Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3042,2,Mod(1,3042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3042 = 2 \cdot 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3042.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: | \(24.2904922949\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 78) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3042.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.73205 | −1.66902 | −0.834512 | − | 0.550990i | \(-0.814250\pi\) | ||||
−0.834512 | + | 0.550990i | \(0.814250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.73205 | −1.03262 | −0.516309 | − | 0.856402i | \(-0.672694\pi\) | ||||
−0.516309 | + | 0.856402i | \(0.672694\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.73205 | 1.18018 | ||||||||
\(11\) | −1.26795 | −0.382301 | −0.191151 | − | 0.981561i | \(-0.561222\pi\) | ||||
−0.191151 | + | 0.981561i | \(0.561222\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.73205 | 0.730171 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.73205 | 1.39023 | 0.695113 | − | 0.718900i | \(-0.255354\pi\) | ||||
0.695113 | + | 0.718900i | \(0.255354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.73205 | 1.08561 | 0.542803 | − | 0.839860i | \(-0.317363\pi\) | ||||
0.542803 | + | 0.839860i | \(0.317363\pi\) | |||||||
\(20\) | −3.73205 | −0.834512 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.26795 | 0.270328 | ||||||||
\(23\) | −4.19615 | −0.874958 | −0.437479 | − | 0.899229i | \(-0.644129\pi\) | ||||
−0.437479 | + | 0.899229i | \(0.644129\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.92820 | 1.78564 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.73205 | −0.516309 | ||||||||
\(29\) | 4.46410 | 0.828963 | 0.414481 | − | 0.910058i | \(-0.363963\pi\) | ||||
0.414481 | + | 0.910058i | \(0.363963\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.46410 | 0.262960 | 0.131480 | − | 0.991319i | \(-0.458027\pi\) | ||||
0.131480 | + | 0.991319i | \(0.458027\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.73205 | −0.983039 | ||||||||
\(35\) | 10.1962 | 1.72346 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.53590 | 0.581298 | 0.290649 | − | 0.956830i | \(-0.406129\pi\) | ||||
0.290649 | + | 0.956830i | \(0.406129\pi\) | |||||||
\(38\) | −4.73205 | −0.767640 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.73205 | 0.590089 | ||||||||
\(41\) | 9.39230 | 1.46683 | 0.733416 | − | 0.679780i | \(-0.237925\pi\) | ||||
0.733416 | + | 0.679780i | \(0.237925\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.66025 | −1.47317 | −0.736587 | − | 0.676342i | \(-0.763564\pi\) | ||||
−0.736587 | + | 0.676342i | \(0.763564\pi\) | |||||||
\(44\) | −1.26795 | −0.191151 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.19615 | 0.618689 | ||||||||
\(47\) | −2.19615 | −0.320342 | −0.160171 | − | 0.987089i | \(-0.551205\pi\) | ||||
−0.160171 | + | 0.987089i | \(0.551205\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.464102 | 0.0663002 | ||||||||
\(50\) | −8.92820 | −1.26264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.46410 | 0.887913 | 0.443956 | − | 0.896048i | \(-0.353575\pi\) | ||||
0.443956 | + | 0.896048i | \(0.353575\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.73205 | 0.638070 | ||||||||
\(56\) | 2.73205 | 0.365086 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.46410 | −0.586165 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.19615 | −1.17745 | −0.588723 | − | 0.808335i | \(-0.700369\pi\) | ||||
−0.588723 | + | 0.808335i | \(0.700369\pi\) | |||||||
\(62\) | −1.46410 | −0.185941 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.1244 | 1.60340 | 0.801698 | − | 0.597730i | \(-0.203930\pi\) | ||||
0.801698 | + | 0.597730i | \(0.203930\pi\) | |||||||
\(68\) | 5.73205 | 0.695113 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −10.1962 | −1.21867 | ||||||||
\(71\) | −4.73205 | −0.561591 | −0.280796 | − | 0.959768i | \(-0.590598\pi\) | ||||
−0.280796 | + | 0.959768i | \(0.590598\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.26795 | −0.733608 | −0.366804 | − | 0.930298i | \(-0.619548\pi\) | ||||
−0.366804 | + | 0.930298i | \(0.619548\pi\) | |||||||
\(74\) | −3.53590 | −0.411040 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.73205 | 0.542803 | ||||||||
\(77\) | 3.46410 | 0.394771 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.53590 | −0.285311 | −0.142655 | − | 0.989772i | \(-0.545564\pi\) | ||||
−0.142655 | + | 0.989772i | \(0.545564\pi\) | |||||||
\(80\) | −3.73205 | −0.417256 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.39230 | −1.03721 | ||||||||
\(83\) | 0.196152 | 0.0215305 | 0.0107653 | − | 0.999942i | \(-0.496573\pi\) | ||||
0.0107653 | + | 0.999942i | \(0.496573\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.3923 | −2.32032 | ||||||||
\(86\) | 9.66025 | 1.04169 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.26795 | 0.135164 | ||||||||
\(89\) | 9.46410 | 1.00319 | 0.501596 | − | 0.865102i | \(-0.332746\pi\) | ||||
0.501596 | + | 0.865102i | \(0.332746\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.19615 | −0.437479 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.19615 | 0.226516 | ||||||||
\(95\) | −17.6603 | −1.81190 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | −0.464102 | −0.0468813 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.92820 | 0.892820 | ||||||||
\(101\) | −1.92820 | −0.191863 | −0.0959317 | − | 0.995388i | \(-0.530583\pi\) | ||||
−0.0959317 | + | 0.995388i | \(0.530583\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.2679 | −1.50440 | −0.752198 | − | 0.658937i | \(-0.771006\pi\) | ||||
−0.752198 | + | 0.658937i | \(0.771006\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.46410 | −0.627849 | ||||||||
\(107\) | −10.1962 | −0.985699 | −0.492850 | − | 0.870114i | \(-0.664045\pi\) | ||||
−0.492850 | + | 0.870114i | \(0.664045\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.46410 | 0.140236 | 0.0701178 | − | 0.997539i | \(-0.477662\pi\) | ||||
0.0701178 | + | 0.997539i | \(0.477662\pi\) | |||||||
\(110\) | −4.73205 | −0.451183 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.73205 | −0.258155 | ||||||||
\(113\) | 1.33975 | 0.126033 | 0.0630163 | − | 0.998012i | \(-0.479928\pi\) | ||||
0.0630163 | + | 0.998012i | \(0.479928\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.6603 | 1.46033 | ||||||||
\(116\) | 4.46410 | 0.414481 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.00000 | 0.736460 | ||||||||
\(119\) | −15.6603 | −1.43557 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | 9.19615 | 0.832581 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.46410 | 0.131480 | ||||||||
\(125\) | −14.6603 | −1.31125 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.85641 | −0.874615 | −0.437307 | − | 0.899312i | \(-0.644068\pi\) | ||||
−0.437307 | + | 0.899312i | \(0.644068\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.53590 | −0.571044 | −0.285522 | − | 0.958372i | \(-0.592167\pi\) | ||||
−0.285522 | + | 0.958372i | \(0.592167\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.9282 | −1.12102 | ||||||||
\(134\) | −13.1244 | −1.13377 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.73205 | −0.491519 | ||||||||
\(137\) | −11.9282 | −1.01910 | −0.509548 | − | 0.860442i | \(-0.670187\pi\) | ||||
−0.509548 | + | 0.860442i | \(0.670187\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.8564 | 1.51456 | 0.757280 | − | 0.653090i | \(-0.226528\pi\) | ||||
0.757280 | + | 0.653090i | \(0.226528\pi\) | |||||||
\(140\) | 10.1962 | 0.861732 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.73205 | 0.397105 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.6603 | −1.38356 | ||||||||
\(146\) | 6.26795 | 0.518739 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.53590 | 0.290649 | ||||||||
\(149\) | −13.1962 | −1.08107 | −0.540535 | − | 0.841321i | \(-0.681778\pi\) | ||||
−0.540535 | + | 0.841321i | \(0.681778\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.73205 | 0.547847 | 0.273923 | − | 0.961752i | \(-0.411679\pi\) | ||||
0.273923 | + | 0.961752i | \(0.411679\pi\) | |||||||
\(152\) | −4.73205 | −0.383820 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.46410 | −0.279145 | ||||||||
\(155\) | −5.46410 | −0.438887 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.58846 | 0.605625 | 0.302812 | − | 0.953050i | \(-0.402074\pi\) | ||||
0.302812 | + | 0.953050i | \(0.402074\pi\) | |||||||
\(158\) | 2.53590 | 0.201745 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.73205 | 0.295045 | ||||||||
\(161\) | 11.4641 | 0.903498 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.4641 | −1.05459 | −0.527295 | − | 0.849682i | \(-0.676794\pi\) | ||||
−0.527295 | + | 0.849682i | \(0.676794\pi\) | |||||||
\(164\) | 9.39230 | 0.733416 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.196152 | −0.0152244 | ||||||||
\(167\) | 9.46410 | 0.732354 | 0.366177 | − | 0.930545i | \(-0.380666\pi\) | ||||
0.366177 | + | 0.930545i | \(0.380666\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 21.3923 | 1.64071 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.66025 | −0.736587 | ||||||||
\(173\) | −4.39230 | −0.333941 | −0.166970 | − | 0.985962i | \(-0.553398\pi\) | ||||
−0.166970 | + | 0.985962i | \(0.553398\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.3923 | −1.84388 | ||||||||
\(176\) | −1.26795 | −0.0955753 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.46410 | −0.709364 | ||||||||
\(179\) | 16.0526 | 1.19982 | 0.599912 | − | 0.800066i | \(-0.295202\pi\) | ||||
0.599912 | + | 0.800066i | \(0.295202\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.1962 | 1.42684 | 0.713419 | − | 0.700737i | \(-0.247145\pi\) | ||||
0.713419 | + | 0.700737i | \(0.247145\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.19615 | 0.309344 | ||||||||
\(185\) | −13.1962 | −0.970200 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.26795 | −0.531485 | ||||||||
\(188\) | −2.19615 | −0.160171 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.6603 | 1.28121 | ||||||||
\(191\) | 6.92820 | 0.501307 | 0.250654 | − | 0.968077i | \(-0.419354\pi\) | ||||
0.250654 | + | 0.968077i | \(0.419354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7321 | −0.844491 | −0.422246 | − | 0.906481i | \(-0.638758\pi\) | ||||
−0.422246 | + | 0.906481i | \(0.638758\pi\) | |||||||
\(194\) | 6.00000 | 0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.464102 | 0.0331501 | ||||||||
\(197\) | 17.8564 | 1.27222 | 0.636108 | − | 0.771600i | \(-0.280543\pi\) | ||||
0.636108 | + | 0.771600i | \(0.280543\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.1962 | −1.00634 | −0.503169 | − | 0.864188i | \(-0.667833\pi\) | ||||
−0.503169 | + | 0.864188i | \(0.667833\pi\) | |||||||
\(200\) | −8.92820 | −0.631319 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.92820 | 0.135668 | ||||||||
\(203\) | −12.1962 | −0.856002 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −35.0526 | −2.44818 | ||||||||
\(206\) | 15.2679 | 1.06377 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.3923 | 1.12849 | 0.564246 | − | 0.825606i | \(-0.309167\pi\) | ||||
0.564246 | + | 0.825606i | \(0.309167\pi\) | |||||||
\(212\) | 6.46410 | 0.443956 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.1962 | 0.696995 | ||||||||
\(215\) | 36.0526 | 2.45876 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | −1.46410 | −0.0991615 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.73205 | 0.319035 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.9282 | −1.80325 | −0.901623 | − | 0.432523i | \(-0.857623\pi\) | ||||
−0.901623 | + | 0.432523i | \(0.857623\pi\) | |||||||
\(224\) | 2.73205 | 0.182543 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.33975 | −0.0891186 | ||||||||
\(227\) | 12.1962 | 0.809487 | 0.404744 | − | 0.914430i | \(-0.367361\pi\) | ||||
0.404744 | + | 0.914430i | \(0.367361\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.8564 | −0.783493 | −0.391747 | − | 0.920073i | \(-0.628129\pi\) | ||||
−0.391747 | + | 0.920073i | \(0.628129\pi\) | |||||||
\(230\) | −15.6603 | −1.03261 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.46410 | −0.293083 | ||||||||
\(233\) | 7.85641 | 0.514690 | 0.257345 | − | 0.966320i | \(-0.417152\pi\) | ||||
0.257345 | + | 0.966320i | \(0.417152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.19615 | 0.534658 | ||||||||
\(236\) | −8.00000 | −0.520756 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.6603 | 1.01510 | ||||||||
\(239\) | −7.66025 | −0.495501 | −0.247750 | − | 0.968824i | \(-0.579691\pi\) | ||||
−0.247750 | + | 0.968824i | \(0.579691\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.5885 | 0.875309 | 0.437655 | − | 0.899143i | \(-0.355809\pi\) | ||||
0.437655 | + | 0.899143i | \(0.355809\pi\) | |||||||
\(242\) | 9.39230 | 0.603760 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.19615 | −0.588723 | ||||||||
\(245\) | −1.73205 | −0.110657 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.46410 | −0.0929705 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.6603 | 0.927196 | ||||||||
\(251\) | −13.4641 | −0.849847 | −0.424923 | − | 0.905229i | \(-0.639699\pi\) | ||||
−0.424923 | + | 0.905229i | \(0.639699\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.32051 | 0.334497 | ||||||||
\(254\) | 9.85641 | 0.618446 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.33975 | −0.582597 | −0.291299 | − | 0.956632i | \(-0.594087\pi\) | ||||
−0.291299 | + | 0.956632i | \(0.594087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.66025 | −0.600259 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.53590 | 0.403789 | ||||||||
\(263\) | 10.0526 | 0.619867 | 0.309934 | − | 0.950758i | \(-0.399693\pi\) | ||||
0.309934 | + | 0.950758i | \(0.399693\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.1244 | −1.48195 | ||||||||
\(266\) | 12.9282 | 0.792679 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.1244 | 0.801698 | ||||||||
\(269\) | −5.46410 | −0.333152 | −0.166576 | − | 0.986029i | \(-0.553271\pi\) | ||||
−0.166576 | + | 0.986029i | \(0.553271\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.8564 | −1.32768 | −0.663841 | − | 0.747874i | \(-0.731075\pi\) | ||||
−0.663841 | + | 0.747874i | \(0.731075\pi\) | |||||||
\(272\) | 5.73205 | 0.347557 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.9282 | 0.720609 | ||||||||
\(275\) | −11.3205 | −0.682652 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.73205 | −0.344406 | −0.172203 | − | 0.985062i | \(-0.555088\pi\) | ||||
−0.172203 | + | 0.985062i | \(0.555088\pi\) | |||||||
\(278\) | −17.8564 | −1.07096 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.1962 | −0.609337 | ||||||||
\(281\) | −12.3205 | −0.734980 | −0.367490 | − | 0.930027i | \(-0.619783\pi\) | ||||
−0.367490 | + | 0.930027i | \(0.619783\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.6603 | 1.52534 | 0.762672 | − | 0.646786i | \(-0.223887\pi\) | ||||
0.762672 | + | 0.646786i | \(0.223887\pi\) | |||||||
\(284\) | −4.73205 | −0.280796 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.6603 | −1.51468 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8564 | 0.932730 | ||||||||
\(290\) | 16.6603 | 0.978324 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.26795 | −0.366804 | ||||||||
\(293\) | −30.5167 | −1.78280 | −0.891401 | − | 0.453215i | \(-0.850277\pi\) | ||||
−0.891401 | + | 0.453215i | \(0.850277\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.8564 | 1.73831 | ||||||||
\(296\) | −3.53590 | −0.205520 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.1962 | 0.764433 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.3923 | 1.52123 | ||||||||
\(302\) | −6.73205 | −0.387386 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.73205 | 0.271402 | ||||||||
\(305\) | 34.3205 | 1.96519 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.5885 | −1.28919 | −0.644596 | − | 0.764524i | \(-0.722974\pi\) | ||||
−0.644596 | + | 0.764524i | \(0.722974\pi\) | |||||||
\(308\) | 3.46410 | 0.197386 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.46410 | 0.310340 | ||||||||
\(311\) | 1.66025 | 0.0941444 | 0.0470722 | − | 0.998891i | \(-0.485011\pi\) | ||||
0.0470722 | + | 0.998891i | \(0.485011\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.53590 | 0.369431 | 0.184715 | − | 0.982792i | \(-0.440864\pi\) | ||||
0.184715 | + | 0.982792i | \(0.440864\pi\) | |||||||
\(314\) | −7.58846 | −0.428241 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.53590 | −0.142655 | ||||||||
\(317\) | −20.6603 | −1.16040 | −0.580198 | − | 0.814476i | \(-0.697025\pi\) | ||||
−0.580198 | + | 0.814476i | \(0.697025\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.66025 | −0.316913 | ||||||||
\(320\) | −3.73205 | −0.208628 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.4641 | −0.638869 | ||||||||
\(323\) | 27.1244 | 1.50924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.4641 | 0.745708 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.39230 | −0.518603 | ||||||||
\(329\) | 6.00000 | 0.330791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | 0.196152 | 0.0107653 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.46410 | −0.517853 | ||||||||
\(335\) | −48.9808 | −2.67610 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.8564 | −1.13612 | −0.568060 | − | 0.822987i | \(-0.692306\pi\) | ||||
−0.568060 | + | 0.822987i | \(0.692306\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −21.3923 | −1.16016 | ||||||||
\(341\) | −1.85641 | −0.100530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8564 | 0.964155 | ||||||||
\(344\) | 9.66025 | 0.520846 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.39230 | 0.236132 | ||||||||
\(347\) | −33.1244 | −1.77821 | −0.889104 | − | 0.457705i | \(-0.848672\pi\) | ||||
−0.889104 | + | 0.457705i | \(0.848672\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.3205 | 0.820088 | 0.410044 | − | 0.912066i | \(-0.365513\pi\) | ||||
0.410044 | + | 0.912066i | \(0.365513\pi\) | |||||||
\(350\) | 24.3923 | 1.30382 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.26795 | 0.0675819 | ||||||||
\(353\) | 21.7846 | 1.15948 | 0.579739 | − | 0.814802i | \(-0.303155\pi\) | ||||
0.579739 | + | 0.814802i | \(0.303155\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.6603 | 0.937309 | ||||||||
\(356\) | 9.46410 | 0.501596 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.0526 | −0.848404 | ||||||||
\(359\) | 1.12436 | 0.0593412 | 0.0296706 | − | 0.999560i | \(-0.490554\pi\) | ||||
0.0296706 | + | 0.999560i | \(0.490554\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.39230 | 0.178542 | ||||||||
\(362\) | −19.1962 | −1.00893 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.3923 | 1.22441 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.2679 | −0.588182 | −0.294091 | − | 0.955777i | \(-0.595017\pi\) | ||||
−0.294091 | + | 0.955777i | \(0.595017\pi\) | |||||||
\(368\) | −4.19615 | −0.218740 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 13.1962 | 0.686035 | ||||||||
\(371\) | −17.6603 | −0.916875 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.7321 | −0.711019 | −0.355509 | − | 0.934673i | \(-0.615693\pi\) | ||||
−0.355509 | + | 0.934673i | \(0.615693\pi\) | |||||||
\(374\) | 7.26795 | 0.375817 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.19615 | 0.113258 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.46410 | −0.280672 | −0.140336 | − | 0.990104i | \(-0.544818\pi\) | ||||
−0.140336 | + | 0.990104i | \(0.544818\pi\) | |||||||
\(380\) | −17.6603 | −0.905952 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.92820 | −0.354478 | ||||||||
\(383\) | 1.46410 | 0.0748121 | 0.0374060 | − | 0.999300i | \(-0.488091\pi\) | ||||
0.0374060 | + | 0.999300i | \(0.488091\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.9282 | −0.658882 | ||||||||
\(386\) | 11.7321 | 0.597146 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.00000 | −0.304604 | ||||||||
\(389\) | −11.7846 | −0.597503 | −0.298752 | − | 0.954331i | \(-0.596570\pi\) | ||||
−0.298752 | + | 0.954331i | \(0.596570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0526 | −1.21639 | ||||||||
\(392\) | −0.464102 | −0.0234407 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.8564 | −0.899593 | ||||||||
\(395\) | 9.46410 | 0.476191 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.3923 | 1.02346 | 0.511730 | − | 0.859146i | \(-0.329005\pi\) | ||||
0.511730 | + | 0.859146i | \(0.329005\pi\) | |||||||
\(398\) | 14.1962 | 0.711589 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.92820 | 0.446410 | ||||||||
\(401\) | −8.07180 | −0.403086 | −0.201543 | − | 0.979480i | \(-0.564596\pi\) | ||||
−0.201543 | + | 0.979480i | \(0.564596\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.92820 | −0.0959317 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.1962 | 0.605285 | ||||||||
\(407\) | −4.48334 | −0.222231 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.7321 | 0.876793 | 0.438397 | − | 0.898782i | \(-0.355546\pi\) | ||||
0.438397 | + | 0.898782i | \(0.355546\pi\) | |||||||
\(410\) | 35.0526 | 1.73112 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.2679 | −0.752198 | ||||||||
\(413\) | 21.8564 | 1.07548 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.732051 | −0.0359350 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.00000 | 0.293470 | ||||||||
\(419\) | 17.4641 | 0.853177 | 0.426589 | − | 0.904446i | \(-0.359715\pi\) | ||||
0.426589 | + | 0.904446i | \(0.359715\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.7128 | −1.10695 | −0.553477 | − | 0.832864i | \(-0.686699\pi\) | ||||
−0.553477 | + | 0.832864i | \(0.686699\pi\) | |||||||
\(422\) | −16.3923 | −0.797965 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.46410 | −0.313925 | ||||||||
\(425\) | 51.1769 | 2.48244 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.1244 | 1.21585 | ||||||||
\(428\) | −10.1962 | −0.492850 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −36.0526 | −1.73861 | ||||||||
\(431\) | −13.1244 | −0.632178 | −0.316089 | − | 0.948730i | \(-0.602370\pi\) | ||||
−0.316089 | + | 0.948730i | \(0.602370\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.8564 | 0.617839 | 0.308920 | − | 0.951088i | \(-0.400033\pi\) | ||||
0.308920 | + | 0.951088i | \(0.400033\pi\) | |||||||
\(434\) | 4.00000 | 0.192006 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.46410 | 0.0701178 | ||||||||
\(437\) | −19.8564 | −0.949861 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.339746 | −0.0162152 | −0.00810760 | − | 0.999967i | \(-0.502581\pi\) | ||||
−0.00810760 | + | 0.999967i | \(0.502581\pi\) | |||||||
\(440\) | −4.73205 | −0.225592 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.6077 | −0.741544 | −0.370772 | − | 0.928724i | \(-0.620907\pi\) | ||||
−0.370772 | + | 0.928724i | \(0.620907\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −35.3205 | −1.67435 | ||||||||
\(446\) | 26.9282 | 1.27509 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.73205 | −0.129077 | ||||||||
\(449\) | −11.3205 | −0.534248 | −0.267124 | − | 0.963662i | \(-0.586073\pi\) | ||||
−0.267124 | + | 0.963662i | \(0.586073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.9090 | −0.560771 | ||||||||
\(452\) | 1.33975 | 0.0630163 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.1962 | −0.572394 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.33975 | 0.0626707 | 0.0313353 | − | 0.999509i | \(-0.490024\pi\) | ||||
0.0313353 | + | 0.999509i | \(0.490024\pi\) | |||||||
\(458\) | 11.8564 | 0.554013 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 15.6603 | 0.730163 | ||||||||
\(461\) | −22.2679 | −1.03712 | −0.518561 | − | 0.855041i | \(-0.673532\pi\) | ||||
−0.518561 | + | 0.855041i | \(0.673532\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.0526 | 0.467182 | 0.233591 | − | 0.972335i | \(-0.424952\pi\) | ||||
0.233591 | + | 0.972335i | \(0.424952\pi\) | |||||||
\(464\) | 4.46410 | 0.207241 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.85641 | −0.363941 | ||||||||
\(467\) | −18.5885 | −0.860171 | −0.430086 | − | 0.902788i | \(-0.641517\pi\) | ||||
−0.430086 | + | 0.902788i | \(0.641517\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −35.8564 | −1.65570 | ||||||||
\(470\) | −8.19615 | −0.378060 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.00000 | 0.368230 | ||||||||
\(473\) | 12.2487 | 0.563196 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 42.2487 | 1.93850 | ||||||||
\(476\) | −15.6603 | −0.717787 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.66025 | 0.350372 | ||||||||
\(479\) | −33.4641 | −1.52901 | −0.764507 | − | 0.644616i | \(-0.777017\pi\) | ||||
−0.764507 | + | 0.644616i | \(0.777017\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −13.5885 | −0.618937 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.39230 | −0.426923 | ||||||||
\(485\) | 22.3923 | 1.01678 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.12436 | −0.141578 | −0.0707890 | − | 0.997491i | \(-0.522552\pi\) | ||||
−0.0707890 | + | 0.997491i | \(0.522552\pi\) | |||||||
\(488\) | 9.19615 | 0.416290 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.73205 | 0.0782461 | ||||||||
\(491\) | −8.73205 | −0.394072 | −0.197036 | − | 0.980396i | \(-0.563132\pi\) | ||||
−0.197036 | + | 0.980396i | \(0.563132\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.5885 | 1.15245 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.46410 | 0.0657401 | ||||||||
\(497\) | 12.9282 | 0.579909 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0000 | 1.43252 | 0.716258 | − | 0.697835i | \(-0.245853\pi\) | ||||
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | −14.6603 | −0.655626 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.4641 | 0.600932 | ||||||||
\(503\) | −40.9808 | −1.82724 | −0.913621 | − | 0.406567i | \(-0.866726\pi\) | ||||
−0.913621 | + | 0.406567i | \(0.866726\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.19615 | 0.320225 | ||||||||
\(506\) | −5.32051 | −0.236525 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.85641 | −0.437307 | ||||||||
\(509\) | −13.7321 | −0.608662 | −0.304331 | − | 0.952566i | \(-0.598433\pi\) | ||||
−0.304331 | + | 0.952566i | \(0.598433\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.1244 | 0.757537 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.33975 | 0.411959 | ||||||||
\(515\) | 56.9808 | 2.51087 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.78461 | 0.122467 | ||||||||
\(518\) | 9.66025 | 0.424447 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.4449 | −1.81573 | −0.907866 | − | 0.419260i | \(-0.862290\pi\) | ||||
−0.907866 | + | 0.419260i | \(0.862290\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.4449 | −0.981445 | −0.490723 | − | 0.871316i | \(-0.663267\pi\) | ||||
−0.490723 | + | 0.871316i | \(0.663267\pi\) | |||||||
\(524\) | −6.53590 | −0.285522 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.0526 | −0.438312 | ||||||||
\(527\) | 8.39230 | 0.365575 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.39230 | −0.234448 | ||||||||
\(530\) | 24.1244 | 1.04790 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.9282 | −0.560509 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 38.0526 | 1.64516 | ||||||||
\(536\) | −13.1244 | −0.566886 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.46410 | 0.235574 | ||||||||
\(539\) | −0.588457 | −0.0253466 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.67949 | 0.244180 | 0.122090 | − | 0.992519i | \(-0.461040\pi\) | ||||
0.122090 | + | 0.992519i | \(0.461040\pi\) | |||||||
\(542\) | 21.8564 | 0.938813 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.73205 | −0.245760 | ||||||||
\(545\) | −5.46410 | −0.234056 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.19615 | −0.179415 | −0.0897073 | − | 0.995968i | \(-0.528593\pi\) | ||||
−0.0897073 | + | 0.995968i | \(0.528593\pi\) | |||||||
\(548\) | −11.9282 | −0.509548 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.3205 | 0.482708 | ||||||||
\(551\) | 21.1244 | 0.899928 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.92820 | 0.294617 | ||||||||
\(554\) | 5.73205 | 0.243532 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.8564 | 0.757280 | ||||||||
\(557\) | −42.3731 | −1.79540 | −0.897702 | − | 0.440603i | \(-0.854765\pi\) | ||||
−0.897702 | + | 0.440603i | \(0.854765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 10.1962 | 0.430866 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.3205 | 0.519709 | ||||||||
\(563\) | −34.9282 | −1.47205 | −0.736024 | − | 0.676955i | \(-0.763299\pi\) | ||||
−0.736024 | + | 0.676955i | \(0.763299\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.00000 | −0.210352 | ||||||||
\(566\) | −25.6603 | −1.07858 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.73205 | 0.198552 | ||||||||
\(569\) | −30.6410 | −1.28454 | −0.642269 | − | 0.766479i | \(-0.722007\pi\) | ||||
−0.642269 | + | 0.766479i | \(0.722007\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0526 | 0.588081 | 0.294041 | − | 0.955793i | \(-0.405000\pi\) | ||||
0.294041 | + | 0.955793i | \(0.405000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 25.6603 | 1.07104 | ||||||||
\(575\) | −37.4641 | −1.56236 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.73205 | 0.155367 | 0.0776837 | − | 0.996978i | \(-0.475248\pi\) | ||||
0.0776837 | + | 0.996978i | \(0.475248\pi\) | |||||||
\(578\) | −15.8564 | −0.659540 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −16.6603 | −0.691779 | ||||||||
\(581\) | −0.535898 | −0.0222328 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.19615 | −0.339450 | ||||||||
\(584\) | 6.26795 | 0.259370 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.5167 | 1.26063 | ||||||||
\(587\) | −16.0000 | −0.660391 | −0.330195 | − | 0.943913i | \(-0.607115\pi\) | ||||
−0.330195 | + | 0.943913i | \(0.607115\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.92820 | 0.285472 | ||||||||
\(590\) | −29.8564 | −1.22917 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.53590 | 0.145325 | ||||||||
\(593\) | 9.14359 | 0.375482 | 0.187741 | − | 0.982219i | \(-0.439883\pi\) | ||||
0.187741 | + | 0.982219i | \(0.439883\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 58.4449 | 2.39601 | ||||||||
\(596\) | −13.1962 | −0.540535 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.53590 | 0.103614 | 0.0518070 | − | 0.998657i | \(-0.483502\pi\) | ||||
0.0518070 | + | 0.998657i | \(0.483502\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.92820 | 0.323398 | 0.161699 | − | 0.986840i | \(-0.448303\pi\) | ||||
0.161699 | + | 0.986840i | \(0.448303\pi\) | |||||||
\(602\) | −26.3923 | −1.07567 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.73205 | 0.273923 | ||||||||
\(605\) | 35.0526 | 1.42509 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.7846 | −1.65540 | −0.827698 | − | 0.561174i | \(-0.810350\pi\) | ||||
−0.827698 | + | 0.561174i | \(0.810350\pi\) | |||||||
\(608\) | −4.73205 | −0.191910 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −34.3205 | −1.38960 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.39230 | −0.379352 | −0.189676 | − | 0.981847i | \(-0.560744\pi\) | ||||
−0.189676 | + | 0.981847i | \(0.560744\pi\) | |||||||
\(614\) | 22.5885 | 0.911596 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.46410 | −0.139573 | ||||||||
\(617\) | 13.2487 | 0.533373 | 0.266687 | − | 0.963783i | \(-0.414071\pi\) | ||||
0.266687 | + | 0.963783i | \(0.414071\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.4641 | 0.701942 | 0.350971 | − | 0.936386i | \(-0.385852\pi\) | ||||
0.350971 | + | 0.936386i | \(0.385852\pi\) | |||||||
\(620\) | −5.46410 | −0.219444 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.66025 | −0.0665701 | ||||||||
\(623\) | −25.8564 | −1.03592 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | −6.53590 | −0.261227 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.58846 | 0.302812 | ||||||||
\(629\) | 20.2679 | 0.808136 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.71281 | −0.307042 | −0.153521 | − | 0.988145i | \(-0.549061\pi\) | ||||
−0.153521 | + | 0.988145i | \(0.549061\pi\) | |||||||
\(632\) | 2.53590 | 0.100873 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.6603 | 0.820524 | ||||||||
\(635\) | 36.7846 | 1.45975 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.66025 | 0.224092 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.73205 | 0.147522 | ||||||||
\(641\) | 25.9808 | 1.02618 | 0.513089 | − | 0.858335i | \(-0.328501\pi\) | ||||
0.513089 | + | 0.858335i | \(0.328501\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.8564 | −0.546443 | −0.273222 | − | 0.961951i | \(-0.588089\pi\) | ||||
−0.273222 | + | 0.961951i | \(0.588089\pi\) | |||||||
\(644\) | 11.4641 | 0.451749 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27.1244 | −1.06719 | ||||||||
\(647\) | 22.2487 | 0.874687 | 0.437344 | − | 0.899295i | \(-0.355919\pi\) | ||||
0.437344 | + | 0.899295i | \(0.355919\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.1436 | 0.398171 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.4641 | −0.527295 | ||||||||
\(653\) | 17.4641 | 0.683423 | 0.341712 | − | 0.939805i | \(-0.388993\pi\) | ||||
0.341712 | + | 0.939805i | \(0.388993\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.3923 | 0.953086 | ||||||||
\(656\) | 9.39230 | 0.366708 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.00000 | −0.233904 | ||||||||
\(659\) | 10.2487 | 0.399233 | 0.199617 | − | 0.979874i | \(-0.436030\pi\) | ||||
0.199617 | + | 0.979874i | \(0.436030\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.3923 | 0.443109 | 0.221555 | − | 0.975148i | \(-0.428887\pi\) | ||||
0.221555 | + | 0.975148i | \(0.428887\pi\) | |||||||
\(662\) | −20.0000 | −0.777322 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.196152 | −0.00761219 | ||||||||
\(665\) | 48.2487 | 1.87100 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.7321 | −0.725308 | ||||||||
\(668\) | 9.46410 | 0.366177 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 48.9808 | 1.89229 | ||||||||
\(671\) | 11.6603 | 0.450139 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.9282 | 1.07655 | 0.538277 | − | 0.842768i | \(-0.319076\pi\) | ||||
0.538277 | + | 0.842768i | \(0.319076\pi\) | |||||||
\(674\) | 20.8564 | 0.803359 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.4641 | 1.74733 | 0.873664 | − | 0.486530i | \(-0.161738\pi\) | ||||
0.873664 | + | 0.486530i | \(0.161738\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.3923 | 0.629079 | ||||||||
\(680\) | 21.3923 | 0.820357 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.85641 | 0.0710855 | ||||||||
\(683\) | 10.1436 | 0.388134 | 0.194067 | − | 0.980988i | \(-0.437832\pi\) | ||||
0.194067 | + | 0.980988i | \(0.437832\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44.5167 | 1.70089 | ||||||||
\(686\) | −17.8564 | −0.681761 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.66025 | −0.368294 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.6603 | 1.66091 | 0.830457 | − | 0.557082i | \(-0.188079\pi\) | ||||
0.830457 | + | 0.557082i | \(0.188079\pi\) | |||||||
\(692\) | −4.39230 | −0.166970 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.1244 | 1.25738 | ||||||||
\(695\) | −66.6410 | −2.52784 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 53.8372 | 2.03923 | ||||||||
\(698\) | −15.3205 | −0.579890 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −24.3923 | −0.921942 | ||||||||
\(701\) | 3.32051 | 0.125414 | 0.0627069 | − | 0.998032i | \(-0.480027\pi\) | ||||
0.0627069 | + | 0.998032i | \(0.480027\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.7321 | 0.631061 | ||||||||
\(704\) | −1.26795 | −0.0477876 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.7846 | −0.819875 | ||||||||
\(707\) | 5.26795 | 0.198122 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.1436 | 0.493618 | 0.246809 | − | 0.969064i | \(-0.420618\pi\) | ||||
0.246809 | + | 0.969064i | \(0.420618\pi\) | |||||||
\(710\) | −17.6603 | −0.662778 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.46410 | −0.354682 | ||||||||
\(713\) | −6.14359 | −0.230079 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.0526 | 0.599912 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.12436 | −0.0419606 | ||||||||
\(719\) | 29.4641 | 1.09883 | 0.549413 | − | 0.835551i | \(-0.314851\pi\) | ||||
0.549413 | + | 0.835551i | \(0.314851\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.7128 | 1.55347 | ||||||||
\(722\) | −3.39230 | −0.126249 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19.1962 | 0.713419 | ||||||||
\(725\) | 39.8564 | 1.48023 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.9808 | −1.14901 | −0.574506 | − | 0.818500i | \(-0.694806\pi\) | ||||
−0.574506 | + | 0.818500i | \(0.694806\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −23.3923 | −0.865788 | ||||||||
\(731\) | −55.3731 | −2.04805 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.0000 | 0.701781 | 0.350891 | − | 0.936416i | \(-0.385879\pi\) | ||||
0.350891 | + | 0.936416i | \(0.385879\pi\) | |||||||
\(734\) | 11.2679 | 0.415908 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.19615 | 0.154672 | ||||||||
\(737\) | −16.6410 | −0.612980 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.92820 | 0.107716 | 0.0538578 | − | 0.998549i | \(-0.482848\pi\) | ||||
0.0538578 | + | 0.998549i | \(0.482848\pi\) | |||||||
\(740\) | −13.1962 | −0.485100 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.6603 | 0.648328 | ||||||||
\(743\) | 48.3923 | 1.77534 | 0.887671 | − | 0.460479i | \(-0.152322\pi\) | ||||
0.887671 | + | 0.460479i | \(0.152322\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 49.2487 | 1.80433 | ||||||||
\(746\) | 13.7321 | 0.502766 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.26795 | −0.265743 | ||||||||
\(749\) | 27.8564 | 1.01785 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.9090 | −1.82120 | −0.910602 | − | 0.413284i | \(-0.864382\pi\) | ||||
−0.910602 | + | 0.413284i | \(0.864382\pi\) | |||||||
\(752\) | −2.19615 | −0.0800854 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.1244 | −0.914369 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.9282 | 0.760648 | 0.380324 | − | 0.924853i | \(-0.375812\pi\) | ||||
0.380324 | + | 0.924853i | \(0.375812\pi\) | |||||||
\(758\) | 5.46410 | 0.198465 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17.6603 | 0.640605 | ||||||||
\(761\) | −11.3205 | −0.410368 | −0.205184 | − | 0.978723i | \(-0.565779\pi\) | ||||
−0.205184 | + | 0.978723i | \(0.565779\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.00000 | −0.144810 | ||||||||
\(764\) | 6.92820 | 0.250654 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.46410 | −0.0529001 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.8564 | −1.58150 | −0.790751 | − | 0.612138i | \(-0.790310\pi\) | ||||
−0.790751 | + | 0.612138i | \(0.790310\pi\) | |||||||
\(770\) | 12.9282 | 0.465900 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.7321 | −0.422246 | ||||||||
\(773\) | 48.9282 | 1.75983 | 0.879913 | − | 0.475136i | \(-0.157601\pi\) | ||||
0.879913 | + | 0.475136i | \(0.157601\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.0718 | 0.469553 | ||||||||
\(776\) | 6.00000 | 0.215387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.7846 | 0.422499 | ||||||||
\(779\) | 44.4449 | 1.59240 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | 24.0526 | 0.860118 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.464102 | 0.0165751 | ||||||||
\(785\) | −28.3205 | −1.01080 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.67949 | 0.166806 | 0.0834029 | − | 0.996516i | \(-0.473421\pi\) | ||||
0.0834029 | + | 0.996516i | \(0.473421\pi\) | |||||||
\(788\) | 17.8564 | 0.636108 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.46410 | −0.336718 | ||||||||
\(791\) | −3.66025 | −0.130144 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.3923 | −0.723696 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.1962 | −0.503169 | ||||||||
\(797\) | 34.0000 | 1.20434 | 0.602171 | − | 0.798367i | \(-0.294303\pi\) | ||||
0.602171 | + | 0.798367i | \(0.294303\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.5885 | −0.445348 | ||||||||
\(800\) | −8.92820 | −0.315660 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.07180 | 0.285025 | ||||||||
\(803\) | 7.94744 | 0.280459 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −42.7846 | −1.50796 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.92820 | 0.0678340 | ||||||||
\(809\) | 53.5885 | 1.88407 | 0.942035 | − | 0.335515i | \(-0.108910\pi\) | ||||
0.942035 | + | 0.335515i | \(0.108910\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.1769 | 0.603163 | 0.301582 | − | 0.953440i | \(-0.402485\pi\) | ||||
0.301582 | + | 0.953440i | \(0.402485\pi\) | |||||||
\(812\) | −12.1962 | −0.428001 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.48334 | 0.157141 | ||||||||
\(815\) | 50.2487 | 1.76014 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −45.7128 | −1.59929 | ||||||||
\(818\) | −17.7321 | −0.619987 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −35.0526 | −1.22409 | ||||||||
\(821\) | 0.928203 | 0.0323945 | 0.0161973 | − | 0.999869i | \(-0.494844\pi\) | ||||
0.0161973 | + | 0.999869i | \(0.494844\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.5692 | 1.44901 | 0.724506 | − | 0.689269i | \(-0.242068\pi\) | ||||
0.724506 | + | 0.689269i | \(0.242068\pi\) | |||||||
\(824\) | 15.2679 | 0.531884 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.8564 | −0.760482 | ||||||||
\(827\) | −26.5359 | −0.922744 | −0.461372 | − | 0.887207i | \(-0.652643\pi\) | ||||
−0.461372 | + | 0.887207i | \(0.652643\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.1244 | −0.421096 | −0.210548 | − | 0.977583i | \(-0.567525\pi\) | ||||
−0.210548 | + | 0.977583i | \(0.567525\pi\) | |||||||
\(830\) | 0.732051 | 0.0254099 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.66025 | 0.0921723 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.3205 | −1.22232 | ||||||||
\(836\) | −6.00000 | −0.207514 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17.4641 | −0.603287 | ||||||||
\(839\) | −41.8564 | −1.44504 | −0.722522 | − | 0.691348i | \(-0.757017\pi\) | ||||
−0.722522 | + | 0.691348i | \(0.757017\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.07180 | −0.312821 | ||||||||
\(842\) | 22.7128 | 0.782735 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.3923 | 0.564246 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.6603 | 0.881697 | ||||||||
\(848\) | 6.46410 | 0.221978 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −51.1769 | −1.75535 | ||||||||
\(851\) | −14.8372 | −0.508612 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −54.1769 | −1.85498 | −0.927491 | − | 0.373845i | \(-0.878039\pi\) | ||||
−0.927491 | + | 0.373845i | \(0.878039\pi\) | |||||||
\(854\) | −25.1244 | −0.859738 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.1962 | 0.348497 | ||||||||
\(857\) | −39.4449 | −1.34741 | −0.673705 | − | 0.739000i | \(-0.735298\pi\) | ||||
−0.673705 | + | 0.739000i | \(0.735298\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.1244 | −1.60786 | −0.803931 | − | 0.594722i | \(-0.797262\pi\) | ||||
−0.803931 | + | 0.594722i | \(0.797262\pi\) | |||||||
\(860\) | 36.0526 | 1.22938 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.1244 | 0.447017 | ||||||||
\(863\) | 17.1244 | 0.582920 | 0.291460 | − | 0.956583i | \(-0.405859\pi\) | ||||
0.291460 | + | 0.956583i | \(0.405859\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.3923 | 0.557355 | ||||||||
\(866\) | −12.8564 | −0.436878 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.00000 | −0.135769 | ||||||||
\(869\) | 3.21539 | 0.109075 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.46410 | −0.0495807 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.8564 | 0.671653 | ||||||||
\(875\) | 40.0526 | 1.35402 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.9282 | 0.807998 | 0.403999 | − | 0.914759i | \(-0.367620\pi\) | ||||
0.403999 | + | 0.914759i | \(0.367620\pi\) | |||||||
\(878\) | 0.339746 | 0.0114659 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.73205 | 0.159517 | ||||||||
\(881\) | 27.8372 | 0.937858 | 0.468929 | − | 0.883236i | \(-0.344640\pi\) | ||||
0.468929 | + | 0.883236i | \(0.344640\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.9282 | 1.44465 | 0.722325 | − | 0.691554i | \(-0.243074\pi\) | ||||
0.722325 | + | 0.691554i | \(0.243074\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.6077 | 0.524351 | ||||||||
\(887\) | −37.8564 | −1.27109 | −0.635547 | − | 0.772062i | \(-0.719225\pi\) | ||||
−0.635547 | + | 0.772062i | \(0.719225\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.9282 | 0.903143 | ||||||||
\(890\) | 35.3205 | 1.18395 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −26.9282 | −0.901623 | ||||||||
\(893\) | −10.3923 | −0.347765 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −59.9090 | −2.00254 | ||||||||
\(896\) | 2.73205 | 0.0912714 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.3205 | 0.377770 | ||||||||
\(899\) | 6.53590 | 0.217984 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.0526 | 1.23440 | ||||||||
\(902\) | 11.9090 | 0.396525 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.33975 | −0.0445593 | ||||||||
\(905\) | −71.6410 | −2.38143 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.3923 | 1.20839 | 0.604193 | − | 0.796838i | \(-0.293495\pi\) | ||||
0.604193 | + | 0.796838i | \(0.293495\pi\) | |||||||
\(908\) | 12.1962 | 0.404744 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.53590 | 0.0840181 | 0.0420090 | − | 0.999117i | \(-0.486624\pi\) | ||||
0.0420090 | + | 0.999117i | \(0.486624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.248711 | −0.00823114 | ||||||||
\(914\) | −1.33975 | −0.0443149 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.8564 | −0.391747 | ||||||||
\(917\) | 17.8564 | 0.589670 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.9615 | 1.51613 | 0.758065 | − | 0.652179i | \(-0.226145\pi\) | ||||
0.758065 | + | 0.652179i | \(0.226145\pi\) | |||||||
\(920\) | −15.6603 | −0.516303 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.2679 | 0.733356 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.5692 | 1.03799 | ||||||||
\(926\) | −10.0526 | −0.330348 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.46410 | −0.146541 | ||||||||
\(929\) | 39.2487 | 1.28771 | 0.643854 | − | 0.765148i | \(-0.277334\pi\) | ||||
0.643854 | + | 0.765148i | \(0.277334\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.19615 | 0.0719760 | ||||||||
\(932\) | 7.85641 | 0.257345 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.5885 | 0.608233 | ||||||||
\(935\) | 27.1244 | 0.887061 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.24871 | −0.171468 | −0.0857340 | − | 0.996318i | \(-0.527324\pi\) | ||||
−0.0857340 | + | 0.996318i | \(0.527324\pi\) | |||||||
\(938\) | 35.8564 | 1.17075 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.19615 | 0.267329 | ||||||||
\(941\) | −12.6410 | −0.412085 | −0.206043 | − | 0.978543i | \(-0.566059\pi\) | ||||
−0.206043 | + | 0.978543i | \(0.566059\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.4115 | −1.28342 | ||||||||
\(944\) | −8.00000 | −0.260378 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.2487 | −0.398240 | ||||||||
\(947\) | −21.0718 | −0.684741 | −0.342371 | − | 0.939565i | \(-0.611230\pi\) | ||||
−0.342371 | + | 0.939565i | \(0.611230\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −42.2487 | −1.37073 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 15.6603 | 0.507552 | ||||||||
\(953\) | −41.5692 | −1.34656 | −0.673280 | − | 0.739388i | \(-0.735115\pi\) | ||||
−0.673280 | + | 0.739388i | \(0.735115\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.8564 | −0.836694 | ||||||||
\(956\) | −7.66025 | −0.247750 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.4641 | 1.08118 | ||||||||
\(959\) | 32.5885 | 1.05234 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8564 | −0.930852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.5885 | 0.437655 | ||||||||
\(965\) | 43.7846 | 1.40948 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.1244 | −1.38679 | −0.693393 | − | 0.720560i | \(-0.743885\pi\) | ||||
−0.693393 | + | 0.720560i | \(0.743885\pi\) | |||||||
\(968\) | 9.39230 | 0.301880 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.3923 | −0.718974 | ||||||||
\(971\) | −30.2487 | −0.970727 | −0.485364 | − | 0.874312i | \(-0.661313\pi\) | ||||
−0.485364 | + | 0.874312i | \(0.661313\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −48.7846 | −1.56396 | ||||||||
\(974\) | 3.12436 | 0.100111 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.19615 | −0.294362 | ||||||||
\(977\) | −45.9282 | −1.46937 | −0.734687 | − | 0.678407i | \(-0.762671\pi\) | ||||
−0.734687 | + | 0.678407i | \(0.762671\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0000 | −0.383522 | ||||||||
\(980\) | −1.73205 | −0.0553283 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.73205 | 0.278651 | ||||||||
\(983\) | −20.7846 | −0.662926 | −0.331463 | − | 0.943468i | \(-0.607542\pi\) | ||||
−0.331463 | + | 0.943468i | \(0.607542\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −66.6410 | −2.12336 | ||||||||
\(986\) | −25.5885 | −0.814902 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40.5359 | 1.28897 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.5885 | 0.717546 | 0.358773 | − | 0.933425i | \(-0.383195\pi\) | ||||
0.358773 | + | 0.933425i | \(0.383195\pi\) | |||||||
\(992\) | −1.46410 | −0.0464853 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.9282 | −0.410058 | ||||||||
\(995\) | 52.9808 | 1.67960 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.3397 | 0.675837 | 0.337918 | − | 0.941175i | \(-0.390277\pi\) | ||||
0.337918 | + | 0.941175i | \(0.390277\pi\) | |||||||
\(998\) | −32.0000 | −1.01294 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))