Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,2,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, 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("1856.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(14.8202346151\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 232) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | 1.36333 | 0.787118 | 0.393559 | − | 0.919299i | \(-0.371244\pi\) | ||||
0.393559 | + | 0.919299i | \(0.371244\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.14134 | −1.85206 | −0.926031 | − | 0.377448i | \(-0.876802\pi\) | ||||
−0.926031 | + | 0.377448i | \(0.876802\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.14134 | −0.380445 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.64600 | −1.70233 | −0.851167 | − | 0.524896i | \(-0.824104\pi\) | ||||
−0.851167 | + | 0.524896i | \(0.824104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.86799 | 0.795438 | 0.397719 | − | 0.917507i | \(-0.369802\pi\) | ||||
0.397719 | + | 0.917507i | \(0.369802\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.64600 | −1.45779 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.28267 | 0.982512 | 0.491256 | − | 0.871015i | \(-0.336538\pi\) | ||||
0.491256 | + | 0.871015i | \(0.336538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.72666 | 0.568547 | 0.284274 | − | 0.958743i | \(-0.408248\pi\) | ||||
0.284274 | + | 0.958743i | \(0.408248\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.1507 | 2.43013 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.64600 | −1.08657 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.36333 | 0.963282 | 0.481641 | − | 0.876369i | \(-0.340041\pi\) | ||||
0.481641 | + | 0.876369i | \(0.340041\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.69735 | −1.33994 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.28267 | 1.03286 | 0.516432 | − | 0.856328i | \(-0.327260\pi\) | ||||
0.516432 | + | 0.856328i | \(0.327260\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.91002 | 0.626104 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.7360 | 1.83285 | 0.916426 | − | 0.400203i | \(-0.131060\pi\) | ||||
0.916426 | + | 0.400203i | \(0.131060\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.91934 | 0.445196 | 0.222598 | − | 0.974910i | \(-0.428546\pi\) | ||||
0.222598 | + | 0.974910i | \(0.428546\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.72666 | 0.704608 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.19269 | 0.611566 | 0.305783 | − | 0.952101i | \(-0.401082\pi\) | ||||
0.305783 | + | 0.952101i | \(0.401082\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.72666 | 0.381808 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.41468 | −0.194321 | −0.0971606 | − | 0.995269i | \(-0.530976\pi\) | ||||
−0.0971606 | + | 0.995269i | \(0.530976\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 23.3820 | 3.15283 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.83869 | 0.773353 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.27334 | 0.165775 | 0.0828876 | − | 0.996559i | \(-0.473586\pi\) | ||||
0.0828876 | + | 0.996559i | \(0.473586\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.45331 | −0.442151 | −0.221076 | − | 0.975257i | \(-0.570957\pi\) | ||||
−0.221076 | + | 0.975257i | \(0.570957\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.8773 | −1.47320 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.45331 | 1.15491 | 0.577453 | − | 0.816424i | \(-0.304047\pi\) | ||||
0.577453 | + | 0.816424i | \(0.304047\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.71733 | 0.447514 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.8387 | −1.64235 | −0.821175 | − | 0.570676i | \(-0.806681\pi\) | ||||
−0.821175 | + | 0.570676i | \(0.806681\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.73599 | −0.905429 | −0.452714 | − | 0.891656i | \(-0.649544\pi\) | ||||
−0.452714 | + | 0.891656i | \(0.649544\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 16.5653 | 1.91280 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.9193 | 1.67856 | 0.839279 | − | 0.543701i | \(-0.182978\pi\) | ||||
0.839279 | + | 0.543701i | \(0.182978\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.27334 | −0.474816 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.27334 | 1.01788 | 0.508941 | − | 0.860801i | \(-0.330037\pi\) | ||||
0.508941 | + | 0.860801i | \(0.330037\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.28267 | −0.898382 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.36333 | −0.146164 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.3013 | −1.72794 | −0.863969 | − | 0.503545i | \(-0.832029\pi\) | ||||
−0.863969 | + | 0.503545i | \(0.832029\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.31198 | 0.758217 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17.7360 | −1.81967 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.2827 | −1.04405 | −0.522024 | − | 0.852931i | \(-0.674823\pi\) | ||||
−0.522024 | + | 0.852931i | \(0.674823\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.44398 | 0.647645 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.829359 | 0.0825243 | 0.0412622 | − | 0.999148i | \(-0.486862\pi\) | ||||
0.0412622 | + | 0.999148i | \(0.486862\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.72666 | 0.268665 | 0.134333 | − | 0.990936i | \(-0.457111\pi\) | ||||
0.134333 | + | 0.990936i | \(0.457111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.0187 | 1.74193 | 0.870965 | − | 0.491346i | \(-0.163495\pi\) | ||||
0.870965 | + | 0.491346i | \(0.163495\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.97070 | 0.667672 | 0.333836 | − | 0.942631i | \(-0.391657\pi\) | ||||
0.333836 | + | 0.942631i | \(0.391657\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.56534 | 0.812987 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5653 | 0.993904 | 0.496952 | − | 0.867778i | \(-0.334452\pi\) | ||||
0.496952 | + | 0.867778i | \(0.334452\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.2920 | −1.05298 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.27334 | −0.302621 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.8773 | 1.89794 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.0000 | 1.44267 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −29.6133 | −2.64869 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.73599 | −0.508986 | −0.254493 | − | 0.967075i | \(-0.581909\pi\) | ||||
−0.254493 | + | 0.967075i | \(0.581909\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.98002 | 0.350422 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.71733 | 0.324784 | 0.162392 | − | 0.986726i | \(-0.448079\pi\) | ||||
0.162392 | + | 0.986726i | \(0.448079\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 23.3820 | 2.01240 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.28267 | 0.536765 | 0.268382 | − | 0.963312i | \(-0.413511\pi\) | ||||
0.268382 | + | 0.963312i | \(0.413511\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.17997 | −0.354540 | −0.177270 | − | 0.984162i | \(-0.556727\pi\) | ||||
−0.177270 | + | 0.984162i | \(0.556727\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.71601 | 0.481375 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.1927 | −1.35410 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.14134 | 0.343919 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.54330 | −0.787118 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.60398 | −0.704865 | −0.352433 | − | 0.935837i | \(-0.614645\pi\) | ||||
−0.352433 | + | 0.935837i | \(0.614645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.01866 | −0.489791 | −0.244896 | − | 0.969549i | \(-0.578754\pi\) | ||||
−0.244896 | + | 0.969549i | \(0.578754\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.28267 | −0.184543 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.2113 | −1.78406 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.71733 | −0.137058 | −0.0685288 | − | 0.997649i | \(-0.521831\pi\) | ||||
−0.0685288 | + | 0.997649i | \(0.521831\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.92867 | −0.152954 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1086 | 0.791770 | 0.395885 | − | 0.918300i | \(-0.370438\pi\) | ||||
0.395885 | + | 0.918300i | \(0.370438\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 31.8773 | 2.48165 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.8387 | −1.07087 | −0.535435 | − | 0.844576i | \(-0.679852\pi\) | ||||
−0.535435 | + | 0.844576i | \(0.679852\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.77462 | −0.367278 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.88797 | −0.373792 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5653 | 0.803268 | 0.401634 | − | 0.915800i | \(-0.368442\pi\) | ||||
0.401634 | + | 0.915800i | \(0.368442\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.73599 | 0.130485 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.8387 | −1.33333 | −0.666663 | − | 0.745359i | \(-0.732278\pi\) | ||||
−0.666663 | + | 0.745359i | \(0.732278\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9707 | −0.815445 | −0.407723 | − | 0.913106i | \(-0.633677\pi\) | ||||
−0.407723 | + | 0.913106i | \(0.633677\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.70800 | −0.348025 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −26.0187 | −1.91293 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.2920 | −0.825753 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.3013 | 1.61367 | 0.806834 | − | 0.590778i | \(-0.201179\pi\) | ||||
0.806834 | + | 0.590778i | \(0.201179\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.82936 | −0.347625 | −0.173812 | − | 0.984779i | \(-0.555609\pi\) | ||||
−0.173812 | + | 0.984779i | \(0.555609\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.1927 | −1.15958 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.5653 | 1.32273 | 0.661363 | − | 0.750066i | \(-0.269978\pi\) | ||||
0.661363 | + | 0.750066i | \(0.269978\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.98134 | 0.140454 | 0.0702268 | − | 0.997531i | \(-0.477628\pi\) | ||||
0.0702268 | + | 0.997531i | \(0.477628\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.8880 | 0.909047 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −48.6027 | −3.39456 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.11203 | −0.216301 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −24.1800 | −1.67256 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.6553 | 1.42197 | 0.710986 | − | 0.703206i | \(-0.248249\pi\) | ||||
0.710986 | + | 0.703206i | \(0.248249\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.8667 | −1.29272 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.0900 | −0.824530 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.5467 | −0.712679 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.73599 | 0.385844 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.4040 | 1.50028 | 0.750142 | − | 0.661276i | \(-0.229985\pi\) | ||||
0.750142 | + | 0.661276i | \(0.229985\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.8680 | −0.924533 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.7640 | 1.77639 | 0.888194 | − | 0.459469i | \(-0.151960\pi\) | ||||
0.888194 | + | 0.459469i | \(0.151960\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.829359 | 0.0548056 | 0.0274028 | − | 0.999624i | \(-0.491276\pi\) | ||||
0.0274028 | + | 0.999624i | \(0.491276\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.1507 | 1.51665 | 0.758325 | − | 0.651876i | \(-0.226018\pi\) | ||||
0.758325 | + | 0.651876i | \(0.226018\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.3633 | −1.13266 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.3400 | 1.32122 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.7267 | −0.693850 | −0.346925 | − | 0.937893i | \(-0.612774\pi\) | ||||
−0.346925 | + | 0.937893i | \(0.612774\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.603978 | −0.0389056 | −0.0194528 | − | 0.999811i | \(-0.506192\pi\) | ||||
−0.0194528 | + | 0.999811i | \(0.506192\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.1120 | 0.712837 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 28.9894 | 1.85206 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.2827 | 0.781528 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.6426 | 0.801193 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.92867 | 0.121737 | 0.0608684 | − | 0.998146i | \(-0.480613\pi\) | ||||
0.0608684 | + | 0.998146i | \(0.480613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.3947 | −0.967857 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.2920 | −0.707133 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.5946 | 1.34704 | 0.673519 | − | 0.739170i | \(-0.264782\pi\) | ||||
0.673519 | + | 0.739170i | \(0.264782\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.14134 | 0.0706469 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.08998 | −0.498850 | −0.249425 | − | 0.968394i | \(-0.580242\pi\) | ||||
−0.249425 | + | 0.968394i | \(0.580242\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.85866 | 0.359895 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.2241 | −1.36009 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.6587 | −0.710845 | −0.355422 | − | 0.934706i | \(-0.615663\pi\) | ||||
−0.355422 | + | 0.934706i | \(0.615663\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.07133 | 0.125824 | 0.0629121 | − | 0.998019i | \(-0.479961\pi\) | ||||
0.0629121 | + | 0.998019i | \(0.479961\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −68.6027 | −4.13690 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.4720 | 0.809452 | 0.404726 | − | 0.914438i | \(-0.367367\pi\) | ||||
0.404726 | + | 0.914438i | \(0.367367\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.12136 | −0.366476 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.8680 | −1.36419 | −0.682095 | − | 0.731264i | \(-0.738931\pi\) | ||||
−0.682095 | + | 0.731264i | \(0.738931\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.707999 | 0.0420862 | 0.0210431 | − | 0.999779i | \(-0.493301\pi\) | ||||
0.0210431 | + | 0.999779i | \(0.493301\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −24.1800 | −1.43230 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.0187 | −0.821788 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.5653 | 1.08460 | 0.542300 | − | 0.840185i | \(-0.317554\pi\) | ||||
0.542300 | + | 0.840185i | \(0.317554\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.27334 | −0.307026 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 31.8773 | 1.84971 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.82003 | 0.452244 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.13069 | 0.0649564 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.3013 | 0.818892 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.55263 | −0.488124 | −0.244062 | − | 0.969760i | \(-0.578480\pi\) | ||||
−0.244062 | + | 0.969760i | \(0.578480\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.71733 | 0.211471 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.1706 | 0.746839 | 0.373419 | − | 0.927663i | \(-0.378185\pi\) | ||||
0.373419 | + | 0.927663i | \(0.378185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.14134 | 0.460176 | 0.230088 | − | 0.973170i | \(-0.426099\pi\) | ||||
0.230088 | + | 0.973170i | \(0.426099\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.1120 | −0.961107 | −0.480554 | − | 0.876965i | \(-0.659564\pi\) | ||||
−0.480554 | + | 0.876965i | \(0.659564\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.64600 | 0.316115 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.5653 | 1.37110 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.56534 | 0.476589 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.8480 | 1.93302 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.50335 | 0.525536 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.7487 | 0.975557 | 0.487778 | − | 0.872967i | \(-0.337807\pi\) | ||||
0.487778 | + | 0.872967i | \(0.337807\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.17064 | −0.392949 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −39.1493 | −2.13896 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5467 | 0.683462 | 0.341731 | − | 0.939798i | \(-0.388987\pi\) | ||||
0.341731 | + | 0.939798i | \(0.388987\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.4040 | 0.782320 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.2814 | −1.63983 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.3947 | −0.828823 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.3107 | 1.14402 | 0.572008 | − | 0.820248i | \(-0.306165\pi\) | ||||
0.572008 | + | 0.820248i | \(0.306165\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.3213 | −1.08777 | −0.543887 | − | 0.839158i | \(-0.683048\pi\) | ||||
−0.543887 | + | 0.839158i | \(0.683048\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.1927 | −0.864302 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.09337 | −0.164644 | −0.0823218 | − | 0.996606i | \(-0.526234\pi\) | ||||
−0.0823218 | + | 0.996606i | \(0.526234\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 57.3107 | 3.04173 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.4847 | 0.817251 | 0.408625 | − | 0.912702i | \(-0.366008\pi\) | ||||
0.408625 | + | 0.912702i | \(0.366008\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.658719 | −0.0346694 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.4626 | 1.49390 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.0373 | 1.67691 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.8480 | 1.71465 | 0.857326 | − | 0.514773i | \(-0.172124\pi\) | ||||
0.857326 | + | 0.514773i | \(0.172124\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.3947 | −0.697300 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.706681 | 0.0365905 | 0.0182953 | − | 0.999833i | \(-0.494176\pi\) | ||||
0.0182953 | + | 0.999833i | \(0.494176\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −40.3727 | −2.08484 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.86799 | −0.147709 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.3947 | −0.790773 | −0.395386 | − | 0.918515i | \(-0.629389\pi\) | ||||
−0.395386 | + | 0.918515i | \(0.629389\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.82003 | −0.400632 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.43466 | −0.379893 | −0.189947 | − | 0.981794i | \(-0.560831\pi\) | ||||
−0.189947 | + | 0.981794i | \(0.560831\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.33195 | −0.169373 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.1893 | 1.68276 | 0.841382 | − | 0.540441i | \(-0.181742\pi\) | ||||
0.841382 | + | 0.540441i | \(0.181742\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.45331 | 0.275786 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.06794 | 0.255644 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −61.7860 | −3.10879 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.44267 | −0.323348 | −0.161674 | − | 0.986844i | \(-0.551689\pi\) | ||||
−0.161674 | + | 0.986844i | \(0.551689\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.32131 | −0.215796 | −0.107898 | − | 0.994162i | \(-0.534412\pi\) | ||||
−0.107898 | + | 0.994162i | \(0.534412\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.3820 | 0.766231 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.6974 | 0.879388 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.4720 | −1.75828 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.3599 | −1.10563 | −0.552814 | − | 0.833305i | \(-0.686446\pi\) | ||||
−0.552814 | + | 0.833305i | \(0.686446\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.56534 | 0.422497 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.4040 | −1.88518 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.69867 | −0.279065 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.63328 | 0.0797911 | 0.0398955 | − | 0.999204i | \(-0.487297\pi\) | ||||
0.0398955 | + | 0.999204i | \(0.487297\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.5653 | −0.709871 | −0.354936 | − | 0.934891i | \(-0.615497\pi\) | ||||
−0.354936 | + | 0.934891i | \(0.615497\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.78527 | −0.232668 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.3013 | 1.17879 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −22.0759 | −1.06584 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.7640 | 1.86719 | 0.933597 | − | 0.358324i | \(-0.116652\pi\) | ||||
0.933597 | + | 0.358324i | \(0.116652\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.73599 | 0.179540 | 0.0897700 | − | 0.995963i | \(-0.471387\pi\) | ||||
0.0897700 | + | 0.995963i | \(0.471387\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.64600 | 0.270705 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.6774 | 0.558605 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.3107 | 1.58983 | 0.794915 | − | 0.606720i | \(-0.207515\pi\) | ||||
0.794915 | + | 0.606720i | \(0.207515\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.98935 | 0.380445 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.8480 | 0.610428 | 0.305214 | − | 0.952284i | \(-0.401272\pi\) | ||||
0.305214 | + | 0.952284i | \(0.401272\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 67.5093 | 3.20025 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.7300 | −0.554812 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.341281 | −0.0161061 | −0.00805303 | − | 0.999968i | \(-0.502563\pi\) | ||||
−0.00805303 | + | 0.999968i | \(0.502563\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −66.2614 | −3.12013 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.20541 | −0.385524 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.9066 | −0.790859 | −0.395429 | − | 0.918496i | \(-0.629404\pi\) | ||||
−0.395429 | + | 0.918496i | \(0.629404\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.2920 | −0.527065 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.0373 | −1.21268 | −0.606339 | − | 0.795206i | \(-0.707363\pi\) | ||||
−0.606339 | + | 0.795206i | \(0.707363\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.3107 | −1.91987 | −0.959935 | − | 0.280224i | \(-0.909591\pi\) | ||||
−0.959935 | + | 0.280224i | \(0.909591\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −30.2814 | −1.40426 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.1180 | −1.53252 | −0.766258 | − | 0.642532i | \(-0.777884\pi\) | ||||
−0.766258 | + | 0.642532i | \(0.777884\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.34128 | −0.107881 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.4826 | −0.757872 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 52.0373 | 2.38764 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.61462 | 0.0739286 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.6553 | 1.12653 | 0.563265 | − | 0.826276i | \(-0.309545\pi\) | ||||
0.563265 | + | 0.826276i | \(0.309545\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0187 | 0.821580 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 42.5840 | 1.93364 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.45331 | −0.247113 | −0.123557 | − | 0.992338i | \(-0.539430\pi\) | ||||
−0.123557 | + | 0.992338i | \(0.539430\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.7814 | 0.623216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.3727 | −0.738888 | −0.369444 | − | 0.929253i | \(-0.620452\pi\) | ||||
−0.369444 | + | 0.929253i | \(0.620452\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.00000 | −0.0900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −26.6867 | −1.19948 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.6333 | −1.14750 | −0.573752 | − | 0.819029i | \(-0.694513\pi\) | ||||
−0.573752 | + | 0.819029i | \(0.694513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.8667 | −0.842901 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.475360 | −0.0211952 | −0.0105976 | − | 0.999944i | \(-0.503373\pi\) | ||||
−0.0105976 | + | 0.999944i | \(0.503373\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.43466 | −0.152840 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.50937 | −0.289091 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.9987 | −1.41832 | −0.709158 | − | 0.705049i | \(-0.750925\pi\) | ||||
−0.709158 | + | 0.705049i | \(0.750925\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.1800 | −1.06757 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.2920 | −0.497585 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.6719 | −1.04109 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.4040 | 0.632267 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.7253 | −1.17086 | −0.585429 | − | 0.810724i | \(-0.699074\pi\) | ||||
−0.585429 | + | 0.810724i | \(0.699074\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.45331 | 0.413365 | 0.206682 | − | 0.978408i | \(-0.433733\pi\) | ||||
0.206682 | + | 0.978408i | \(0.433733\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.7267 | 0.467260 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.5653 | −0.676754 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.45331 | −0.0630684 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.6587 | 1.45792 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −74.6213 | −3.22616 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.3200 | −1.04948 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 39.5220 | 1.70233 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.8667 | 0.897128 | 0.448564 | − | 0.893751i | \(-0.351936\pi\) | ||||
0.448564 | + | 0.893751i | \(0.351936\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.9567 | −0.641852 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28.8680 | −1.23657 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.5653 | −0.537255 | −0.268628 | − | 0.963244i | \(-0.586570\pi\) | ||||
−0.268628 | + | 0.963244i | \(0.586570\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.94139 | 0.168214 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.28267 | −0.182448 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −35.4720 | −1.50570 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.3786 | −1.20244 | −0.601220 | − | 0.799084i | \(-0.705318\pi\) | ||||
−0.601220 | + | 0.799084i | \(0.705318\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.37266 | 0.354126 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.3947 | −0.649965 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.16470 | 0.133376 | 0.0666881 | − | 0.997774i | \(-0.478757\pi\) | ||||
0.0666881 | + | 0.997774i | \(0.478757\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −43.7546 | −1.84077 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.3599 | 0.434311 | 0.217156 | − | 0.976137i | \(-0.430322\pi\) | ||||
0.217156 | + | 0.976137i | \(0.430322\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.5840 | −0.777716 | −0.388858 | − | 0.921298i | \(-0.627130\pi\) | ||||
−0.388858 | + | 0.921298i | \(0.627130\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.4040 | 1.27015 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33.1307 | 1.38165 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.0187 | −1.16643 | −0.583216 | − | 0.812317i | \(-0.698206\pi\) | ||||
−0.583216 | + | 0.812317i | \(0.698206\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.58400 | −0.273622 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.98728 | 0.330799 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.5560 | 0.560472 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −45.8760 | −1.89351 | −0.946753 | − | 0.321962i | \(-0.895658\pi\) | ||||
−0.946753 | + | 0.321962i | \(0.895658\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.9694 | 0.946437 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.3107 | 1.04114 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.8026 | 1.75769 | 0.878846 | − | 0.477105i | \(-0.158314\pi\) | ||||
0.878846 | + | 0.477105i | \(0.158314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.70122 | 0.110554 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.90069 | 0.363672 | 0.181836 | − | 0.983329i | \(-0.441796\pi\) | ||||
0.181836 | + | 0.983329i | \(0.441796\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.7173 | 0.559541 | 0.279771 | − | 0.960067i | \(-0.409742\pi\) | ||||
0.279771 | + | 0.960067i | \(0.409742\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.7894 | −0.439379 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −86.4600 | −3.51510 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.4754 | −0.993424 | −0.496712 | − | 0.867915i | \(-0.665460\pi\) | ||||
−0.496712 | + | 0.867915i | \(0.665460\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0246 | 0.486463 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.74663 | 0.353273 | 0.176637 | − | 0.984276i | \(-0.443478\pi\) | ||||
0.176637 | + | 0.984276i | \(0.443478\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −66.2614 | −2.67192 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.2827 | 0.897067 | 0.448533 | − | 0.893766i | \(-0.351947\pi\) | ||||
0.448533 | + | 0.893766i | \(0.351947\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.9966 | 0.602765 | 0.301382 | − | 0.953503i | \(-0.402552\pi\) | ||||
0.301382 | + | 0.953503i | \(0.402552\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.3947 | −0.617768 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 61.8853 | 2.47541 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −32.9652 | −1.31650 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.5653 | 0.501013 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.7267 | 0.427021 | 0.213511 | − | 0.976941i | \(-0.431510\pi\) | ||||
0.213511 | + | 0.976941i | \(0.431510\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.1600 | 1.11926 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.7546 | 0.942674 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.0759 | −0.795438 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.7946 | 0.624824 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.9253 | −0.905494 | −0.452747 | − | 0.891639i | \(-0.649556\pi\) | ||||
−0.452747 | + | 0.891639i | \(0.649556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.5467 | 1.20464 | 0.602322 | − | 0.798253i | \(-0.294242\pi\) | ||||
0.602322 | + | 0.798253i | \(0.294242\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.4826 | −0.649002 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.7453 | −0.972839 | −0.486419 | − | 0.873725i | \(-0.661697\pi\) | ||||
−0.486419 | + | 0.873725i | \(0.661697\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.18930 | −0.282205 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.4134 | 0.603171 | 0.301586 | − | 0.953439i | \(-0.402484\pi\) | ||||
0.301586 | + | 0.953439i | \(0.402484\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.3947 | −0.601521 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.82936 | 0.344466 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.1341 | 0.706403 | 0.353202 | − | 0.935547i | \(-0.385093\pi\) | ||||
0.353202 | + | 0.935547i | \(0.385093\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0934 | −0.431482 | −0.215741 | − | 0.976451i | \(-0.569217\pi\) | ||||
−0.215741 | + | 0.976451i | \(0.569217\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.82003 | 0.303705 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.72666 | −0.105577 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 30.5441 | 1.18090 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.4974 | 0.752689 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.7160 | −1.37675 | −0.688375 | − | 0.725355i | \(-0.741676\pi\) | ||||
−0.688375 | + | 0.725355i | \(0.741676\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −68.6027 | −2.64052 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.64006 | −0.216765 | −0.108383 | − | 0.994109i | \(-0.534567\pi\) | ||||
−0.108383 | + | 0.994109i | \(0.534567\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.4881 | 1.39823 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.0187 | −0.995576 | −0.497788 | − | 0.867299i | \(-0.665854\pi\) | ||||
−0.497788 | + | 0.867299i | \(0.665854\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.0187 | −0.994122 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.13069 | 0.0431385 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.05729 | −0.154570 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.65872 | 0.367435 | 0.183717 | − | 0.982979i | \(-0.441187\pi\) | ||||
0.183717 | + | 0.982979i | \(0.441187\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.3107 | 0.656631 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.4720 | 0.889064 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.5620 | 1.19378 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.8867 | 0.637800 | 0.318900 | − | 0.947788i | \(-0.396687\pi\) | ||||
0.318900 | + | 0.947788i | \(0.396687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.9066 | 1.01480 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23.6719 | −0.891536 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.2814 | −1.36257 | −0.681287 | − | 0.732016i | \(-0.738580\pi\) | ||||
−0.681287 | + | 0.732016i | \(0.738580\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.0280 | −0.638599 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.6240 | 0.547671 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 67.0594 | 2.50788 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.6240 | −0.546142 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.3293 | 1.76509 | 0.882543 | − | 0.470232i | \(-0.155830\pi\) | ||||
0.882543 | + | 0.470232i | \(0.155830\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.823420 | −0.0306233 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.1507 | −0.451264 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 52.5254 | 1.94806 | 0.974029 | − | 0.226421i | \(-0.0727026\pi\) | ||||
0.974029 | + | 0.226421i | \(0.0727026\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.9694 | 1.03590 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.83869 | 0.215952 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.4320 | 1.08710 | 0.543548 | − | 0.839378i | \(-0.317081\pi\) | ||||
0.543548 | + | 0.839378i | \(0.317081\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 39.5220 | 1.45779 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −53.3734 | −1.96603 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.08998 | −0.150453 | −0.0752263 | − | 0.997166i | \(-0.523968\pi\) | ||||
−0.0752263 | + | 0.997166i | \(0.523968\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.7453 | 0.615154 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.8294 | 0.690782 | 0.345391 | − | 0.938459i | \(-0.387746\pi\) | ||||
0.345391 | + | 0.938459i | \(0.387746\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.6320 | 1.30545 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.5840 | −0.387248 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.6613 | −0.826921 | −0.413461 | − | 0.910522i | \(-0.635680\pi\) | ||||
−0.413461 | + | 0.910522i | \(0.635680\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.62941 | 0.0958212 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.9253 | 0.907124 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.1680 | −1.27820 | −0.639101 | − | 0.769122i | \(-0.720694\pi\) | ||||
−0.639101 | + | 0.769122i | \(0.720694\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.9880 | −0.761817 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.4720 | 0.488359 | 0.244179 | − | 0.969730i | \(-0.421481\pi\) | ||||
0.244179 | + | 0.969730i | \(0.421481\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.45331 | 0.341785 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.65194 | 0.131864 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.0560 | 1.58870 | 0.794349 | − | 0.607461i | \(-0.207812\pi\) | ||||
0.794349 | + | 0.607461i | \(0.207812\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.4406 | 1.06028 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.26401 | −0.153366 | −0.0766830 | − | 0.997056i | \(-0.524433\pi\) | ||||
−0.0766830 | + | 0.997056i | \(0.524433\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 65.1680 | 2.34090 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 50.2614 | 1.80080 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 78.1332 | 2.79583 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.64600 | 0.201772 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.11203 | 0.253839 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.08660 | 0.252610 | 0.126305 | − | 0.991991i | \(-0.459688\pi\) | ||||
0.126305 | + | 0.991991i | \(0.459688\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.0293 | −0.392654 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.90408 | −0.351704 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.98728 | 0.283280 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.4533 | −0.689072 | −0.344536 | − | 0.938773i | \(-0.611964\pi\) | ||||
−0.344536 | + | 0.938773i | \(0.611964\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.38538 | 0.296653 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.6053 | 0.657386 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 43.6774 | 1.54134 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.8947 | −0.559519 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.3200 | −0.503464 | −0.251732 | − | 0.967797i | \(-0.581000\pi\) | ||||
−0.251732 | + | 0.967797i | \(0.581000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.43466 | 0.120607 | 0.0603035 | − | 0.998180i | \(-0.480793\pi\) | ||||
0.0603035 | + | 0.998180i | \(0.480793\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.82390 | 0.0990385 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −41.8633 | −1.46641 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.5026 | 0.437410 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.0921 | 1.15492 | 0.577460 | − | 0.816419i | \(-0.304044\pi\) | ||||
0.577460 | + | 0.816419i | \(0.304044\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.20796 | 0.320969 | 0.160485 | − | 0.987038i | \(-0.448694\pi\) | ||||
0.160485 | + | 0.987038i | \(0.448694\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −93.5279 | −3.25623 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.8607 | 0.725399 | 0.362699 | − | 0.931906i | \(-0.381855\pi\) | ||||
0.362699 | + | 0.931906i | \(0.381855\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.4160 | 0.396494 | 0.198247 | − | 0.980152i | \(-0.436475\pi\) | ||||
0.198247 | + | 0.980152i | \(0.436475\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.3667 | 0.637134 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.0000 | −0.485071 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 57.3107 | 1.98332 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.2814 | −1.04668 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.8260 | −1.16780 | −0.583901 | − | 0.811825i | \(-0.698474\pi\) | ||||
−0.583901 | + | 0.811825i | \(0.698474\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −31.1766 | −1.07378 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.7733 | 0.680222 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.965235 | 0.0331268 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.1307 | 0.587232 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.4347 | 0.596951 | 0.298476 | − | 0.954417i | \(-0.403522\pi\) | ||||
0.298476 | + | 0.954417i | \(0.403522\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.2427 | 0.692286 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.98935 | −0.307070 | −0.153535 | − | 0.988143i | \(-0.549066\pi\) | ||||
−0.153535 | + | 0.988143i | \(0.549066\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.48469 | −0.118896 | −0.0594480 | − | 0.998231i | \(-0.518934\pi\) | ||||
−0.0594480 | + | 0.998231i | \(0.518934\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.8947 | −1.08571 | −0.542853 | − | 0.839827i | \(-0.682656\pi\) | ||||
−0.542853 | + | 0.839827i | \(0.682656\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43.7546 | −1.48770 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.7233 | −0.601914 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −84.2346 | −2.85746 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.1120 | 0.918656 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.7360 | 0.397203 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.5853 | 1.30293 | 0.651467 | − | 0.758677i | \(-0.274154\pi\) | ||||
0.651467 | + | 0.758677i | \(0.274154\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.3107 | 0.853707 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.54669 | −0.287945 | −0.143973 | − | 0.989582i | \(-0.545988\pi\) | ||||
−0.143973 | + | 0.989582i | \(0.545988\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.9253 | −0.704192 | −0.352096 | − | 0.935964i | \(-0.614531\pi\) | ||||
−0.352096 | + | 0.935964i | \(0.614531\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.18930 | −0.241666 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.2886 | 1.28561 | 0.642803 | − | 0.766032i | \(-0.277771\pi\) | ||||
0.642803 | + | 0.766032i | \(0.277771\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.1273 | 0.808295 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.9559 | 0.600871 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 73.8760 | 2.46940 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.6613 | 0.355969 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.36333 | −0.178877 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.82936 | −0.0942596 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 45.4333 | 1.51026 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.28267 | −0.142204 | −0.0711019 | − | 0.997469i | \(-0.522652\pi\) | ||||
−0.0711019 | + | 0.997469i | \(0.522652\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.946578 | −0.0313960 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.9660 | −1.39040 | −0.695198 | − | 0.718819i | \(-0.744683\pi\) | ||||
−0.695198 | + | 0.718819i | \(0.744683\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.3573 | −1.73277 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.4974 | 0.644564 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.06794 | 0.167176 | 0.0835879 | − | 0.996500i | \(-0.473362\pi\) | ||||
0.0835879 | + | 0.996500i | \(0.473362\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.6600 | −0.384211 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −39.6893 | −1.30639 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 76.3386 | 2.51000 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.11203 | −0.102213 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.6960 | 0.908677 | 0.454339 | − | 0.890829i | \(-0.349876\pi\) | ||||
0.454339 | + | 0.890829i | \(0.349876\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.9787 | −0.982512 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.9559 | 0.587850 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 46.7640 | 1.52935 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.6027 | 0.477048 | 0.238524 | − | 0.971137i | \(-0.423336\pi\) | ||||
0.238524 | + | 0.971137i | \(0.423336\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.0993 | 0.362212 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.1600 | −0.331206 | −0.165603 | − | 0.986192i | \(-0.552957\pi\) | ||||
−0.165603 | + | 0.986192i | \(0.552957\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0000 | 1.04206 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.2487 | −0.593002 | −0.296501 | − | 0.955033i | \(-0.595820\pi\) | ||||
−0.296501 | + | 0.955033i | \(0.595820\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.1867 | −0.720212 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.3293 | −0.756505 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.5640 | −1.05485 | −0.527426 | − | 0.849601i | \(-0.676843\pi\) | ||||
−0.527426 | + | 0.849601i | \(0.676843\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −92.3573 | −2.98861 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.69735 | 0.248820 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.23471 | −0.0720874 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.5653 | −0.662709 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.0000 | 0.643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.1247 | −0.486379 | −0.243190 | − | 0.969979i | \(-0.578194\pi\) | ||||
−0.243190 | + | 0.969979i | \(0.578194\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.6774 | 0.375131 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.81070 | −0.282749 | −0.141374 | − | 0.989956i | \(-0.545152\pi\) | ||||
−0.141374 | + | 0.989956i | \(0.545152\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 47.5093 | 1.52151 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.08273 | −0.194604 | −0.0973018 | − | 0.995255i | \(-0.531021\pi\) | ||||
−0.0973018 | + | 0.995255i | \(0.531021\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 92.0373 | 2.94153 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.95591 | −0.254013 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.335342 | −0.0106958 | −0.00534788 | − | 0.999986i | \(-0.501702\pi\) | ||||
−0.00534788 | + | 0.999986i | \(0.501702\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −76.8853 | −2.44977 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.96005 | 0.253115 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.1986 | −0.705163 | −0.352581 | − | 0.935781i | \(-0.614696\pi\) | ||||
−0.352581 | + | 0.935781i | \(0.614696\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.1973 | 0.767878 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.20541 | −0.260129 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.1893 | −0.924434 | −0.462217 | − | 0.886767i | \(-0.652946\pi\) | ||||
−0.462217 | + | 0.886767i | \(0.652946\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −35.4720 | −1.12228 |
(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 | 1856.2.a.y.1.2 | 3 | ||
4.3 | odd | 2 | 1856.2.a.x.1.2 | 3 | |||
8.3 | odd | 2 | 232.2.a.d.1.2 | ✓ | 3 | ||
8.5 | even | 2 | 464.2.a.j.1.2 | 3 | |||
24.5 | odd | 2 | 4176.2.a.bu.1.1 | 3 | |||
24.11 | even | 2 | 2088.2.a.s.1.1 | 3 | |||
40.19 | odd | 2 | 5800.2.a.p.1.2 | 3 | |||
232.115 | odd | 2 | 6728.2.a.j.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.2.a.d.1.2 | ✓ | 3 | 8.3 | odd | 2 | ||
464.2.a.j.1.2 | 3 | 8.5 | even | 2 | |||
1856.2.a.x.1.2 | 3 | 4.3 | odd | 2 | |||
1856.2.a.y.1.2 | 3 | 1.1 | even | 1 | trivial | ||
2088.2.a.s.1.1 | 3 | 24.11 | even | 2 | |||
4176.2.a.bu.1.1 | 3 | 24.5 | odd | 2 | |||
5800.2.a.p.1.2 | 3 | 40.19 | odd | 2 | |||
6728.2.a.j.1.2 | 3 | 232.115 | odd | 2 |