Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [120,2,Mod(59,120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("120.59");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 120 = 2^{3} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 120.m (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(0.958204824255\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + x^{2} + 4 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 59.2 | ||
Root | \(-0.866025 + 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 120.59 |
Dual form | 120.2.m.a.59.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(41\) | \(61\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 1.11803i | −0.612372 | + | 0.790569i | ||||
\(3\) | 1.73205 | 1.00000 | ||||||||
\(4\) | −0.500000 | − | 1.93649i | −0.250000 | − | 0.968246i | ||||
\(5\) | 2.23607i | 1.00000i | ||||||||
\(6\) | −1.50000 | + | 1.93649i | −0.612372 | + | 0.790569i | ||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 2.59808 | + | 1.11803i | 0.918559 | + | 0.395285i | ||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | −2.50000 | − | 1.93649i | −0.790569 | − | 0.612372i | ||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | −0.866025 | − | 3.35410i | −0.250000 | − | 0.968246i | ||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.87298i | 1.00000i | ||||||||
\(16\) | −3.50000 | + | 1.93649i | −0.875000 | + | 0.484123i | ||||
\(17\) | −6.92820 | −1.68034 | −0.840168 | − | 0.542326i | \(-0.817544\pi\) | ||||
−0.840168 | + | 0.542326i | \(0.817544\pi\) | |||||||
\(18\) | −2.59808 | + | 3.35410i | −0.612372 | + | 0.790569i | ||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 4.33013 | − | 1.11803i | 0.968246 | − | 0.250000i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.94427i | − | 1.86501i | −0.361158 | − | 0.932505i | \(-0.617618\pi\) | ||
0.361158 | − | 0.932505i | \(-0.382382\pi\) | |||||||
\(24\) | 4.50000 | + | 1.93649i | 0.918559 | + | 0.395285i | ||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | −4.33013 | − | 3.35410i | −0.790569 | − | 0.612372i | ||||
\(31\) | − | 7.74597i | − | 1.39122i | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||
0.718421 | − | 0.695608i | \(-0.244865\pi\) | |||||||
\(32\) | 0.866025 | − | 5.59017i | 0.153093 | − | 0.988212i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | − | 7.74597i | 1.02899 | − | 1.32842i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.50000 | − | 5.80948i | −0.250000 | − | 0.968246i | ||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | −3.46410 | + | 4.47214i | −0.561951 | + | 0.725476i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.50000 | + | 5.80948i | −0.395285 | + | 0.918559i | ||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.70820i | 1.00000i | ||||||||
\(46\) | 10.0000 | + | 7.74597i | 1.47442 | + | 1.14208i | ||||
\(47\) | 8.94427i | 1.30466i | 0.757937 | + | 0.652328i | \(0.226208\pi\) | ||||
−0.757937 | + | 0.652328i | \(0.773792\pi\) | |||||||
\(48\) | −6.06218 | + | 3.35410i | −0.875000 | + | 0.484123i | ||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 4.33013 | − | 5.59017i | 0.612372 | − | 0.790569i | ||||
\(51\) | −12.0000 | −1.68034 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.47214i | − | 0.614295i | −0.951662 | − | 0.307148i | \(-0.900625\pi\) | ||
0.951662 | − | 0.307148i | \(-0.0993745\pi\) | |||||||
\(54\) | −4.50000 | + | 5.80948i | −0.612372 | + | 0.790569i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.92820 | 0.917663 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 7.50000 | − | 1.93649i | 0.968246 | − | 0.250000i | ||||
\(61\) | 15.4919i | 1.98354i | 0.128037 | + | 0.991769i | \(0.459132\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 8.66025 | + | 6.70820i | 1.09985 | + | 0.851943i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.50000 | + | 5.80948i | 0.687500 | + | 0.726184i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 3.46410 | + | 13.4164i | 0.420084 | + | 1.62698i | ||||
\(69\) | − | 15.4919i | − | 1.86501i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 7.79423 | + | 3.35410i | 0.918559 | + | 0.395285i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.66025 | −1.00000 | ||||||||
\(76\) | −2.00000 | − | 7.74597i | −0.229416 | − | 0.888523i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.74597i | 0.871489i | 0.900070 | + | 0.435745i | \(0.143515\pi\) | ||||
−0.900070 | + | 0.435745i | \(0.856485\pi\) | |||||||
\(80\) | −4.33013 | − | 7.82624i | −0.484123 | − | 0.875000i | ||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.46410 | −0.380235 | −0.190117 | − | 0.981761i | \(-0.560887\pi\) | ||||
−0.190117 | + | 0.981761i | \(0.560887\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 15.4919i | − | 1.68034i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | −7.50000 | − | 5.80948i | −0.790569 | − | 0.612372i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −17.3205 | + | 4.47214i | −1.80579 | + | 0.466252i | ||||
\(93\) | − | 13.4164i | − | 1.39122i | ||||||
\(94\) | −10.0000 | − | 7.74597i | −1.03142 | − | 0.798935i | ||||
\(95\) | 8.94427i | 0.917663i | ||||||||
\(96\) | 1.50000 | − | 9.68246i | 0.153093 | − | 0.988212i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 6.06218 | − | 7.82624i | 0.612372 | − | 0.790569i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.50000 | + | 9.68246i | 0.250000 | + | 0.968246i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 10.3923 | − | 13.4164i | 1.02899 | − | 1.32842i | ||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.00000 | + | 3.87298i | 0.485643 | + | 0.376177i | ||||
\(107\) | −10.3923 | −1.00466 | −0.502331 | − | 0.864675i | \(-0.667524\pi\) | ||||
−0.502331 | + | 0.864675i | \(0.667524\pi\) | |||||||
\(108\) | −2.59808 | − | 10.0623i | −0.250000 | − | 0.968246i | ||||
\(109\) | 15.4919i | 1.48386i | 0.670478 | + | 0.741929i | \(0.266089\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.7846 | 1.95525 | 0.977626 | − | 0.210352i | \(-0.0674609\pi\) | ||||
0.977626 | + | 0.210352i | \(0.0674609\pi\) | |||||||
\(114\) | −6.00000 | + | 7.74597i | −0.561951 | + | 0.725476i | ||||
\(115\) | 20.0000 | 1.86501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.33013 | + | 10.0623i | −0.395285 | + | 0.918559i | ||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | −17.3205 | − | 13.4164i | −1.56813 | − | 1.21466i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.0000 | + | 3.87298i | −1.34704 | + | 0.347804i | ||||
\(125\) | − | 11.1803i | − | 1.00000i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | −11.2583 | + | 1.11803i | −0.995105 | + | 0.0988212i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.6190i | 1.00000i | ||||||||
\(136\) | −18.0000 | − | 7.74597i | −1.54349 | − | 0.664211i | ||||
\(137\) | 6.92820 | 0.591916 | 0.295958 | − | 0.955201i | \(-0.404361\pi\) | ||||
0.295958 | + | 0.955201i | \(0.404361\pi\) | |||||||
\(138\) | 17.3205 | + | 13.4164i | 1.47442 | + | 1.14208i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.4919i | 1.30466i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −10.5000 | + | 5.80948i | −0.875000 | + | 0.484123i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.1244 | −1.00000 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 7.50000 | − | 9.68246i | 0.612372 | − | 0.790569i | ||||
\(151\) | − | 23.2379i | − | 1.89107i | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||
0.325515 | − | 0.945537i | \(-0.394462\pi\) | |||||||
\(152\) | 10.3923 | + | 4.47214i | 0.842927 | + | 0.362738i | ||||
\(153\) | −20.7846 | −1.68034 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.3205 | 1.39122 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(158\) | −8.66025 | − | 6.70820i | −0.688973 | − | 0.533676i | ||||
\(159\) | − | 7.74597i | − | 0.614295i | ||||||
\(160\) | 12.5000 | + | 1.93649i | 0.988212 | + | 0.153093i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.79423 | + | 10.0623i | −0.612372 | + | 0.790569i | ||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | − | 3.87298i | 0.232845 | − | 0.300602i | ||||
\(167\) | − | 8.94427i | − | 0.692129i | −0.938211 | − | 0.346064i | \(-0.887518\pi\) | ||
0.938211 | − | 0.346064i | \(-0.112482\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 17.3205 | + | 13.4164i | 1.32842 | + | 1.02899i | ||||
\(171\) | 12.0000 | 0.917663 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.3607i | 1.70005i | 0.526742 | + | 0.850026i | \(0.323414\pi\) | ||||
−0.526742 | + | 0.850026i | \(0.676586\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | 12.9904 | − | 3.35410i | 0.968246 | − | 0.250000i | ||||
\(181\) | − | 15.4919i | − | 1.15151i | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||
0.817624 | − | 0.575753i | \(-0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.8328i | 1.98354i | ||||||||
\(184\) | 10.0000 | − | 23.2379i | 0.737210 | − | 1.71312i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 15.0000 | + | 11.6190i | 1.09985 | + | 0.851943i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 17.3205 | − | 4.47214i | 1.26323 | − | 0.326164i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.0000 | − | 7.74597i | −0.725476 | − | 0.561951i | ||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 9.52628 | + | 10.0623i | 0.687500 | + | 0.726184i | ||||
\(193\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.50000 | + | 13.5554i | 0.250000 | + | 0.968246i | ||||
\(197\) | 4.47214i | 0.318626i | 0.987228 | + | 0.159313i | \(0.0509280\pi\) | ||||
−0.987228 | + | 0.159313i | \(0.949072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.2379i | 1.64729i | 0.567105 | + | 0.823646i | \(0.308063\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | −12.9904 | − | 5.59017i | −0.918559 | − | 0.395285i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.00000 | + | 23.2379i | 0.420084 | + | 1.62698i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 26.8328i | − | 1.86501i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.0000 | −1.92760 | −0.963800 | − | 0.266627i | \(-0.914091\pi\) | ||||
−0.963800 | + | 0.266627i | \(0.914091\pi\) | |||||||
\(212\) | −8.66025 | + | 2.23607i | −0.594789 | + | 0.153574i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.00000 | − | 11.6190i | 0.615227 | − | 0.794255i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.5000 | + | 5.80948i | 0.918559 | + | 0.395285i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −17.3205 | − | 13.4164i | −1.17309 | − | 0.908674i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.0000 | −1.00000 | ||||||||
\(226\) | −18.0000 | + | 23.2379i | −1.19734 | + | 1.54576i | ||||
\(227\) | 24.2487 | 1.60944 | 0.804722 | − | 0.593652i | \(-0.202314\pi\) | ||||
0.804722 | + | 0.593652i | \(0.202314\pi\) | |||||||
\(228\) | −3.46410 | − | 13.4164i | −0.229416 | − | 0.888523i | ||||
\(229\) | − | 15.4919i | − | 1.02374i | −0.859064 | − | 0.511868i | \(-0.828954\pi\) | ||
0.859064 | − | 0.511868i | \(-0.171046\pi\) | |||||||
\(230\) | −17.3205 | + | 22.3607i | −1.14208 | + | 1.47442i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.7846 | −1.36165 | −0.680823 | − | 0.732448i | \(-0.738378\pi\) | ||||
−0.680823 | + | 0.732448i | \(0.738378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.0000 | −1.30466 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.4164i | 0.871489i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | −7.50000 | − | 13.5554i | −0.484123 | − | 0.875000i | ||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | −9.52628 | + | 12.2984i | −0.612372 | + | 0.790569i | ||||
\(243\) | 15.5885 | 1.00000 | ||||||||
\(244\) | 30.0000 | − | 7.74597i | 1.92055 | − | 0.495885i | ||||
\(245\) | − | 15.6525i | − | 1.00000i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.66025 | − | 20.1246i | 0.549927 | − | 1.27791i | ||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 12.5000 | + | 9.68246i | 0.790569 | + | 0.612372i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 26.8328i | − | 1.68034i | ||||||
\(256\) | 8.50000 | − | 13.5554i | 0.531250 | − | 0.847215i | ||||
\(257\) | −6.92820 | −0.432169 | −0.216085 | − | 0.976375i | \(-0.569329\pi\) | ||||
−0.216085 | + | 0.976375i | \(0.569329\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 8.94427i | − | 0.551527i | −0.961225 | − | 0.275764i | \(-0.911069\pi\) | ||
0.961225 | − | 0.275764i | \(-0.0889307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0000 | 0.614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | −12.9904 | − | 10.0623i | −0.790569 | − | 0.612372i | ||||
\(271\) | 7.74597i | 0.470534i | 0.971931 | + | 0.235267i | \(0.0755965\pi\) | ||||
−0.971931 | + | 0.235267i | \(0.924404\pi\) | |||||||
\(272\) | 24.2487 | − | 13.4164i | 1.47029 | − | 0.813489i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | + | 7.74597i | −0.362473 | + | 0.467951i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −30.0000 | + | 7.74597i | −1.80579 | + | 0.466252i | ||||
\(277\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(278\) | 3.46410 | − | 4.47214i | 0.207763 | − | 0.268221i | ||||
\(279\) | − | 23.2379i | − | 1.39122i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | −17.3205 | − | 13.4164i | −1.03142 | − | 0.798935i | ||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.4919i | 0.917663i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.59808 | − | 16.7705i | 0.153093 | − | 0.988212i | ||||
\(289\) | 31.0000 | 1.82353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 31.3050i | 1.82885i | 0.404750 | + | 0.914427i | \(0.367359\pi\) | ||||
−0.404750 | + | 0.914427i | \(0.632641\pi\) | |||||||
\(294\) | 10.5000 | − | 13.5554i | 0.612372 | − | 0.790569i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.33013 | + | 16.7705i | 0.250000 | + | 0.968246i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 25.9808 | + | 20.1246i | 1.49502 | + | 1.15804i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.0000 | + | 7.74597i | −0.802955 | + | 0.444262i | ||||
\(305\) | −34.6410 | −1.98354 | ||||||||
\(306\) | 18.0000 | − | 23.2379i | 1.02899 | − | 1.32842i | ||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.0000 | + | 19.3649i | −0.851943 | + | 1.09985i | ||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.0000 | − | 3.87298i | 0.843816 | − | 0.217872i | ||||
\(317\) | − | 22.3607i | − | 1.25590i | −0.778253 | − | 0.627950i | \(-0.783894\pi\) | ||
0.778253 | − | 0.627950i | \(-0.216106\pi\) | |||||||
\(318\) | 8.66025 | + | 6.70820i | 0.485643 | + | 0.376177i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −12.9904 | + | 12.2984i | −0.726184 | + | 0.687500i | ||||
\(321\) | −18.0000 | −1.00466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −27.7128 | −1.54198 | ||||||||
\(324\) | −4.50000 | − | 17.4284i | −0.250000 | − | 0.968246i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.8328i | 1.48386i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.0000 | 1.53902 | 0.769510 | − | 0.638635i | \(-0.220501\pi\) | ||||
0.769510 | + | 0.638635i | \(0.220501\pi\) | |||||||
\(332\) | 1.73205 | + | 6.70820i | 0.0950586 | + | 0.368161i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.0000 | + | 7.74597i | 0.547176 | + | 0.423840i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 11.2583 | − | 14.5344i | 0.612372 | − | 0.790569i | ||||
\(339\) | 36.0000 | 1.95525 | ||||||||
\(340\) | −30.0000 | + | 7.74597i | −1.62698 | + | 0.420084i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −10.3923 | + | 13.4164i | −0.561951 | + | 0.725476i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 34.6410 | 1.86501 | ||||||||
\(346\) | −25.0000 | − | 19.3649i | −1.34401 | − | 1.04106i | ||||
\(347\) | 10.3923 | 0.557888 | 0.278944 | − | 0.960307i | \(-0.410016\pi\) | ||||
0.278944 | + | 0.960307i | \(0.410016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.4919i | 0.829264i | 0.909989 | + | 0.414632i | \(0.136090\pi\) | ||||
−0.909989 | + | 0.414632i | \(0.863910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.7846 | 1.10625 | 0.553127 | − | 0.833097i | \(-0.313435\pi\) | ||||
0.553127 | + | 0.833097i | \(0.313435\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | −7.50000 | + | 17.4284i | −0.395285 | + | 0.918559i | ||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 17.3205 | + | 13.4164i | 0.910346 | + | 0.705151i | ||||
\(363\) | 19.0526 | 1.00000 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −30.0000 | − | 23.2379i | −1.56813 | − | 1.21466i | ||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | 17.3205 | + | 31.3050i | 0.902894 | + | 1.63188i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −25.9808 | + | 6.70820i | −1.34704 | + | 0.347804i | ||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 19.3649i | − | 1.00000i | ||||||
\(376\) | −10.0000 | + | 23.2379i | −0.515711 | + | 1.19840i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | 17.3205 | − | 4.47214i | 0.888523 | − | 0.229416i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.94427i | 0.457031i | 0.973540 | + | 0.228515i | \(0.0733872\pi\) | ||||
−0.973540 | + | 0.228515i | \(0.926613\pi\) | |||||||
\(384\) | −19.5000 | + | 1.93649i | −0.995105 | + | 0.0988212i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 61.9677i | 3.13384i | ||||||||
\(392\) | −18.1865 | − | 7.82624i | −0.918559 | − | 0.395285i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.00000 | − | 3.87298i | −0.251896 | − | 0.195118i | ||||
\(395\) | −17.3205 | −0.871489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(398\) | −25.9808 | − | 20.1246i | −1.30230 | − | 1.00876i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.5000 | − | 9.68246i | 0.875000 | − | 0.484123i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.1246i | 1.00000i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −31.1769 | − | 13.4164i | −1.54349 | − | 0.664211i | ||||
\(409\) | 26.0000 | 1.28562 | 0.642809 | − | 0.766027i | \(-0.277769\pi\) | ||||
0.642809 | + | 0.766027i | \(0.277769\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 30.0000 | + | 23.2379i | 1.47442 | + | 1.14208i | ||||
\(415\) | − | 7.74597i | − | 0.380235i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.92820 | −0.339276 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 15.4919i | − | 0.755031i | −0.926003 | − | 0.377515i | \(-0.876779\pi\) | ||
0.926003 | − | 0.377515i | \(-0.123221\pi\) | |||||||
\(422\) | 24.2487 | − | 31.3050i | 1.18041 | − | 1.52390i | ||||
\(423\) | 26.8328i | 1.30466i | ||||||||
\(424\) | 5.00000 | − | 11.6190i | 0.242821 | − | 0.564266i | ||||
\(425\) | 34.6410 | 1.68034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.19615 | + | 20.1246i | 0.251166 | + | 0.972760i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −18.1865 | + | 10.0623i | −0.875000 | + | 0.484123i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 30.0000 | − | 7.74597i | 1.43674 | − | 0.370965i | ||||
\(437\) | − | 35.7771i | − | 1.71145i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 38.7298i | − | 1.84847i | −0.381819 | − | 0.924237i | \(-0.624702\pi\) | ||
0.381819 | − | 0.924237i | \(-0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.0000 | −1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −38.1051 | −1.81043 | −0.905214 | − | 0.424955i | \(-0.860290\pi\) | ||||
−0.905214 | + | 0.424955i | \(0.860290\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 12.9904 | − | 16.7705i | 0.612372 | − | 0.790569i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −10.3923 | − | 40.2492i | −0.488813 | − | 1.89316i | ||||
\(453\) | − | 40.2492i | − | 1.89107i | ||||||
\(454\) | −21.0000 | + | 27.1109i | −0.985579 | + | 1.27238i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 18.0000 | + | 7.74597i | 0.842927 | + | 0.362738i | ||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 17.3205 | + | 13.4164i | 0.809334 | + | 0.626908i | ||||
\(459\) | −36.0000 | −1.68034 | ||||||||
\(460\) | −10.0000 | − | 38.7298i | −0.466252 | − | 1.80579i | ||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 30.0000 | 1.39122 | ||||||||
\(466\) | 18.0000 | − | 23.2379i | 0.833834 | − | 1.07647i | ||||
\(467\) | −24.2487 | −1.12210 | −0.561048 | − | 0.827783i | \(-0.689602\pi\) | ||||
−0.561048 | + | 0.827783i | \(0.689602\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 17.3205 | − | 22.3607i | 0.798935 | − | 1.03142i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −15.0000 | − | 11.6190i | −0.688973 | − | 0.533676i | ||||
\(475\) | −20.0000 | −0.917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 13.4164i | − | 0.614295i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 21.6506 | + | 3.35410i | 0.988212 | + | 0.153093i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.73205 | − | 2.23607i | 0.0788928 | − | 0.101850i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.50000 | − | 21.3014i | −0.250000 | − | 0.968246i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.5000 | + | 17.4284i | −0.612372 | + | 0.790569i | ||||
\(487\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(488\) | −17.3205 | + | 40.2492i | −0.784063 | + | 1.82200i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 17.5000 | + | 13.5554i | 0.790569 | + | 0.612372i | ||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.0000 | + | 27.1109i | 0.673520 | + | 1.21731i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.19615 | − | 6.70820i | 0.232845 | − | 0.300602i | ||||
\(499\) | −44.0000 | −1.96971 | −0.984855 | − | 0.173379i | \(-0.944532\pi\) | ||||
−0.984855 | + | 0.173379i | \(0.944532\pi\) | |||||||
\(500\) | −21.6506 | + | 5.59017i | −0.968246 | + | 0.250000i | ||||
\(501\) | − | 15.4919i | − | 0.692129i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 44.7214i | − | 1.99403i | −0.0772283 | − | 0.997013i | \(-0.524607\pi\) | ||
0.0772283 | − | 0.997013i | \(-0.475393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.5167 | −1.00000 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 30.0000 | + | 23.2379i | 1.32842 | + | 1.02899i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7.79423 | + | 21.2426i | 0.344459 | + | 0.938801i | ||||
\(513\) | 20.7846 | 0.917663 | ||||||||
\(514\) | 6.00000 | − | 7.74597i | 0.264649 | − | 0.341660i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 38.7298i | 1.70005i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.0000 | + | 7.74597i | 0.436021 | + | 0.337740i | ||||
\(527\) | 53.6656i | 2.33771i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −57.0000 | −2.47826 | ||||||||
\(530\) | −8.66025 | + | 11.1803i | −0.376177 | + | 0.485643i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 23.2379i | − | 1.00466i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 22.5000 | − | 5.80948i | 0.968246 | − | 0.250000i | ||||
\(541\) | − | 46.4758i | − | 1.99815i | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||
0.0429934 | − | 0.999075i | \(-0.486311\pi\) | |||||||
\(542\) | −8.66025 | − | 6.70820i | −0.371990 | − | 0.288142i | ||||
\(543\) | − | 26.8328i | − | 1.15151i | ||||||
\(544\) | −6.00000 | + | 38.7298i | −0.257248 | + | 1.66053i | ||||
\(545\) | −34.6410 | −1.48386 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | −3.46410 | − | 13.4164i | −0.147979 | − | 0.573121i | ||||
\(549\) | 46.4758i | 1.98354i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 17.3205 | − | 40.2492i | 0.737210 | − | 1.71312i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 7.74597i | 0.0848189 | + | 0.328502i | ||||
\(557\) | 22.3607i | 0.947452i | 0.880672 | + | 0.473726i | \(0.157091\pi\) | ||||
−0.880672 | + | 0.473726i | \(0.842909\pi\) | |||||||
\(558\) | 25.9808 | + | 20.1246i | 1.09985 | + | 0.851943i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.1769 | 1.31395 | 0.656975 | − | 0.753912i | \(-0.271836\pi\) | ||||
0.656975 | + | 0.753912i | \(0.271836\pi\) | |||||||
\(564\) | 30.0000 | − | 7.74597i | 1.26323 | − | 0.326164i | ||||
\(565\) | 46.4758i | 1.95525i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | −17.3205 | − | 13.4164i | −0.725476 | − | 0.561951i | ||||
\(571\) | 28.0000 | 1.17176 | 0.585882 | − | 0.810397i | \(-0.300748\pi\) | ||||
0.585882 | + | 0.810397i | \(0.300748\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 44.7214i | 1.86501i | ||||||||
\(576\) | 16.5000 | + | 17.4284i | 0.687500 | + | 0.726184i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −26.8468 | + | 34.6591i | −1.11668 | + | 1.44163i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −35.0000 | − | 27.1109i | −1.44584 | − | 1.11994i | ||||
\(587\) | 45.0333 | 1.85872 | 0.929362 | − | 0.369170i | \(-0.120358\pi\) | ||||
0.929362 | + | 0.369170i | \(0.120358\pi\) | |||||||
\(588\) | 6.06218 | + | 23.4787i | 0.250000 | + | 0.968246i | ||||
\(589\) | − | 30.9839i | − | 1.27667i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.74597i | 0.318626i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 48.4974 | 1.99155 | 0.995775 | − | 0.0918243i | \(-0.0292698\pi\) | ||||
0.995775 | + | 0.0918243i | \(0.0292698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 40.2492i | 1.64729i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | −22.5000 | − | 9.68246i | −0.918559 | − | 0.395285i | ||||
\(601\) | −38.0000 | −1.55005 | −0.775026 | − | 0.631929i | \(-0.782263\pi\) | ||||
−0.775026 | + | 0.631929i | \(0.782263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −45.0000 | + | 11.6190i | −1.83102 | + | 0.472768i | ||||
\(605\) | 24.5967i | 1.00000i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 3.46410 | − | 22.3607i | 0.140488 | − | 0.906845i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 30.0000 | − | 38.7298i | 1.21466 | − | 1.56813i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 10.3923 | + | 40.2492i | 0.420084 | + | 1.62698i | ||||
\(613\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.92820 | 0.278919 | 0.139459 | − | 0.990228i | \(-0.455464\pi\) | ||||
0.139459 | + | 0.990228i | \(0.455464\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.0000 | 1.76851 | 0.884255 | − | 0.467005i | \(-0.154667\pi\) | ||||
0.884255 | + | 0.467005i | \(0.154667\pi\) | |||||||
\(620\) | −8.66025 | − | 33.5410i | −0.347804 | − | 1.34704i | ||||
\(621\) | − | 46.4758i | − | 1.86501i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 38.7298i | − | 1.54181i | −0.636950 | − | 0.770905i | \(-0.719804\pi\) | ||
0.636950 | − | 0.770905i | \(-0.280196\pi\) | |||||||
\(632\) | −8.66025 | + | 20.1246i | −0.344486 | + | 0.800514i | ||||
\(633\) | −48.4974 | −1.92760 | ||||||||
\(634\) | 25.0000 | + | 19.3649i | 0.992877 | + | 0.769079i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −15.0000 | + | 3.87298i | −0.594789 | + | 0.153574i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.50000 | − | 25.1744i | −0.0988212 | − | 0.995105i | ||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 15.5885 | − | 20.1246i | 0.615227 | − | 0.794255i | ||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.0000 | − | 30.9839i | 0.944267 | − | 1.21904i | ||||
\(647\) | − | 44.7214i | − | 1.75818i | −0.476658 | − | 0.879089i | \(-0.658152\pi\) | ||
0.476658 | − | 0.879089i | \(-0.341848\pi\) | |||||||
\(648\) | 23.3827 | + | 10.0623i | 0.918559 | + | 0.395285i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 49.1935i | − | 1.92509i | −0.271122 | − | 0.962545i | \(-0.587395\pi\) | ||
0.271122 | − | 0.962545i | \(-0.412605\pi\) | |||||||
\(654\) | −30.0000 | − | 23.2379i | −1.17309 | − | 0.908674i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.4758i | 1.80770i | 0.427850 | + | 0.903850i | \(0.359271\pi\) | ||||
−0.427850 | + | 0.903850i | \(0.640729\pi\) | |||||||
\(662\) | −24.2487 | + | 31.3050i | −0.942453 | + | 1.21670i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.00000 | − | 3.87298i | −0.349268 | − | 0.150301i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −17.3205 | + | 4.47214i | −0.670151 | + | 0.173032i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.9808 | −1.00000 | ||||||||
\(676\) | 6.50000 | + | 25.1744i | 0.250000 | + | 0.968246i | ||||
\(677\) | 31.3050i | 1.20315i | 0.798817 | + | 0.601574i | \(0.205459\pi\) | ||||
−0.798817 | + | 0.601574i | \(0.794541\pi\) | |||||||
\(678\) | −31.1769 | + | 40.2492i | −1.19734 | + | 1.54576i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 17.3205 | − | 40.2492i | 0.664211 | − | 1.54349i | ||||
\(681\) | 42.0000 | 1.60944 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.1051 | 1.45805 | 0.729026 | − | 0.684486i | \(-0.239973\pi\) | ||||
0.729026 | + | 0.684486i | \(0.239973\pi\) | |||||||
\(684\) | −6.00000 | − | 23.2379i | −0.229416 | − | 0.888523i | ||||
\(685\) | 15.4919i | 0.591916i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 26.8328i | − | 1.02374i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −30.0000 | + | 38.7298i | −1.14208 | + | 1.47442i | ||||
\(691\) | 52.0000 | 1.97817 | 0.989087 | − | 0.147335i | \(-0.0470696\pi\) | ||||
0.989087 | + | 0.147335i | \(0.0470696\pi\) | |||||||
\(692\) | 43.3013 | − | 11.1803i | 1.64607 | − | 0.425013i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.00000 | + | 11.6190i | −0.341635 | + | 0.441049i | ||||
\(695\) | − | 8.94427i | − | 0.339276i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −17.3205 | − | 13.4164i | −0.655591 | − | 0.507819i | ||||
\(699\) | −36.0000 | −1.36165 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −34.6410 | −1.30466 | ||||||||
\(706\) | −18.0000 | + | 23.2379i | −0.677439 | + | 0.874570i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.4758i | 1.74544i | 0.488225 | + | 0.872718i | \(0.337644\pi\) | ||||
−0.488225 | + | 0.872718i | \(0.662356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.2379i | 0.871489i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −69.2820 | −2.59463 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | −12.9904 | − | 23.4787i | −0.484123 | − | 0.875000i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.59808 | − | 3.35410i | 0.0966904 | − | 0.124827i | ||||
\(723\) | −3.46410 | −0.128831 | ||||||||
\(724\) | −30.0000 | + | 7.74597i | −1.11494 | + | 0.287877i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −16.5000 | + | 21.3014i | −0.612372 | + | 0.790569i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 51.9615 | − | 13.4164i | 1.92055 | − | 0.495885i | ||||
\(733\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 27.1109i | − | 1.00000i | ||||||
\(736\) | −50.0000 | − | 7.74597i | −1.84302 | − | 0.285520i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.00000 | 0.147142 | 0.0735712 | − | 0.997290i | \(-0.476560\pi\) | ||||
0.0735712 | + | 0.997290i | \(0.476560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 44.7214i | − | 1.64067i | −0.571885 | − | 0.820334i | \(-0.693788\pi\) | ||
0.571885 | − | 0.820334i | \(-0.306212\pi\) | |||||||
\(744\) | 15.0000 | − | 34.8569i | 0.549927 | − | 1.27791i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.3923 | −0.380235 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 21.6506 | + | 16.7705i | 0.790569 | + | 0.612372i | ||||
\(751\) | 54.2218i | 1.97858i | 0.145962 | + | 0.989290i | \(0.453372\pi\) | ||||
−0.145962 | + | 0.989290i | \(0.546628\pi\) | |||||||
\(752\) | −17.3205 | − | 31.3050i | −0.631614 | − | 1.14157i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 51.9615 | 1.89107 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(758\) | 3.46410 | − | 4.47214i | 0.125822 | − | 0.162435i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.0000 | + | 23.2379i | −0.362738 | + | 0.842927i | ||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 46.4758i | − | 1.68034i | ||||||
\(766\) | −10.0000 | − | 7.74597i | −0.361315 | − | 0.279873i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 14.7224 | − | 23.4787i | 0.531250 | − | 0.847215i | ||||
\(769\) | 46.0000 | 1.65880 | 0.829401 | − | 0.558653i | \(-0.188682\pi\) | ||||
0.829401 | + | 0.558653i | \(0.188682\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.47214i | 0.160852i | 0.996761 | + | 0.0804258i | \(0.0256280\pi\) | ||||
−0.996761 | + | 0.0804258i | \(0.974372\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38.7298i | 1.39122i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −69.2820 | − | 53.6656i | −2.47752 | − | 1.91908i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 24.5000 | − | 13.5554i | 0.875000 | − | 0.484123i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(788\) | 8.66025 | − | 2.23607i | 0.308509 | − | 0.0796566i | ||||
\(789\) | − | 15.4919i | − | 0.551527i | ||||||
\(790\) | 15.0000 | − | 19.3649i | 0.533676 | − | 0.688973i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.3205 | 0.614295 | ||||||||
\(796\) | 45.0000 | − | 11.6190i | 1.59498 | − | 0.411823i | ||||
\(797\) |