Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4704,2,Mod(1,4704)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4704, 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("4704.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4704 = 2^{5} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4704.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: | \(37.5616291108\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.66908\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4704.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.454904 | −0.203439 | −0.101720 | − | 0.994813i | \(-0.532434\pi\) | ||||
−0.101720 | + | 0.994813i | \(0.532434\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.79306 | −1.74667 | −0.873337 | − | 0.487117i | \(-0.838049\pi\) | ||||
−0.873337 | + | 0.487117i | \(0.838049\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.88325 | 1.63172 | 0.815861 | − | 0.578249i | \(-0.196264\pi\) | ||||
0.815861 | + | 0.578249i | \(0.196264\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.454904 | 0.117456 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.90981 | −0.705732 | −0.352866 | − | 0.935674i | \(-0.614793\pi\) | ||||
−0.352866 | + | 0.935674i | \(0.614793\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.88325 | −1.34971 | −0.674856 | − | 0.737950i | \(-0.735794\pi\) | ||||
−0.674856 | + | 0.737950i | \(0.735794\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.90981 | −0.606737 | −0.303368 | − | 0.952873i | \(-0.598111\pi\) | ||||
−0.303368 | + | 0.952873i | \(0.598111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.79306 | −0.958612 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.54510 | 0.658308 | 0.329154 | − | 0.944276i | \(-0.393237\pi\) | ||||
0.329154 | + | 0.944276i | \(0.393237\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.33816 | 0.779156 | 0.389578 | − | 0.920993i | \(-0.372621\pi\) | ||||
0.389578 | + | 0.920993i | \(0.372621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.79306 | 1.00844 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.70287 | 1.26634 | 0.633172 | − | 0.774011i | \(-0.281753\pi\) | ||||
0.633172 | + | 0.774011i | \(0.281753\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.88325 | −0.942075 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.58612 | −1.49710 | −0.748551 | − | 0.663078i | \(-0.769250\pi\) | ||||
−0.748551 | + | 0.663078i | \(0.769250\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7931 | 1.64593 | 0.822963 | − | 0.568095i | \(-0.192319\pi\) | ||||
0.822963 | + | 0.568095i | \(0.192319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.454904 | −0.0678131 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.90981 | −0.716169 | −0.358085 | − | 0.933689i | \(-0.616570\pi\) | ||||
−0.358085 | + | 0.933689i | \(0.616570\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.90981 | 0.407455 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.1312 | 1.80371 | 0.901856 | − | 0.432037i | \(-0.142205\pi\) | ||||
0.901856 | + | 0.432037i | \(0.142205\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.63529 | 0.355342 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.88325 | 0.779256 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.79306 | 0.233437 | 0.116718 | − | 0.993165i | \(-0.462762\pi\) | ||||
0.116718 | + | 0.993165i | \(0.462762\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.67632 | −0.598741 | −0.299370 | − | 0.954137i | \(-0.596777\pi\) | ||||
−0.299370 | + | 0.954137i | \(0.596777\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.67632 | −0.331956 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.88325 | 0.963093 | 0.481546 | − | 0.876421i | \(-0.340075\pi\) | ||||
0.481546 | + | 0.876421i | \(0.340075\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.90981 | 0.350300 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.909808 | −0.107974 | −0.0539872 | − | 0.998542i | \(-0.517193\pi\) | ||||
−0.0539872 | + | 0.998542i | \(0.517193\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.20694 | −0.609426 | −0.304713 | − | 0.952444i | \(-0.598561\pi\) | ||||
−0.304713 | + | 0.952444i | \(0.598561\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.79306 | 0.553455 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.75203 | −0.309628 | −0.154814 | − | 0.987944i | \(-0.549478\pi\) | ||||
−0.154814 | + | 0.987944i | \(0.549478\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.97345 | −1.09473 | −0.547364 | − | 0.836895i | \(-0.684369\pi\) | ||||
−0.547364 | + | 0.836895i | \(0.684369\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.32368 | 0.143574 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.54510 | −0.380074 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.90981 | 0.520439 | 0.260219 | − | 0.965550i | \(-0.416205\pi\) | ||||
0.260219 | + | 0.965550i | \(0.416205\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.33816 | −0.449846 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.67632 | 0.274584 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.79306 | 0.588196 | 0.294098 | − | 0.955775i | \(-0.404981\pi\) | ||||
0.294098 | + | 0.955775i | \(0.404981\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.79306 | −0.582225 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.6763 | −1.65936 | −0.829678 | − | 0.558243i | \(-0.811476\pi\) | ||||
−0.829678 | + | 0.558243i | \(0.811476\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.793062 | 0.0781427 | 0.0390714 | − | 0.999236i | \(-0.487560\pi\) | ||||
0.0390714 | + | 0.999236i | \(0.487560\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.9734 | 1.15752 | 0.578758 | − | 0.815499i | \(-0.303537\pi\) | ||||
0.578758 | + | 0.815499i | \(0.303537\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.61268 | −0.441814 | −0.220907 | − | 0.975295i | \(-0.570902\pi\) | ||||
−0.220907 | + | 0.975295i | \(0.570902\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.70287 | −0.731124 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.00000 | 0.752577 | 0.376288 | − | 0.926503i | \(-0.377200\pi\) | ||||
0.376288 | + | 0.926503i | \(0.377200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.32368 | 0.123434 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.88325 | 0.543907 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.5596 | 2.05087 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.58612 | 0.864352 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.45490 | 0.398459 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.24797 | −0.110739 | −0.0553696 | − | 0.998466i | \(-0.517634\pi\) | ||||
−0.0553696 | + | 0.998466i | \(0.517634\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.7931 | −0.950276 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.79306 | 0.506142 | 0.253071 | − | 0.967448i | \(-0.418559\pi\) | ||||
0.253071 | + | 0.967448i | \(0.418559\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.454904 | 0.0391519 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.09019 | −0.264013 | −0.132006 | − | 0.991249i | \(-0.542142\pi\) | ||||
−0.132006 | + | 0.991249i | \(0.542142\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.70287 | 0.483711 | 0.241856 | − | 0.970312i | \(-0.422244\pi\) | ||||
0.241856 | + | 0.970312i | \(0.422244\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.90981 | 0.413480 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −34.0821 | −2.85008 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.61268 | −0.133926 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.09019 | 0.253158 | 0.126579 | − | 0.991957i | \(-0.459600\pi\) | ||||
0.126579 | + | 0.991957i | \(0.459600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.72548 | −0.140418 | −0.0702088 | − | 0.997532i | \(-0.522367\pi\) | ||||
−0.0702088 | + | 0.997532i | \(0.522367\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.90981 | −0.235244 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.97345 | −0.158511 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.58612 | 0.445821 | 0.222911 | − | 0.974839i | \(-0.428444\pi\) | ||||
0.222911 | + | 0.974839i | \(0.428444\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.1312 | −1.04137 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.85670 | −0.693710 | −0.346855 | − | 0.937919i | \(-0.612750\pi\) | ||||
−0.346855 | + | 0.937919i | \(0.612750\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.63529 | −0.205157 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.4057 | 1.34690 | 0.673448 | − | 0.739234i | \(-0.264812\pi\) | ||||
0.673448 | + | 0.739234i | \(0.264812\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.6127 | 1.66251 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.88325 | −0.449904 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.6763 | 1.26788 | 0.633938 | − | 0.773384i | \(-0.281437\pi\) | ||||
0.633938 | + | 0.773384i | \(0.281437\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.79306 | −0.134775 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.18038 | 0.461944 | 0.230972 | − | 0.972960i | \(-0.425809\pi\) | ||||
0.230972 | + | 0.972960i | \(0.425809\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.20694 | 0.238370 | 0.119185 | − | 0.992872i | \(-0.461972\pi\) | ||||
0.119185 | + | 0.992872i | \(0.461972\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.67632 | 0.345683 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.50407 | −0.257624 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.8567 | 1.23268 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.3526 | −1.54502 | −0.772511 | − | 0.635001i | \(-0.781000\pi\) | ||||
−0.772511 | + | 0.635001i | \(0.781000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.4057 | 1.18091 | 0.590456 | − | 0.807070i | \(-0.298948\pi\) | ||||
0.590456 | + | 0.807070i | \(0.298948\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.67632 | 0.191655 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.6763 | 1.75811 | 0.879057 | − | 0.476716i | \(-0.158173\pi\) | ||||
0.879057 | + | 0.476716i | \(0.158173\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.8196 | 0.979647 | 0.489823 | − | 0.871822i | \(-0.337061\pi\) | ||||
0.489823 | + | 0.871822i | \(0.337061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.88325 | −0.556042 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.36077 | 0.304569 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.90981 | −0.202246 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 34.0821 | 2.35751 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.5861 | −0.797622 | −0.398811 | − | 0.917033i | \(-0.630577\pi\) | ||||
−0.398811 | + | 0.917033i | \(0.630577\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.909808 | 0.0623390 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.90981 | −0.334846 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.20694 | 0.351852 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.1191 | −1.15156 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.4549 | 1.36976 | 0.684881 | − | 0.728655i | \(-0.259854\pi\) | ||||
0.684881 | + | 0.728655i | \(0.259854\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.79306 | −0.319537 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.7400 | 1.17744 | 0.588721 | − | 0.808336i | \(-0.299632\pi\) | ||||
0.588721 | + | 0.808336i | \(0.299632\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.1988 | 1.59910 | 0.799551 | − | 0.600598i | \(-0.205071\pi\) | ||||
0.799551 | + | 0.600598i | \(0.205071\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.6763 | 1.48557 | 0.742787 | − | 0.669527i | \(-0.233503\pi\) | ||||
0.742787 | + | 0.669527i | \(0.233503\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.23349 | 0.145697 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.75203 | 0.178764 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.90981 | −0.188220 | −0.0941099 | − | 0.995562i | \(-0.530001\pi\) | ||||
−0.0941099 | + | 0.995562i | \(0.530001\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.7400 | −1.40039 | −0.700197 | − | 0.713950i | \(-0.746904\pi\) | ||||
−0.700197 | + | 0.713950i | \(0.746904\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −34.6127 | −2.20235 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.97345 | 0.632041 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.02655 | −0.506632 | −0.253316 | − | 0.967384i | \(-0.581521\pi\) | ||||
−0.253316 | + | 0.967384i | \(0.581521\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.8567 | 1.05977 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.32368 | −0.0828923 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.9098 | 0.805292 | 0.402646 | − | 0.915356i | \(-0.368091\pi\) | ||||
0.402646 | + | 0.915356i | \(0.368091\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.54510 | 0.219436 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.90981 | −0.549402 | −0.274701 | − | 0.961530i | \(-0.588579\pi\) | ||||
−0.274701 | + | 0.961530i | \(0.588579\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.97345 | −0.366946 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.90981 | −0.300475 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.04103 | 0.368328 | 0.184164 | − | 0.982896i | \(-0.441042\pi\) | ||||
0.184164 | + | 0.982896i | \(0.441042\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.3647 | 0.811848 | 0.405924 | − | 0.913907i | \(-0.366950\pi\) | ||||
0.405924 | + | 0.913907i | \(0.366950\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 27.7665 | 1.67438 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.79306 | 0.287987 | 0.143994 | − | 0.989579i | \(-0.454006\pi\) | ||||
0.143994 | + | 0.989579i | \(0.454006\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.33816 | 0.259719 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.32368 | 0.436894 | 0.218447 | − | 0.975849i | \(-0.429901\pi\) | ||||
0.218447 | + | 0.975849i | \(0.429901\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.2069 | 0.785071 | 0.392535 | − | 0.919737i | \(-0.371598\pi\) | ||||
0.392535 | + | 0.919737i | \(0.371598\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.67632 | −0.158531 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.53302 | −0.501942 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.79306 | −0.339595 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.54510 | −0.440789 | −0.220395 | − | 0.975411i | \(-0.570735\pi\) | ||||
−0.220395 | + | 0.975411i | \(0.570735\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.815671 | −0.0474902 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.79306 | 0.336148 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.1191 | −0.990025 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.6763 | 0.958029 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.12728 | 0.121807 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.1086 | −1.31888 | −0.659439 | − | 0.751758i | \(-0.729206\pi\) | ||||
−0.659439 | + | 0.751758i | \(0.729206\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.793062 | −0.0451157 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.40574 | 0.419941 | 0.209971 | − | 0.977708i | \(-0.432663\pi\) | ||||
0.209971 | + | 0.977708i | \(0.432663\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.5861 | −0.824457 | −0.412228 | − | 0.911081i | \(-0.635249\pi\) | ||||
−0.412228 | + | 0.911081i | \(0.635249\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.36471 | 0.0766499 | 0.0383249 | − | 0.999265i | \(-0.487798\pi\) | ||||
0.0383249 | + | 0.999265i | \(0.487798\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.5370 | −1.14985 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.9734 | −0.668293 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.1191 | 0.952534 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28.1988 | −1.56419 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.61268 | 0.255082 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9734 | 0.603155 | 0.301578 | − | 0.953442i | \(-0.402487\pi\) | ||||
0.301578 | + | 0.953442i | \(0.402487\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.70287 | 0.422115 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.58612 | −0.195931 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.1722 | −1.20780 | −0.603900 | − | 0.797060i | \(-0.706387\pi\) | ||||
−0.603900 | + | 0.797060i | \(0.706387\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.00000 | −0.434500 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.1312 | −1.36093 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.32368 | −0.0712647 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.233492 | 0.0125345 | 0.00626725 | − | 0.999980i | \(-0.498005\pi\) | ||||
0.00626725 | + | 0.999980i | \(0.498005\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.35263 | −0.393577 | −0.196789 | − | 0.980446i | \(-0.563051\pi\) | ||||
−0.196789 | + | 0.980446i | \(0.563051\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.88325 | −0.314025 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.1722 | −1.02044 | −0.510218 | − | 0.860045i | \(-0.670435\pi\) | ||||
−0.510218 | + | 0.860045i | \(0.670435\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.413875 | 0.0219662 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.9388 | 1.10511 | 0.552553 | − | 0.833478i | \(-0.313654\pi\) | ||||
0.552553 | + | 0.833478i | \(0.313654\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.6127 | 0.821720 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −22.5596 | −1.18407 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.36866 | 0.123981 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.0145 | 1.30574 | 0.652872 | − | 0.757468i | \(-0.273564\pi\) | ||||
0.652872 | + | 0.757468i | \(0.273564\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.58612 | −0.499034 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.3261 | −1.05244 | −0.526222 | − | 0.850347i | \(-0.676392\pi\) | ||||
−0.526222 | + | 0.850347i | \(0.676392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.45490 | −0.230050 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.8567 | 1.07417 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.7931 | 1.06807 | 0.534034 | − | 0.845463i | \(-0.320675\pi\) | ||||
0.534034 | + | 0.845463i | \(0.320675\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.24797 | 0.0639353 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.1722 | 1.28624 | 0.643121 | − | 0.765765i | \(-0.277639\pi\) | ||||
0.643121 | + | 0.765765i | \(0.277639\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.7931 | 0.548642 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.4428 | 1.23930 | 0.619650 | − | 0.784878i | \(-0.287274\pi\) | ||||
0.619650 | + | 0.784878i | \(0.287274\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.46698 | 0.428194 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.79306 | −0.292221 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.25191 | 0.0629905 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.79306 | 0.441311 | 0.220656 | − | 0.975352i | \(-0.429180\pi\) | ||||
0.220656 | + | 0.975352i | \(0.429180\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.1191 | 1.65389 | 0.826945 | − | 0.562282i | \(-0.190076\pi\) | ||||
0.826945 | + | 0.562282i | \(0.190076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.5225 | 1.27137 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.454904 | −0.0226044 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −44.6232 | −2.21189 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.94689 | 0.343502 | 0.171751 | − | 0.985140i | \(-0.445058\pi\) | ||||
0.171751 | + | 0.985140i | \(0.445058\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.09019 | 0.152428 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.53696 | 0.222711 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.70287 | −0.279271 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.2254 | −1.42775 | −0.713876 | − | 0.700272i | \(-0.753062\pi\) | ||||
−0.713876 | + | 0.700272i | \(0.753062\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.2359 | 1.61982 | 0.809909 | − | 0.586556i | \(-0.199516\pi\) | ||||
0.809909 | + | 0.586556i | \(0.199516\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.90981 | −0.238723 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.9469 | 0.676524 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 34.0821 | 1.64550 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.18038 | −0.297699 | −0.148849 | − | 0.988860i | \(-0.547557\pi\) | ||||
−0.148849 | + | 0.988860i | \(0.547557\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6127 | −0.798354 | −0.399177 | − | 0.916874i | \(-0.630704\pi\) | ||||
−0.399177 | + | 0.916874i | \(0.630704\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.61268 | 0.0773220 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.1191 | 0.818920 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.6272 | −1.31857 | −0.659286 | − | 0.751892i | \(-0.729141\pi\) | ||||
−0.659286 | + | 0.751892i | \(0.729141\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.0266 | 0.951490 | 0.475745 | − | 0.879583i | \(-0.342178\pi\) | ||||
0.475745 | + | 0.879583i | \(0.342178\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.23349 | −0.105878 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.09019 | −0.146161 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.0371 | 0.709644 | 0.354822 | − | 0.934934i | \(-0.384541\pi\) | ||||
0.354822 | + | 0.934934i | \(0.384541\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 55.5330 | 2.61495 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.72548 | 0.0810701 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −42.1191 | −1.97025 | −0.985125 | − | 0.171838i | \(-0.945029\pi\) | ||||
−0.985125 | + | 0.171838i | \(0.945029\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.90981 | 0.135818 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.9098 | −0.973867 | −0.486933 | − | 0.873439i | \(-0.661885\pi\) | ||||
−0.486933 | + | 0.873439i | \(0.661885\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.1457 | 1.77278 | 0.886390 | − | 0.462939i | \(-0.153205\pi\) | ||||
0.886390 | + | 0.462939i | \(0.153205\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.97345 | 0.0915164 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.5330 | 0.533684 | 0.266842 | − | 0.963740i | \(-0.414020\pi\) | ||||
0.266842 | + | 0.963740i | \(0.414020\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.58612 | −0.257395 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −62.5249 | −2.87490 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.1988 | 1.29385 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.1312 | 0.601237 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.32368 | −0.334628 | −0.167314 | − | 0.985904i | \(-0.553509\pi\) | ||||
−0.167314 | + | 0.985904i | \(0.553509\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 45.3179 | 2.06632 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.63529 | −0.119662 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.0516 | 1.18051 | 0.590254 | − | 0.807217i | \(-0.299027\pi\) | ||||
0.590254 | + | 0.807217i | \(0.299027\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.85670 | 0.400514 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.37919 | −0.333018 | −0.166509 | − | 0.986040i | \(-0.553249\pi\) | ||||
−0.166509 | + | 0.986040i | \(0.553249\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.3155 | −0.464589 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.63529 | 0.118447 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.350238 | −0.0156788 | −0.00783940 | − | 0.999969i | \(-0.502495\pi\) | ||||
−0.00783940 | + | 0.999969i | \(0.502495\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.4057 | −0.777631 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.9098 | −0.664795 | −0.332398 | − | 0.943139i | \(-0.607858\pi\) | ||||
−0.332398 | + | 0.943139i | \(0.607858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.58612 | 0.337578 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.6127 | −0.959853 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.8977 | −0.748979 | −0.374489 | − | 0.927231i | \(-0.622182\pi\) | ||||
−0.374489 | + | 0.927231i | \(0.622182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.88325 | 0.259752 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.360767 | −0.0158973 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.4428 | 1.25091 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.6763 | −0.732009 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.58612 | −0.332354 | −0.166177 | − | 0.986096i | \(-0.553142\pi\) | ||||
−0.166177 | + | 0.986096i | \(0.553142\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.5144 | 1.85902 | 0.929511 | − | 0.368793i | \(-0.120229\pi\) | ||||
0.929511 | + | 0.368793i | \(0.120229\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.6232 | −0.549876 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.5330 | −0.631870 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.79306 | 0.0778123 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −56.3976 | −2.44285 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.44677 | −0.235484 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.18038 | −0.266703 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0636 | 0.604643 | 0.302322 | − | 0.953206i | \(-0.402238\pi\) | ||||
0.302322 | + | 0.953206i | \(0.402238\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.20694 | −0.137623 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.09833 | 0.0898824 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.49593 | −0.192232 | −0.0961161 | − | 0.995370i | \(-0.530642\pi\) | ||||
−0.0961161 | + | 0.995370i | \(0.530642\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.67632 | −0.199580 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.8567 | −0.888525 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.50407 | 0.148739 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.8606 | 1.34998 | 0.674989 | − | 0.737827i | \(-0.264148\pi\) | ||||
0.674989 | + | 0.737827i | \(0.264148\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 63.4983 | 2.68569 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.8567 | −0.711690 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −46.1376 | −1.94447 | −0.972233 | − | 0.234014i | \(-0.924814\pi\) | ||||
−0.972233 | + | 0.234014i | \(0.924814\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.63923 | −0.153104 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.6232 | −0.696881 | −0.348441 | − | 0.937331i | \(-0.613289\pi\) | ||||
−0.348441 | + | 0.937331i | \(0.613289\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.5065 | 1.52775 | 0.763874 | − | 0.645365i | \(-0.223295\pi\) | ||||
0.763874 | + | 0.645365i | \(0.223295\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.3526 | 0.892019 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.9469 | 0.581626 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.1804 | 0.631968 | 0.315984 | − | 0.948765i | \(-0.397665\pi\) | ||||
0.315984 | + | 0.948765i | \(0.397665\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.4057 | −0.681799 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −76.0700 | −3.15050 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.67632 | −0.110652 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.20694 | −0.338737 | −0.169368 | − | 0.985553i | \(-0.554173\pi\) | ||||
−0.169368 | + | 0.985553i | \(0.554173\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.5225 | −1.05164 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.6763 | −1.01505 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.55718 | 0.228206 | 0.114103 | − | 0.993469i | \(-0.463601\pi\) | ||||
0.114103 | + | 0.993469i | \(0.463601\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.8196 | −0.565599 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.5861 | −1.45401 | −0.727005 | − | 0.686632i | \(-0.759088\pi\) | ||||
−0.727005 | + | 0.686632i | \(0.759088\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.18038 | −0.0481489 | −0.0240744 | − | 0.999710i | \(-0.507664\pi\) | ||||
−0.0240744 | + | 0.999710i | \(0.507664\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.88325 | 0.321031 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.2624 | −0.417228 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.3382 | −0.500790 | −0.250395 | − | 0.968144i | \(-0.580561\pi\) | ||||
−0.250395 | + | 0.968144i | \(0.580561\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.8856 | −1.16859 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.0902 | −0.851825 | −0.425912 | − | 0.904764i | \(-0.640047\pi\) | ||||
−0.425912 | + | 0.904764i | \(0.640047\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.36077 | −0.175843 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.3526 | 0.618074 | 0.309037 | − | 0.951050i | \(-0.399993\pi\) | ||||
0.309037 | + | 0.951050i | \(0.399993\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.4323 | 0.740856 | 0.370428 | − | 0.928861i | \(-0.379211\pi\) | ||||
0.370428 | + | 0.928861i | \(0.379211\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.90981 | 0.116767 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.9388 | 0.877550 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −34.0821 | −1.36111 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.4139 | −0.893700 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.91375 | −0.235423 | −0.117711 | − | 0.993048i | \(-0.537556\pi\) | ||||
−0.117711 | + | 0.993048i | \(0.537556\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.5861 | 0.460507 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.567705 | 0.0225287 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.909808 | −0.0359915 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.1641 | 1.82337 | 0.911686 | − | 0.410887i | \(-0.134781\pi\) | ||||
0.911686 | + | 0.410887i | \(0.134781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.0555 | 1.22471 | 0.612355 | − | 0.790583i | \(-0.290222\pi\) | ||||
0.612355 | + | 0.790583i | \(0.290222\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.90981 | 0.193324 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.0371 | −0.669797 | −0.334898 | − | 0.942254i | \(-0.608702\pi\) | ||||
−0.334898 | + | 0.942254i | \(0.608702\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.3873 | −0.407738 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.13936 | −0.318518 | −0.159259 | − | 0.987237i | \(-0.550910\pi\) | ||||
−0.159259 | + | 0.987237i | \(0.550910\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.63529 | −0.102969 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.20694 | −0.203142 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.1191 | −1.60177 | −0.800887 | − | 0.598815i | \(-0.795638\pi\) | ||||
−0.800887 | + | 0.598815i | \(0.795638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.3421 | 0.518948 | 0.259474 | − | 0.965750i | \(-0.416451\pi\) | ||||
0.259474 | + | 0.965750i | \(0.416451\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.1191 | 0.664852 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.3155 | −0.399420 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.4549 | −0.790832 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.0902 | 1.04581 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.75837 | 0.376158 | 0.188079 | − | 0.982154i | \(-0.439774\pi\) | ||||
0.188079 | + | 0.982154i | \(0.439774\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.79306 | 0.184485 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.4549 | −1.24734 | −0.623672 | − | 0.781686i | \(-0.714360\pi\) | ||||
−0.623672 | + | 0.781686i | \(0.714360\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.7400 | −0.679797 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.9653 | 1.41444 | 0.707219 | − | 0.706994i | \(-0.249949\pi\) | ||||
0.707219 | + | 0.706994i | \(0.249949\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.40574 | 0.0537106 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.1988 | −0.923242 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 77.2543 | 2.94315 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.2519 | −0.542168 | −0.271084 | − | 0.962556i | \(-0.587382\pi\) | ||||
−0.271084 | + | 0.962556i | \(0.587382\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.59426 | −0.0984059 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.8938 | 1.05655 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.6763 | −0.857697 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.3937 | −1.94111 | −0.970556 | − | 0.240876i | \(-0.922565\pi\) | ||||
−0.970556 | + | 0.240876i | \(0.922565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −45.3179 | −1.70920 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.23349 | −0.0841182 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.1722 | 0.945364 | 0.472682 | − | 0.881233i | \(-0.343286\pi\) | ||||
0.472682 | + | 0.881233i | \(0.343286\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.75203 | −0.103209 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.6232 | −0.472743 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.5041 | 0.579819 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.90981 | 0.108669 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.18038 | −0.305077 | −0.152538 | − | 0.988298i | \(-0.548745\pi\) | ||||
−0.152538 | + | 0.988298i | \(0.548745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.7400 | 0.808518 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.9919 | −0.631062 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.9614 | −0.999942 | −0.499971 | − | 0.866042i | \(-0.666656\pi\) | ||||
−0.499971 | + | 0.866042i | \(0.666656\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.4057 | −1.16158 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.4694 | 0.792990 | 0.396495 | − | 0.918037i | \(-0.370226\pi\) | ||||
0.396495 | + | 0.918037i | \(0.370226\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −45.6682 | −1.68221 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.34210 | −0.0493701 | −0.0246850 | − | 0.999695i | \(-0.507858\pi\) | ||||
−0.0246850 | + | 0.999695i | \(0.507858\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.6127 | 1.27153 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.9919 | 0.990236 | 0.495118 | − | 0.868826i | \(-0.335125\pi\) | ||||
0.495118 | + | 0.868826i | \(0.335125\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.40574 | −0.0515024 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.97345 | −0.364909 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.8872 | −0.470261 | −0.235130 | − | 0.971964i | \(-0.575552\pi\) | ||||
−0.235130 | + | 0.971964i | \(0.575552\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.02655 | 0.292504 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.784928 | 0.0285664 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.3897 | −0.959151 | −0.479575 | − | 0.877501i | \(-0.659209\pi\) | ||||
−0.479575 | + | 0.877501i | \(0.659209\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.8567 | −0.611859 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.4428 | −1.10355 | −0.551776 | − | 0.833993i | \(-0.686050\pi\) | ||||
−0.551776 | + | 0.833993i | \(0.686050\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.32368 | 0.0478579 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.5490 | 0.380904 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.1191 | −1.51886 | −0.759428 | − | 0.650592i | \(-0.774521\pi\) | ||||
−0.759428 | + | 0.650592i | \(0.774521\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.9098 | −0.464935 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.0289 | −1.36781 | −0.683903 | − | 0.729573i | \(-0.739719\pi\) | ||||
−0.683903 | + | 0.729573i | \(0.739719\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.7931 | −0.746909 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 56.3976 | 2.02065 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.27058 | 0.188596 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.54510 | −0.126691 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.54115 | −0.0906976 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.5861 | 1.12592 | 0.562962 | − | 0.826483i | \(-0.309662\pi\) | ||||
0.562962 | + | 0.826483i | \(0.309662\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.90981 | 0.317198 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.5120 | −0.976978 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.97345 | 0.211856 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −45.2133 | −1.60154 | −0.800768 | − | 0.598974i | \(-0.795575\pi\) | ||||
−0.800768 | + | 0.598974i | \(0.795575\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.2866 | 0.505424 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.90981 | 0.173480 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.1641 | 1.06447 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.04103 | −0.212654 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.991865 | 0.0348721 | 0.0174361 | − | 0.999848i | \(-0.494450\pi\) | ||||
0.0174361 | + | 0.999848i | \(0.494450\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.6151 | −0.829237 | −0.414619 | − | 0.909995i | \(-0.636085\pi\) | ||||
−0.414619 | + | 0.909995i | \(0.636085\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.3647 | −0.468721 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.02895 | 0.141128 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −63.4983 | −2.22153 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.2664 | −1.23081 | −0.615403 | − | 0.788213i | \(-0.711007\pi\) | ||||
−0.615403 | + | 0.788213i | \(0.711007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.5412 | −0.367441 | −0.183721 | − | 0.982978i | \(-0.558814\pi\) | ||||
−0.183721 | + | 0.982978i | \(0.558814\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.7665 | −0.966706 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.4323 | 1.09301 | 0.546504 | − | 0.837456i | \(-0.315958\pi\) | ||||
0.546504 | + | 0.837456i | \(0.315958\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.5225 | 0.886433 | 0.443216 | − | 0.896415i | \(-0.353837\pi\) | ||||
0.443216 | + | 0.896415i | \(0.353837\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.79306 | −0.166269 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.91794 | −0.274012 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.33816 | −0.149949 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.78253 | −0.0960637 | −0.0480318 | − | 0.998846i | \(-0.515295\pi\) | ||||
−0.0480318 | + | 0.998846i | \(0.515295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.4323 | −0.566631 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.32368 | −0.252241 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.83170 | −0.338221 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.2069 | −0.453261 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.4139 | −0.768338 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.7931 | −0.643462 | −0.321731 | − | 0.946831i | \(-0.604265\pi\) | ||||
−0.321731 | + | 0.946831i | \(0.604265\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.67632 | 0.0915281 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.9388 | −0.715254 | −0.357627 | − | 0.933864i | \(-0.616414\pi\) | ||||
−0.357627 | + | 0.933864i | \(0.616414\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.5861 | −0.395313 | −0.197657 | − | 0.980271i | \(-0.563333\pi\) | ||||
−0.197657 | + | 0.980271i | \(0.563333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.5330 | 1.00532 | 0.502658 | − | 0.864485i | \(-0.332356\pi\) | ||||
0.502658 | + | 0.864485i | \(0.332356\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.58612 | −0.257936 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.53302 | 0.289796 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.9427 | 0.540819 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.3792 | 1.57150 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.79306 | 0.196065 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.22536 | 0.176448 | 0.0882239 | − | 0.996101i | \(-0.471881\pi\) | ||||
0.0882239 | + | 0.996101i | \(0.471881\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.54510 | 0.254490 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.1433 | 0.442809 | 0.221405 | − | 0.975182i | \(-0.428936\pi\) | ||||
0.221405 | + | 0.975182i | \(0.428936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.96531 | 0.268054 | 0.134027 | − | 0.990978i | \(-0.457209\pi\) | ||||
0.134027 | + | 0.990978i | \(0.457209\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.815671 | 0.0274185 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.7955 | −1.33620 | −0.668100 | − | 0.744071i | \(-0.732892\pi\) | ||||
−0.668100 | + | 0.744071i | \(0.732892\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.79306 | −0.194075 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.8856 | 0.966621 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.81148 | −0.0939775 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.1191 | 0.571591 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.3792 | 0.512925 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.2093 | −1.27294 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.45885 | −0.0484938 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.5967 | −0.385061 | −0.192530 | − | 0.981291i | \(-0.561669\pi\) | ||||
−0.192530 | + | 0.981291i | \(0.561669\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.6763 | −0.553118 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.4959 | 1.14290 | 0.571451 | − | 0.820636i | \(-0.306381\pi\) | ||||
0.571451 | + | 0.820636i | \(0.306381\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57.7768 | 1.91213 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.12728 | −0.0703256 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.85431 | −0.0611679 | −0.0305839 | − | 0.999532i | \(-0.509737\pi\) | ||||
−0.0305839 | + | 0.999532i | \(0.509737\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.1086 | 0.761455 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.35263 | −0.176184 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.9203 | −1.21393 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.793062 | 0.0260476 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.1191 | 0.758514 | 0.379257 | − | 0.925291i | \(-0.376180\pi\) | ||||
0.379257 | + | 0.925291i | \(0.376180\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.40574 | −0.242453 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.66818 | −0.250776 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.3445 | 1.41600 | 0.708002 | − | 0.706211i | \(-0.249597\pi\) | ||||
0.708002 | + | 0.706211i | \(0.249597\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.5861 | 0.476000 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.1312 | 0.949651 | 0.474825 | − | 0.880080i | \(-0.342511\pi\) | ||||
0.474825 | + | 0.880080i | \(0.342511\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.8938 | 0.908347 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.9469 | −0.453213 | −0.226607 | − | 0.973986i | \(-0.572763\pi\) | ||||
−0.226607 | + | 0.973986i | \(0.572763\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.6337 | −0.994413 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.36471 | −0.0442538 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.7134 | −1.28644 | −0.643222 | − | 0.765680i | \(-0.722403\pi\) | ||||
−0.643222 | + | 0.765680i | \(0.722403\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.71340 | 0.314318 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.5370 | 0.663866 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.1804 | −0.392916 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.9734 | 0.385839 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.46304 | −0.240244 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.5717 | −0.404277 | −0.202139 | − | 0.979357i | \(-0.564789\pi\) | ||||
−0.202139 | + | 0.979357i | \(0.564789\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.1191 | −0.549946 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.1538 | −0.454218 | −0.227109 | − | 0.973869i | \(-0.572927\pi\) | ||||
−0.227109 | + | 0.973869i | \(0.572927\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 28.1988 | 0.903084 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.5249 | −1.48846 | −0.744231 | − | 0.667922i | \(-0.767184\pi\) | ||||
−0.744231 | + | 0.667922i | \(0.767184\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.4428 | −0.909037 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.61268 | −0.147271 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.4718 | 1.60980 | 0.804900 | − | 0.593411i | \(-0.202219\pi\) | ||||
0.804900 | + | 0.593411i | \(0.202219\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.2254 | −0.357670 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31.4057 | −0.998644 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.97739 | −0.126346 | −0.0631730 | − | 0.998003i | \(-0.520122\pi\) | ||||
−0.0631730 | + | 0.998003i | \(0.520122\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.9734 | −0.348232 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.28660 | −0.199299 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.0184 | 1.39408 | 0.697039 | − | 0.717034i | \(-0.254501\pi\) | ||||
0.697039 | + | 0.717034i | \(0.254501\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.70287 | −0.243708 |
(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 | 4704.2.a.bt.1.2 | 3 | ||
4.3 | odd | 2 | 4704.2.a.bv.1.2 | 3 | |||
7.3 | odd | 6 | 672.2.q.k.289.2 | yes | 6 | ||
7.5 | odd | 6 | 672.2.q.k.193.2 | ✓ | 6 | ||
7.6 | odd | 2 | 4704.2.a.bu.1.2 | 3 | |||
8.3 | odd | 2 | 9408.2.a.eg.1.2 | 3 | |||
8.5 | even | 2 | 9408.2.a.ei.1.2 | 3 | |||
21.5 | even | 6 | 2016.2.s.u.865.2 | 6 | |||
21.17 | even | 6 | 2016.2.s.u.289.2 | 6 | |||
28.3 | even | 6 | 672.2.q.l.289.2 | yes | 6 | ||
28.19 | even | 6 | 672.2.q.l.193.2 | yes | 6 | ||
28.27 | even | 2 | 4704.2.a.bs.1.2 | 3 | |||
56.3 | even | 6 | 1344.2.q.y.961.2 | 6 | |||
56.5 | odd | 6 | 1344.2.q.z.193.2 | 6 | |||
56.13 | odd | 2 | 9408.2.a.eh.1.2 | 3 | |||
56.19 | even | 6 | 1344.2.q.y.193.2 | 6 | |||
56.27 | even | 2 | 9408.2.a.ej.1.2 | 3 | |||
56.45 | odd | 6 | 1344.2.q.z.961.2 | 6 | |||
84.47 | odd | 6 | 2016.2.s.v.865.2 | 6 | |||
84.59 | odd | 6 | 2016.2.s.v.289.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.q.k.193.2 | ✓ | 6 | 7.5 | odd | 6 | ||
672.2.q.k.289.2 | yes | 6 | 7.3 | odd | 6 | ||
672.2.q.l.193.2 | yes | 6 | 28.19 | even | 6 | ||
672.2.q.l.289.2 | yes | 6 | 28.3 | even | 6 | ||
1344.2.q.y.193.2 | 6 | 56.19 | even | 6 | |||
1344.2.q.y.961.2 | 6 | 56.3 | even | 6 | |||
1344.2.q.z.193.2 | 6 | 56.5 | odd | 6 | |||
1344.2.q.z.961.2 | 6 | 56.45 | odd | 6 | |||
2016.2.s.u.289.2 | 6 | 21.17 | even | 6 | |||
2016.2.s.u.865.2 | 6 | 21.5 | even | 6 | |||
2016.2.s.v.289.2 | 6 | 84.59 | odd | 6 | |||
2016.2.s.v.865.2 | 6 | 84.47 | odd | 6 | |||
4704.2.a.bs.1.2 | 3 | 28.27 | even | 2 | |||
4704.2.a.bt.1.2 | 3 | 1.1 | even | 1 | trivial | ||
4704.2.a.bu.1.2 | 3 | 7.6 | odd | 2 | |||
4704.2.a.bv.1.2 | 3 | 4.3 | odd | 2 | |||
9408.2.a.eg.1.2 | 3 | 8.3 | odd | 2 | |||
9408.2.a.eh.1.2 | 3 | 56.13 | odd | 2 | |||
9408.2.a.ei.1.2 | 3 | 8.5 | even | 2 | |||
9408.2.a.ej.1.2 | 3 | 56.27 | even | 2 |