Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(59,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.59");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.bd (of order \(6\), degree \(2\), 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: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 59.4 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.59 |
Dual form | 360.2.bd.a.299.4 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | − | 0.707107i | 0.866025 | − | 0.500000i | ||||
\(3\) | 0.866025 | + | 1.50000i | 0.500000 | + | 0.866025i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | −1.67303 | + | 1.48356i | −0.748203 | + | 0.663470i | ||||
\(6\) | 2.12132 | + | 1.22474i | 0.866025 | + | 0.500000i | ||||
\(7\) | 1.22474 | + | 2.12132i | 0.462910 | + | 0.801784i | 0.999104 | − | 0.0423108i | \(-0.0134720\pi\) |
−0.536194 | + | 0.844094i | \(0.680139\pi\) | |||||||
\(8\) | − | 2.82843i | − | 1.00000i | ||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | −1.00000 | + | 3.00000i | −0.316228 | + | 0.948683i | ||||
\(11\) | 4.50000 | − | 2.59808i | 1.35680 | − | 0.783349i | 0.367610 | − | 0.929980i | \(-0.380176\pi\) |
0.989191 | + | 0.146631i | \(0.0468429\pi\) | |||||||
\(12\) | 3.46410 | 1.00000 | ||||||||
\(13\) | −1.22474 | + | 2.12132i | −0.339683 | + | 0.588348i | −0.984373 | − | 0.176096i | \(-0.943653\pi\) |
0.644690 | + | 0.764444i | \(0.276986\pi\) | |||||||
\(14\) | 3.00000 | + | 1.73205i | 0.801784 | + | 0.462910i | ||||
\(15\) | −3.67423 | − | 1.22474i | −0.948683 | − | 0.316228i | ||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | 5.19615 | 1.26025 | 0.630126 | − | 0.776493i | \(-0.283003\pi\) | ||||
0.630126 | + | 0.776493i | \(0.283003\pi\) | |||||||
\(18\) | 4.24264i | 1.00000i | ||||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | 0.896575 | + | 4.38134i | 0.200480 | + | 0.979698i | ||||
\(21\) | −2.12132 | + | 3.67423i | −0.462910 | + | 0.801784i | ||||
\(22\) | 3.67423 | − | 6.36396i | 0.783349 | − | 1.35680i | ||||
\(23\) | 2.44949 | + | 1.41421i | 0.510754 | + | 0.294884i | 0.733144 | − | 0.680074i | \(-0.238052\pi\) |
−0.222390 | + | 0.974958i | \(0.571386\pi\) | |||||||
\(24\) | 4.24264 | − | 2.44949i | 0.866025 | − | 0.500000i | ||||
\(25\) | 0.598076 | − | 4.96410i | 0.119615 | − | 0.992820i | ||||
\(26\) | 3.46410i | 0.679366i | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 4.89898 | 0.925820 | ||||||||
\(29\) | −4.24264 | − | 7.34847i | −0.787839 | − | 1.36458i | −0.927289 | − | 0.374347i | \(-0.877867\pi\) |
0.139450 | − | 0.990229i | \(-0.455467\pi\) | |||||||
\(30\) | −5.36603 | + | 1.09808i | −0.979698 | + | 0.200480i | ||||
\(31\) | −6.36396 | − | 3.67423i | −1.14300 | − | 0.659912i | −0.195829 | − | 0.980638i | \(-0.562740\pi\) |
−0.947172 | + | 0.320726i | \(0.896073\pi\) | |||||||
\(32\) | −4.89898 | − | 2.82843i | −0.866025 | − | 0.500000i | ||||
\(33\) | 7.79423 | + | 4.50000i | 1.35680 | + | 0.783349i | ||||
\(34\) | 6.36396 | − | 3.67423i | 1.09141 | − | 0.630126i | ||||
\(35\) | −5.19615 | − | 1.73205i | −0.878310 | − | 0.292770i | ||||
\(36\) | 3.00000 | + | 5.19615i | 0.500000 | + | 0.866025i | ||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | −6.12372 | + | 3.53553i | −0.993399 | + | 0.573539i | ||||
\(39\) | −4.24264 | −0.679366 | ||||||||
\(40\) | 4.19615 | + | 4.73205i | 0.663470 | + | 0.748203i | ||||
\(41\) | 1.50000 | + | 0.866025i | 0.234261 | + | 0.135250i | 0.612536 | − | 0.790443i | \(-0.290149\pi\) |
−0.378275 | + | 0.925693i | \(0.623483\pi\) | |||||||
\(42\) | 6.00000i | 0.925820i | ||||||||
\(43\) | −7.79423 | + | 4.50000i | −1.18861 | + | 0.686244i | −0.957990 | − | 0.286801i | \(-0.907408\pi\) |
−0.230618 | + | 0.973044i | \(0.574075\pi\) | |||||||
\(44\) | − | 10.3923i | − | 1.56670i | ||||||
\(45\) | −1.34486 | − | 6.57201i | −0.200480 | − | 0.979698i | ||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | 6.12372 | − | 3.53553i | 0.893237 | − | 0.515711i | 0.0182371 | − | 0.999834i | \(-0.494195\pi\) |
0.875000 | + | 0.484123i | \(0.160861\pi\) | |||||||
\(48\) | 3.46410 | − | 6.00000i | 0.500000 | − | 0.866025i | ||||
\(49\) | 0.500000 | − | 0.866025i | 0.0714286 | − | 0.123718i | ||||
\(50\) | −2.77766 | − | 6.50266i | −0.392820 | − | 0.919615i | ||||
\(51\) | 4.50000 | + | 7.79423i | 0.630126 | + | 1.09141i | ||||
\(52\) | 2.44949 | + | 4.24264i | 0.339683 | + | 0.588348i | ||||
\(53\) | − | 1.41421i | − | 0.194257i | −0.995272 | − | 0.0971286i | \(-0.969034\pi\) | ||
0.995272 | − | 0.0971286i | \(-0.0309658\pi\) | |||||||
\(54\) | −6.36396 | + | 3.67423i | −0.866025 | + | 0.500000i | ||||
\(55\) | −3.67423 | + | 11.0227i | −0.495434 | + | 1.48630i | ||||
\(56\) | 6.00000 | − | 3.46410i | 0.801784 | − | 0.462910i | ||||
\(57\) | −4.33013 | − | 7.50000i | −0.573539 | − | 0.993399i | ||||
\(58\) | −10.3923 | − | 6.00000i | −1.36458 | − | 0.787839i | ||||
\(59\) | −1.50000 | − | 0.866025i | −0.195283 | − | 0.112747i | 0.399170 | − | 0.916877i | \(-0.369298\pi\) |
−0.594454 | + | 0.804130i | \(0.702632\pi\) | |||||||
\(60\) | −5.79555 | + | 5.13922i | −0.748203 | + | 0.663470i | ||||
\(61\) | 6.36396 | − | 3.67423i | 0.814822 | − | 0.470438i | −0.0338058 | − | 0.999428i | \(-0.510763\pi\) |
0.848628 | + | 0.528991i | \(0.177429\pi\) | |||||||
\(62\) | −10.3923 | −1.31982 | ||||||||
\(63\) | −7.34847 | −0.925820 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −1.09808 | − | 5.36603i | −0.136200 | − | 0.665574i | ||||
\(66\) | 12.7279 | 1.56670 | ||||||||
\(67\) | 2.59808 | + | 1.50000i | 0.317406 | + | 0.183254i | 0.650236 | − | 0.759733i | \(-0.274670\pi\) |
−0.332830 | + | 0.942987i | \(0.608004\pi\) | |||||||
\(68\) | 5.19615 | − | 9.00000i | 0.630126 | − | 1.09141i | ||||
\(69\) | 4.89898i | 0.589768i | ||||||||
\(70\) | −7.58871 | + | 1.55291i | −0.907024 | + | 0.185609i | ||||
\(71\) | −4.24264 | −0.503509 | −0.251754 | − | 0.967791i | \(-0.581008\pi\) | ||||
−0.251754 | + | 0.967791i | \(0.581008\pi\) | |||||||
\(72\) | 7.34847 | + | 4.24264i | 0.866025 | + | 0.500000i | ||||
\(73\) | − | 3.00000i | − | 0.351123i | −0.984468 | − | 0.175562i | \(-0.943826\pi\) | ||
0.984468 | − | 0.175562i | \(-0.0561742\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.96410 | − | 3.40192i | 0.919615 | − | 0.392820i | ||||
\(76\) | −5.00000 | + | 8.66025i | −0.573539 | + | 0.993399i | ||||
\(77\) | 11.0227 | + | 6.36396i | 1.25615 | + | 0.725241i | ||||
\(78\) | −5.19615 | + | 3.00000i | −0.588348 | + | 0.339683i | ||||
\(79\) | 6.36396 | − | 3.67423i | 0.716002 | − | 0.413384i | −0.0972777 | − | 0.995257i | \(-0.531013\pi\) |
0.813279 | + | 0.581874i | \(0.197680\pi\) | |||||||
\(80\) | 8.48528 | + | 2.82843i | 0.948683 | + | 0.316228i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 2.44949 | 0.270501 | ||||||||
\(83\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(84\) | 4.24264 | + | 7.34847i | 0.462910 | + | 0.801784i | ||||
\(85\) | −8.69333 | + | 7.70882i | −0.942924 | + | 0.836139i | ||||
\(86\) | −6.36396 | + | 11.0227i | −0.686244 | + | 1.18861i | ||||
\(87\) | 7.34847 | − | 12.7279i | 0.787839 | − | 1.36458i | ||||
\(88\) | −7.34847 | − | 12.7279i | −0.783349 | − | 1.35680i | ||||
\(89\) | 10.3923i | 1.10158i | 0.834643 | + | 0.550791i | \(0.185674\pi\) | ||||
−0.834643 | + | 0.550791i | \(0.814326\pi\) | |||||||
\(90\) | −6.29423 | − | 7.09808i | −0.663470 | − | 0.748203i | ||||
\(91\) | −6.00000 | −0.628971 | ||||||||
\(92\) | 4.89898 | − | 2.82843i | 0.510754 | − | 0.294884i | ||||
\(93\) | − | 12.7279i | − | 1.31982i | ||||||
\(94\) | 5.00000 | − | 8.66025i | 0.515711 | − | 0.893237i | ||||
\(95\) | 8.36516 | − | 7.41782i | 0.858248 | − | 0.761052i | ||||
\(96\) | − | 9.79796i | − | 1.00000i | ||||||
\(97\) | 2.59808 | − | 1.50000i | 0.263795 | − | 0.152302i | −0.362270 | − | 0.932073i | \(-0.617998\pi\) |
0.626064 | + | 0.779771i | \(0.284665\pi\) | |||||||
\(98\) | − | 1.41421i | − | 0.142857i | ||||||
\(99\) | 15.5885i | 1.56670i | ||||||||
\(100\) | −8.00000 | − | 6.00000i | −0.800000 | − | 0.600000i | ||||
\(101\) | 4.24264 | + | 7.34847i | 0.422159 | + | 0.731200i | 0.996150 | − | 0.0876610i | \(-0.0279392\pi\) |
−0.573992 | + | 0.818861i | \(0.694606\pi\) | |||||||
\(102\) | 11.0227 | + | 6.36396i | 1.09141 | + | 0.630126i | ||||
\(103\) | −8.57321 | + | 14.8492i | −0.844744 | + | 1.46314i | 0.0410996 | + | 0.999155i | \(0.486914\pi\) |
−0.885843 | + | 0.463984i | \(0.846419\pi\) | |||||||
\(104\) | 6.00000 | + | 3.46410i | 0.588348 | + | 0.339683i | ||||
\(105\) | −1.90192 | − | 9.29423i | −0.185609 | − | 0.907024i | ||||
\(106\) | −1.00000 | − | 1.73205i | −0.0971286 | − | 0.168232i | ||||
\(107\) | −15.5885 | −1.50699 | −0.753497 | − | 0.657452i | \(-0.771634\pi\) | ||||
−0.753497 | + | 0.657452i | \(0.771634\pi\) | |||||||
\(108\) | −5.19615 | + | 9.00000i | −0.500000 | + | 0.866025i | ||||
\(109\) | 14.6969i | 1.40771i | 0.710343 | + | 0.703856i | \(0.248540\pi\) | ||||
−0.710343 | + | 0.703856i | \(0.751460\pi\) | |||||||
\(110\) | 3.29423 | + | 16.0981i | 0.314092 | + | 1.53489i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.89898 | − | 8.48528i | 0.462910 | − | 0.801784i | ||||
\(113\) | 5.19615 | − | 9.00000i | 0.488813 | − | 0.846649i | −0.511104 | − | 0.859519i | \(-0.670763\pi\) |
0.999917 | + | 0.0128699i | \(0.00409674\pi\) | |||||||
\(114\) | −10.6066 | − | 6.12372i | −0.993399 | − | 0.573539i | ||||
\(115\) | −6.19615 | + | 1.26795i | −0.577794 | + | 0.118237i | ||||
\(116\) | −16.9706 | −1.57568 | ||||||||
\(117\) | −3.67423 | − | 6.36396i | −0.339683 | − | 0.588348i | ||||
\(118\) | −2.44949 | −0.225494 | ||||||||
\(119\) | 6.36396 | + | 11.0227i | 0.583383 | + | 1.01045i | ||||
\(120\) | −3.46410 | + | 10.3923i | −0.316228 | + | 0.948683i | ||||
\(121\) | 8.00000 | − | 13.8564i | 0.727273 | − | 1.25967i | ||||
\(122\) | 5.19615 | − | 9.00000i | 0.470438 | − | 0.814822i | ||||
\(123\) | 3.00000i | 0.270501i | ||||||||
\(124\) | −12.7279 | + | 7.34847i | −1.14300 | + | 0.659912i | ||||
\(125\) | 6.36396 | + | 9.19239i | 0.569210 | + | 0.822192i | ||||
\(126\) | −9.00000 | + | 5.19615i | −0.801784 | + | 0.462910i | ||||
\(127\) | −4.89898 | −0.434714 | −0.217357 | − | 0.976092i | \(-0.569744\pi\) | ||||
−0.217357 | + | 0.976092i | \(0.569744\pi\) | |||||||
\(128\) | −9.79796 | + | 5.65685i | −0.866025 | + | 0.500000i | ||||
\(129\) | −13.5000 | − | 7.79423i | −1.18861 | − | 0.686244i | ||||
\(130\) | −5.13922 | − | 5.79555i | −0.450739 | − | 0.508304i | ||||
\(131\) | −6.00000 | − | 3.46410i | −0.524222 | − | 0.302660i | 0.214438 | − | 0.976738i | \(-0.431208\pi\) |
−0.738661 | + | 0.674078i | \(0.764541\pi\) | |||||||
\(132\) | 15.5885 | − | 9.00000i | 1.35680 | − | 0.783349i | ||||
\(133\) | −6.12372 | − | 10.6066i | −0.530994 | − | 0.919709i | ||||
\(134\) | 4.24264 | 0.366508 | ||||||||
\(135\) | 8.69333 | − | 7.70882i | 0.748203 | − | 0.663470i | ||||
\(136\) | − | 14.6969i | − | 1.26025i | ||||||
\(137\) | 7.79423 | + | 13.5000i | 0.665906 | + | 1.15338i | 0.979039 | + | 0.203674i | \(0.0652881\pi\) |
−0.313133 | + | 0.949709i | \(0.601379\pi\) | |||||||
\(138\) | 3.46410 | + | 6.00000i | 0.294884 | + | 0.510754i | ||||
\(139\) | −8.50000 | + | 14.7224i | −0.720961 | + | 1.24874i | 0.239655 | + | 0.970858i | \(0.422966\pi\) |
−0.960615 | + | 0.277882i | \(0.910368\pi\) | |||||||
\(140\) | −8.19615 | + | 7.26795i | −0.692701 | + | 0.614254i | ||||
\(141\) | 10.6066 | + | 6.12372i | 0.893237 | + | 0.515711i | ||||
\(142\) | −5.19615 | + | 3.00000i | −0.436051 | + | 0.251754i | ||||
\(143\) | 12.7279i | 1.06436i | ||||||||
\(144\) | 12.0000 | 1.00000 | ||||||||
\(145\) | 18.0000 | + | 6.00000i | 1.49482 | + | 0.498273i | ||||
\(146\) | −2.12132 | − | 3.67423i | −0.175562 | − | 0.304082i | ||||
\(147\) | 1.73205 | 0.142857 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.36396 | − | 11.0227i | 0.521356 | − | 0.903015i | −0.478335 | − | 0.878177i | \(-0.658760\pi\) |
0.999691 | − | 0.0248379i | \(-0.00790696\pi\) | |||||||
\(150\) | 7.34847 | − | 9.79796i | 0.600000 | − | 0.800000i | ||||
\(151\) | 12.7279 | − | 7.34847i | 1.03578 | − | 0.598010i | 0.117147 | − | 0.993115i | \(-0.462625\pi\) |
0.918636 | + | 0.395105i | \(0.129292\pi\) | |||||||
\(152\) | 14.1421i | 1.14708i | ||||||||
\(153\) | −7.79423 | + | 13.5000i | −0.630126 | + | 1.09141i | ||||
\(154\) | 18.0000 | 1.45048 | ||||||||
\(155\) | 16.0981 | − | 3.29423i | 1.29303 | − | 0.264599i | ||||
\(156\) | −4.24264 | + | 7.34847i | −0.339683 | + | 0.588348i | ||||
\(157\) | −2.44949 | + | 4.24264i | −0.195491 | + | 0.338600i | −0.947061 | − | 0.321053i | \(-0.895963\pi\) |
0.751571 | + | 0.659653i | \(0.229297\pi\) | |||||||
\(158\) | 5.19615 | − | 9.00000i | 0.413384 | − | 0.716002i | ||||
\(159\) | 2.12132 | − | 1.22474i | 0.168232 | − | 0.0971286i | ||||
\(160\) | 12.3923 | − | 2.53590i | 0.979698 | − | 0.200480i | ||||
\(161\) | 6.92820i | 0.546019i | ||||||||
\(162\) | −11.0227 | − | 6.36396i | −0.866025 | − | 0.500000i | ||||
\(163\) | 6.00000i | 0.469956i | 0.972001 | + | 0.234978i | \(0.0755019\pi\) | ||||
−0.972001 | + | 0.234978i | \(0.924498\pi\) | |||||||
\(164\) | 3.00000 | − | 1.73205i | 0.234261 | − | 0.135250i | ||||
\(165\) | −19.7160 | + | 4.03459i | −1.53489 | + | 0.314092i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.22474 | − | 0.707107i | −0.0947736 | − | 0.0547176i | 0.451864 | − | 0.892087i | \(-0.350759\pi\) |
−0.546638 | + | 0.837369i | \(0.684093\pi\) | |||||||
\(168\) | 10.3923 | + | 6.00000i | 0.801784 | + | 0.462910i | ||||
\(169\) | 3.50000 | + | 6.06218i | 0.269231 | + | 0.466321i | ||||
\(170\) | −5.19615 | + | 15.5885i | −0.398527 | + | 1.19558i | ||||
\(171\) | 7.50000 | − | 12.9904i | 0.573539 | − | 0.993399i | ||||
\(172\) | 18.0000i | 1.37249i | ||||||||
\(173\) | 17.1464 | − | 9.89949i | 1.30362 | − | 0.752645i | 0.322596 | − | 0.946537i | \(-0.395445\pi\) |
0.981023 | + | 0.193892i | \(0.0621112\pi\) | |||||||
\(174\) | − | 20.7846i | − | 1.57568i | ||||||
\(175\) | 11.2629 | − | 4.81105i | 0.851398 | − | 0.363681i | ||||
\(176\) | −18.0000 | − | 10.3923i | −1.35680 | − | 0.783349i | ||||
\(177\) | − | 3.00000i | − | 0.225494i | ||||||
\(178\) | 7.34847 | + | 12.7279i | 0.550791 | + | 0.953998i | ||||
\(179\) | − | 6.92820i | − | 0.517838i | −0.965899 | − | 0.258919i | \(-0.916634\pi\) | ||
0.965899 | − | 0.258919i | \(-0.0833663\pi\) | |||||||
\(180\) | −12.7279 | − | 4.24264i | −0.948683 | − | 0.316228i | ||||
\(181\) | − | 7.34847i | − | 0.546207i | −0.961985 | − | 0.273104i | \(-0.911950\pi\) | ||
0.961985 | − | 0.273104i | \(-0.0880502\pi\) | |||||||
\(182\) | −7.34847 | + | 4.24264i | −0.544705 | + | 0.314485i | ||||
\(183\) | 11.0227 | + | 6.36396i | 0.814822 | + | 0.470438i | ||||
\(184\) | 4.00000 | − | 6.92820i | 0.294884 | − | 0.510754i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.00000 | − | 15.5885i | −0.659912 | − | 1.14300i | ||||
\(187\) | 23.3827 | − | 13.5000i | 1.70991 | − | 0.987218i | ||||
\(188\) | − | 14.1421i | − | 1.03142i | ||||||
\(189\) | −6.36396 | − | 11.0227i | −0.462910 | − | 0.801784i | ||||
\(190\) | 5.00000 | − | 15.0000i | 0.362738 | − | 1.08821i | ||||
\(191\) | −10.6066 | − | 18.3712i | −0.767467 | − | 1.32929i | −0.938933 | − | 0.344101i | \(-0.888184\pi\) |
0.171466 | − | 0.985190i | \(-0.445150\pi\) | |||||||
\(192\) | −6.92820 | − | 12.0000i | −0.500000 | − | 0.866025i | ||||
\(193\) | −7.79423 | − | 4.50000i | −0.561041 | − | 0.323917i | 0.192522 | − | 0.981293i | \(-0.438333\pi\) |
−0.753563 | + | 0.657376i | \(0.771667\pi\) | |||||||
\(194\) | 2.12132 | − | 3.67423i | 0.152302 | − | 0.263795i | ||||
\(195\) | 7.09808 | − | 6.29423i | 0.508304 | − | 0.450739i | ||||
\(196\) | −1.00000 | − | 1.73205i | −0.0714286 | − | 0.123718i | ||||
\(197\) | − | 11.3137i | − | 0.806068i | −0.915185 | − | 0.403034i | \(-0.867956\pi\) | ||
0.915185 | − | 0.403034i | \(-0.132044\pi\) | |||||||
\(198\) | 11.0227 | + | 19.0919i | 0.783349 | + | 1.35680i | ||||
\(199\) | 7.34847i | 0.520919i | 0.965485 | + | 0.260460i | \(0.0838741\pi\) | ||||
−0.965485 | + | 0.260460i | \(0.916126\pi\) | |||||||
\(200\) | −14.0406 | − | 1.69161i | −0.992820 | − | 0.119615i | ||||
\(201\) | 5.19615i | 0.366508i | ||||||||
\(202\) | 10.3923 | + | 6.00000i | 0.731200 | + | 0.422159i | ||||
\(203\) | 10.3923 | − | 18.0000i | 0.729397 | − | 1.26335i | ||||
\(204\) | 18.0000 | 1.26025 | ||||||||
\(205\) | −3.79435 | + | 0.776457i | −0.265009 | + | 0.0542301i | ||||
\(206\) | 24.2487i | 1.68949i | ||||||||
\(207\) | −7.34847 | + | 4.24264i | −0.510754 | + | 0.294884i | ||||
\(208\) | 9.79796 | 0.679366 | ||||||||
\(209\) | −22.5000 | + | 12.9904i | −1.55636 | + | 0.898563i | ||||
\(210\) | −8.90138 | − | 10.0382i | −0.614254 | − | 0.692701i | ||||
\(211\) | −4.00000 | + | 6.92820i | −0.275371 | + | 0.476957i | −0.970229 | − | 0.242190i | \(-0.922134\pi\) |
0.694857 | + | 0.719148i | \(0.255467\pi\) | |||||||
\(212\) | −2.44949 | − | 1.41421i | −0.168232 | − | 0.0971286i | ||||
\(213\) | −3.67423 | − | 6.36396i | −0.251754 | − | 0.436051i | ||||
\(214\) | −19.0919 | + | 11.0227i | −1.30509 | + | 0.753497i | ||||
\(215\) | 6.36396 | − | 19.0919i | 0.434019 | − | 1.30206i | ||||
\(216\) | 14.6969i | 1.00000i | ||||||||
\(217\) | − | 18.0000i | − | 1.22192i | ||||||
\(218\) | 10.3923 | + | 18.0000i | 0.703856 | + | 1.21911i | ||||
\(219\) | 4.50000 | − | 2.59808i | 0.304082 | − | 0.175562i | ||||
\(220\) | 15.4176 | + | 17.3867i | 1.03946 | + | 1.17221i | ||||
\(221\) | −6.36396 | + | 11.0227i | −0.428086 | + | 0.741467i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(224\) | − | 13.8564i | − | 0.925820i | ||||||
\(225\) | 12.0000 | + | 9.00000i | 0.800000 | + | 0.600000i | ||||
\(226\) | − | 14.6969i | − | 0.977626i | ||||||
\(227\) | 12.9904 | + | 22.5000i | 0.862202 | + | 1.49338i | 0.869799 | + | 0.493406i | \(0.164248\pi\) |
−0.00759708 | + | 0.999971i | \(0.502418\pi\) | |||||||
\(228\) | −17.3205 | −1.14708 | ||||||||
\(229\) | 6.36396 | + | 3.67423i | 0.420542 | + | 0.242800i | 0.695309 | − | 0.718711i | \(-0.255267\pi\) |
−0.274767 | + | 0.961511i | \(0.588601\pi\) | |||||||
\(230\) | −6.69213 | + | 5.93426i | −0.441266 | + | 0.391293i | ||||
\(231\) | 22.0454i | 1.45048i | ||||||||
\(232\) | −20.7846 | + | 12.0000i | −1.36458 | + | 0.787839i | ||||
\(233\) | 5.19615 | 0.340411 | 0.170206 | − | 0.985409i | \(-0.445557\pi\) | ||||
0.170206 | + | 0.985409i | \(0.445557\pi\) | |||||||
\(234\) | −9.00000 | − | 5.19615i | −0.588348 | − | 0.339683i | ||||
\(235\) | −5.00000 | + | 15.0000i | −0.326164 | + | 0.978492i | ||||
\(236\) | −3.00000 | + | 1.73205i | −0.195283 | + | 0.112747i | ||||
\(237\) | 11.0227 | + | 6.36396i | 0.716002 | + | 0.413384i | ||||
\(238\) | 15.5885 | + | 9.00000i | 1.01045 | + | 0.583383i | ||||
\(239\) | −4.24264 | + | 7.34847i | −0.274434 | + | 0.475333i | −0.969992 | − | 0.243137i | \(-0.921824\pi\) |
0.695558 | + | 0.718470i | \(0.255157\pi\) | |||||||
\(240\) | 3.10583 | + | 15.1774i | 0.200480 | + | 0.979698i | ||||
\(241\) | 8.50000 | + | 14.7224i | 0.547533 | + | 0.948355i | 0.998443 | + | 0.0557856i | \(0.0177663\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | − | 22.6274i | − | 1.45455i | ||||||
\(243\) | 7.79423 | − | 13.5000i | 0.500000 | − | 0.866025i | ||||
\(244\) | − | 14.6969i | − | 0.940875i | ||||||
\(245\) | 0.448288 | + | 2.19067i | 0.0286401 | + | 0.139957i | ||||
\(246\) | 2.12132 | + | 3.67423i | 0.135250 | + | 0.234261i | ||||
\(247\) | 6.12372 | − | 10.6066i | 0.389643 | − | 0.674882i | ||||
\(248\) | −10.3923 | + | 18.0000i | −0.659912 | + | 1.14300i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.2942 | + | 6.75833i | 0.904046 | + | 0.427434i | ||||
\(251\) | − | 19.0526i | − | 1.20259i | −0.799028 | − | 0.601293i | \(-0.794652\pi\) | ||
0.799028 | − | 0.601293i | \(-0.205348\pi\) | |||||||
\(252\) | −7.34847 | + | 12.7279i | −0.462910 | + | 0.801784i | ||||
\(253\) | 14.6969 | 0.923989 | ||||||||
\(254\) | −6.00000 | + | 3.46410i | −0.376473 | + | 0.217357i | ||||
\(255\) | −19.0919 | − | 6.36396i | −1.19558 | − | 0.398527i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −12.9904 | + | 22.5000i | −0.810318 | + | 1.40351i | 0.102324 | + | 0.994751i | \(0.467372\pi\) |
−0.912642 | + | 0.408760i | \(0.865961\pi\) | |||||||
\(258\) | −22.0454 | −1.37249 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −10.3923 | − | 3.46410i | −0.644503 | − | 0.214834i | ||||
\(261\) | 25.4558 | 1.57568 | ||||||||
\(262\) | −9.79796 | −0.605320 | ||||||||
\(263\) | −6.12372 | + | 3.53553i | −0.377605 | + | 0.218010i | −0.676776 | − | 0.736189i | \(-0.736623\pi\) |
0.299171 | + | 0.954200i | \(0.403290\pi\) | |||||||
\(264\) | 12.7279 | − | 22.0454i | 0.783349 | − | 1.35680i | ||||
\(265\) | 2.09808 | + | 2.36603i | 0.128884 | + | 0.145344i | ||||
\(266\) | −15.0000 | − | 8.66025i | −0.919709 | − | 0.530994i | ||||
\(267\) | −15.5885 | + | 9.00000i | −0.953998 | + | 0.550791i | ||||
\(268\) | 5.19615 | − | 3.00000i | 0.317406 | − | 0.183254i | ||||
\(269\) | 12.7279 | 0.776035 | 0.388018 | − | 0.921652i | \(-0.373160\pi\) | ||||
0.388018 | + | 0.921652i | \(0.373160\pi\) | |||||||
\(270\) | 5.19615 | − | 15.5885i | 0.316228 | − | 0.948683i | ||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −10.3923 | − | 18.0000i | −0.630126 | − | 1.09141i | ||||
\(273\) | −5.19615 | − | 9.00000i | −0.314485 | − | 0.544705i | ||||
\(274\) | 19.0919 | + | 11.0227i | 1.15338 | + | 0.665906i | ||||
\(275\) | −10.2058 | − | 23.8923i | −0.615431 | − | 1.44076i | ||||
\(276\) | 8.48528 | + | 4.89898i | 0.510754 | + | 0.294884i | ||||
\(277\) | 9.79796 | + | 16.9706i | 0.588702 | + | 1.01966i | 0.994403 | + | 0.105656i | \(0.0336943\pi\) |
−0.405700 | + | 0.914006i | \(0.632972\pi\) | |||||||
\(278\) | 24.0416i | 1.44192i | ||||||||
\(279\) | 19.0919 | − | 11.0227i | 1.14300 | − | 0.659912i | ||||
\(280\) | −4.89898 | + | 14.6969i | −0.292770 | + | 0.878310i | ||||
\(281\) | −15.0000 | + | 8.66025i | −0.894825 | + | 0.516627i | −0.875518 | − | 0.483186i | \(-0.839479\pi\) |
−0.0193073 | + | 0.999814i | \(0.506146\pi\) | |||||||
\(282\) | 17.3205 | 1.03142 | ||||||||
\(283\) | −5.19615 | − | 3.00000i | −0.308879 | − | 0.178331i | 0.337546 | − | 0.941309i | \(-0.390403\pi\) |
−0.646425 | + | 0.762978i | \(0.723737\pi\) | |||||||
\(284\) | −4.24264 | + | 7.34847i | −0.251754 | + | 0.436051i | ||||
\(285\) | 18.3712 | + | 6.12372i | 1.08821 | + | 0.362738i | ||||
\(286\) | 9.00000 | + | 15.5885i | 0.532181 | + | 0.921765i | ||||
\(287\) | 4.24264i | 0.250435i | ||||||||
\(288\) | 14.6969 | − | 8.48528i | 0.866025 | − | 0.500000i | ||||
\(289\) | 10.0000 | 0.588235 | ||||||||
\(290\) | 26.2880 | − | 5.37945i | 1.54369 | − | 0.315892i | ||||
\(291\) | 4.50000 | + | 2.59808i | 0.263795 | + | 0.152302i | ||||
\(292\) | −5.19615 | − | 3.00000i | −0.304082 | − | 0.175562i | ||||
\(293\) | −19.5959 | − | 11.3137i | −1.14481 | − | 0.660954i | −0.197190 | − | 0.980365i | \(-0.563181\pi\) |
−0.947616 | + | 0.319411i | \(0.896515\pi\) | |||||||
\(294\) | 2.12132 | − | 1.22474i | 0.123718 | − | 0.0714286i | ||||
\(295\) | 3.79435 | − | 0.776457i | 0.220916 | − | 0.0452071i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23.3827 | + | 13.5000i | −1.35680 | + | 0.783349i | ||||
\(298\) | − | 18.0000i | − | 1.04271i | ||||||
\(299\) | −6.00000 | + | 3.46410i | −0.346989 | + | 0.200334i | ||||
\(300\) | 2.07180 | − | 17.1962i | 0.119615 | − | 0.992820i | ||||
\(301\) | −19.0919 | − | 11.0227i | −1.10044 | − | 0.635338i | ||||
\(302\) | 10.3923 | − | 18.0000i | 0.598010 | − | 1.03578i | ||||
\(303\) | −7.34847 | + | 12.7279i | −0.422159 | + | 0.731200i | ||||
\(304\) | 10.0000 | + | 17.3205i | 0.573539 | + | 0.993399i | ||||
\(305\) | −5.19615 | + | 15.5885i | −0.297531 | + | 0.892592i | ||||
\(306\) | 22.0454i | 1.26025i | ||||||||
\(307\) | − | 15.0000i | − | 0.856095i | −0.903756 | − | 0.428048i | \(-0.859202\pi\) | ||
0.903756 | − | 0.428048i | \(-0.140798\pi\) | |||||||
\(308\) | 22.0454 | − | 12.7279i | 1.25615 | − | 0.725241i | ||||
\(309\) | −29.6985 | −1.68949 | ||||||||
\(310\) | 17.3867 | − | 15.4176i | 0.987496 | − | 0.875664i | ||||
\(311\) | −8.48528 | + | 14.6969i | −0.481156 | + | 0.833387i | −0.999766 | − | 0.0216240i | \(-0.993116\pi\) |
0.518610 | + | 0.855011i | \(0.326450\pi\) | |||||||
\(312\) | 12.0000i | 0.679366i | ||||||||
\(313\) | −12.9904 | + | 7.50000i | −0.734260 | + | 0.423925i | −0.819979 | − | 0.572394i | \(-0.806015\pi\) |
0.0857188 | + | 0.996319i | \(0.472681\pi\) | |||||||
\(314\) | 6.92820i | 0.390981i | ||||||||
\(315\) | 12.2942 | − | 10.9019i | 0.692701 | − | 0.614254i | ||||
\(316\) | − | 14.6969i | − | 0.826767i | ||||||
\(317\) | −28.1691 | + | 16.2635i | −1.58214 | + | 0.913447i | −0.587589 | + | 0.809160i | \(0.699923\pi\) |
−0.994547 | + | 0.104287i | \(0.966744\pi\) | |||||||
\(318\) | 1.73205 | − | 3.00000i | 0.0971286 | − | 0.168232i | ||||
\(319\) | −38.1838 | − | 22.0454i | −2.13788 | − | 1.23431i | ||||
\(320\) | 13.3843 | − | 11.8685i | 0.748203 | − | 0.663470i | ||||
\(321\) | −13.5000 | − | 23.3827i | −0.753497 | − | 1.30509i | ||||
\(322\) | 4.89898 | + | 8.48528i | 0.273009 | + | 0.472866i | ||||
\(323\) | −25.9808 | −1.44561 | ||||||||
\(324\) | −18.0000 | −1.00000 | ||||||||
\(325\) | 9.79796 | + | 7.34847i | 0.543493 | + | 0.407620i | ||||
\(326\) | 4.24264 | + | 7.34847i | 0.234978 | + | 0.406994i | ||||
\(327\) | −22.0454 | + | 12.7279i | −1.21911 | + | 0.703856i | ||||
\(328\) | 2.44949 | − | 4.24264i | 0.135250 | − | 0.234261i | ||||
\(329\) | 15.0000 | + | 8.66025i | 0.826977 | + | 0.477455i | ||||
\(330\) | −21.2942 | + | 18.8827i | −1.17221 | + | 1.03946i | ||||
\(331\) | −5.00000 | − | 8.66025i | −0.274825 | − | 0.476011i | 0.695266 | − | 0.718752i | \(-0.255287\pi\) |
−0.970091 | + | 0.242742i | \(0.921953\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.00000 | −0.109435 | ||||||||
\(335\) | −6.57201 | + | 1.34486i | −0.359067 | + | 0.0734777i | ||||
\(336\) | 16.9706 | 0.925820 | ||||||||
\(337\) | −2.59808 | − | 1.50000i | −0.141526 | − | 0.0817102i | 0.427565 | − | 0.903985i | \(-0.359372\pi\) |
−0.569091 | + | 0.822274i | \(0.692705\pi\) | |||||||
\(338\) | 8.57321 | + | 4.94975i | 0.466321 | + | 0.269231i | ||||
\(339\) | 18.0000 | 0.977626 | ||||||||
\(340\) | 4.65874 | + | 22.7661i | 0.252656 | + | 1.23467i | ||||
\(341\) | −38.1838 | −2.06777 | ||||||||
\(342\) | − | 21.2132i | − | 1.14708i | ||||||
\(343\) | 19.5959 | 1.05808 | ||||||||
\(344\) | 12.7279 | + | 22.0454i | 0.686244 | + | 1.18861i | ||||
\(345\) | −7.26795 | − | 8.19615i | −0.391293 | − | 0.441266i | ||||
\(346\) | 14.0000 | − | 24.2487i | 0.752645 | − | 1.30362i | ||||
\(347\) | 2.59808 | − | 4.50000i | 0.139472 | − | 0.241573i | −0.787825 | − | 0.615899i | \(-0.788793\pi\) |
0.927297 | + | 0.374327i | \(0.122126\pi\) | |||||||
\(348\) | −14.6969 | − | 25.4558i | −0.787839 | − | 1.36458i | ||||
\(349\) | 12.7279 | − | 7.34847i | 0.681310 | − | 0.393355i | −0.119038 | − | 0.992890i | \(-0.537981\pi\) |
0.800348 | + | 0.599535i | \(0.204648\pi\) | |||||||
\(350\) | 10.3923 | − | 13.8564i | 0.555492 | − | 0.740656i | ||||
\(351\) | 6.36396 | − | 11.0227i | 0.339683 | − | 0.588348i | ||||
\(352\) | −29.3939 | −1.56670 | ||||||||
\(353\) | −12.9904 | − | 22.5000i | −0.691408 | − | 1.19755i | −0.971377 | − | 0.237545i | \(-0.923657\pi\) |
0.279968 | − | 0.960009i | \(-0.409676\pi\) | |||||||
\(354\) | −2.12132 | − | 3.67423i | −0.112747 | − | 0.195283i | ||||
\(355\) | 7.09808 | − | 6.29423i | 0.376727 | − | 0.334063i | ||||
\(356\) | 18.0000 | + | 10.3923i | 0.953998 | + | 0.550791i | ||||
\(357\) | −11.0227 | + | 19.0919i | −0.583383 | + | 1.01045i | ||||
\(358\) | −4.89898 | − | 8.48528i | −0.258919 | − | 0.448461i | ||||
\(359\) | 4.24264 | 0.223918 | 0.111959 | − | 0.993713i | \(-0.464287\pi\) | ||||
0.111959 | + | 0.993713i | \(0.464287\pi\) | |||||||
\(360\) | −18.5885 | + | 3.80385i | −0.979698 | + | 0.200480i | ||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | −5.19615 | − | 9.00000i | −0.273104 | − | 0.473029i | ||||
\(363\) | 27.7128 | 1.45455 | ||||||||
\(364\) | −6.00000 | + | 10.3923i | −0.314485 | + | 0.544705i | ||||
\(365\) | 4.45069 | + | 5.01910i | 0.232960 | + | 0.262712i | ||||
\(366\) | 18.0000 | 0.940875 | ||||||||
\(367\) | −7.34847 | − | 12.7279i | −0.383587 | − | 0.664392i | 0.607985 | − | 0.793948i | \(-0.291978\pi\) |
−0.991572 | + | 0.129556i | \(0.958645\pi\) | |||||||
\(368\) | − | 11.3137i | − | 0.589768i | ||||||
\(369\) | −4.50000 | + | 2.59808i | −0.234261 | + | 0.135250i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.00000 | − | 1.73205i | 0.155752 | − | 0.0899236i | ||||
\(372\) | −22.0454 | − | 12.7279i | −1.14300 | − | 0.659912i | ||||
\(373\) | 7.34847 | − | 12.7279i | 0.380489 | − | 0.659027i | −0.610643 | − | 0.791906i | \(-0.709089\pi\) |
0.991132 | + | 0.132879i | \(0.0424222\pi\) | |||||||
\(374\) | 19.0919 | − | 33.0681i | 0.987218 | − | 1.70991i | ||||
\(375\) | −8.27723 | + | 17.5068i | −0.427434 | + | 0.904046i | ||||
\(376\) | −10.0000 | − | 17.3205i | −0.515711 | − | 0.893237i | ||||
\(377\) | 20.7846 | 1.07046 | ||||||||
\(378\) | −15.5885 | − | 9.00000i | −0.801784 | − | 0.462910i | ||||
\(379\) | −13.0000 | −0.667765 | −0.333883 | − | 0.942615i | \(-0.608359\pi\) | ||||
−0.333883 | + | 0.942615i | \(0.608359\pi\) | |||||||
\(380\) | −4.48288 | − | 21.9067i | −0.229967 | − | 1.12379i | ||||
\(381\) | −4.24264 | − | 7.34847i | −0.217357 | − | 0.376473i | ||||
\(382\) | −25.9808 | − | 15.0000i | −1.32929 | − | 0.767467i | ||||
\(383\) | −2.44949 | − | 1.41421i | −0.125163 | − | 0.0722629i | 0.436111 | − | 0.899893i | \(-0.356355\pi\) |
−0.561274 | + | 0.827630i | \(0.689689\pi\) | |||||||
\(384\) | −16.9706 | − | 9.79796i | −0.866025 | − | 0.500000i | ||||
\(385\) | −27.8827 | + | 5.70577i | −1.42103 | + | 0.290793i | ||||
\(386\) | −12.7279 | −0.647834 | ||||||||
\(387\) | − | 27.0000i | − | 1.37249i | ||||||
\(388\) | − | 6.00000i | − | 0.304604i | ||||||
\(389\) | 2.12132 | + | 3.67423i | 0.107555 | + | 0.186291i | 0.914779 | − | 0.403954i | \(-0.132364\pi\) |
−0.807224 | + | 0.590245i | \(0.799031\pi\) | |||||||
\(390\) | 4.24264 | − | 12.7279i | 0.214834 | − | 0.644503i | ||||
\(391\) | 12.7279 | + | 7.34847i | 0.643679 | + | 0.371628i | ||||
\(392\) | −2.44949 | − | 1.41421i | −0.123718 | − | 0.0714286i | ||||
\(393\) | − | 12.0000i | − | 0.605320i | ||||||
\(394\) | −8.00000 | − | 13.8564i | −0.403034 | − | 0.698076i | ||||
\(395\) | −5.19615 | + | 15.5885i | −0.261447 | + | 0.784340i | ||||
\(396\) | 27.0000 | + | 15.5885i | 1.35680 | + | 0.783349i | ||||
\(397\) | −29.3939 | −1.47524 | −0.737618 | − | 0.675218i | \(-0.764050\pi\) | ||||
−0.737618 | + | 0.675218i | \(0.764050\pi\) | |||||||
\(398\) | 5.19615 | + | 9.00000i | 0.260460 | + | 0.451129i | ||||
\(399\) | 10.6066 | − | 18.3712i | 0.530994 | − | 0.919709i | ||||
\(400\) | −18.3923 | + | 7.85641i | −0.919615 | + | 0.392820i | ||||
\(401\) | 19.5000 | + | 11.2583i | 0.973784 | + | 0.562214i | 0.900388 | − | 0.435089i | \(-0.143283\pi\) |
0.0733959 | + | 0.997303i | \(0.476616\pi\) | |||||||
\(402\) | 3.67423 | + | 6.36396i | 0.183254 | + | 0.317406i | ||||
\(403\) | 15.5885 | − | 9.00000i | 0.776516 | − | 0.448322i | ||||
\(404\) | 16.9706 | 0.844317 | ||||||||
\(405\) | 19.0919 | + | 6.36396i | 0.948683 | + | 0.316228i | ||||
\(406\) | − | 29.3939i | − | 1.45879i | ||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 22.0454 | − | 12.7279i | 1.09141 | − | 0.630126i | ||||
\(409\) | 0.500000 | − | 0.866025i | 0.0247234 | − | 0.0428222i | −0.853399 | − | 0.521258i | \(-0.825463\pi\) |
0.878122 | + | 0.478436i | \(0.158796\pi\) | |||||||
\(410\) | −4.09808 | + | 3.63397i | −0.202390 | + | 0.179469i | ||||
\(411\) | −13.5000 | + | 23.3827i | −0.665906 | + | 1.15338i | ||||
\(412\) | 17.1464 | + | 29.6985i | 0.844744 | + | 1.46314i | ||||
\(413\) | − | 4.24264i | − | 0.208767i | ||||||
\(414\) | −6.00000 | + | 10.3923i | −0.294884 | + | 0.510754i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.0000 | − | 6.92820i | 0.588348 | − | 0.339683i | ||||
\(417\) | −29.4449 | −1.44192 | ||||||||
\(418\) | −18.3712 | + | 31.8198i | −0.898563 | + | 1.55636i | ||||
\(419\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(420\) | −18.0000 | − | 6.00000i | −0.878310 | − | 0.292770i | ||||
\(421\) | 6.36396 | − | 3.67423i | 0.310160 | − | 0.179071i | −0.336838 | − | 0.941563i | \(-0.609357\pi\) |
0.646998 | + | 0.762491i | \(0.276024\pi\) | |||||||
\(422\) | 11.3137i | 0.550743i | ||||||||
\(423\) | 21.2132i | 1.03142i | ||||||||
\(424\) | −4.00000 | −0.194257 | ||||||||
\(425\) | 3.10770 | − | 25.7942i | 0.150745 | − | 1.25120i | ||||
\(426\) | −9.00000 | − | 5.19615i | −0.436051 | − | 0.251754i | ||||
\(427\) | 15.5885 | + | 9.00000i | 0.754378 | + | 0.435541i | ||||
\(428\) | −15.5885 | + | 27.0000i | −0.753497 | + | 1.30509i | ||||
\(429\) | −19.0919 | + | 11.0227i | −0.921765 | + | 0.532181i | ||||
\(430\) | −5.70577 | − | 27.8827i | −0.275157 | − | 1.34462i | ||||
\(431\) | −4.24264 | −0.204361 | −0.102180 | − | 0.994766i | \(-0.532582\pi\) | ||||
−0.102180 | + | 0.994766i | \(0.532582\pi\) | |||||||
\(432\) | 10.3923 | + | 18.0000i | 0.500000 | + | 0.866025i | ||||
\(433\) | 15.0000i | 0.720854i | 0.932787 | + | 0.360427i | \(0.117369\pi\) | ||||
−0.932787 | + | 0.360427i | \(0.882631\pi\) | |||||||
\(434\) | −12.7279 | − | 22.0454i | −0.610960 | − | 1.05821i | ||||
\(435\) | 6.58846 | + | 32.1962i | 0.315892 | + | 1.54369i | ||||
\(436\) | 25.4558 | + | 14.6969i | 1.21911 | + | 0.703856i | ||||
\(437\) | −12.2474 | − | 7.07107i | −0.585875 | − | 0.338255i | ||||
\(438\) | 3.67423 | − | 6.36396i | 0.175562 | − | 0.304082i | ||||
\(439\) | −31.8198 | + | 18.3712i | −1.51868 | + | 0.876808i | −0.518918 | + | 0.854824i | \(0.673665\pi\) |
−0.999758 | + | 0.0219843i | \(0.993002\pi\) | |||||||
\(440\) | 31.1769 | + | 10.3923i | 1.48630 | + | 0.495434i | ||||
\(441\) | 1.50000 | + | 2.59808i | 0.0714286 | + | 0.123718i | ||||
\(442\) | 18.0000i | 0.856173i | ||||||||
\(443\) | 7.79423 | + | 13.5000i | 0.370315 | + | 0.641404i | 0.989614 | − | 0.143751i | \(-0.0459164\pi\) |
−0.619299 | + | 0.785155i | \(0.712583\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.4176 | − | 17.3867i | −0.730867 | − | 0.824207i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.0454 | 1.04271 | ||||||||
\(448\) | −9.79796 | − | 16.9706i | −0.462910 | − | 0.801784i | ||||
\(449\) | − | 19.0526i | − | 0.899146i | −0.893244 | − | 0.449573i | \(-0.851576\pi\) | ||
0.893244 | − | 0.449573i | \(-0.148424\pi\) | |||||||
\(450\) | 21.0609 | + | 2.53742i | 0.992820 | + | 0.119615i | ||||
\(451\) | 9.00000 | 0.423793 | ||||||||
\(452\) | −10.3923 | − | 18.0000i | −0.488813 | − | 0.846649i | ||||
\(453\) | 22.0454 | + | 12.7279i | 1.03578 | + | 0.598010i | ||||
\(454\) | 31.8198 | + | 18.3712i | 1.49338 | + | 0.862202i | ||||
\(455\) | 10.0382 | − | 8.90138i | 0.470598 | − | 0.417303i | ||||
\(456\) | −21.2132 | + | 12.2474i | −0.993399 | + | 0.573539i | ||||
\(457\) | 23.3827 | − | 13.5000i | 1.09380 | − | 0.631503i | 0.159211 | − | 0.987245i | \(-0.449105\pi\) |
0.934585 | + | 0.355741i | \(0.115772\pi\) | |||||||
\(458\) | 10.3923 | 0.485601 | ||||||||
\(459\) | −27.0000 | −1.26025 | ||||||||
\(460\) | −4.00000 | + | 12.0000i | −0.186501 | + | 0.559503i | ||||
\(461\) | −6.36396 | − | 11.0227i | −0.296399 | − | 0.513378i | 0.678910 | − | 0.734221i | \(-0.262453\pi\) |
−0.975309 | + | 0.220843i | \(0.929119\pi\) | |||||||
\(462\) | 15.5885 | + | 27.0000i | 0.725241 | + | 1.25615i | ||||
\(463\) | −9.79796 | + | 16.9706i | −0.455350 | + | 0.788689i | −0.998708 | − | 0.0508118i | \(-0.983819\pi\) |
0.543358 | + | 0.839501i | \(0.317152\pi\) | |||||||
\(464\) | −16.9706 | + | 29.3939i | −0.787839 | + | 1.36458i | ||||
\(465\) | 18.8827 | + | 21.2942i | 0.875664 | + | 0.987496i | ||||
\(466\) | 6.36396 | − | 3.67423i | 0.294805 | − | 0.170206i | ||||
\(467\) | 25.9808 | 1.20225 | 0.601123 | − | 0.799156i | \(-0.294720\pi\) | ||||
0.601123 | + | 0.799156i | \(0.294720\pi\) | |||||||
\(468\) | −14.6969 | −0.679366 | ||||||||
\(469\) | 7.34847i | 0.339321i | ||||||||
\(470\) | 4.48288 | + | 21.9067i | 0.206780 | + | 1.01048i | ||||
\(471\) | −8.48528 | −0.390981 | ||||||||
\(472\) | −2.44949 | + | 4.24264i | −0.112747 | + | 0.195283i | ||||
\(473\) | −23.3827 | + | 40.5000i | −1.07514 | + | 1.86219i | ||||
\(474\) | 18.0000 | 0.826767 | ||||||||
\(475\) | −2.99038 | + | 24.8205i | −0.137208 | + | 1.13884i | ||||
\(476\) | 25.4558 | 1.16677 | ||||||||
\(477\) | 3.67423 | + | 2.12132i | 0.168232 | + | 0.0971286i | ||||
\(478\) | 12.0000i | 0.548867i | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 14.5359 | + | 16.3923i | 0.663470 | + | 0.748203i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 20.8207 | + | 12.0208i | 0.948355 | + | 0.547533i | ||||
\(483\) | −10.3923 | + | 6.00000i | −0.472866 | + | 0.273009i | ||||
\(484\) | −16.0000 | − | 27.7128i | −0.727273 | − | 1.25967i | ||||
\(485\) | −2.12132 | + | 6.36396i | −0.0963242 | + | 0.288973i | ||||
\(486\) | − | 22.0454i | − | 1.00000i | ||||||
\(487\) | 19.5959 | 0.887976 | 0.443988 | − | 0.896033i | \(-0.353563\pi\) | ||||
0.443988 | + | 0.896033i | \(0.353563\pi\) | |||||||
\(488\) | −10.3923 | − | 18.0000i | −0.470438 | − | 0.814822i | ||||
\(489\) | −9.00000 | + | 5.19615i | −0.406994 | + | 0.234978i | ||||
\(490\) | 2.09808 | + | 2.36603i | 0.0947814 | + | 0.106886i | ||||
\(491\) | 19.5000 | + | 11.2583i | 0.880023 | + | 0.508081i | 0.870666 | − | 0.491875i | \(-0.163688\pi\) |
0.00935679 | + | 0.999956i | \(0.497022\pi\) | |||||||
\(492\) | 5.19615 | + | 3.00000i | 0.234261 | + | 0.135250i | ||||
\(493\) | −22.0454 | − | 38.1838i | −0.992875 | − | 1.71971i | ||||
\(494\) | − | 17.3205i | − | 0.779287i | ||||||
\(495\) | −23.1265 | − | 26.0800i | −1.03946 | − | 1.17221i | ||||
\(496\) | 29.3939i | 1.31982i | ||||||||
\(497\) | −5.19615 | − | 9.00000i | −0.233079 | − | 0.403705i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.50000 | − | 14.7224i | 0.380512 | − | 0.659067i | −0.610623 | − | 0.791921i | \(-0.709081\pi\) |
0.991136 | + | 0.132855i | \(0.0424144\pi\) | |||||||
\(500\) | 22.2856 | − | 1.83032i | 0.996644 | − | 0.0818542i | ||||
\(501\) | − | 2.44949i | − | 0.109435i | ||||||
\(502\) | −13.4722 | − | 23.3345i | −0.601293 | − | 1.04147i | ||||
\(503\) | 7.07107i | 0.315283i | 0.987496 | + | 0.157642i | \(0.0503891\pi\) | ||||
−0.987496 | + | 0.157642i | \(0.949611\pi\) | |||||||
\(504\) | 20.7846i | 0.925820i | ||||||||
\(505\) | −18.0000 | − | 6.00000i | −0.800989 | − | 0.266996i | ||||
\(506\) | 18.0000 | − | 10.3923i | 0.800198 | − | 0.461994i | ||||
\(507\) | −6.06218 | + | 10.5000i | −0.269231 | + | 0.466321i | ||||
\(508\) | −4.89898 | + | 8.48528i | −0.217357 | + | 0.376473i | ||||
\(509\) | 8.48528 | − | 14.6969i | 0.376103 | − | 0.651430i | −0.614388 | − | 0.789004i | \(-0.710597\pi\) |
0.990492 | + | 0.137574i | \(0.0439304\pi\) | |||||||
\(510\) | −27.8827 | + | 5.70577i | −1.23467 | + | 0.252656i | ||||
\(511\) | 6.36396 | − | 3.67423i | 0.281525 | − | 0.162539i | ||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | 25.9808 | 1.14708 | ||||||||
\(514\) | 36.7423i | 1.62064i | ||||||||
\(515\) | −7.68653 | − | 37.5622i | −0.338709 | − | 1.65519i | ||||
\(516\) | −27.0000 | + | 15.5885i | −1.18861 | + | 0.686244i | ||||
\(517\) | 18.3712 | − | 31.8198i | 0.807963 | − | 1.39943i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.6985 | + | 17.1464i | 1.30362 | + | 0.752645i | ||||
\(520\) | −15.1774 | + | 3.10583i | −0.665574 | + | 0.136200i | ||||
\(521\) | − | 29.4449i | − | 1.29000i | −0.764181 | − | 0.645001i | \(-0.776857\pi\) | ||
0.764181 | − | 0.645001i | \(-0.223143\pi\) | |||||||
\(522\) | 31.1769 | − | 18.0000i | 1.36458 | − | 0.787839i | ||||
\(523\) | 6.00000i | 0.262362i | 0.991358 | + | 0.131181i | \(0.0418769\pi\) | ||||
−0.991358 | + | 0.131181i | \(0.958123\pi\) | |||||||
\(524\) | −12.0000 | + | 6.92820i | −0.524222 | + | 0.302660i | ||||
\(525\) | 16.9706 | + | 12.7279i | 0.740656 | + | 0.555492i | ||||
\(526\) | −5.00000 | + | 8.66025i | −0.218010 | + | 0.377605i | ||||
\(527\) | −33.0681 | − | 19.0919i | −1.44047 | − | 0.831655i | ||||
\(528\) | − | 36.0000i | − | 1.56670i | ||||||
\(529\) | −7.50000 | − | 12.9904i | −0.326087 | − | 0.564799i | ||||
\(530\) | 4.24264 | + | 1.41421i | 0.184289 | + | 0.0614295i | ||||
\(531\) | 4.50000 | − | 2.59808i | 0.195283 | − | 0.112747i | ||||
\(532\) | −24.4949 | −1.06199 | ||||||||
\(533\) | −3.67423 | + | 2.12132i | −0.159149 | + | 0.0918846i | ||||
\(534\) | −12.7279 | + | 22.0454i | −0.550791 | + | 0.953998i | ||||
\(535\) | 26.0800 | − | 23.1265i | 1.12754 | − | 0.999845i | ||||
\(536\) | 4.24264 | − | 7.34847i | 0.183254 | − | 0.317406i | ||||
\(537\) | 10.3923 | − | 6.00000i | 0.448461 | − | 0.258919i | ||||
\(538\) | 15.5885 | − | 9.00000i | 0.672066 | − | 0.388018i | ||||
\(539\) | − | 5.19615i | − | 0.223814i | ||||||
\(540\) | −4.65874 | − | 22.7661i | −0.200480 | − | 0.979698i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.0227 | − | 6.36396i | 0.473029 | − | 0.273104i | ||||
\(544\) | −25.4558 | − | 14.6969i | −1.09141 | − | 0.630126i | ||||
\(545\) | −21.8038 | − | 24.5885i | −0.933974 | − | 1.05325i | ||||
\(546\) | −12.7279 | − | 7.34847i | −0.544705 | − | 0.314485i | ||||
\(547\) | −28.5788 | + | 16.5000i | −1.22194 | + | 0.705489i | −0.965332 | − | 0.261026i | \(-0.915939\pi\) |
−0.256611 | + | 0.966515i | \(0.582606\pi\) | |||||||
\(548\) | 31.1769 | 1.33181 | ||||||||
\(549\) | 22.0454i | 0.940875i | ||||||||
\(550\) | −29.3939 | − | 22.0454i | −1.25336 | − | 0.940019i | ||||
\(551\) | 21.2132 | + | 36.7423i | 0.903713 | + | 1.56528i | ||||
\(552\) | 13.8564 | 0.589768 | ||||||||
\(553\) | 15.5885 | + | 9.00000i | 0.662889 | + | 0.382719i | ||||
\(554\) | 24.0000 | + | 13.8564i | 1.01966 | + | 0.588702i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.0000 | + | 29.4449i | 0.720961 | + | 1.24874i | ||||
\(557\) | 24.0416i | 1.01868i | 0.860566 | + | 0.509338i | \(0.170110\pi\) | ||||
−0.860566 | + | 0.509338i | \(0.829890\pi\) | |||||||
\(558\) | 15.5885 | − | 27.0000i | 0.659912 | − | 1.14300i | ||||
\(559\) | − | 22.0454i | − | 0.932421i | ||||||
\(560\) | 4.39230 | + | 21.4641i | 0.185609 | + | 0.907024i | ||||
\(561\) | 40.5000 | + | 23.3827i | 1.70991 | + | 0.987218i | ||||
\(562\) | −12.2474 | + | 21.2132i | −0.516627 | + | 0.894825i | ||||
\(563\) | −2.59808 | + | 4.50000i | −0.109496 | + | 0.189652i | −0.915566 | − | 0.402167i | \(-0.868257\pi\) |
0.806070 | + | 0.591820i | \(0.201590\pi\) | |||||||
\(564\) | 21.2132 | − | 12.2474i | 0.893237 | − | 0.515711i | ||||
\(565\) | 4.65874 | + | 22.7661i | 0.195995 | + | 0.957778i | ||||
\(566\) | −8.48528 | −0.356663 | ||||||||
\(567\) | 11.0227 | − | 19.0919i | 0.462910 | − | 0.801784i | ||||
\(568\) | 12.0000i | 0.503509i | ||||||||
\(569\) | 19.5000 | − | 11.2583i | 0.817483 | − | 0.471974i | −0.0320650 | − | 0.999486i | \(-0.510208\pi\) |
0.849548 | + | 0.527512i | \(0.176875\pi\) | |||||||
\(570\) | 26.8301 | − | 5.49038i | 1.12379 | − | 0.229967i | ||||
\(571\) | −6.50000 | + | 11.2583i | −0.272017 | + | 0.471146i | −0.969378 | − | 0.245573i | \(-0.921024\pi\) |
0.697362 | + | 0.716720i | \(0.254357\pi\) | |||||||
\(572\) | 22.0454 | + | 12.7279i | 0.921765 | + | 0.532181i | ||||
\(573\) | 18.3712 | − | 31.8198i | 0.767467 | − | 1.32929i | ||||
\(574\) | 3.00000 | + | 5.19615i | 0.125218 | + | 0.216883i | ||||
\(575\) | 8.48528 | − | 11.3137i | 0.353861 | − | 0.471814i | ||||
\(576\) | 12.0000 | − | 20.7846i | 0.500000 | − | 0.866025i | ||||
\(577\) | 3.00000i | 0.124892i | 0.998048 | + | 0.0624458i | \(0.0198901\pi\) | ||||
−0.998048 | + | 0.0624458i | \(0.980110\pi\) | |||||||
\(578\) | 12.2474 | − | 7.07107i | 0.509427 | − | 0.294118i | ||||
\(579\) | − | 15.5885i | − | 0.647834i | ||||||
\(580\) | 28.3923 | − | 25.1769i | 1.17893 | − | 1.04541i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.34847 | 0.304604 | ||||||||
\(583\) | −3.67423 | − | 6.36396i | −0.152171 | − | 0.263568i | ||||
\(584\) | −8.48528 | −0.351123 | ||||||||
\(585\) | 15.5885 | + | 5.19615i | 0.644503 | + | 0.214834i | ||||
\(586\) | −32.0000 | −1.32191 | ||||||||
\(587\) | 12.9904 | + | 22.5000i | 0.536170 | + | 0.928674i | 0.999106 | + | 0.0422823i | \(0.0134629\pi\) |
−0.462935 | + | 0.886392i | \(0.653204\pi\) | |||||||
\(588\) | 1.73205 | − | 3.00000i | 0.0714286 | − | 0.123718i | ||||
\(589\) | 31.8198 | + | 18.3712i | 1.31111 | + | 0.756971i | ||||
\(590\) | 4.09808 | − | 3.63397i | 0.168715 | − | 0.149608i | ||||
\(591\) | 16.9706 | − | 9.79796i | 0.698076 | − | 0.403034i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.1769 | 1.28028 | 0.640141 | − | 0.768257i | \(-0.278876\pi\) | ||||
0.640141 | + | 0.768257i | \(0.278876\pi\) | |||||||
\(594\) | −19.0919 | + | 33.0681i | −0.783349 | + | 1.35680i | ||||
\(595\) | −27.0000 | − | 9.00000i | −1.10689 | − | 0.368964i | ||||
\(596\) | −12.7279 | − | 22.0454i | −0.521356 | − | 0.903015i | ||||
\(597\) | −11.0227 | + | 6.36396i | −0.451129 | + | 0.260460i | ||||
\(598\) | −4.89898 | + | 8.48528i | −0.200334 | + | 0.346989i | ||||
\(599\) | −16.9706 | + | 29.3939i | −0.693398 | + | 1.20100i | 0.277319 | + | 0.960778i | \(0.410554\pi\) |
−0.970718 | + | 0.240223i | \(0.922779\pi\) | |||||||
\(600\) | −9.62209 | − | 22.5259i | −0.392820 | − | 0.919615i | ||||
\(601\) | −12.5000 | − | 21.6506i | −0.509886 | − | 0.883148i | −0.999934 | − | 0.0114528i | \(-0.996354\pi\) |
0.490049 | − | 0.871695i | \(-0.336979\pi\) | |||||||
\(602\) | −31.1769 | −1.27068 | ||||||||
\(603\) | −7.79423 | + | 4.50000i | −0.317406 | + | 0.183254i | ||||
\(604\) | − | 29.3939i | − | 1.19602i | ||||||
\(605\) | 7.17260 | + | 35.0507i | 0.291608 | + | 1.42501i | ||||
\(606\) | 20.7846i | 0.844317i | ||||||||
\(607\) | −14.6969 | + | 25.4558i | −0.596530 | + | 1.03322i | 0.396799 | + | 0.917906i | \(0.370121\pi\) |
−0.993329 | + | 0.115315i | \(0.963212\pi\) | |||||||
\(608\) | 24.4949 | + | 14.1421i | 0.993399 | + | 0.573539i | ||||
\(609\) | 36.0000 | 1.45879 | ||||||||
\(610\) | 4.65874 | + | 22.7661i | 0.188627 | + | 0.921773i | ||||
\(611\) | 17.3205i | 0.700713i | ||||||||
\(612\) | 15.5885 | + | 27.0000i | 0.630126 | + | 1.09141i | ||||
\(613\) | 41.6413 | 1.68188 | 0.840939 | − | 0.541130i | \(-0.182003\pi\) | ||||
0.840939 | + | 0.541130i | \(0.182003\pi\) | |||||||
\(614\) | −10.6066 | − | 18.3712i | −0.428048 | − | 0.741400i | ||||
\(615\) | −4.45069 | − | 5.01910i | −0.179469 | − | 0.202390i | ||||
\(616\) | 18.0000 | − | 31.1769i | 0.725241 | − | 1.25615i | ||||
\(617\) | −2.59808 | + | 4.50000i | −0.104595 | + | 0.181163i | −0.913573 | − | 0.406676i | \(-0.866688\pi\) |
0.808978 | + | 0.587839i | \(0.200021\pi\) | |||||||
\(618\) | −36.3731 | + | 21.0000i | −1.46314 | + | 0.844744i | ||||
\(619\) | −5.50000 | − | 9.52628i | −0.221064 | − | 0.382893i | 0.734068 | − | 0.679076i | \(-0.237620\pi\) |
−0.955131 | + | 0.296183i | \(0.904286\pi\) | |||||||
\(620\) | 10.3923 | − | 31.1769i | 0.417365 | − | 1.25210i | ||||
\(621\) | −12.7279 | − | 7.34847i | −0.510754 | − | 0.294884i | ||||
\(622\) | 24.0000i | 0.962312i | ||||||||
\(623\) | −22.0454 | + | 12.7279i | −0.883231 | + | 0.509933i | ||||
\(624\) | 8.48528 | + | 14.6969i | 0.339683 | + | 0.588348i | ||||
\(625\) | −24.2846 | − | 5.93782i | −0.971384 | − | 0.237513i | ||||
\(626\) | −10.6066 | + | 18.3712i | −0.423925 | + | 0.734260i | ||||
\(627\) | −38.9711 | − | 22.5000i | −1.55636 | − | 0.898563i | ||||
\(628\) | 4.89898 | + | 8.48528i | 0.195491 | + | 0.338600i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 7.34847 | − | 22.0454i | 0.292770 | − | 0.878310i | ||||
\(631\) | 7.34847i | 0.292538i | 0.989245 | + | 0.146269i | \(0.0467265\pi\) | ||||
−0.989245 | + | 0.146269i | \(0.953274\pi\) | |||||||
\(632\) | −10.3923 | − | 18.0000i | −0.413384 | − | 0.716002i | ||||
\(633\) | −13.8564 | −0.550743 | ||||||||
\(634\) | −23.0000 | + | 39.8372i | −0.913447 | + | 1.58214i | ||||
\(635\) | 8.19615 | − | 7.26795i | 0.325254 | − | 0.288420i | ||||
\(636\) | − | 4.89898i | − | 0.194257i | ||||||
\(637\) | 1.22474 | + | 2.12132i | 0.0485262 | + | 0.0840498i | ||||
\(638\) | −62.3538 | −2.46861 | ||||||||
\(639\) | 6.36396 | − | 11.0227i | 0.251754 | − | 0.436051i | ||||
\(640\) | 8.00000 | − | 24.0000i | 0.316228 | − | 0.948683i | ||||
\(641\) | −4.50000 | + | 2.59808i | −0.177739 | + | 0.102618i | −0.586230 | − | 0.810145i | \(-0.699389\pi\) |
0.408491 | + | 0.912762i | \(0.366055\pi\) | |||||||
\(642\) | −33.0681 | − | 19.0919i | −1.30509 | − | 0.753497i | ||||
\(643\) | 18.1865 | + | 10.5000i | 0.717207 | + | 0.414080i | 0.813724 | − | 0.581252i | \(-0.197437\pi\) |
−0.0965169 | + | 0.995331i | \(0.530770\pi\) | |||||||
\(644\) | 12.0000 | + | 6.92820i | 0.472866 | + | 0.273009i | ||||
\(645\) | 34.1492 | − | 6.98811i | 1.34462 | − | 0.275157i | ||||
\(646\) | −31.8198 | + | 18.3712i | −1.25193 | + | 0.722804i | ||||
\(647\) | − | 5.65685i | − | 0.222394i | −0.993798 | − | 0.111197i | \(-0.964532\pi\) | ||
0.993798 | − | 0.111197i | \(-0.0354684\pi\) | |||||||
\(648\) | −22.0454 | + | 12.7279i | −0.866025 | + | 0.500000i | ||||
\(649\) | −9.00000 | −0.353281 | ||||||||
\(650\) | 17.1962 | + | 2.07180i | 0.674489 | + | 0.0812626i | ||||
\(651\) | 27.0000 | − | 15.5885i | 1.05821 | − | 0.610960i | ||||
\(652\) | 10.3923 | + | 6.00000i | 0.406994 | + | 0.234978i | ||||
\(653\) | 9.79796 | + | 5.65685i | 0.383424 | + | 0.221370i | 0.679307 | − | 0.733854i | \(-0.262281\pi\) |
−0.295883 | + | 0.955224i | \(0.595614\pi\) | |||||||
\(654\) | −18.0000 | + | 31.1769i | −0.703856 | + | 1.21911i | ||||
\(655\) | 15.1774 | − | 3.10583i | 0.593031 | − | 0.121355i | ||||
\(656\) | − | 6.92820i | − | 0.270501i | ||||||
\(657\) | 7.79423 | + | 4.50000i | 0.304082 | + | 0.175562i | ||||
\(658\) | 24.4949 | 0.954911 | ||||||||
\(659\) | 33.0000 | − | 19.0526i | 1.28550 | − | 0.742182i | 0.307650 | − | 0.951500i | \(-0.400458\pi\) |
0.977848 | + | 0.209317i | \(0.0671242\pi\) | |||||||
\(660\) | −12.7279 | + | 38.1838i | −0.495434 | + | 1.48630i | ||||
\(661\) | −25.4558 | − | 14.6969i | −0.990118 | − | 0.571645i | −0.0848081 | − | 0.996397i | \(-0.527028\pi\) |
−0.905309 | + | 0.424753i | \(0.860361\pi\) | |||||||
\(662\) | −12.2474 | − | 7.07107i | −0.476011 | − | 0.274825i | ||||
\(663\) | −22.0454 | −0.856173 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.9808 | + | 8.66025i | 1.00749 | + | 0.335830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 24.0000i | − | 0.929284i | ||||||
\(668\) | −2.44949 | + | 1.41421i | −0.0947736 | + | 0.0547176i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.09808 | + | 6.29423i | −0.274223 | + | 0.243167i | ||||
\(671\) | 19.0919 | − | 33.0681i | 0.737034 | − | 1.27658i | ||||
\(672\) | 20.7846 | − | 12.0000i | 0.801784 | − | 0.462910i | ||||
\(673\) | 20.7846 | − | 12.0000i | 0.801188 | − | 0.462566i | −0.0426985 | − | 0.999088i | \(-0.513595\pi\) |
0.843886 | + | 0.536522i | \(0.180262\pi\) | |||||||
\(674\) | −4.24264 | −0.163420 | ||||||||
\(675\) | −3.10770 | + | 25.7942i | −0.119615 | + | 0.992820i | ||||
\(676\) | 14.0000 | 0.538462 | ||||||||
\(677\) | 26.9444 | − | 15.5563i | 1.03556 | − | 0.597879i | 0.116985 | − | 0.993134i | \(-0.462677\pi\) |
0.918572 | + | 0.395255i | \(0.129344\pi\) | |||||||
\(678\) | 22.0454 | − | 12.7279i | 0.846649 | − | 0.488813i | ||||
\(679\) | 6.36396 | + | 3.67423i | 0.244226 | + | 0.141004i | ||||
\(680\) | 21.8038 | + | 24.5885i | 0.836139 | + | 0.942924i | ||||
\(681\) | −22.5000 | + | 38.9711i | −0.862202 | + | 1.49338i | ||||
\(682\) | −46.7654 | + | 27.0000i | −1.79074 | + | 1.03388i | ||||
\(683\) | −15.5885 | −0.596476 | −0.298238 | − | 0.954492i | \(-0.596399\pi\) | ||||
−0.298238 | + | 0.954492i | \(0.596399\pi\) | |||||||
\(684\) | −15.0000 | − | 25.9808i | −0.573539 | − | 0.993399i | ||||
\(685\) | −33.0681 | − | 11.0227i | −1.26347 | − | 0.421156i | ||||
\(686\) | 24.0000 | − | 13.8564i | 0.916324 | − | 0.529040i | ||||
\(687\) | 12.7279i | 0.485601i | ||||||||
\(688\) | 31.1769 | + | 18.0000i | 1.18861 | + | 0.686244i | ||||
\(689\) | 3.00000 | + | 1.73205i | 0.114291 | + | 0.0659859i | ||||
\(690\) | −14.6969 | − | 4.89898i | −0.559503 | − | 0.186501i | ||||
\(691\) | −8.00000 | − | 13.8564i | −0.304334 | − | 0.527123i | 0.672779 | − | 0.739844i | \(-0.265101\pi\) |
−0.977113 | + | 0.212721i | \(0.931767\pi\) | |||||||
\(692\) | − | 39.5980i | − | 1.50529i | ||||||
\(693\) | −33.0681 | + | 19.0919i | −1.25615 | + | 0.725241i | ||||
\(694\) | − | 7.34847i | − | 0.278944i | ||||||
\(695\) | −7.62089 | − | 37.2414i | −0.289077 | − | 1.41265i | ||||
\(696\) | −36.0000 | − | 20.7846i | −1.36458 | − | 0.787839i | ||||
\(697\) | 7.79423 | + | 4.50000i | 0.295227 | + | 0.170450i | ||||
\(698\) | 10.3923 | − | 18.0000i | 0.393355 | − | 0.681310i | ||||
\(699\) | 4.50000 | + | 7.79423i | 0.170206 | + | 0.294805i | ||||
\(700\) | 2.92996 | − | 24.3190i | 0.110742 | − | 0.919173i | ||||
\(701\) | 50.9117 | 1.92291 | 0.961454 | − | 0.274966i | \(-0.0886666\pi\) | ||||
0.961454 | + | 0.274966i | \(0.0886666\pi\) | |||||||
\(702\) | − | 18.0000i | − | 0.679366i | ||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −36.0000 | + | 20.7846i | −1.35680 | + | 0.783349i | ||||
\(705\) | −26.8301 | + | 5.49038i | −1.01048 | + | 0.206780i | ||||
\(706\) | −31.8198 | − | 18.3712i | −1.19755 | − | 0.691408i | ||||
\(707\) | −10.3923 | + | 18.0000i | −0.390843 | + | 0.676960i | ||||
\(708\) | −5.19615 | − | 3.00000i | −0.195283 | − | 0.112747i | ||||
\(709\) | 31.8198 | − | 18.3712i | 1.19502 | − | 0.689944i | 0.235578 | − | 0.971856i | \(-0.424302\pi\) |
0.959440 | + | 0.281912i | \(0.0909685\pi\) | |||||||
\(710\) | 4.24264 | − | 12.7279i | 0.159223 | − | 0.477670i | ||||
\(711\) | 22.0454i | 0.826767i | ||||||||
\(712\) | 29.3939 | 1.10158 | ||||||||
\(713\) | −10.3923 | − | 18.0000i | −0.389195 | − | 0.674105i | ||||
\(714\) | 31.1769i | 1.16677i | ||||||||
\(715\) | −18.8827 | − | 21.2942i | −0.706172 | − | 0.796359i | ||||
\(716\) | −12.0000 | − | 6.92820i | −0.448461 | − | 0.258919i | ||||
\(717\) | −14.6969 | −0.548867 | ||||||||
\(718\) | 5.19615 | − | 3.00000i | 0.193919 | − | 0.111959i | ||||
\(719\) | −25.4558 | −0.949343 | −0.474671 | − | 0.880163i | \(-0.657433\pi\) | ||||
−0.474671 | + | 0.880163i | \(0.657433\pi\) | |||||||
\(720\) | −20.0764 | + | 17.8028i | −0.748203 | + | 0.663470i | ||||
\(721\) | −42.0000 | −1.56416 | ||||||||
\(722\) | 7.34847 | − | 4.24264i | 0.273482 | − | 0.157895i | ||||
\(723\) | −14.7224 | + | 25.5000i | −0.547533 | + | 0.948355i | ||||
\(724\) | −12.7279 | − | 7.34847i | −0.473029 | − | 0.273104i | ||||
\(725\) | −39.0160 | + | 16.6660i | −1.44902 | + | 0.618958i | ||||
\(726\) | 33.9411 | − | 19.5959i | 1.25967 | − | 0.727273i | ||||
\(727\) | −13.4722 | − | 23.3345i | −0.499656 | − | 0.865430i | 0.500344 | − | 0.865827i | \(-0.333207\pi\) |
−1.00000 | 0.000397168i | \(0.999874\pi\) | ||||||||
\(728\) | 16.9706i | 0.628971i | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 9.00000 | + | 3.00000i | 0.333105 | + | 0.111035i | ||||
\(731\) | −40.5000 | + | 23.3827i | −1.49795 | + | 0.864840i | ||||
\(732\) | 22.0454 | − | 12.7279i | 0.814822 | − | 0.470438i | ||||
\(733\) | −18.3712 | + | 31.8198i | −0.678555 | + | 1.17529i | 0.296861 | + | 0.954921i | \(0.404060\pi\) |
−0.975416 | + | 0.220371i | \(0.929273\pi\) | |||||||
\(734\) | −18.0000 | − | 10.3923i | −0.664392 | − | 0.383587i | ||||
\(735\) | −2.89778 | + | 2.56961i | −0.106886 | + | 0.0947814i | ||||
\(736\) | −8.00000 | − | 13.8564i | −0.294884 | − | 0.510754i | ||||
\(737\) | 15.5885 | 0.574208 | ||||||||
\(738\) | −3.67423 | + | 6.36396i | −0.135250 | + | 0.234261i | ||||
\(739\) | 43.0000 | 1.58178 | 0.790890 | − | 0.611958i | \(-0.209618\pi\) | ||||
0.790890 | + | 0.611958i | \(0.209618\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.2132 | 0.779287 | ||||||||
\(742\) | 2.44949 | − | 4.24264i | 0.0899236 | − | 0.155752i | ||||
\(743\) | 12.2474 | + | 7.07107i | 0.449315 | + | 0.259412i | 0.707541 | − | 0.706672i | \(-0.249804\pi\) |
−0.258226 | + | 0.966085i | \(0.583138\pi\) | |||||||
\(744\) | −36.0000 | −1.31982 | ||||||||
\(745\) | 5.70577 | + | 27.8827i | 0.209043 | + | 1.02154i | ||||
\(746\) | − | 20.7846i | − | 0.760979i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 54.0000i | − | 1.97444i | ||||||
\(749\) | −19.0919 | − | 33.0681i | −0.697602 | − | 1.20828i | ||||
\(750\) | 2.24167 | + | 27.2942i | 0.0818542 | + | 0.996644i | ||||
\(751\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(752\) | −24.4949 | − | 14.1421i | −0.893237 | − | 0.515711i | ||||
\(753\) | 28.5788 | − | 16.5000i | 1.04147 | − | 0.601293i | ||||
\(754\) | 25.4558 | − | 14.6969i | 0.927047 | − | 0.535231i | ||||
\(755\) | −10.3923 | + | 31.1769i | −0.378215 | + | 1.13464i | ||||
\(756\) | −25.4558 | −0.925820 | ||||||||
\(757\) | 19.5959 | 0.712226 | 0.356113 | − | 0.934443i | \(-0.384102\pi\) | ||||
0.356113 | + | 0.934443i | \(0.384102\pi\) | |||||||
\(758\) | −15.9217 | + | 9.19239i | −0.578302 | + | 0.333883i | ||||
\(759\) | 12.7279 | + | 22.0454i | 0.461994 | + | 0.800198i | ||||
\(760\) | −20.9808 | − | 23.6603i | −0.761052 | − | 0.858248i | ||||
\(761\) | 3.00000 | + | 1.73205i | 0.108750 | + | 0.0627868i | 0.553388 | − | 0.832923i | \(-0.313335\pi\) |
−0.444639 | + | 0.895710i | \(0.646668\pi\) | |||||||
\(762\) | −10.3923 | − | 6.00000i | −0.376473 | − | 0.217357i | ||||
\(763\) | −31.1769 | + | 18.0000i | −1.12868 | + | 0.651644i | ||||
\(764\) | −42.4264 | −1.53493 | ||||||||
\(765\) | −6.98811 | − | 34.1492i | −0.252656 | − | 1.23467i | ||||
\(766\) | −4.00000 | −0.144526 | ||||||||
\(767\) | 3.67423 | − | 2.12132i | 0.132669 | − | 0.0765964i | ||||
\(768\) | −27.7128 | −1.00000 | ||||||||
\(769\) | −2.00000 | + | 3.46410i | −0.0721218 | + | 0.124919i | −0.899831 | − | 0.436239i | \(-0.856310\pi\) |
0.827709 | + | 0.561157i | \(0.189644\pi\) | |||||||
\(770\) | −30.1146 | + | 26.7042i | −1.08525 | + | 0.962351i | ||||
\(771\) | −45.0000 | −1.62064 | ||||||||
\(772\) | −15.5885 | + | 9.00000i | −0.561041 | + | 0.323917i | ||||
\(773\) | − | 45.2548i | − | 1.62770i | −0.581073 | − | 0.813852i | \(-0.697367\pi\) | ||
0.581073 | − | 0.813852i | \(-0.302633\pi\) | |||||||
\(774\) | −19.0919 | − | 33.0681i | −0.686244 | − | 1.18861i | ||||
\(775\) | −22.0454 | + | 29.3939i | −0.791894 | + | 1.05586i | ||||
\(776\) | −4.24264 | − | 7.34847i | −0.152302 | − | 0.263795i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.19615 | + | 3.00000i | 0.186291 | + | 0.107555i | ||||
\(779\) | −7.50000 | − | 4.33013i | −0.268715 | − | 0.155143i | ||||
\(780\) | −3.80385 | − | 18.5885i | −0.136200 | − | 0.665574i | ||||
\(781\) | −19.0919 | + | 11.0227i | −0.683161 | + | 0.394423i | ||||
\(782\) | 20.7846 | 0.743256 | ||||||||
\(783\) | 22.0454 | + | 38.1838i | 0.787839 | + | 1.36458i | ||||
\(784\) | −4.00000 | −0.142857 | ||||||||
\(785\) | −2.19615 | − | 10.7321i | −0.0783840 | − | 0.383043i | ||||
\(786\) | −8.48528 | − | 14.6969i | −0.302660 | − | 0.524222i | ||||
\(787\) | −41.5692 | − | 24.0000i | −1.48178 | − | 0.855508i | −0.481996 | − | 0.876173i | \(-0.660088\pi\) |
−0.999786 | + | 0.0206657i | \(0.993421\pi\) | |||||||
\(788\) | −19.5959 | − | 11.3137i | −0.698076 | − | 0.403034i | ||||
\(789\) | −10.6066 | − | 6.12372i | −0.377605 | − | 0.218010i | ||||
\(790\) | 4.65874 | + | 22.7661i | 0.165751 | + | 0.809982i | ||||
\(791\) | 25.4558 | 0.905106 | ||||||||
\(792\) | 44.0908 | 1.56670 | ||||||||
\(793\) | 18.0000i | 0.639199i | ||||||||
\(794\) | −36.0000 | + | 20.7846i | −1.27759 | + | 0.737618i | ||||
\(795\) | −1.73205 | + | 5.19615i | −0.0614295 | + | 0.184289i | ||||
\(796\) | 12.7279 | + | 7.34847i | 0.451129 | + | 0.260460i | ||||
\(797\) | 12.2474 | + | 7.07107i | 0.433827 | + | 0.250470i | 0.700976 | − | 0.713185i | \(-0.252748\pi\) |
−0.267149 | + | 0.963655i | \(0.586081\pi\) | |||||||
\(798\) | − | 30.0000i | − | 1.06199i | ||||||
\(799\) | 31.8198 | − | 18.3712i | 1.12570 | − | 0.649925i | ||||
\(800\) | −16.9706 | + | 22.6274i | −0.600000 | + | 0.800000i | ||||
\(801\) | −27.0000 | − | 15.5885i | −0.953998 | − | 0.550791i | ||||
\(802\) | 31.8434 | 1.12443 | ||||||||
\(803\) | −7.79423 | − | 13.5000i | −0.275052 | − | 0.476405i | ||||
\(804\) | 9.00000 | + | 5.19615i | 0.317406 | + | 0.183254i | ||||
\(805\) | −10.2784 | − | 11.5911i | −0.362267 | − | 0.408533i | ||||
\(806\) | 12.7279 | − | 22.0454i | 0.448322 | − | 0.776516i | ||||
\(807\) | 11.0227 | + | 19.0919i | 0.388018 | + | 0.672066i | ||||
\(808\) | 20.7846 | − | 12.0000i | 0.731200 | − | 0.422159i | ||||
\(809\) | − | 32.9090i | − | 1.15702i | −0.815676 | − | 0.578509i | \(-0.803635\pi\) | ||
0.815676 | − | 0.578509i | \(-0.196365\pi\) | |||||||
\(810\) | 27.8827 | − | 5.70577i | 0.979698 | − | 0.200480i | ||||
\(811\) | 47.0000 | 1.65039 | 0.825197 | − | 0.564846i | \(-0.191064\pi\) | ||||
0.825197 | + | 0.564846i | \(0.191064\pi\) | |||||||
\(812\) | −20.7846 | − | 36.0000i | −0.729397 | − | 1.26335i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.90138 | − | 10.0382i | −0.311802 | − | 0.351623i | ||||
\(816\) | 18.0000 | − | 31.1769i | 0.630126 | − | 1.09141i | ||||
\(817\) | 38.9711 | − | 22.5000i | 1.36343 | − | 0.787175i | ||||
\(818\) | − | 1.41421i | − | 0.0494468i | ||||||
\(819\) | 9.00000 | − | 15.5885i | 0.314485 | − | 0.544705i | ||||
\(820\) | −2.44949 | + | 7.34847i | −0.0855399 | + | 0.256620i | ||||
\(821\) | 10.6066 | + | 18.3712i | 0.370173 | + | 0.641158i | 0.989592 | − | 0.143902i | \(-0.0459651\pi\) |
−0.619419 | + | 0.785061i | \(0.712632\pi\) | |||||||
\(822\) | 38.1838i | 1.33181i | ||||||||
\(823\) | 14.6969 | − | 25.4558i | 0.512303 | − | 0.887335i | −0.487595 | − | 0.873070i | \(-0.662126\pi\) |
0.999898 | − | 0.0142651i | \(-0.00454088\pi\) | |||||||
\(824\) | 42.0000 | + | 24.2487i | 1.46314 | + | 0.844744i | ||||
\(825\) | 27.0000 | − | 36.0000i | 0.940019 | − | 1.25336i | ||||
\(826\) | −3.00000 | − | 5.19615i | −0.104383 | − | 0.180797i | ||||
\(827\) | −20.7846 | −0.722752 | −0.361376 | − | 0.932420i | \(-0.617693\pi\) | ||||
−0.361376 | + | 0.932420i | \(0.617693\pi\) | |||||||
\(828\) | 16.9706i | 0.589768i | ||||||||
\(829\) | 51.4393i | 1.78656i | 0.449500 | + | 0.893280i | \(0.351602\pi\) | ||||
−0.449500 | + | 0.893280i | \(0.648398\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.9706 | + | 29.3939i | −0.588702 | + | 1.01966i | ||||
\(832\) | 9.79796 | − | 16.9706i | 0.339683 | − | 0.588348i | ||||
\(833\) | 2.59808 | − | 4.50000i | 0.0900180 | − | 0.155916i | ||||
\(834\) | −36.0624 | + | 20.8207i | −1.24874 | + | 0.720961i | ||||
\(835\) | 3.09808 | − | 0.633975i | 0.107213 | − | 0.0219396i | ||||
\(836\) | 51.9615i | 1.79713i | ||||||||
\(837\) | 33.0681 | + | 19.0919i | 1.14300 | + | 0.659912i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.8492 | + | 25.7196i | 0.512653 | + | 0.887941i | 0.999892 | + | 0.0146723i | \(0.00467051\pi\) |
−0.487240 | + | 0.873268i | \(0.661996\pi\) | |||||||
\(840\) | −26.2880 | + | 5.37945i | −0.907024 | + | 0.185609i | ||||
\(841\) | −21.5000 | + | 37.2391i | −0.741379 | + | 1.28411i | ||||
\(842\) | 5.19615 | − | 9.00000i | 0.179071 | − | 0.310160i | ||||
\(843\) | −25.9808 | − | 15.0000i | −0.894825 | − | 0.516627i | ||||
\(844\) | 8.00000 | + | 13.8564i | 0.275371 | + | 0.476957i | ||||
\(845\) | −14.8492 | − | 4.94975i | −0.510829 | − | 0.170276i | ||||
\(846\) | 15.0000 | + | 25.9808i | 0.515711 | + | 0.893237i | ||||
\(847\) | 39.1918 | 1.34665 | ||||||||
\(848\) | −4.89898 | + | 2.82843i | −0.168232 | + | 0.0971286i | ||||
\(849\) | − | 10.3923i | − | 0.356663i | ||||||
\(850\) | −14.4331 | − | 33.7888i | −0.495053 | − | 1.15895i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −14.6969 | −0.503509 | ||||||||
\(853\) | 11.0227 | + | 19.0919i | 0.377410 | + | 0.653694i | 0.990685 | − | 0.136176i | \(-0.0434814\pi\) |
−0.613274 | + | 0.789870i | \(0.710148\pi\) | |||||||
\(854\) | 25.4558 | 0.871081 | ||||||||
\(855\) | 6.72432 | + | 32.8601i | 0.229967 | + | 1.12379i | ||||
\(856\) | 44.0908i | 1.50699i | ||||||||
\(857\) | −15.5885 | − | 27.0000i | −0.532492 | − | 0.922302i | −0.999280 | − | 0.0379336i | \(-0.987922\pi\) |
0.466789 | − | 0.884369i | \(-0.345411\pi\) | |||||||
\(858\) | −15.5885 | + | 27.0000i | −0.532181 | + | 0.921765i | ||||
\(859\) | 24.5000 | − | 42.4352i | 0.835929 | − | 1.44787i | −0.0573424 | − | 0.998355i | \(-0.518263\pi\) |
0.893272 | − | 0.449517i | \(-0.148404\pi\) | |||||||
\(860\) | −26.7042 | − | 30.1146i | −0.910604 | − | 1.02690i | ||||
\(861\) | −6.36396 | + | 3.67423i | −0.216883 | + | 0.125218i | ||||
\(862\) | −5.19615 | + | 3.00000i | −0.176982 | + | 0.102180i | ||||
\(863\) | − | 24.0416i | − | 0.818387i | −0.912448 | − | 0.409193i | \(-0.865810\pi\) | ||
0.912448 | − | 0.409193i | \(-0.134190\pi\) | |||||||
\(864\) | 25.4558 | + | 14.6969i | 0.866025 | + | 0.500000i | ||||
\(865\) | −14.0000 | + | 42.0000i | −0.476014 | + | 1.42804i | ||||
\(866\) | 10.6066 | + | 18.3712i | 0.360427 | + | 0.624278i | ||||
\(867\) | 8.66025 | + | 15.0000i | 0.294118 | + | 0.509427i | ||||
\(868\) | −31.1769 | − | 18.0000i | −1.05821 | − | 0.610960i | ||||
\(869\) | 19.0919 | − | 33.0681i | 0.647648 | − | 1.12176i | ||||
\(870\) | 30.8353 | + | 34.7733i | 1.04541 | + | 1.17893i | ||||
\(871\) | −6.36396 | + | 3.67423i | −0.215635 | + | 0.124497i | ||||
\(872\) | 41.5692 | 1.40771 | ||||||||
\(873\) | 9.00000i | 0.304604i | ||||||||
\(874\) | −20.0000 | −0.676510 | ||||||||
\(875\) | −11.7058 | + | 24.7583i | −0.395727 | + | 0.836984i | ||||
\(876\) | − | 10.3923i | − | 0.351123i | ||||||
\(877\) | 1.22474 | − | 2.12132i | 0.0413567 | − | 0.0716319i | −0.844606 | − | 0.535388i | \(-0.820165\pi\) |
0.885963 | + | 0.463756i | \(0.153499\pi\) | |||||||
\(878\) | −25.9808 | + | 45.0000i | −0.876808 | + | 1.51868i | ||||
\(879\) | − | 39.1918i | − | 1.32191i | ||||||
\(880\) | 45.5322 | − | 9.31749i | 1.53489 | − | 0.314092i | ||||
\(881\) | − | 41.5692i | − | 1.40050i | −0.713896 | − | 0.700251i | \(-0.753071\pi\) | ||
0.713896 | − | 0.700251i | \(-0.246929\pi\) | |||||||
\(882\) | 3.67423 | + | 2.12132i | 0.123718 | + | 0.0714286i | ||||
\(883\) | 9.00000i | 0.302874i | 0.988467 | + | 0.151437i | \(0.0483901\pi\) | ||||
−0.988467 | + | 0.151437i | \(0.951610\pi\) | |||||||
\(884\) | 12.7279 | + | 22.0454i | 0.428086 | + | 0.741467i | ||||
\(885\) | 4.45069 | + | 5.01910i | 0.149608 | + | 0.168715i | ||||
\(886\) | 19.0919 | + | 11.0227i | 0.641404 | + | 0.370315i | ||||
\(887\) | 35.5176 | + | 20.5061i | 1.19256 | + | 0.688527i | 0.958887 | − | 0.283787i | \(-0.0915908\pi\) |
0.233677 | + | 0.972314i | \(0.424924\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.00000 | − | 10.3923i | −0.201234 | − | 0.348547i | ||||
\(890\) | −31.1769 | − | 10.3923i | −1.04505 | − | 0.348351i | ||||
\(891\) | −40.5000 | − | 23.3827i | −1.35680 | − | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30.6186 | + | 17.6777i | −1.02461 | + | 0.591561i | ||||
\(894\) | 27.0000 | − | 15.5885i | 0.903015 | − | 0.521356i | ||||
\(895\) | 10.2784 | + | 11.5911i | 0.343570 | + | 0.387448i | ||||
\(896\) | −24.0000 | − | 13.8564i | −0.801784 | − | 0.462910i | ||||
\(897\) | −10.3923 | − | 6.00000i | −0.346989 | − | 0.200334i | ||||
\(898\) | −13.4722 | − | 23.3345i | −0.449573 | − | 0.778683i | ||||
\(899\) | 62.3538i | 2.07962i | ||||||||
\(900\) | 27.5885 | − | 11.7846i | 0.919615 | − | 0.392820i | ||||
\(901\) | − | 7.34847i | − | 0.244813i | ||||||
\(902\) | 11.0227 | − | 6.36396i | 0.367016 | − | 0.211897i | ||||
\(903\) | − | 38.1838i | − | 1.27068i | ||||||
\(904\) | −25.4558 | − | 14.6969i | −0.846649 | − | 0.488813i | ||||
\(905\) | 10.9019 | + | 12.2942i | 0.362392 | + | 0.408674i | ||||
\(906\) | 36.0000 | 1.19602 | ||||||||
\(907\) | 44.1673 | − | 25.5000i | 1.46655 | − | 0.846714i | 0.467251 | − | 0.884125i | \(-0.345244\pi\) |
0.999300 | + | 0.0374111i | \(0.0119111\pi\) | |||||||
\(908\) | 51.9615 | 1.72440 | ||||||||
\(909\) | −25.4558 | −0.844317 | ||||||||
\(910\) | 6.00000 | − | 18.0000i | 0.198898 | − | 0.596694i | ||||
\(911\) | −23.3345 | − | 40.4166i | −0.773107 | − | 1.33906i | −0.935852 | − | 0.352393i | \(-0.885368\pi\) |
0.162745 | − | 0.986668i | \(-0.447965\pi\) | |||||||
\(912\) | −17.3205 | + | 30.0000i | −0.573539 | + | 0.993399i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 19.0919 | − | 33.0681i | 0.631503 | − | 1.09380i | ||||
\(915\) | −27.8827 | + | 5.70577i | −0.921773 | + | 0.188627i | ||||
\(916\) | 12.7279 | − | 7.34847i | 0.420542 | − | 0.242800i | ||||
\(917\) | − | 16.9706i | − | 0.560417i | ||||||
\(918\) | −33.0681 | + | 19.0919i | −1.09141 | + | 0.630126i | ||||
\(919\) | − | 58.7878i | − | 1.93923i | −0.244638 | − | 0.969615i | \(-0.578669\pi\) | ||
0.244638 | − | 0.969615i | \(-0.421331\pi\) | |||||||
\(920\) | 3.58630 | + | 17.5254i | 0.118237 | + | 0.577794i | ||||
\(921\) | 22.5000 | − | 12.9904i | 0.741400 | − | 0.428048i | ||||
\(922\) | −15.5885 | − | 9.00000i | −0.513378 | − | 0.296399i | ||||
\(923\) | 5.19615 | − | 9.00000i | 0.171033 | − | 0.296239i | ||||
\(924\) | 38.1838 | + | 22.0454i | 1.25615 | + | 0.725241i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 27.7128i | 0.910700i | ||||||||
\(927\) | −25.7196 | − | 44.5477i | −0.844744 | − | 1.46314i | ||||
\(928\) | 48.0000i | 1.57568i | ||||||||
\(929\) | 27.0000 | − | 15.5885i | 0.885841 | − | 0.511441i | 0.0132613 | − | 0.999912i | \(-0.495779\pi\) |
0.872580 | + | 0.488471i | \(0.162445\pi\) | |||||||
\(930\) | 38.1838 | + | 12.7279i | 1.25210 | + | 0.417365i | ||||
\(931\) | −2.50000 | + | 4.33013i | −0.0819342 | + | 0.141914i | ||||
\(932\) | 5.19615 | − | 9.00000i | 0.170206 | − | 0.294805i | ||||
\(933\) | −29.3939 | −0.962312 | ||||||||
\(934\) | 31.8198 | − | 18.3712i | 1.04118 | − | 0.601123i | ||||
\(935\) | −19.0919 | + | 57.2756i | −0.624371 | + | 1.87311i | ||||
\(936\) | −18.0000 | + | 10.3923i | −0.588348 | + | 0.339683i | ||||
\(937\) | − | 36.0000i | − | 1.17607i | −0.808836 | − | 0.588034i | \(-0.799902\pi\) | ||
0.808836 | − | 0.588034i | \(-0.200098\pi\) | |||||||
\(938\) | 5.19615 | + | 9.00000i | 0.169660 | + | 0.293860i | ||||
\(939\) | −22.5000 | − | 12.9904i | −0.734260 | − | 0.423925i | ||||
\(940\) | 20.9808 | + | 23.6603i | 0.684317 | + | 0.771712i | ||||
\(941\) | −16.9706 | + | 29.3939i | −0.553225 | + | 0.958213i | 0.444815 | + | 0.895623i | \(0.353270\pi\) |
−0.998039 | + | 0.0625904i | \(0.980064\pi\) | |||||||
\(942\) | −10.3923 | + | 6.00000i | −0.338600 | + | 0.195491i | ||||
\(943\) | 2.44949 | + | 4.24264i | 0.0797664 | + | 0.138159i | ||||
\(944\) | 6.92820i | 0.225494i | ||||||||
\(945\) | 27.0000 | + | 9.00000i | 0.878310 | + | 0.292770i | ||||
\(946\) | 66.1362i | 2.15027i | ||||||||
\(947\) | 18.1865 | + | 31.5000i | 0.590983 | + | 1.02361i | 0.994100 | + | 0.108464i | \(0.0345933\pi\) |
−0.403117 | + | 0.915148i | \(0.632073\pi\) | |||||||
\(948\) | 22.0454 | − | 12.7279i | 0.716002 | − | 0.413384i | ||||
\(949\) | 6.36396 | + | 3.67423i | 0.206583 | + | 0.119271i | ||||
\(950\) | 13.8883 | + | 32.5133i | 0.450596 | + | 1.05487i | ||||
\(951\) | −48.7904 | − | 28.1691i | −1.58214 | − | 0.913447i | ||||
\(952\) | 31.1769 | − | 18.0000i | 1.01045 | − | 0.583383i | ||||
\(953\) | −15.5885 | −0.504960 | −0.252480 | − | 0.967602i | \(-0.581246\pi\) | ||||
−0.252480 | + | 0.967602i | \(0.581246\pi\) | |||||||
\(954\) | 6.00000 | 0.194257 | ||||||||
\(955\) | 45.0000 | + | 15.0000i | 1.45617 | + | 0.485389i | ||||
\(956\) | 8.48528 | + | 14.6969i | 0.274434 | + | 0.475333i | ||||
\(957\) | − | 76.3675i | − | 2.46861i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.0919 | + | 33.0681i | −0.616509 | + | 1.06783i | ||||
\(960\) | 29.3939 | + | 9.79796i | 0.948683 | + | 0.316228i | ||||
\(961\) | 11.5000 | + | 19.9186i | 0.370968 | + | 0.642535i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 23.3827 | − | 40.5000i | 0.753497 | − | 1.30509i | ||||
\(964\) | 34.0000 | 1.09507 | ||||||||
\(965\) | 19.7160 | − | 4.03459i | 0.634682 | − | 0.129878i | ||||
\(966\) | −8.48528 | + | 14.6969i | −0.273009 | + | 0.472866i | ||||
\(967\) | −14.6969 | + | 25.4558i | −0.472622 | + | 0.818605i | −0.999509 | − | 0.0313303i | \(-0.990026\pi\) |
0.526887 | + | 0.849935i | \(0.323359\pi\) | |||||||
\(968\) | −39.1918 | − | 22.6274i | −1.25967 | − | 0.727273i | ||||
\(969\) | −22.5000 | − | 38.9711i | −0.722804 | − | 1.25193i | ||||
\(970\) | 1.90192 | + | 9.29423i | 0.0610671 | + | 0.298420i | ||||
\(971\) | 3.46410i | 0.111168i | 0.998454 | + | 0.0555842i | \(0.0177021\pi\) | ||||
−0.998454 | + | 0.0555842i | \(0.982298\pi\) | |||||||
\(972\) | −15.5885 | − | 27.0000i | −0.500000 | − | 0.866025i | ||||
\(973\) | −41.6413 | −1.33496 | ||||||||
\(974\) | 24.0000 | − | 13.8564i | 0.769010 | − | 0.443988i | ||||
\(975\) | −2.53742 | + | 21.0609i | −0.0812626 | + | 0.674489i | ||||
\(976\) | −25.4558 | − | 14.6969i | −0.814822 | − | 0.470438i | ||||
\(977\) | −28.5788 | + | 49.5000i | −0.914318 | + | 1.58365i | −0.106421 | + | 0.994321i | \(0.533939\pi\) |
−0.807897 | + | 0.589324i | \(0.799394\pi\) | |||||||
\(978\) | −7.34847 | + | 12.7279i | −0.234978 | + | 0.406994i | ||||
\(979\) | 27.0000 | + | 46.7654i | 0.862924 | + | 1.49463i | ||||
\(980\) | 4.24264 | + | 1.41421i | 0.135526 | + | 0.0451754i | ||||
\(981\) | −38.1838 | − | 22.0454i | −1.21911 | − | 0.703856i | ||||
\(982\) | 31.8434 | 1.01616 | ||||||||
\(983\) | 24.4949 | − | 14.1421i | 0.781266 | − | 0.451064i | −0.0556128 | − | 0.998452i | \(-0.517711\pi\) |
0.836879 | + | 0.547388i | \(0.184378\pi\) | |||||||
\(984\) | 8.48528 | 0.270501 | ||||||||
\(985\) | 16.7846 | + | 18.9282i | 0.534802 | + | 0.603103i | ||||
\(986\) | −54.0000 | − | 31.1769i | −1.71971 | − | 0.992875i | ||||
\(987\) | 30.0000i | 0.954911i | ||||||||
\(988\) | −12.2474 | − | 21.2132i | −0.389643 | − | 0.674882i | ||||
\(989\) | −25.4558 | −0.809449 | ||||||||
\(990\) | −46.7654 | − | 15.5885i | −1.48630 | − | 0.495434i | ||||
\(991\) | 44.0908i | 1.40059i | 0.713853 | + | 0.700295i | \(0.246948\pi\) | ||||
−0.713853 | + | 0.700295i | \(0.753052\pi\) | |||||||
\(992\) | 20.7846 | + | 36.0000i | 0.659912 | + | 1.14300i | ||||
\(993\) | 8.66025 | − | 15.0000i | 0.274825 | − | 0.476011i | ||||
\(994\) | −12.7279 | − | 7.34847i | −0.403705 | − | 0.233079i | ||||
\(995\) | −10.9019 | − | 12.2942i | −0.345614 | − | 0.389753i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.8207 | + | 36.0624i | 0.659397 | + | 1.14211i | 0.980772 | + | 0.195157i | \(0.0625217\pi\) |
−0.321375 | + | 0.946952i | \(0.604145\pi\) | |||||||
\(998\) | − | 24.0416i | − | 0.761025i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 360.2.bd.a.59.4 | yes | 8 | |
5.4 | even | 2 | inner | 360.2.bd.a.59.1 | ✓ | 8 | |
8.3 | odd | 2 | inner | 360.2.bd.a.59.2 | yes | 8 | |
9.2 | odd | 6 | inner | 360.2.bd.a.299.3 | yes | 8 | |
40.19 | odd | 2 | inner | 360.2.bd.a.59.3 | yes | 8 | |
45.29 | odd | 6 | inner | 360.2.bd.a.299.2 | yes | 8 | |
72.11 | even | 6 | inner | 360.2.bd.a.299.1 | yes | 8 | |
360.299 | even | 6 | inner | 360.2.bd.a.299.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bd.a.59.1 | ✓ | 8 | 5.4 | even | 2 | inner | |
360.2.bd.a.59.2 | yes | 8 | 8.3 | odd | 2 | inner | |
360.2.bd.a.59.3 | yes | 8 | 40.19 | odd | 2 | inner | |
360.2.bd.a.59.4 | yes | 8 | 1.1 | even | 1 | trivial | |
360.2.bd.a.299.1 | yes | 8 | 72.11 | even | 6 | inner | |
360.2.bd.a.299.2 | yes | 8 | 45.29 | odd | 6 | inner | |
360.2.bd.a.299.3 | yes | 8 | 9.2 | odd | 6 | inner | |
360.2.bd.a.299.4 | yes | 8 | 360.299 | even | 6 | inner |