Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3200,2,Mod(1,3200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3200 = 2^{7} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3200.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: | \(25.5521286468\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3200.1 |
$q$-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 | ||||||||
\(3\) | −2.41421 | −1.39385 | −0.696923 | − | 0.717146i | \(-0.745448\pi\) | ||||
−0.696923 | + | 0.717146i | \(0.745448\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.828427 | 0.313116 | 0.156558 | − | 0.987669i | \(-0.449960\pi\) | ||||
0.156558 | + | 0.987669i | \(0.449960\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.24264 | 1.58072 | 0.790358 | − | 0.612646i | \(-0.209895\pi\) | ||||
0.790358 | + | 0.612646i | \(0.209895\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.65685 | 1.56893 | 0.784465 | − | 0.620174i | \(-0.212938\pi\) | ||||
0.784465 | + | 0.620174i | \(0.212938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.171573 | 0.0416125 | 0.0208063 | − | 0.999784i | \(-0.493377\pi\) | ||||
0.0208063 | + | 0.999784i | \(0.493377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.58579 | 0.363804 | 0.181902 | − | 0.983317i | \(-0.441775\pi\) | ||||
0.181902 | + | 0.983317i | \(0.441775\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.82843 | −1.00680 | −0.503398 | − | 0.864054i | \(-0.667917\pi\) | ||||
−0.503398 | + | 0.864054i | \(0.667917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.414214 | 0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.00000 | 1.48556 | 0.742781 | − | 0.669534i | \(-0.233506\pi\) | ||||
0.742781 | + | 0.669534i | \(0.233506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.828427 | 0.148790 | 0.0743950 | − | 0.997229i | \(-0.476297\pi\) | ||||
0.0743950 | + | 0.997229i | \(0.476297\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.6569 | −2.20328 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.65685 | 1.25878 | 0.629390 | − | 0.777090i | \(-0.283305\pi\) | ||||
0.629390 | + | 0.777090i | \(0.283305\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.6569 | −2.18685 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.6569 | 1.66432 | 0.832161 | − | 0.554535i | \(-0.187104\pi\) | ||||
0.832161 | + | 0.554535i | \(0.187104\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.65685 | −1.40860 | −0.704298 | − | 0.709904i | \(-0.748738\pi\) | ||||
−0.704298 | + | 0.709904i | \(0.748738\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.31371 | −0.901958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.414214 | −0.0580015 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.65685 | −1.05175 | −0.525875 | − | 0.850562i | \(-0.676262\pi\) | ||||
−0.525875 | + | 0.850562i | \(0.676262\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.82843 | −0.507088 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.65685 | −0.476082 | −0.238041 | − | 0.971255i | \(-0.576505\pi\) | ||||
−0.238041 | + | 0.971255i | \(0.576505\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.34315 | 0.295209 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.75736 | 0.336865 | 0.168433 | − | 0.985713i | \(-0.446129\pi\) | ||||
0.168433 | + | 0.985713i | \(0.446129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.6569 | 1.40332 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.65685 | 1.14606 | 0.573029 | − | 0.819535i | \(-0.305768\pi\) | ||||
0.573029 | + | 0.819535i | \(0.305768\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.82843 | −0.682166 | −0.341083 | − | 0.940033i | \(-0.610794\pi\) | ||||
−0.341083 | + | 0.940033i | \(0.610794\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.34315 | 0.494947 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8284 | −1.44331 | −0.721655 | − | 0.692252i | \(-0.756618\pi\) | ||||
−0.721655 | + | 0.692252i | \(0.756618\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.24264 | −0.136398 | −0.0681988 | − | 0.997672i | \(-0.521725\pi\) | ||||
−0.0681988 | + | 0.997672i | \(0.521725\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.3137 | −2.07065 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.17157 | 0.654185 | 0.327093 | − | 0.944992i | \(-0.393931\pi\) | ||||
0.327093 | + | 0.944992i | \(0.393931\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.68629 | 0.491257 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | −0.207390 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.3137 | 1.75794 | 0.878970 | − | 0.476876i | \(-0.158231\pi\) | ||||
0.878970 | + | 0.476876i | \(0.158231\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.8284 | 1.49031 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.9706 | −1.88764 | −0.943821 | − | 0.330458i | \(-0.892797\pi\) | ||||
−0.943821 | + | 0.330458i | \(0.892797\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.65685 | 0.163255 | 0.0816274 | − | 0.996663i | \(-0.473988\pi\) | ||||
0.0816274 | + | 0.996663i | \(0.473988\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.92893 | 0.186477 | 0.0932385 | − | 0.995644i | \(-0.470278\pi\) | ||||
0.0932385 | + | 0.995644i | \(0.470278\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.6569 | 1.11652 | 0.558262 | − | 0.829665i | \(-0.311468\pi\) | ||||
0.558262 | + | 0.829665i | \(0.311468\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.4853 | −1.75455 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.34315 | −0.314497 | −0.157248 | − | 0.987559i | \(-0.550262\pi\) | ||||
−0.157248 | + | 0.987559i | \(0.550262\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.0000 | 1.47920 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.142136 | 0.0130296 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.4853 | 1.49866 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −25.7279 | −2.31981 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.1421 | 1.78733 | 0.893663 | − | 0.448739i | \(-0.148127\pi\) | ||||
0.893663 | + | 0.448739i | \(0.148127\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.1421 | 2.12560 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.31371 | 0.464261 | 0.232130 | − | 0.972685i | \(-0.425430\pi\) | ||||
0.232130 | + | 0.972685i | \(0.425430\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.31371 | 0.113913 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.00000 | 0.427179 | 0.213589 | − | 0.976924i | \(-0.431485\pi\) | ||||
0.213589 | + | 0.976924i | \(0.431485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8995 | 0.924483 | 0.462242 | − | 0.886754i | \(-0.347045\pi\) | ||||
0.462242 | + | 0.886754i | \(0.347045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23.3137 | 1.96337 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29.6569 | 2.48003 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.2426 | 1.25719 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.31371 | −0.271470 | −0.135735 | − | 0.990745i | \(-0.543340\pi\) | ||||
−0.135735 | + | 0.990745i | \(0.543340\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.48528 | −0.527765 | −0.263882 | − | 0.964555i | \(-0.585003\pi\) | ||||
−0.263882 | + | 0.964555i | \(0.585003\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.485281 | 0.0392327 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.6569 | −1.56879 | −0.784394 | − | 0.620263i | \(-0.787026\pi\) | ||||
−0.784394 | + | 0.620263i | \(0.787026\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 18.4853 | 1.46598 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.7279 | 1.54521 | 0.772605 | − | 0.634887i | \(-0.218953\pi\) | ||||
0.772605 | + | 0.634887i | \(0.218953\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.34315 | −0.181318 | −0.0906590 | − | 0.995882i | \(-0.528897\pi\) | ||||
−0.0906590 | + | 0.995882i | \(0.528897\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.48528 | 0.342998 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.65685 | −0.734197 | −0.367099 | − | 0.930182i | \(-0.619649\pi\) | ||||
−0.367099 | + | 0.930182i | \(0.619649\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.82843 | 0.663585 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.5858 | 1.61340 | 0.806699 | − | 0.590963i | \(-0.201252\pi\) | ||||
0.806699 | + | 0.590963i | \(0.201252\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.6569 | 1.16376 | 0.581882 | − | 0.813273i | \(-0.302316\pi\) | ||||
0.581882 | + | 0.813273i | \(0.302316\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.4853 | −1.07078 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.899495 | 0.0657776 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.343146 | 0.0249602 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.51472 | −0.109601 | −0.0548006 | − | 0.998497i | \(-0.517452\pi\) | ||||
−0.0548006 | + | 0.998497i | \(0.517452\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.17157 | 0.588203 | 0.294101 | − | 0.955774i | \(-0.404980\pi\) | ||||
0.294101 | + | 0.955774i | \(0.404980\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.65685 | −0.545528 | −0.272764 | − | 0.962081i | \(-0.587938\pi\) | ||||
−0.272764 | + | 0.962081i | \(0.587938\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.6569 | −1.81877 | −0.909383 | − | 0.415960i | \(-0.863446\pi\) | ||||
−0.909383 | + | 0.415960i | \(0.863446\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.65685 | −0.469538 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.62742 | 0.465153 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.6569 | −0.949217 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.31371 | 0.575071 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.8995 | −0.750352 | −0.375176 | − | 0.926954i | \(-0.622418\pi\) | ||||
−0.375176 | + | 0.926954i | \(0.622418\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −23.3137 | −1.59743 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.686292 | 0.0465885 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.0711 | 0.950835 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.970563 | 0.0652871 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.6569 | 0.914531 | 0.457265 | − | 0.889330i | \(-0.348829\pi\) | ||||
0.457265 | + | 0.889330i | \(0.348829\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.3137 | 1.41464 | 0.707320 | − | 0.706893i | \(-0.249904\pi\) | ||||
0.707320 | + | 0.706893i | \(0.249904\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.686292 | 0.0453514 | 0.0226757 | − | 0.999743i | \(-0.492781\pi\) | ||||
0.0226757 | + | 0.999743i | \(0.492781\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.4853 | −0.689881 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.3137 | 0.872210 | 0.436105 | − | 0.899896i | \(-0.356358\pi\) | ||||
0.436105 | + | 0.899896i | \(0.356358\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 30.9706 | 2.01175 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.6274 | −1.20491 | −0.602454 | − | 0.798154i | \(-0.705810\pi\) | ||||
−0.602454 | + | 0.798154i | \(0.705810\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.82843 | 0.633105 | 0.316552 | − | 0.948575i | \(-0.397475\pi\) | ||||
0.316552 | + | 0.948575i | \(0.397475\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.6569 | 1.38929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.97056 | 0.570783 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.00000 | 0.190117 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.75736 | 0.552760 | 0.276380 | − | 0.961048i | \(-0.410865\pi\) | ||||
0.276380 | + | 0.961048i | \(0.410865\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.3137 | −1.59146 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.31371 | −0.331460 | −0.165730 | − | 0.986171i | \(-0.552998\pi\) | ||||
−0.165730 | + | 0.986171i | \(0.552998\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.34315 | 0.394144 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.6274 | 1.40060 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.4853 | 0.646550 | 0.323275 | − | 0.946305i | \(-0.395216\pi\) | ||||
0.323275 | + | 0.946305i | \(0.395216\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.8995 | −0.911834 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.34315 | −0.386748 | −0.193374 | − | 0.981125i | \(-0.561943\pi\) | ||||
−0.193374 | + | 0.981125i | \(0.561943\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.1716 | −1.16459 | −0.582295 | − | 0.812978i | \(-0.697845\pi\) | ||||
−0.582295 | + | 0.812978i | \(0.697845\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.3137 | −0.684737 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.65685 | −0.580224 | −0.290112 | − | 0.956993i | \(-0.593693\pi\) | ||||
−0.290112 | + | 0.956993i | \(0.593693\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.34315 | 0.140280 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.6274 | −1.23053 | −0.615264 | − | 0.788321i | \(-0.710951\pi\) | ||||
−0.615264 | + | 0.788321i | \(0.710951\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.72792 | 0.578265 | 0.289132 | − | 0.957289i | \(-0.406633\pi\) | ||||
0.289132 | + | 0.957289i | \(0.406633\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.82843 | 0.521126 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9706 | −0.998268 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −41.7990 | −2.45030 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.3137 | −1.01148 | −0.505739 | − | 0.862687i | \(-0.668780\pi\) | ||||
−0.505739 | + | 0.862687i | \(0.668780\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.17157 | 0.126007 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.3137 | −1.57959 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.28427 | −0.477497 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 45.7990 | 2.63108 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.24264 | 0.185067 | 0.0925336 | − | 0.995710i | \(-0.470503\pi\) | ||||
0.0925336 | + | 0.995710i | \(0.470503\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.4853 | 1.27502 | 0.637512 | − | 0.770441i | \(-0.279964\pi\) | ||||
0.637512 | + | 0.770441i | \(0.279964\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0000 | 0.565233 | 0.282617 | − | 0.959233i | \(-0.408798\pi\) | ||||
0.282617 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.34315 | −0.131604 | −0.0658021 | − | 0.997833i | \(-0.520961\pi\) | ||||
−0.0658021 | + | 0.997833i | \(0.520961\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 41.9411 | 2.34825 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.65685 | −0.259920 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.272078 | 0.0151388 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −28.1421 | −1.55626 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.00000 | −0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.8995 | 1.25867 | 0.629335 | − | 0.777134i | \(-0.283327\pi\) | ||||
0.629335 | + | 0.777134i | \(0.283327\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.6569 | 1.18679 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.34315 | −0.400007 | −0.200003 | − | 0.979795i | \(-0.564095\pi\) | ||||
−0.200003 | + | 0.979795i | \(0.564095\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.07107 | 0.438360 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.34315 | 0.235195 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.0294 | −0.595534 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.8995 | 1.01458 | 0.507289 | − | 0.861776i | \(-0.330648\pi\) | ||||
0.507289 | + | 0.861776i | \(0.330648\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.3137 | 1.56913 | 0.784563 | − | 0.620049i | \(-0.212887\pi\) | ||||
0.784563 | + | 0.620049i | \(0.212887\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.34315 | 0.125068 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.6274 | 0.672090 | 0.336045 | − | 0.941846i | \(-0.390911\pi\) | ||||
0.336045 | + | 0.941846i | \(0.390911\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.343146 | −0.0181612 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.82843 | −0.465947 | −0.232973 | − | 0.972483i | \(-0.574845\pi\) | ||||
−0.232973 | + | 0.972483i | \(0.574845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4853 | −0.867646 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −39.7990 | −2.08891 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.970563 | −0.0506630 | −0.0253315 | − | 0.999679i | \(-0.508064\pi\) | ||||
−0.0253315 | + | 0.999679i | \(0.508064\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 30.1421 | 1.56914 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.34315 | −0.329320 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.3137 | 1.72492 | 0.862459 | − | 0.506127i | \(-0.168923\pi\) | ||||
0.862459 | + | 0.506127i | \(0.168923\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 45.2548 | 2.33074 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.8995 | −0.868069 | −0.434034 | − | 0.900896i | \(-0.642910\pi\) | ||||
−0.434034 | + | 0.900896i | \(0.642910\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −48.6274 | −2.49126 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.4558 | −1.40293 | −0.701464 | − | 0.712705i | \(-0.747470\pi\) | ||||
−0.701464 | + | 0.712705i | \(0.747470\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −28.2843 | −1.43777 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.31371 | 0.269416 | 0.134708 | − | 0.990885i | \(-0.456990\pi\) | ||||
0.134708 | + | 0.990885i | \(0.456990\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.828427 | −0.0418954 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.8284 | −0.647109 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.68629 | 0.435952 | 0.217976 | − | 0.975954i | \(-0.430054\pi\) | ||||
0.217976 | + | 0.975954i | \(0.430054\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.17157 | −0.158777 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.4558 | 1.02152 | 0.510758 | − | 0.859724i | \(-0.329365\pi\) | ||||
0.510758 | + | 0.859724i | \(0.329365\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.68629 | 0.233441 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 40.1421 | 1.98977 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.97056 | 0.295225 | 0.147613 | − | 0.989045i | \(-0.452841\pi\) | ||||
0.147613 | + | 0.989045i | \(0.452841\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.0711 | −0.595422 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.02944 | −0.149069 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.3137 | −1.28859 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.55635 | 0.320299 | 0.160149 | − | 0.987093i | \(-0.448802\pi\) | ||||
0.160149 | + | 0.987093i | \(0.448802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −27.3137 | −1.32804 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.97056 | 0.240542 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −71.5980 | −3.45678 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.1421 | −0.584866 | −0.292433 | − | 0.956286i | \(-0.594465\pi\) | ||||
−0.292433 | + | 0.956286i | \(0.594465\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.8284 | 1.04901 | 0.524504 | − | 0.851408i | \(-0.324251\pi\) | ||||
0.524504 | + | 0.851408i | \(0.324251\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.65685 | −0.366277 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.686292 | −0.0327549 | −0.0163775 | − | 0.999866i | \(-0.505213\pi\) | ||||
−0.0163775 | + | 0.999866i | \(0.505213\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.8579 | −0.850374 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.5563 | −1.07168 | −0.535842 | − | 0.844318i | \(-0.680006\pi\) | ||||
−0.535842 | + | 0.844318i | \(0.680006\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.00000 | 0.378387 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.4558 | −1.62607 | −0.813036 | − | 0.582214i | \(-0.802187\pi\) | ||||
−0.813036 | + | 0.582214i | \(0.802187\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 55.8701 | 2.63082 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.6569 | 0.735623 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.3431 | −0.811278 | −0.405639 | − | 0.914033i | \(-0.632951\pi\) | ||||
−0.405639 | + | 0.914033i | \(0.632951\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.0710678 | 0.00331716 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.65685 | 0.263466 | 0.131733 | − | 0.991285i | \(-0.457946\pi\) | ||||
0.131733 | + | 0.991285i | \(0.457946\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.9706 | −0.602793 | −0.301397 | − | 0.953499i | \(-0.597453\pi\) | ||||
−0.301397 | + | 0.953499i | \(0.597453\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.31371 | −0.430987 | −0.215494 | − | 0.976505i | \(-0.569136\pi\) | ||||
−0.215494 | + | 0.976505i | \(0.569136\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.28427 | 0.105478 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 47.4558 | 2.18665 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −52.4264 | −2.41057 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.6569 | −0.991599 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.1716 | 1.60703 | 0.803515 | − | 0.595284i | \(-0.202961\pi\) | ||||
0.803515 | + | 0.595284i | \(0.202961\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 43.3137 | 1.97494 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.65685 | 0.439402 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.1127 | −1.13796 | −0.568982 | − | 0.822350i | \(-0.692663\pi\) | ||||
−0.568982 | + | 0.822350i | \(0.692663\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −47.6274 | −2.15379 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.6274 | −0.750385 | −0.375192 | − | 0.926947i | \(-0.622423\pi\) | ||||
−0.375192 | + | 0.926947i | \(0.622423\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.37258 | 0.0618180 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0000 | −0.626726 | −0.313363 | − | 0.949633i | \(-0.601456\pi\) | ||||
−0.313363 | + | 0.949633i | \(0.601456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.65685 | 0.252730 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.9706 | −0.756680 | −0.378340 | − | 0.925667i | \(-0.623505\pi\) | ||||
−0.378340 | + | 0.925667i | \(0.623505\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −45.8701 | −2.03716 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0000 | 0.620539 | 0.310270 | − | 0.950649i | \(-0.399581\pi\) | ||||
0.310270 | + | 0.950649i | \(0.399581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.82843 | −0.213597 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.656854 | 0.0290008 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −50.6274 | −2.22659 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.3137 | 1.02336 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.3137 | 0.714717 | 0.357358 | − | 0.933967i | \(-0.383678\pi\) | ||||
0.357358 | + | 0.933967i | \(0.383678\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.5858 | 0.856427 | 0.428213 | − | 0.903678i | \(-0.359143\pi\) | ||||
0.428213 | + | 0.903678i | \(0.359143\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.142136 | 0.00619153 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.313708 | 0.0136395 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.3431 | −0.448854 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 60.2843 | 2.61120 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −52.1127 | −2.24883 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −33.1005 | −1.42574 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.6569 | −0.759127 | −0.379564 | − | 0.925166i | \(-0.623926\pi\) | ||||
−0.379564 | + | 0.925166i | \(0.623926\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −37.7990 | −1.62211 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.5563 | 0.622385 | 0.311192 | − | 0.950347i | \(-0.399272\pi\) | ||||
0.311192 | + | 0.950347i | \(0.399272\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.9706 | 0.724286 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.6863 | 0.540454 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.6274 | −0.451924 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.3431 | 1.11619 | 0.558097 | − | 0.829775i | \(-0.311532\pi\) | ||||
0.558097 | + | 0.829775i | \(0.311532\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.5685 | −2.39259 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.17157 | −0.0916839 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.97056 | 0.293774 | 0.146887 | − | 0.989153i | \(-0.453075\pi\) | ||||
0.146887 | + | 0.989153i | \(0.453075\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.85786 | −0.329999 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.3137 | −1.10313 | −0.551564 | − | 0.834133i | \(-0.685969\pi\) | ||||
−0.551564 | + | 0.834133i | \(0.685969\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.9411 | 1.33669 | 0.668347 | − | 0.743849i | \(-0.267002\pi\) | ||||
0.668347 | + | 0.743849i | \(0.267002\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.65685 | 0.152767 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.2843 | −1.71869 | −0.859343 | − | 0.511399i | \(-0.829127\pi\) | ||||
−0.859343 | + | 0.511399i | \(0.829127\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.7279 | −0.819864 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.02944 | −0.0427083 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −40.1421 | −1.66252 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.0710678 | 0.00293328 | 0.00146664 | − | 0.999999i | \(-0.499533\pi\) | ||||
0.00146664 | + | 0.999999i | \(0.499533\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.31371 | 0.0541304 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.4853 | 0.760383 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.00000 | 0.287456 | 0.143728 | − | 0.989617i | \(-0.454091\pi\) | ||||
0.143728 | + | 0.989617i | \(0.454091\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 61.9411 | 2.53508 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.7696 | −1.09377 | −0.546887 | − | 0.837206i | \(-0.684187\pi\) | ||||
−0.546887 | + | 0.837206i | \(0.684187\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.1421 | 1.43348 | 0.716739 | − | 0.697342i | \(-0.245634\pi\) | ||||
0.716739 | + | 0.697342i | \(0.245634\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.79899 | 0.317599 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.0000 | 1.46119 | 0.730597 | − | 0.682808i | \(-0.239242\pi\) | ||||
0.730597 | + | 0.682808i | \(0.239242\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16.0000 | −0.648353 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −54.6274 | −2.20999 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.68629 | 0.270057 | 0.135028 | − | 0.990842i | \(-0.456887\pi\) | ||||
0.135028 | + | 0.990842i | \(0.456887\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000 | 0.724653 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.3137 | −0.535123 | −0.267562 | − | 0.963541i | \(-0.586218\pi\) | ||||
−0.267562 | + | 0.963541i | \(0.586218\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | −0.0802572 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.11270 | 0.204836 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.0711 | −0.801561 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.31371 | 0.0523810 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.8579 | −0.631292 | −0.315646 | − | 0.948877i | \(-0.602221\pi\) | ||||
−0.315646 | + | 0.948877i | \(0.602221\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.3137 | 1.04588 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −35.7157 | −1.41511 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.3137 | 1.08051 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −45.3137 | −1.78978 | −0.894892 | − | 0.446283i | \(-0.852748\pi\) | ||||
−0.894892 | + | 0.446283i | \(0.852748\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.6863 | 0.579171 | 0.289585 | − | 0.957152i | \(-0.406483\pi\) | ||||
0.289585 | + | 0.957152i | \(0.406483\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.65685 | −0.222394 | −0.111197 | − | 0.993798i | \(-0.535468\pi\) | ||||
−0.111197 | + | 0.993798i | \(0.535468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.1716 | −0.752550 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.65685 | −0.0649372 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.4853 | −0.643152 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −51.1838 | −1.99384 | −0.996918 | − | 0.0784478i | \(-0.975004\pi\) | ||||
−0.996918 | + | 0.0784478i | \(0.975004\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.34315 | 0.246720 | 0.123360 | − | 0.992362i | \(-0.460633\pi\) | ||||
0.123360 | + | 0.992362i | \(0.460633\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.34315 | −0.0910002 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.6274 | −1.49566 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.9706 | −1.27472 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.4558 | 1.21434 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.3137 | 0.975772 | 0.487886 | − | 0.872907i | \(-0.337768\pi\) | ||||
0.487886 | + | 0.872907i | \(0.337768\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.6863 | −1.10250 | −0.551252 | − | 0.834339i | \(-0.685850\pi\) | ||||
−0.551252 | + | 0.834339i | \(0.685850\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.3431 | 0.550439 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −51.4558 | −1.97179 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.6985 | −0.638950 | −0.319475 | − | 0.947595i | \(-0.603507\pi\) | ||||
−0.319475 | + | 0.947595i | \(0.603507\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.65685 | −0.0632129 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −43.3137 | −1.65012 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.2132 | 1.37762 | 0.688808 | − | 0.724944i | \(-0.258134\pi\) | ||||
0.688808 | + | 0.724944i | \(0.258134\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.2843 | 0.466641 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.82843 | 0.0692566 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −32.1421 | −1.21573 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −47.3137 | −1.78701 | −0.893507 | − | 0.449049i | \(-0.851763\pi\) | ||||
−0.893507 | + | 0.449049i | \(0.851763\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.1421 | 0.457949 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.7157 | −0.591051 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.9411 | −0.824016 | −0.412008 | − | 0.911180i | \(-0.635172\pi\) | ||||
−0.412008 | + | 0.911180i | \(0.635172\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.2843 | −1.36077 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.00000 | −0.149801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 44.9706 | 1.67946 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.4558 | 0.874755 | 0.437378 | − | 0.899278i | \(-0.355907\pi\) | ||||
0.437378 | + | 0.899278i | \(0.355907\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.37258 | 0.0511177 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.7279 | −0.882451 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.71573 | −0.0634585 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.3431 | 0.973006 | 0.486503 | − | 0.873679i | \(-0.338272\pi\) | ||||
0.486503 | + | 0.873679i | \(0.338272\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.4558 | 0.532488 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.6274 | −1.05308 | −0.526538 | − | 0.850151i | \(-0.676510\pi\) | ||||
−0.526538 | + | 0.850151i | \(0.676510\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.6569 | −0.795584 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.7990 | 0.946473 | 0.473237 | − | 0.880935i | \(-0.343086\pi\) | ||||
0.473237 | + | 0.880935i | \(0.343086\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.51472 | −0.128597 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.59798 | 0.0583889 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.6274 | 1.26357 | 0.631786 | − | 0.775143i | \(-0.282322\pi\) | ||||
0.631786 | + | 0.775143i | \(0.282322\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.1421 | −0.770462 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.6569 | −0.932514 | −0.466257 | − | 0.884649i | \(-0.654398\pi\) | ||||
−0.466257 | + | 0.884649i | \(0.654398\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 61.1127 | 2.21825 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.2843 | −1.42405 | −0.712027 | − | 0.702152i | \(-0.752223\pi\) | ||||
−0.712027 | + | 0.702152i | \(0.752223\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.65685 | 0.349602 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.6863 | −0.746939 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.1127 | 1.23014 | 0.615068 | − | 0.788474i | \(-0.289129\pi\) | ||||
0.615068 | + | 0.788474i | \(0.289129\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.8284 | 0.462005 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.3137 | −0.694666 | −0.347333 | − | 0.937742i | \(-0.612913\pi\) | ||||
−0.347333 | + | 0.937742i | \(0.612913\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.3137 | −0.549376 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.8995 | 0.605487 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.6274 | 1.81159 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.31371 | 0.118422 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.6274 | 0.592703 | 0.296352 | − | 0.955079i | \(-0.404230\pi\) | ||||
0.296352 | + | 0.955079i | \(0.404230\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.3137 | −0.901192 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.76955 | −0.0984740 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.9411 | 1.20528 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.0000 | −1.48772 | −0.743858 | − | 0.668338i | \(-0.767006\pi\) | ||||
−0.743858 | + | 0.668338i | \(0.767006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.65685 | −0.0586153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.4558 | 0.616772 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −30.5563 | −1.07831 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.3137 | 0.539068 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.6274 | 1.42838 | 0.714192 | − | 0.699950i | \(-0.246794\pi\) | ||||
0.714192 | + | 0.699950i | \(0.246794\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.9411 | −1.26206 | −0.631032 | − | 0.775757i | \(-0.717368\pi\) | ||||
−0.631032 | + | 0.775757i | \(0.717368\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 46.2843 | 1.62326 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.8579 | −0.554796 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.2548 | 0.463161 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.6274 | −1.41791 | −0.708953 | − | 0.705255i | \(-0.750832\pi\) | ||||
−0.708953 | + | 0.705255i | \(0.750832\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.9706 | −0.452125 | −0.226063 | − | 0.974113i | \(-0.572585\pi\) | ||||
−0.226063 | + | 0.974113i | \(0.572585\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.0711 | 1.67159 | 0.835797 | − | 0.549038i | \(-0.185006\pi\) | ||||
0.835797 | + | 0.549038i | \(0.185006\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.0000 | 0.694629 | 0.347314 | − | 0.937749i | \(-0.387094\pi\) | ||||
0.347314 | + | 0.937749i | \(0.387094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.3137 | 0.808744 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.08326 | −0.0375328 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.343146 | 0.0118609 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.00000 | −0.138095 | −0.0690477 | − | 0.997613i | \(-0.521996\pi\) | ||||
−0.0690477 | + | 0.997613i | \(0.521996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 49.7990 | 1.71517 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.6569 | 0.469255 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.4853 | −0.806013 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.9706 | −1.26733 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.6274 | −0.569312 | −0.284656 | − | 0.958630i | \(-0.591879\pi\) | ||||
−0.284656 | + | 0.958630i | \(0.591879\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.0000 | −0.375753 | −0.187876 | − | 0.982193i | \(-0.560160\pi\) | ||||
−0.187876 | + | 0.982193i | \(0.560160\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 54.2132 | 1.84973 | 0.924865 | − | 0.380295i | \(-0.124177\pi\) | ||||
0.924865 | + | 0.380295i | \(0.124177\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.3137 | −0.726369 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.00000 | −0.136162 | −0.0680808 | − | 0.997680i | \(-0.521688\pi\) | ||||
−0.0680808 | + | 0.997680i | \(0.521688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.9706 | 1.39143 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −67.2548 | −2.28146 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.5980 | 0.528517 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 48.9706 | 1.65740 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.3431 | 0.889545 | 0.444772 | − | 0.895644i | \(-0.353285\pi\) | ||||
0.444772 | + | 0.895644i | \(0.353285\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 41.7990 | 1.40984 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.6863 | −0.494794 | −0.247397 | − | 0.968914i | \(-0.579575\pi\) | ||||
−0.247397 | + | 0.968914i | \(0.579575\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.2426 | 1.45523 | 0.727615 | − | 0.685985i | \(-0.240629\pi\) | ||||
0.727615 | + | 0.685985i | \(0.240629\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.3431 | 0.750209 | 0.375105 | − | 0.926982i | \(-0.377607\pi\) | ||||
0.375105 | + | 0.926982i | \(0.377607\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.6863 | 0.559640 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −49.7279 | −1.66595 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.3137 | −0.512454 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 65.9411 | 2.20171 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.62742 | 0.221037 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.31371 | −0.0437660 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.0000 | 0.665558 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.3137 | −1.50462 | −0.752308 | − | 0.658811i | \(-0.771060\pi\) | ||||
−0.752308 | + | 0.658811i | \(0.771060\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −53.6569 | −1.77969 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.2843 | −1.20215 | −0.601076 | − | 0.799192i | \(-0.705261\pi\) | ||||
−0.601076 | + | 0.799192i | \(0.705261\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.51472 | −0.215606 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.40202 | 0.145368 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.1716 | 1.29215 | 0.646075 | − | 0.763274i | \(-0.276409\pi\) | ||||
0.646075 | + | 0.763274i | \(0.276409\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.82843 | −0.257955 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 54.6274 | 1.79808 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.68629 | 0.153918 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.627417 | 0.0205849 | 0.0102924 | − | 0.999947i | \(-0.496724\pi\) | ||||
0.0102924 | + | 0.999947i | \(0.496724\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.0122 | −0.328136 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −54.2843 | −1.77719 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.1127 | 0.657053 | 0.328527 | − | 0.944495i | \(-0.393448\pi\) | ||||
0.328527 | + | 0.944495i | \(0.393448\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.1421 | −0.787849 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.9706 | 1.33560 | 0.667801 | − | 0.744340i | \(-0.267236\pi\) | ||||
0.667801 | + | 0.744340i | \(0.267236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −51.4558 | −1.67563 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.5980 | −1.09179 | −0.545894 | − | 0.837854i | \(-0.683810\pi\) | ||||
−0.545894 | + | 0.837854i | \(0.683810\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.9706 | −1.07027 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.65685 | 0.183436 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.3137 | 0.398880 | 0.199440 | − | 0.979910i | \(-0.436088\pi\) | ||||
0.199440 | + | 0.979910i | \(0.436088\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −101.255 | −3.27310 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.14214 | 0.133757 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3137 | −0.977862 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.45584 | 0.175812 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.6274 | 1.37081 | 0.685403 | − | 0.728164i | \(-0.259626\pi\) | ||||
0.685403 | + | 0.728164i | \(0.259626\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.656854 | −0.0211012 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.8995 | 1.37671 | 0.688355 | − | 0.725374i | \(-0.258333\pi\) | ||||
0.688355 | + | 0.725374i | \(0.258333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.02944 | 0.289470 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.1127 | −0.771434 | −0.385717 | − | 0.922617i | \(-0.626046\pi\) | ||||
−0.385717 | + | 0.922617i | \(0.626046\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.3553 | 1.03408 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32.9706 | 1.05267 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.7990 | 1.07802 | 0.539010 | − | 0.842299i | \(-0.318798\pi\) | ||||
0.539010 | + | 0.842299i | \(0.318798\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.3137 | 0.614762 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.2843 | 1.53535 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −62.0833 | −1.97214 | −0.986070 | − | 0.166331i | \(-0.946808\pi\) | ||||
−0.986070 | + | 0.166331i | \(0.946808\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −55.2843 | −1.75439 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.9706 | −0.537463 | −0.268732 | − | 0.963215i | \(-0.586604\pi\) | ||||
−0.268732 | + | 0.963215i | \(0.586604\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.17157 | 0.100344 |
(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 | 3200.2.a.bd.1.1 | yes | 2 | |
4.3 | odd | 2 | 3200.2.a.bm.1.2 | yes | 2 | ||
5.2 | odd | 4 | 3200.2.c.ba.2049.4 | 4 | |||
5.3 | odd | 4 | 3200.2.c.ba.2049.1 | 4 | |||
5.4 | even | 2 | 3200.2.a.bn.1.2 | yes | 2 | ||
8.3 | odd | 2 | 3200.2.a.bh.1.1 | yes | 2 | ||
8.5 | even | 2 | 3200.2.a.bi.1.2 | yes | 2 | ||
20.3 | even | 4 | 3200.2.c.y.2049.4 | 4 | |||
20.7 | even | 4 | 3200.2.c.y.2049.1 | 4 | |||
20.19 | odd | 2 | 3200.2.a.bc.1.1 | ✓ | 2 | ||
40.3 | even | 4 | 3200.2.c.bb.2049.1 | 4 | |||
40.13 | odd | 4 | 3200.2.c.z.2049.4 | 4 | |||
40.19 | odd | 2 | 3200.2.a.bj.1.2 | yes | 2 | ||
40.27 | even | 4 | 3200.2.c.bb.2049.4 | 4 | |||
40.29 | even | 2 | 3200.2.a.bg.1.1 | yes | 2 | ||
40.37 | odd | 4 | 3200.2.c.z.2049.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3200.2.a.bc.1.1 | ✓ | 2 | 20.19 | odd | 2 | ||
3200.2.a.bd.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
3200.2.a.bg.1.1 | yes | 2 | 40.29 | even | 2 | ||
3200.2.a.bh.1.1 | yes | 2 | 8.3 | odd | 2 | ||
3200.2.a.bi.1.2 | yes | 2 | 8.5 | even | 2 | ||
3200.2.a.bj.1.2 | yes | 2 | 40.19 | odd | 2 | ||
3200.2.a.bm.1.2 | yes | 2 | 4.3 | odd | 2 | ||
3200.2.a.bn.1.2 | yes | 2 | 5.4 | even | 2 | ||
3200.2.c.y.2049.1 | 4 | 20.7 | even | 4 | |||
3200.2.c.y.2049.4 | 4 | 20.3 | even | 4 | |||
3200.2.c.z.2049.1 | 4 | 40.37 | odd | 4 | |||
3200.2.c.z.2049.4 | 4 | 40.13 | odd | 4 | |||
3200.2.c.ba.2049.1 | 4 | 5.3 | odd | 4 | |||
3200.2.c.ba.2049.4 | 4 | 5.2 | odd | 4 | |||
3200.2.c.bb.2049.1 | 4 | 40.3 | even | 4 | |||
3200.2.c.bb.2049.4 | 4 | 40.27 | even | 4 |