.464855 | + | 0.885387i | \(0.346107\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.6863 | 1.17611 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.20101 | 0.198388 | 0.0991939 | − | 0.995068i | \(-0.468374\pi\) | ||||
0.0991939 | + | 0.995068i | \(0.468374\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.6274 | 1.49022 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.9411 | 0.508961 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.3137 | −0.488431 | −0.244216 | − | 0.969721i | \(-0.578531\pi\) | ||||
−0.244216 | + | 0.969721i | \(0.578531\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.31371 | 0.0418582 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.0000 | −0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | 0.254128 | 0.127064 | − | 0.991894i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991894i | \(0.459445\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.31371 | 0.231860 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.3431 | 0.390911 | 0.195456 | − | 0.980713i | \(-0.437381\pi\) | ||||
0.195456 | + | 0.980713i | \(0.437381\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 6080.2.a.bd.1.2 | 2 | ||
4.3 | odd | 2 | 6080.2.a.be.1.1 | 2 | |||
8.3 | odd | 2 | 3040.2.a.f.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 3040.2.a.g.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3040.2.a.f.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
3040.2.a.g.1.2 | yes | 2 | 8.5 | even | 2 | ||
6080.2.a.bd.1.2 | 2 | 1.1 | even | 1 | trivial | ||
6080.2.a.be.1.1 | 2 | 4.3 | odd | 2 |