Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(521,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("2646.521");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.l (of order \(6\), degree \(2\), not 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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1097.6 | ||
Root | \(1.40917 + 1.00709i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.1097 |
Dual form | 2646.2.l.b.521.2 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.17468 | − | 2.03460i | −0.525332 | − | 0.909902i | −0.999565 | − | 0.0295026i | \(-0.990608\pi\) |
0.474232 | − | 0.880400i | \(-0.342726\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.03460 | − | 1.17468i | 0.643398 | − | 0.371466i | ||||
\(11\) | −4.91614 | − | 2.83834i | −1.48227 | − | 0.855790i | −0.482475 | − | 0.875910i | \(-0.660262\pi\) |
−0.999798 | + | 0.0201197i | \(0.993595\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.48943 | + | 0.859925i | 0.413094 | + | 0.238500i | 0.692118 | − | 0.721784i | \(-0.256678\pi\) |
−0.279024 | + | 0.960284i | \(0.590011\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.884414 | − | 1.53185i | −0.214502 | − | 0.371528i | 0.738616 | − | 0.674126i | \(-0.235480\pi\) |
−0.953118 | + | 0.302598i | \(0.902146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.986680 | − | 0.569660i | −0.226360 | − | 0.130689i | 0.382532 | − | 0.923942i | \(-0.375052\pi\) |
−0.608892 | + | 0.793253i | \(0.708386\pi\) | |||||||
\(20\) | 1.17468 | + | 2.03460i | 0.262666 | + | 0.454951i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.83834 | − | 4.91614i | 0.605135 | − | 1.04812i | ||||
\(23\) | −3.18272 | + | 1.83755i | −0.663644 | + | 0.383155i | −0.793664 | − | 0.608356i | \(-0.791829\pi\) |
0.130020 | + | 0.991511i | \(0.458496\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.259741 | + | 0.449885i | −0.0519482 | + | 0.0899769i | ||||
\(26\) | −0.859925 | + | 1.48943i | −0.168645 | + | 0.292102i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.59886 | + | 2.07781i | −0.668292 | + | 0.385839i | −0.795429 | − | 0.606046i | \(-0.792755\pi\) |
0.127137 | + | 0.991885i | \(0.459421\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.37019i | 1.50333i | 0.659545 | + | 0.751665i | \(0.270749\pi\) | ||||
−0.659545 | + | 0.751665i | \(0.729251\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.53185 | − | 0.884414i | 0.262710 | − | 0.151676i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.59886 | − | 7.96547i | 0.756049 | − | 1.30951i | −0.188803 | − | 0.982015i | \(-0.560461\pi\) |
0.944851 | − | 0.327500i | \(-0.106206\pi\) | |||||||
\(38\) | 0.569660 | − | 0.986680i | 0.0924111 | − | 0.160061i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.03460 | + | 1.17468i | −0.321699 | + | 0.185733i | ||||
\(41\) | −3.99709 | + | 6.92317i | −0.624241 | + | 1.08122i | 0.364446 | + | 0.931225i | \(0.381258\pi\) |
−0.988687 | + | 0.149993i | \(0.952075\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.76053 | + | 3.04933i | 0.268478 | + | 0.465018i | 0.968469 | − | 0.249134i | \(-0.0801459\pi\) |
−0.699991 | + | 0.714152i | \(0.746813\pi\) | |||||||
\(44\) | 4.91614 | + | 2.83834i | 0.741136 | + | 0.427895i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.83755 | − | 3.18272i | −0.270931 | − | 0.469267i | ||||
\(47\) | 11.8099 | 1.72265 | 0.861324 | − | 0.508055i | \(-0.169635\pi\) | ||||
0.861324 | + | 0.508055i | \(0.169635\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.449885 | − | 0.259741i | −0.0636233 | − | 0.0367329i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.48943 | − | 0.859925i | −0.206547 | − | 0.119250i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.3365i | 1.79830i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.07781 | − | 3.59886i | −0.272829 | − | 0.472554i | ||||
\(59\) | 2.22966 | 0.290277 | 0.145139 | − | 0.989411i | \(-0.453637\pi\) | ||||
0.145139 | + | 0.989411i | \(0.453637\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.99970i | 1.15229i | 0.817346 | + | 0.576146i | \(0.195444\pi\) | ||||
−0.817346 | + | 0.576146i | \(0.804556\pi\) | |||||||
\(62\) | −8.37019 | −1.06301 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 4.04054i | − | 0.501167i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.8712 | 1.32813 | 0.664067 | − | 0.747673i | \(-0.268829\pi\) | ||||
0.664067 | + | 0.747673i | \(0.268829\pi\) | |||||||
\(68\) | 0.884414 | + | 1.53185i | 0.107251 | + | 0.185764i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.52106i | 0.536551i | 0.963342 | + | 0.268276i | \(0.0864538\pi\) | ||||
−0.963342 | + | 0.268276i | \(0.913546\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.62660 | + | 2.67117i | −0.541503 | + | 0.312637i | −0.745688 | − | 0.666295i | \(-0.767879\pi\) |
0.204185 | + | 0.978932i | \(0.434546\pi\) | |||||||
\(74\) | 7.96547 | + | 4.59886i | 0.925967 | + | 0.534607i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.986680 | + | 0.569660i | 0.113180 | + | 0.0653445i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.0284 | −1.46581 | −0.732907 | − | 0.680329i | \(-0.761837\pi\) | ||||
−0.732907 | + | 0.680329i | \(0.761837\pi\) | |||||||
\(80\) | −1.17468 | − | 2.03460i | −0.131333 | − | 0.227476i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.92317 | − | 3.99709i | −0.764536 | − | 0.441405i | ||||
\(83\) | 6.27298 | + | 10.8651i | 0.688549 | + | 1.19260i | 0.972307 | + | 0.233707i | \(0.0750855\pi\) |
−0.283758 | + | 0.958896i | \(0.591581\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.07781 | + | 3.59886i | −0.225370 | + | 0.390352i | ||||
\(86\) | −3.04933 | + | 1.76053i | −0.328817 | + | 0.189843i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.83834 | + | 4.91614i | −0.302568 | + | 0.524062i | ||||
\(89\) | −0.580529 | + | 1.00551i | −0.0615360 | + | 0.106583i | −0.895152 | − | 0.445761i | \(-0.852933\pi\) |
0.833616 | + | 0.552344i | \(0.186267\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.18272 | − | 1.83755i | 0.331822 | − | 0.191577i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.8099i | 1.21810i | ||||||||
\(95\) | 2.67667i | 0.274621i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.97536 | + | 2.29517i | −0.403636 | + | 0.233039i | −0.688052 | − | 0.725662i | \(-0.741534\pi\) |
0.284416 | + | 0.958701i | \(0.408200\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.259741 | − | 0.449885i | 0.0259741 | − | 0.0449885i | ||||
\(101\) | −3.31155 | + | 5.73577i | −0.329511 | + | 0.570730i | −0.982415 | − | 0.186711i | \(-0.940217\pi\) |
0.652904 | + | 0.757441i | \(0.273551\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.07471 | − | 2.92989i | 0.500026 | − | 0.288690i | −0.228698 | − | 0.973497i | \(-0.573447\pi\) |
0.728724 | + | 0.684807i | \(0.240114\pi\) | |||||||
\(104\) | 0.859925 | − | 1.48943i | 0.0843225 | − | 0.146051i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.08386 | + | 2.35782i | 0.394802 | + | 0.227939i | 0.684239 | − | 0.729258i | \(-0.260135\pi\) |
−0.289437 | + | 0.957197i | \(0.593468\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.11835 | − | 3.66908i | −0.202901 | − | 0.351435i | 0.746561 | − | 0.665317i | \(-0.231704\pi\) |
−0.949462 | + | 0.313882i | \(0.898370\pi\) | |||||||
\(110\) | −13.3365 | −1.27159 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.91693 | − | 3.41614i | −0.556618 | − | 0.321363i | 0.195169 | − | 0.980770i | \(-0.437474\pi\) |
−0.751787 | + | 0.659406i | \(0.770808\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.47736 | + | 4.31705i | 0.697267 | + | 0.402567i | ||||
\(116\) | 3.59886 | − | 2.07781i | 0.334146 | − | 0.192919i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.22966i | 0.205257i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6123 | + | 18.3810i | 0.964754 | + | 1.67100i | ||||
\(122\) | −8.99970 | −0.814794 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 8.37019i | − | 0.751665i | ||||||
\(125\) | −10.5263 | −0.941504 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.67667 | −0.592459 | −0.296229 | − | 0.955117i | \(-0.595729\pi\) | ||||
−0.296229 | + | 0.955117i | \(0.595729\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.04054 | 0.354379 | ||||||||
\(131\) | −3.73653 | − | 6.47185i | −0.326462 | − | 0.565448i | 0.655345 | − | 0.755329i | \(-0.272523\pi\) |
−0.981807 | + | 0.189881i | \(0.939190\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10.8712i | 0.939133i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.53185 | + | 0.884414i | −0.131355 | + | 0.0758379i | ||||
\(137\) | 6.91772 | + | 3.99395i | 0.591021 | + | 0.341226i | 0.765501 | − | 0.643435i | \(-0.222491\pi\) |
−0.174480 | + | 0.984661i | \(0.555825\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.9792 | + | 10.3803i | 1.52498 | + | 0.880446i | 0.999562 | + | 0.0295993i | \(0.00942312\pi\) |
0.525415 | + | 0.850846i | \(0.323910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.52106 | −0.379399 | ||||||||
\(143\) | −4.88151 | − | 8.45502i | −0.408212 | − | 0.707044i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.45502 | + | 4.88151i | 0.702151 | + | 0.405387i | ||||
\(146\) | −2.67117 | − | 4.62660i | −0.221068 | − | 0.382900i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.59886 | + | 7.96547i | −0.378024 | + | 0.654757i | ||||
\(149\) | −1.03726 | + | 0.598865i | −0.0849760 | + | 0.0490609i | −0.541886 | − | 0.840452i | \(-0.682290\pi\) |
0.456910 | + | 0.889513i | \(0.348956\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.61229 | + | 13.1849i | −0.619480 | + | 1.07297i | 0.370101 | + | 0.928991i | \(0.379323\pi\) |
−0.989581 | + | 0.143979i | \(0.954010\pi\) | |||||||
\(152\) | −0.569660 | + | 0.986680i | −0.0462055 | + | 0.0800303i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.0300 | − | 9.83228i | 1.36788 | − | 0.789748i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.0269i | − | 0.800237i | −0.916463 | − | 0.400118i | \(-0.868969\pi\) | ||
0.916463 | − | 0.400118i | \(-0.131031\pi\) | |||||||
\(158\) | − | 13.0284i | − | 1.03649i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.03460 | − | 1.17468i | 0.160850 | − | 0.0928665i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.00158 | + | 10.3950i | −0.470080 | + | 0.814202i | −0.999415 | − | 0.0342109i | \(-0.989108\pi\) |
0.529335 | + | 0.848413i | \(0.322442\pi\) | |||||||
\(164\) | 3.99709 | − | 6.92317i | 0.312121 | − | 0.540609i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.8651 | + | 6.27298i | −0.843297 | + | 0.486878i | ||||
\(167\) | −8.57472 | + | 14.8518i | −0.663532 | + | 1.14927i | 0.316150 | + | 0.948709i | \(0.397610\pi\) |
−0.979681 | + | 0.200561i | \(0.935723\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.02106 | − | 8.69673i | −0.386235 | − | 0.668979i | ||||
\(170\) | −3.59886 | − | 2.07781i | −0.276020 | − | 0.159360i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.76053 | − | 3.04933i | −0.134239 | − | 0.232509i | ||||
\(173\) | 1.98748 | 0.151105 | 0.0755525 | − | 0.997142i | \(-0.475928\pi\) | ||||
0.0755525 | + | 0.997142i | \(0.475928\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.91614 | − | 2.83834i | −0.370568 | − | 0.213948i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.00551 | − | 0.580529i | −0.0753659 | − | 0.0435125i | ||||
\(179\) | −7.19773 | + | 4.15561i | −0.537984 | + | 0.310605i | −0.744261 | − | 0.667889i | \(-0.767198\pi\) |
0.206278 | + | 0.978493i | \(0.433865\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.4541i | 1.14870i | 0.818611 | + | 0.574348i | \(0.194744\pi\) | ||||
−0.818611 | + | 0.574348i | \(0.805256\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.83755 | + | 3.18272i | 0.135466 | + | 0.234634i | ||||
\(185\) | −21.6088 | −1.58871 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0411i | 0.734275i | ||||||||
\(188\) | −11.8099 | −0.861324 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.67667 | −0.194186 | ||||||||
\(191\) | − | 12.3381i | − | 0.892752i | −0.894845 | − | 0.446376i | \(-0.852714\pi\) | ||
0.894845 | − | 0.446376i | \(-0.147286\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.39388 | 0.316279 | 0.158139 | − | 0.987417i | \(-0.449451\pi\) | ||||
0.158139 | + | 0.987417i | \(0.449451\pi\) | |||||||
\(194\) | −2.29517 | − | 3.97536i | −0.164784 | − | 0.285414i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 10.8865i | − | 0.775632i | −0.921737 | − | 0.387816i | \(-0.873230\pi\) | ||
0.921737 | − | 0.387816i | \(-0.126770\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.8733 | + | 13.7832i | −1.69233 | + | 0.977068i | −0.739703 | + | 0.672933i | \(0.765034\pi\) |
−0.952629 | + | 0.304135i | \(0.901633\pi\) | |||||||
\(200\) | 0.449885 | + | 0.259741i | 0.0318116 | + | 0.0183665i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.73577 | − | 3.31155i | −0.403567 | − | 0.233000i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.7812 | 1.31174 | ||||||||
\(206\) | 2.92989 | + | 5.07471i | 0.204135 | + | 0.353572i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.48943 | + | 0.859925i | 0.103274 | + | 0.0596250i | ||||
\(209\) | 3.23377 | + | 5.60106i | 0.223685 | + | 0.387433i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.15561 | − | 8.92978i | 0.354927 | − | 0.614751i | −0.632179 | − | 0.774823i | \(-0.717839\pi\) |
0.987105 | + | 0.160071i | \(0.0511724\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.35782 | + | 4.08386i | −0.161177 | + | 0.279167i | ||||
\(215\) | 4.13611 | − | 7.16396i | 0.282081 | − | 0.488578i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.66908 | − | 2.11835i | 0.248502 | − | 0.143473i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 13.3365i | − | 0.899149i | ||||||
\(221\) | − | 3.04212i | − | 0.204635i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.24329 | + | 3.60456i | −0.418081 | + | 0.241379i | −0.694256 | − | 0.719728i | \(-0.744267\pi\) |
0.276175 | + | 0.961107i | \(0.410933\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.41614 | − | 5.91693i | 0.227238 | − | 0.393588i | ||||
\(227\) | −6.37800 | + | 11.0470i | −0.423323 | + | 0.733217i | −0.996262 | − | 0.0863812i | \(-0.972470\pi\) |
0.572939 | + | 0.819598i | \(0.305803\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.89208 | + | 2.24709i | −0.257196 | + | 0.148492i | −0.623055 | − | 0.782178i | \(-0.714109\pi\) |
0.365859 | + | 0.930670i | \(0.380775\pi\) | |||||||
\(230\) | −4.31705 | + | 7.47736i | −0.284658 | + | 0.493042i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.07781 | + | 3.59886i | 0.136415 | + | 0.236277i | ||||
\(233\) | 1.86545 | + | 1.07702i | 0.122210 | + | 0.0705577i | 0.559859 | − | 0.828588i | \(-0.310855\pi\) |
−0.437649 | + | 0.899146i | \(0.644189\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.8728 | − | 24.0284i | −0.904963 | − | 1.56744i | ||||
\(236\) | −2.22966 | −0.145139 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.78317 | + | 5.07096i | 0.568136 | + | 0.328013i | 0.756404 | − | 0.654104i | \(-0.226954\pi\) |
−0.188269 | + | 0.982118i | \(0.560288\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.13490 | − | 5.27404i | −0.588431 | − | 0.339731i | 0.176046 | − | 0.984382i | \(-0.443669\pi\) |
−0.764477 | + | 0.644651i | \(0.777003\pi\) | |||||||
\(242\) | −18.3810 | + | 10.6123i | −1.18158 | + | 0.682184i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 8.99970i | − | 0.576146i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.979729 | − | 1.69694i | −0.0623387 | − | 0.107974i | ||||
\(248\) | 8.37019 | 0.531507 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 10.5263i | − | 0.665744i | ||||||
\(251\) | 29.3005 | 1.84943 | 0.924714 | − | 0.380662i | \(-0.124304\pi\) | ||||
0.924714 | + | 0.380662i | \(0.124304\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.8623 | 1.31160 | ||||||||
\(254\) | − | 6.67667i | − | 0.418932i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.81430 | + | 6.60656i | 0.237930 | + | 0.412106i | 0.960120 | − | 0.279588i | \(-0.0901979\pi\) |
−0.722190 | + | 0.691694i | \(0.756865\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.04054i | 0.250584i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.47185 | − | 3.73653i | 0.399832 | − | 0.230843i | ||||
\(263\) | −10.5531 | − | 6.09281i | −0.650729 | − | 0.375699i | 0.138006 | − | 0.990431i | \(-0.455931\pi\) |
−0.788736 | + | 0.614733i | \(0.789264\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.8712 | −0.664067 | ||||||||
\(269\) | 1.38717 | + | 2.40264i | 0.0845771 | + | 0.146492i | 0.905211 | − | 0.424963i | \(-0.139713\pi\) |
−0.820634 | + | 0.571454i | \(0.806379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.77815 | − | 1.60396i | −0.168760 | − | 0.0974338i | 0.413241 | − | 0.910622i | \(-0.364397\pi\) |
−0.582001 | + | 0.813188i | \(0.697730\pi\) | |||||||
\(272\) | −0.884414 | − | 1.53185i | −0.0536255 | − | 0.0928821i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.99395 | + | 6.91772i | −0.241283 | + | 0.417915i | ||||
\(275\) | 2.55385 | − | 1.47446i | 0.154003 | − | 0.0889135i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.04054 | + | 8.73047i | −0.302857 | + | 0.524563i | −0.976782 | − | 0.214236i | \(-0.931274\pi\) |
0.673925 | + | 0.738800i | \(0.264607\pi\) | |||||||
\(278\) | −10.3803 | + | 17.9792i | −0.622569 | + | 1.07832i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.21999 | + | 2.43641i | −0.251743 | + | 0.145344i | −0.620562 | − | 0.784157i | \(-0.713096\pi\) |
0.368819 | + | 0.929501i | \(0.379762\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.81781i | 0.167502i | 0.996487 | + | 0.0837508i | \(0.0266900\pi\) | ||||
−0.996487 | + | 0.0837508i | \(0.973310\pi\) | |||||||
\(284\) | − | 4.52106i | − | 0.268276i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.45502 | − | 4.88151i | 0.499956 | − | 0.288650i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.93562 | − | 12.0129i | 0.407978 | − | 0.706638i | ||||
\(290\) | −4.88151 | + | 8.45502i | −0.286652 | + | 0.496496i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.62660 | − | 2.67117i | 0.270751 | − | 0.156318i | ||||
\(293\) | 4.05694 | − | 7.02683i | 0.237009 | − | 0.410512i | −0.722846 | − | 0.691010i | \(-0.757166\pi\) |
0.959855 | + | 0.280498i | \(0.0904995\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.61914 | − | 4.53648i | −0.152492 | − | 0.264124i | ||||
\(296\) | −7.96547 | − | 4.59886i | −0.462983 | − | 0.267304i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.598865 | − | 1.03726i | −0.0346913 | − | 0.0600871i | ||||
\(299\) | −6.32061 | −0.365530 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −13.1849 | − | 7.61229i | −0.758705 | − | 0.438038i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.986680 | − | 0.569660i | −0.0565900 | − | 0.0326722i | ||||
\(305\) | 18.3108 | − | 10.5718i | 1.04847 | − | 0.605337i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.8996i | − | 0.622074i | −0.950398 | − | 0.311037i | \(-0.899324\pi\) | ||
0.950398 | − | 0.311037i | \(-0.100676\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.83228 | + | 17.0300i | 0.558436 | + | 0.967240i | ||||
\(311\) | 8.23637 | 0.467042 | 0.233521 | − | 0.972352i | \(-0.424975\pi\) | ||||
0.233521 | + | 0.972352i | \(0.424975\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 33.8023i | − | 1.91062i | −0.295611 | − | 0.955308i | \(-0.595523\pi\) | ||
0.295611 | − | 0.955308i | \(-0.404477\pi\) | |||||||
\(314\) | 10.0269 | 0.565853 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.0284 | 0.732907 | ||||||||
\(317\) | − | 6.73090i | − | 0.378045i | −0.981973 | − | 0.189022i | \(-0.939468\pi\) | ||
0.981973 | − | 0.189022i | \(-0.0605319\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.5900 | 1.32079 | ||||||||
\(320\) | 1.17468 | + | 2.03460i | 0.0656665 | + | 0.113738i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.01526i | 0.112132i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.773734 | + | 0.446715i | −0.0429190 | + | 0.0247793i | ||||
\(326\) | −10.3950 | − | 6.00158i | −0.575728 | − | 0.332397i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.92317 | + | 3.99709i | 0.382268 | + | 0.220703i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.0569 | −1.76200 | −0.881002 | − | 0.473112i | \(-0.843131\pi\) | ||||
−0.881002 | + | 0.473112i | \(0.843131\pi\) | |||||||
\(332\) | −6.27298 | − | 10.8651i | −0.344275 | − | 0.596301i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.8518 | − | 8.57472i | −0.812657 | − | 0.469188i | ||||
\(335\) | −12.7702 | − | 22.1187i | −0.697712 | − | 1.20847i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.1123 | + | 20.9791i | −0.659799 | + | 1.14280i | 0.320869 | + | 0.947124i | \(0.396025\pi\) |
−0.980668 | + | 0.195681i | \(0.937308\pi\) | |||||||
\(338\) | 8.69673 | − | 5.02106i | 0.473040 | − | 0.273110i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.07781 | − | 3.59886i | 0.112685 | − | 0.195176i | ||||
\(341\) | 23.7574 | − | 41.1490i | 1.28654 | − | 2.22834i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.04933 | − | 1.76053i | 0.164409 | − | 0.0949214i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.98748i | 0.106847i | ||||||||
\(347\) | 22.7999i | 1.22396i | 0.790873 | + | 0.611981i | \(0.209627\pi\) | ||||
−0.790873 | + | 0.611981i | \(0.790373\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.46389 | + | 1.42253i | −0.131889 | + | 0.0761461i | −0.564493 | − | 0.825438i | \(-0.690928\pi\) |
0.432604 | + | 0.901584i | \(0.357595\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.83834 | − | 4.91614i | 0.151284 | − | 0.262031i | ||||
\(353\) | 3.57212 | − | 6.18709i | 0.190125 | − | 0.329306i | −0.755167 | − | 0.655533i | \(-0.772444\pi\) |
0.945291 | + | 0.326227i | \(0.105777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.19856 | − | 5.31079i | 0.488209 | − | 0.281868i | ||||
\(356\) | 0.580529 | − | 1.00551i | 0.0307680 | − | 0.0532917i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.15561 | − | 7.19773i | −0.219631 | − | 0.380412i | ||||
\(359\) | 10.0491 | + | 5.80186i | 0.530372 | + | 0.306210i | 0.741168 | − | 0.671320i | \(-0.234272\pi\) |
−0.210796 | + | 0.977530i | \(0.567606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.85097 | − | 15.3303i | −0.465841 | − | 0.806860i | ||||
\(362\) | −15.4541 | −0.812250 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.8695 | + | 6.27554i | 0.568938 | + | 0.328477i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.78525 | − | 3.91747i | −0.354187 | − | 0.204490i | 0.312341 | − | 0.949970i | \(-0.398887\pi\) |
−0.666528 | + | 0.745480i | \(0.732220\pi\) | |||||||
\(368\) | −3.18272 | + | 1.83755i | −0.165911 | + | 0.0957887i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 21.6088i | − | 1.12339i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.8339 | − | 22.2289i | −0.664512 | − | 1.15097i | −0.979417 | − | 0.201845i | \(-0.935306\pi\) |
0.314905 | − | 0.949123i | \(-0.398027\pi\) | |||||||
\(374\) | −10.0411 | −0.519211 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 11.8099i | − | 0.609048i | ||||||
\(377\) | −7.14702 | −0.368091 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.1045 | −0.775868 | −0.387934 | − | 0.921687i | \(-0.626811\pi\) | ||||
−0.387934 | + | 0.921687i | \(0.626811\pi\) | |||||||
\(380\) | − | 2.67667i | − | 0.137310i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.3381 | 0.631271 | ||||||||
\(383\) | −0.763322 | − | 1.32211i | −0.0390040 | − | 0.0675568i | 0.845864 | − | 0.533398i | \(-0.179085\pi\) |
−0.884868 | + | 0.465841i | \(0.845752\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.39388i | 0.223643i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.97536 | − | 2.29517i | 0.201818 | − | 0.116520i | ||||
\(389\) | 12.8948 | + | 7.44483i | 0.653794 | + | 0.377468i | 0.789908 | − | 0.613225i | \(-0.210128\pi\) |
−0.136115 | + | 0.990693i | \(0.543462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.62969 | + | 3.25030i | 0.284706 | + | 0.164375i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.8865 | 0.548454 | ||||||||
\(395\) | 15.3042 | + | 26.5077i | 0.770039 | + | 1.33375i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.9302 | + | 14.3935i | 1.25121 | + | 0.722388i | 0.971350 | − | 0.237653i | \(-0.0763780\pi\) |
0.279862 | + | 0.960040i | \(0.409711\pi\) | |||||||
\(398\) | −13.7832 | − | 23.8733i | −0.690892 | − | 1.19666i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.259741 | + | 0.449885i | −0.0129871 | + | 0.0224942i | ||||
\(401\) | −33.0592 | + | 19.0868i | −1.65090 | + | 0.953147i | −0.674196 | + | 0.738552i | \(0.735510\pi\) |
−0.976703 | + | 0.214595i | \(0.931157\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.19773 | + | 12.4668i | −0.358544 | + | 0.621017i | ||||
\(404\) | 3.31155 | − | 5.73577i | 0.164756 | − | 0.285365i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −45.2173 | + | 26.1062i | −2.24134 | + | 1.29404i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.96694i | − | 0.344493i | −0.985054 | − | 0.172247i | \(-0.944897\pi\) | ||
0.985054 | − | 0.172247i | \(-0.0551026\pi\) | |||||||
\(410\) | 18.7812i | 0.927538i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.07471 | + | 2.92989i | −0.250013 | + | 0.144345i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.7375 | − | 25.5261i | 0.723435 | − | 1.25303i | ||||
\(416\) | −0.859925 | + | 1.48943i | −0.0421613 | + | 0.0730255i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.60106 | + | 3.23377i | −0.273957 | + | 0.158169i | ||||
\(419\) | 17.4232 | − | 30.1778i | 0.851177 | − | 1.47428i | −0.0289690 | − | 0.999580i | \(-0.509222\pi\) |
0.880146 | − | 0.474702i | \(-0.157444\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.84597 | + | 4.92936i | 0.138704 | + | 0.240242i | 0.927006 | − | 0.375046i | \(-0.122373\pi\) |
−0.788302 | + | 0.615288i | \(0.789040\pi\) | |||||||
\(422\) | 8.92978 | + | 5.15561i | 0.434695 | + | 0.250971i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.918875 | 0.0445720 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.08386 | − | 2.35782i | −0.197401 | − | 0.113969i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.16396 | + | 4.13611i | 0.345477 | + | 0.199461i | ||||
\(431\) | 26.2350 | − | 15.1468i | 1.26370 | − | 0.729595i | 0.289908 | − | 0.957055i | \(-0.406375\pi\) |
0.973787 | + | 0.227460i | \(0.0730420\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 23.6094i | − | 1.13459i | −0.823513 | − | 0.567297i | \(-0.807989\pi\) | ||
0.823513 | − | 0.567297i | \(-0.192011\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.11835 | + | 3.66908i | 0.101450 | + | 0.175717i | ||||
\(437\) | 4.18711 | 0.200297 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.0202i | 1.19415i | 0.802185 | + | 0.597075i | \(0.203671\pi\) | ||||
−0.802185 | + | 0.597075i | \(0.796329\pi\) | |||||||
\(440\) | 13.3365 | 0.635794 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.04212 | 0.144699 | ||||||||
\(443\) | 23.0300i | 1.09419i | 0.837071 | + | 0.547094i | \(0.184266\pi\) | ||||
−0.837071 | + | 0.547094i | \(0.815734\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.72774 | 0.129307 | ||||||||
\(446\) | −3.60456 | − | 6.24329i | −0.170681 | − | 0.295628i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15.9028i | − | 0.750501i | −0.926923 | − | 0.375251i | \(-0.877557\pi\) | ||
0.926923 | − | 0.375251i | \(-0.122443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 39.3006 | − | 22.6902i | 1.85059 | − | 1.06844i | ||||
\(452\) | 5.91693 | + | 3.41614i | 0.278309 | + | 0.160682i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.0470 | − | 6.37800i | −0.518462 | − | 0.299334i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.66614 | −0.265051 | −0.132525 | − | 0.991180i | \(-0.542309\pi\) | ||||
−0.132525 | + | 0.991180i | \(0.542309\pi\) | |||||||
\(458\) | −2.24709 | − | 3.89208i | −0.105000 | − | 0.181865i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.47736 | − | 4.31705i | −0.348634 | − | 0.201284i | ||||
\(461\) | 15.7292 | + | 27.2438i | 0.732582 | + | 1.26887i | 0.955776 | + | 0.294095i | \(0.0950183\pi\) |
−0.223194 | + | 0.974774i | \(0.571648\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.55148 | − | 7.88340i | 0.211525 | − | 0.366373i | −0.740667 | − | 0.671873i | \(-0.765490\pi\) |
0.952192 | + | 0.305500i | \(0.0988236\pi\) | |||||||
\(464\) | −3.59886 | + | 2.07781i | −0.167073 | + | 0.0964597i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.07702 | + | 1.86545i | −0.0498918 | + | 0.0864152i | ||||
\(467\) | −15.1516 | + | 26.2433i | −0.701132 | + | 1.21440i | 0.266938 | + | 0.963714i | \(0.413988\pi\) |
−0.968069 | + | 0.250682i | \(0.919345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 24.0284 | − | 13.8728i | 1.10835 | − | 0.639906i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 2.22966i | − | 0.102628i | ||||||
\(473\) | − | 19.9879i | − | 0.919044i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.512563 | − | 0.295928i | 0.0235180 | − | 0.0135781i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.07096 | + | 8.78317i | −0.231940 | + | 0.401733i | ||||
\(479\) | 2.33143 | − | 4.03816i | 0.106526 | − | 0.184508i | −0.807835 | − | 0.589409i | \(-0.799361\pi\) |
0.914361 | + | 0.404901i | \(0.132694\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.6994 | − | 7.90935i | 0.624639 | − | 0.360636i | ||||
\(482\) | 5.27404 | − | 9.13490i | 0.240226 | − | 0.416083i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.6123 | − | 18.3810i | −0.482377 | − | 0.835501i | ||||
\(485\) | 9.33953 | + | 5.39218i | 0.424086 | + | 0.244846i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.74105 | + | 16.8720i | 0.441409 | + | 0.764543i | 0.997794 | − | 0.0663816i | \(-0.0211455\pi\) |
−0.556385 | + | 0.830924i | \(0.687812\pi\) | |||||||
\(488\) | 8.99970 | 0.407397 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.7437 | + | 10.2443i | 0.800762 | + | 0.462320i | 0.843737 | − | 0.536756i | \(-0.180351\pi\) |
−0.0429758 | + | 0.999076i | \(0.513684\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.36577 | + | 3.67528i | 0.286700 | + | 0.165526i | ||||
\(494\) | 1.69694 | − | 0.979729i | 0.0763490 | − | 0.0440801i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.37019i | 0.375832i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.12598 | + | 8.87845i | 0.229470 | + | 0.397454i | 0.957651 | − | 0.287931i | \(-0.0929673\pi\) |
−0.728181 | + | 0.685385i | \(0.759634\pi\) | |||||||
\(500\) | 10.5263 | 0.470752 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 29.3005i | 1.30774i | ||||||||
\(503\) | 14.5521 | 0.648845 | 0.324422 | − | 0.945912i | \(-0.394830\pi\) | ||||
0.324422 | + | 0.945912i | \(0.394830\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.5600 | 0.692412 | ||||||||
\(506\) | 20.8623i | 0.927442i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.67667 | 0.296229 | ||||||||
\(509\) | 16.6617 | + | 28.8589i | 0.738517 | + | 1.27915i | 0.953163 | + | 0.302457i | \(0.0978068\pi\) |
−0.214646 | + | 0.976692i | \(0.568860\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.60656 | + | 3.81430i | −0.291403 | + | 0.168242i | ||||
\(515\) | −11.9223 | − | 6.88335i | −0.525360 | − | 0.303317i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −58.0591 | − | 33.5204i | −2.55343 | − | 1.47423i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.04054 | −0.177189 | ||||||||
\(521\) | −3.26963 | − | 5.66316i | −0.143245 | − | 0.248108i | 0.785472 | − | 0.618897i | \(-0.212420\pi\) |
−0.928717 | + | 0.370790i | \(0.879087\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.681439 | − | 0.393429i | −0.0297972 | − | 0.0172034i | 0.485027 | − | 0.874499i | \(-0.338810\pi\) |
−0.514825 | + | 0.857296i | \(0.672143\pi\) | |||||||
\(524\) | 3.73653 | + | 6.47185i | 0.163231 | + | 0.282724i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.09281 | − | 10.5531i | 0.265659 | − | 0.460135i | ||||
\(527\) | 12.8219 | − | 7.40271i | 0.558530 | − | 0.322467i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.74685 | + | 8.22178i | −0.206385 | + | 0.357469i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.9068 | + | 6.87440i | −0.515741 | + | 0.297763i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 11.0787i | − | 0.478975i | ||||||
\(536\) | − | 10.8712i | − | 0.469566i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.40264 | + | 1.38717i | −0.103585 | + | 0.0598050i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.80227 | + | 4.85367i | −0.120479 | + | 0.208676i | −0.919957 | − | 0.392020i | \(-0.871776\pi\) |
0.799478 | + | 0.600696i | \(0.205110\pi\) | |||||||
\(542\) | 1.60396 | − | 2.77815i | 0.0688961 | − | 0.119332i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.53185 | − | 0.884414i | 0.0656775 | − | 0.0379189i | ||||
\(545\) | −4.97675 | + | 8.61999i | −0.213181 | + | 0.369240i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.91456 | − | 11.9764i | −0.295645 | − | 0.512073i | 0.679489 | − | 0.733685i | \(-0.262201\pi\) |
−0.975135 | + | 0.221612i | \(0.928868\pi\) | |||||||
\(548\) | −6.91772 | − | 3.99395i | −0.295510 | − | 0.170613i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.47446 | + | 2.55385i | 0.0628714 | + | 0.108896i | ||||
\(551\) | 4.73457 | 0.201700 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8.73047 | − | 5.04054i | −0.370922 | − | 0.214152i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.9792 | − | 10.3803i | −0.762488 | − | 0.440223i | ||||
\(557\) | −24.0957 | + | 13.9117i | −1.02097 | + | 0.589456i | −0.914384 | − | 0.404848i | \(-0.867325\pi\) |
−0.106584 | + | 0.994304i | \(0.533991\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.05569i | 0.256128i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.43641 | − | 4.21999i | −0.102774 | − | 0.178009i | ||||
\(563\) | 24.5300 | 1.03382 | 0.516909 | − | 0.856040i | \(-0.327083\pi\) | ||||
0.516909 | + | 0.856040i | \(0.327083\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.0515i | 0.675291i | ||||||||
\(566\) | −2.81781 | −0.118441 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.52106 | 0.189699 | ||||||||
\(569\) | 27.1079i | 1.13642i | 0.822882 | + | 0.568212i | \(0.192365\pi\) | ||||
−0.822882 | + | 0.568212i | \(0.807635\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.8354 | −1.24857 | −0.624287 | − | 0.781195i | \(-0.714610\pi\) | ||||
−0.624287 | + | 0.781195i | \(0.714610\pi\) | |||||||
\(572\) | 4.88151 | + | 8.45502i | 0.204106 | + | 0.353522i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.90915i | − | 0.0796169i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.3930 | − | 14.0833i | 1.01549 | − | 0.586296i | 0.102699 | − | 0.994712i | \(-0.467252\pi\) |
0.912796 | + | 0.408416i | \(0.133919\pi\) | |||||||
\(578\) | 12.0129 | + | 6.93562i | 0.499669 | + | 0.288484i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.45502 | − | 4.88151i | −0.351076 | − | 0.202694i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.67117 | + | 4.62660i | 0.110534 | + | 0.191450i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.02683 | + | 4.05694i | 0.290276 | + | 0.167591i | ||||
\(587\) | −4.95928 | − | 8.58973i | −0.204692 | − | 0.354536i | 0.745343 | − | 0.666681i | \(-0.232286\pi\) |
−0.950034 | + | 0.312145i | \(0.898952\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.76816 | − | 8.25870i | 0.196469 | − | 0.340294i | ||||
\(590\) | 4.53648 | − | 2.61914i | 0.186764 | − | 0.107828i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.59886 | − | 7.96547i | 0.189012 | − | 0.327379i | ||||
\(593\) | −2.34936 | + | 4.06921i | −0.0964766 | + | 0.167102i | −0.910224 | − | 0.414116i | \(-0.864091\pi\) |
0.813747 | + | 0.581219i | \(0.197424\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.03726 | − | 0.598865i | 0.0424880 | − | 0.0245305i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 6.32061i | − | 0.258469i | ||||||
\(599\) | 14.7004i | 0.600641i | 0.953838 | + | 0.300320i | \(0.0970936\pi\) | ||||
−0.953838 | + | 0.300320i | \(0.902906\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.2923 | − | 9.40634i | 0.664575 | − | 0.383693i | −0.129443 | − | 0.991587i | \(-0.541319\pi\) |
0.794018 | + | 0.607894i | \(0.207986\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.61229 | − | 13.1849i | 0.309740 | − | 0.536485i | ||||
\(605\) | 24.9321 | − | 43.1836i | 1.01363 | − | 1.75566i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.9051 | + | 6.29608i | −0.442625 | + | 0.255550i | −0.704711 | − | 0.709495i | \(-0.748923\pi\) |
0.262085 | + | 0.965045i | \(0.415590\pi\) | |||||||
\(608\) | 0.569660 | − | 0.986680i | 0.0231028 | − | 0.0400152i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.5718 | + | 18.3108i | 0.428038 | + | 0.741383i | ||||
\(611\) | 17.5900 | + | 10.1556i | 0.711617 | + | 0.410852i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.91009 | + | 8.50452i | 0.198317 | + | 0.343494i | 0.947983 | − | 0.318322i | \(-0.103119\pi\) |
−0.749666 | + | 0.661816i | \(0.769786\pi\) | |||||||
\(614\) | 10.8996 | 0.439873 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.25158 | + | 1.87730i | 0.130904 | + | 0.0755772i | 0.564022 | − | 0.825760i | \(-0.309253\pi\) |
−0.433118 | + | 0.901337i | \(0.642587\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.56902 | − | 5.52468i | −0.384611 | − | 0.222055i | 0.295211 | − | 0.955432i | \(-0.404610\pi\) |
−0.679823 | + | 0.733376i | \(0.737943\pi\) | |||||||
\(620\) | −17.0300 | + | 9.83228i | −0.683942 | + | 0.394874i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.23637i | 0.330248i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.6638 | + | 23.6664i | 0.546551 | + | 0.946654i | ||||
\(626\) | 33.8023 | 1.35101 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.0269i | 0.400118i | ||||||||
\(629\) | −16.2692 | −0.648696 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.4921 | 0.775969 | 0.387984 | − | 0.921666i | \(-0.373171\pi\) | ||||
0.387984 | + | 0.921666i | \(0.373171\pi\) | |||||||
\(632\) | 13.0284i | 0.518243i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.73090 | 0.267318 | ||||||||
\(635\) | 7.84294 | + | 13.5844i | 0.311238 | + | 0.539080i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 23.5900i | 0.933938i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.03460 | + | 1.17468i | −0.0804248 | + | 0.0464333i | ||||
\(641\) | −22.6669 | − | 13.0868i | −0.895290 | − | 0.516896i | −0.0196208 | − | 0.999807i | \(-0.506246\pi\) |
−0.875669 | + | 0.482912i | \(0.839579\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.50955 | + | 5.49034i | 0.375020 | + | 0.216518i | 0.675649 | − | 0.737223i | \(-0.263863\pi\) |
−0.300629 | + | 0.953741i | \(0.597197\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.01526 | −0.0792894 | ||||||||
\(647\) | 16.0063 | + | 27.7237i | 0.629273 | + | 1.08993i | 0.987698 | + | 0.156374i | \(0.0499805\pi\) |
−0.358425 | + | 0.933558i | \(0.616686\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.9613 | − | 6.32852i | −0.430270 | − | 0.248416i | ||||
\(650\) | −0.446715 | − | 0.773734i | −0.0175216 | − | 0.0303483i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.00158 | − | 10.3950i | 0.235040 | − | 0.407101i | ||||
\(653\) | 19.3686 | − | 11.1825i | 0.757952 | − | 0.437604i | −0.0706080 | − | 0.997504i | \(-0.522494\pi\) |
0.828560 | + | 0.559900i | \(0.189161\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.77843 | + | 15.2047i | −0.343002 | + | 0.594097i | ||||
\(656\) | −3.99709 | + | 6.92317i | −0.156060 | + | 0.270304i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.2546 | − | 11.1166i | 0.750053 | − | 0.433043i | −0.0756603 | − | 0.997134i | \(-0.524106\pi\) |
0.825713 | + | 0.564091i | \(0.190773\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.5499i | 0.410343i | 0.978726 | + | 0.205171i | \(0.0657751\pi\) | ||||
−0.978726 | + | 0.205171i | \(0.934225\pi\) | |||||||
\(662\) | − | 32.0569i | − | 1.24593i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.8651 | − | 6.27298i | 0.421649 | − | 0.243439i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.63613 | − | 13.2262i | 0.295672 | − | 0.512119i | ||||
\(668\) | 8.57472 | − | 14.8518i | 0.331766 | − | 0.574635i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 22.1187 | − | 12.7702i | 0.854519 | − | 0.493357i | ||||
\(671\) | 25.5442 | − | 44.2438i | 0.986121 | − | 1.70801i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.93562 | + | 17.2090i | 0.382990 | + | 0.663358i | 0.991488 | − | 0.130197i | \(-0.0415610\pi\) |
−0.608498 | + | 0.793555i | \(0.708228\pi\) | |||||||
\(674\) | −20.9791 | − | 12.1123i | −0.808085 | − | 0.466548i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.02106 | + | 8.69673i | 0.193118 | + | 0.334490i | ||||
\(677\) | −15.9290 | −0.612201 | −0.306100 | − | 0.951999i | \(-0.599024\pi\) | ||||
−0.306100 | + | 0.951999i | \(0.599024\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.59886 | + | 2.07781i | 0.138010 | + | 0.0796802i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 41.1490 | + | 23.7574i | 1.57568 | + | 0.909718i | ||||
\(683\) | 16.4777 | − | 9.51343i | 0.630503 | − | 0.364021i | −0.150444 | − | 0.988619i | \(-0.548070\pi\) |
0.780947 | + | 0.624597i | \(0.214737\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 18.7664i | − | 0.717028i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.76053 | + | 3.04933i | 0.0671196 | + | 0.116254i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.161055i | 0.00612681i | 0.999995 | + | 0.00306340i | \(0.000975113\pi\) | ||||
−0.999995 | + | 0.00306340i | \(0.999025\pi\) | |||||||
\(692\) | −1.98748 | −0.0755525 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.7999 | −0.865471 | ||||||||
\(695\) | − | 48.7741i | − | 1.85011i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.1403 | 0.535604 | ||||||||
\(698\) | −1.42253 | − | 2.46389i | −0.0538434 | − | 0.0932595i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9.98234i | − | 0.377028i | −0.982071 | − | 0.188514i | \(-0.939633\pi\) | ||
0.982071 | − | 0.188514i | \(-0.0603670\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.07522 | + | 5.23958i | −0.342278 | + | 0.197614i | ||||
\(704\) | 4.91614 | + | 2.83834i | 0.185284 | + | 0.106974i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.18709 | + | 3.57212i | 0.232854 | + | 0.134438i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.3923 | −0.916072 | −0.458036 | − | 0.888934i | \(-0.651447\pi\) | ||||
−0.458036 | + | 0.888934i | \(0.651447\pi\) | |||||||
\(710\) | 5.31079 | + | 9.19856i | 0.199311 | + | 0.345216i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.00551 | + | 0.580529i | 0.0376829 | + | 0.0217563i | ||||
\(713\) | −15.3806 | − | 26.6400i | −0.576008 | − | 0.997676i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.4684 | + | 19.8639i | −0.428894 | + | 0.742867i | ||||
\(716\) | 7.19773 | − | 4.15561i | 0.268992 | − | 0.155302i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.80186 | + | 10.0491i | −0.216523 | + | 0.375030i | ||||
\(719\) | −8.13460 | + | 14.0895i | −0.303370 | + | 0.525451i | −0.976897 | − | 0.213711i | \(-0.931445\pi\) |
0.673527 | + | 0.739162i | \(0.264778\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15.3303 | − | 8.85097i | 0.570536 | − | 0.329399i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 15.4541i | − | 0.574348i | ||||||
\(725\) | − | 2.15877i | − | 0.0801745i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.6626 | − | 11.9296i | 0.766335 | − | 0.442444i | −0.0652306 | − | 0.997870i | \(-0.520778\pi\) |
0.831566 | + | 0.555427i | \(0.187445\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.27554 | + | 10.8695i | −0.232268 | + | 0.402300i | ||||
\(731\) | 3.11408 | − | 5.39374i | 0.115178 | − | 0.199495i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.6259 | + | 6.13486i | −0.392476 | + | 0.226596i | −0.683233 | − | 0.730201i | \(-0.739426\pi\) |
0.290756 | + | 0.956797i | \(0.406093\pi\) | |||||||
\(734\) | 3.91747 | − | 6.78525i | 0.144596 | − | 0.250448i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.83755 | − | 3.18272i | −0.0677329 | − | 0.117317i | ||||
\(737\) | −53.4446 | − | 30.8562i | −1.96866 | − | 1.13660i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.9446 | − | 36.2771i | −0.770459 | − | 1.33447i | −0.937312 | − | 0.348492i | \(-0.886694\pi\) |
0.166853 | − | 0.985982i | \(-0.446639\pi\) | |||||||
\(740\) | 21.6088 | 0.794354 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.9160 | − | 25.3549i | −1.61112 | − | 0.930182i | −0.989111 | − | 0.147173i | \(-0.952982\pi\) |
−0.622011 | − | 0.783008i | \(-0.713684\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.43690 | + | 1.40695i | 0.0892813 | + | 0.0515466i | ||||
\(746\) | 22.2289 | − | 12.8339i | 0.813858 | − | 0.469881i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 10.0411i | − | 0.367137i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.3683 | + | 28.3508i | 0.597289 | + | 1.03454i | 0.993219 | + | 0.116255i | \(0.0370890\pi\) |
−0.395930 | + | 0.918281i | \(0.629578\pi\) | |||||||
\(752\) | 11.8099 | 0.430662 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 7.14702i | − | 0.260279i | ||||||
\(755\) | 35.7680 | 1.30173 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.9255 | −0.651512 | −0.325756 | − | 0.945454i | \(-0.605619\pi\) | ||||
−0.325756 | + | 0.945454i | \(0.605619\pi\) | |||||||
\(758\) | − | 15.1045i | − | 0.548622i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.67667 | 0.0970930 | ||||||||
\(761\) | −21.8509 | − | 37.8469i | −0.792096 | − | 1.37195i | −0.924667 | − | 0.380777i | \(-0.875657\pi\) |
0.132571 | − | 0.991174i | \(-0.457677\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 12.3381i | 0.446376i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.32211 | − | 0.763322i | 0.0477699 | − | 0.0275800i | ||||
\(767\) | 3.32093 | + | 1.91734i | 0.119912 | + | 0.0692311i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.0864 | − | 21.4118i | −1.33737 | − | 0.772131i | −0.350953 | − | 0.936393i | \(-0.614142\pi\) |
−0.986417 | + | 0.164262i | \(0.947476\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.39388 | −0.158139 | ||||||||
\(773\) | −10.8025 | − | 18.7105i | −0.388540 | − | 0.672971i | 0.603714 | − | 0.797201i | \(-0.293687\pi\) |
−0.992253 | + | 0.124231i | \(0.960354\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.76562 | − | 2.17408i | −0.135265 | − | 0.0780953i | ||||
\(776\) | 2.29517 | + | 3.97536i | 0.0823919 | + | 0.142707i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.44483 | + | 12.8948i | −0.266910 | + | 0.462302i | ||||
\(779\) | 7.88771 | − | 4.55397i | 0.282606 | − | 0.163163i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.8323 | − | 22.2262i | 0.459175 | − | 0.795315i | ||||
\(782\) | −3.25030 | + | 5.62969i | −0.116231 | + | 0.201317i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.4008 | + | 11.7784i | −0.728137 | + | 0.420390i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 51.3042i | 1.82880i | 0.404817 | + | 0.914398i | \(0.367335\pi\) | ||||
−0.404817 | + | 0.914398i | \(0.632665\pi\) | |||||||
\(788\) | 10.8865i | 0.387816i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −26.5077 | + | 15.3042i | −0.943102 | + | 0.544500i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.73906 | + | 13.4044i | −0.274822 | + | 0.476006i | ||||
\(794\) | −14.3935 | + | 24.9302i | −0.510805 | + | 0.884740i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.8733 | − | 13.7832i | 0.846166 | − | 0.488534i | ||||
\(797\) | 0.899094 | − | 1.55728i | 0.0318476 | − | 0.0551616i | −0.849662 | − | 0.527327i | \(-0.823194\pi\) |
0.881510 | + | 0.472166i | \(0.156528\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.4448 | − | 18.0910i | −0.369512 | − | 0.640013i | ||||
\(800\) | −0.449885 | − | 0.259741i | −0.0159058 | − | 0.00918323i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.0868 | − | 33.0592i | −0.673977 | − | 1.16736i | ||||
\(803\) | 30.3267 | 1.07021 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.4668 | − | 7.19773i | −0.439125 | − | 0.253529i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.73577 | + | 3.31155i | 0.201784 | + | 0.116500i | ||||
\(809\) | −35.2371 | + | 20.3441i | −1.23887 | + | 0.715262i | −0.968863 | − | 0.247597i | \(-0.920359\pi\) |
−0.270006 | + | 0.962859i | \(0.587026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.378710i | 0.0132983i | 0.999978 | + | 0.00664916i | \(0.00211651\pi\) | ||||
−0.999978 | + | 0.00664916i | \(0.997883\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −26.1062 | − | 45.2173i | −0.915023 | − | 1.58487i | ||||
\(815\) | 28.1997 | 0.987793 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.01161i | − | 0.140349i | ||||||
\(818\) | 6.96694 | 0.243593 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.7812 | −0.655868 | ||||||||
\(821\) | − | 13.2754i | − | 0.463315i | −0.972797 | − | 0.231658i | \(-0.925585\pi\) | ||
0.972797 | − | 0.231658i | \(-0.0744149\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.7422 | 0.967034 | 0.483517 | − | 0.875335i | \(-0.339359\pi\) | ||||
0.483517 | + | 0.875335i | \(0.339359\pi\) | |||||||
\(824\) | −2.92989 | − | 5.07471i | −0.102067 | − | 0.176786i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27.7183i | − | 0.963859i | −0.876210 | − | 0.481929i | \(-0.839936\pi\) | ||
0.876210 | − | 0.481929i | \(-0.160064\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.0105 | − | 21.3680i | 1.28543 | − | 0.742143i | 0.307593 | − | 0.951518i | \(-0.400476\pi\) |
0.977835 | + | 0.209375i | \(0.0671431\pi\) | |||||||
\(830\) | 25.5261 | + | 14.7375i | 0.886023 | + | 0.511545i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.48943 | − | 0.859925i | −0.0516368 | − | 0.0298125i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40.2902 | 1.39430 | ||||||||
\(836\) | −3.23377 | − | 5.60106i | −0.111842 | − | 0.193717i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30.1778 | + | 17.4232i | 1.04248 | + | 0.601873i | ||||
\(839\) | 1.92438 | + | 3.33313i | 0.0664370 | + | 0.115072i | 0.897331 | − | 0.441359i | \(-0.145504\pi\) |
−0.830894 | + | 0.556431i | \(0.812170\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.86545 | + | 10.1593i | −0.202257 | + | 0.350319i | ||||
\(842\) | −4.92936 | + | 2.84597i | −0.169877 | + | 0.0980785i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.15561 | + | 8.92978i | −0.177463 | + | 0.307376i | ||||
\(845\) | −11.7963 | + | 20.4317i | −0.405804 | + | 0.702873i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.918875i | 0.0315171i | ||||||||
\(851\) | 33.8025i | 1.15874i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.3470 | + | 15.2114i | −0.902103 | + | 0.520830i | −0.877882 | − | 0.478877i | \(-0.841044\pi\) |
−0.0242213 | + | 0.999707i | \(0.507711\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.35782 | − | 4.08386i | 0.0805885 | − | 0.139583i | ||||
\(857\) | −19.4657 | + | 33.7156i | −0.664937 | + | 1.15170i | 0.314366 | + | 0.949302i | \(0.398208\pi\) |
−0.979303 | + | 0.202402i | \(0.935125\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.5922 | + | 6.69275i | −0.395520 | + | 0.228354i | −0.684549 | − | 0.728967i | \(-0.740001\pi\) |
0.289029 | + | 0.957320i | \(0.406668\pi\) | |||||||
\(860\) | −4.13611 | + | 7.16396i | −0.141040 | + | 0.244289i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.1468 | + | 26.2350i | 0.515901 | + | 0.893567i | ||||
\(863\) | −18.8118 | − | 10.8610i | −0.640360 | − | 0.369712i | 0.144393 | − | 0.989520i | \(-0.453877\pi\) |
−0.784753 | + | 0.619809i | \(0.787210\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.33465 | − | 4.04373i | −0.0793804 | − | 0.137491i | ||||
\(866\) | 23.6094 | 0.802279 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 64.0496 | + | 36.9791i | 2.17273 | + | 1.25443i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.1920 | + | 9.34845i | 0.548645 | + | 0.316760i | ||||
\(872\) | −3.66908 | + | 2.11835i | −0.124251 | + | 0.0717363i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.18711i | 0.141631i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.196152 | − | 0.339746i | −0.00662360 | − | 0.0114724i | 0.862695 | − | 0.505725i | \(-0.168775\pi\) |
−0.869318 | + | 0.494253i | \(0.835442\pi\) | |||||||
\(878\) | −25.0202 | −0.844392 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13.3365i | 0.449574i | ||||||||
\(881\) | −43.3363 | −1.46004 | −0.730018 | − | 0.683427i | \(-0.760489\pi\) | ||||
−0.730018 | + | 0.683427i | \(0.760489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.17403 | 0.0731618 | 0.0365809 | − | 0.999331i | \(-0.488353\pi\) | ||||
0.0365809 | + | 0.999331i | \(0.488353\pi\) | |||||||
\(884\) | 3.04212i | 0.102318i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.0300 | −0.773708 | ||||||||
\(887\) | 5.72215 | + | 9.91105i | 0.192131 | + | 0.332781i | 0.945956 | − | 0.324294i | \(-0.105127\pi\) |
−0.753825 | + | 0.657075i | \(0.771793\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.72774i | 0.0914341i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.24329 | − | 3.60456i | 0.209041 | − | 0.120690i | ||||
\(893\) | −11.6526 | − | 6.72762i | −0.389939 | − | 0.225131i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.9100 | + | 9.76302i | 0.565240 | + | 0.326342i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.9028 | 0.530684 | ||||||||
\(899\) | −17.3916 | − | 30.1232i | −0.580043 | − | 1.00466i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 22.6902 | + | 39.3006i | 0.755501 | + | 1.30857i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.41614 | + | 5.91693i | −0.113619 | + | 0.196794i | ||||
\(905\) | 31.4430 | − | 18.1536i | 1.04520 | − | 0.603447i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.9446 | − | 46.6694i | 0.894680 | − | 1.54963i | 0.0604797 | − | 0.998169i | \(-0.480737\pi\) |
0.834200 | − | 0.551462i | \(-0.185930\pi\) | |||||||
\(908\) | 6.37800 | − | 11.0470i | 0.211661 | − | 0.366608i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.00460 | − | 4.04411i | 0.232073 | − | 0.133987i | −0.379455 | − | 0.925210i | \(-0.623889\pi\) |
0.611528 | + | 0.791223i | \(0.290555\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 71.2193i | − | 2.35702i | ||||||
\(914\) | − | 5.66614i | − | 0.187419i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.89208 | − | 2.24709i | 0.128598 | − | 0.0742460i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.8375 | + | 22.2353i | −0.423472 | + | 0.733474i | −0.996276 | − | 0.0862175i | \(-0.972522\pi\) |
0.572805 | + | 0.819692i | \(0.305855\pi\) | |||||||
\(920\) | 4.31705 | − | 7.47736i | 0.142329 | − | 0.246521i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27.2438 | + | 15.7292i | −0.897226 | + | 0.518014i | ||||
\(923\) | −3.88777 | + | 6.73382i | −0.127968 | + | 0.221646i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.38903 | + | 4.13792i | 0.0785507 | + | 0.136054i | ||||
\(926\) | 7.88340 | + | 4.55148i | 0.259064 | + | 0.149571i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.07781 | − | 3.59886i | −0.0682073 | − | 0.118139i | ||||
\(929\) | 10.8524 | 0.356055 | 0.178027 | − | 0.984026i | \(-0.443028\pi\) | ||||
0.178027 | + | 0.984026i | \(0.443028\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.86545 | − | 1.07702i | −0.0611048 | − | 0.0352789i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26.2433 | − | 15.1516i | −0.858708 | − | 0.495775i | ||||
\(935\) | 20.4296 | − | 11.7950i | 0.668118 | − | 0.385738i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.458120i | 0.0149661i | 0.999972 | + | 0.00748306i | \(0.00238195\pi\) | ||||
−0.999972 | + | 0.00748306i | \(0.997618\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.8728 | + | 24.0284i | 0.452482 | + | 0.783721i | ||||
\(941\) | −7.37780 | −0.240510 | −0.120255 | − | 0.992743i | \(-0.538371\pi\) | ||||
−0.120255 | + | 0.992743i | \(0.538371\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 29.3794i | − | 0.956725i | ||||||
\(944\) | 2.22966 | 0.0725693 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.9879 | 0.649862 | ||||||||
\(947\) | 11.9910i | 0.389657i | 0.980837 | + | 0.194828i | \(0.0624150\pi\) | ||||
−0.980837 | + | 0.194828i | \(0.937585\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.18802 | −0.298256 | ||||||||
\(950\) | 0.295928 | + | 0.512563i | 0.00960118 | + | 0.0166297i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 58.6883i | − | 1.90110i | −0.310572 | − | 0.950550i | \(-0.600521\pi\) | ||
0.310572 | − | 0.950550i | \(-0.399479\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.1031 | + | 14.4933i | −0.812317 | + | 0.468992i | ||||
\(956\) | −8.78317 | − | 5.07096i | −0.284068 | − | 0.164007i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.03816 | + | 2.33143i | 0.130467 | + | 0.0753251i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −39.0600 | −1.26000 | ||||||||
\(962\) | 7.90935 | + | 13.6994i | 0.255008 | + | 0.441686i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.13490 | + | 5.27404i | 0.294215 | + | 0.169865i | ||||
\(965\) | −5.16140 | − | 8.93981i | −0.166151 | − | 0.287783i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.37560 | + | 5.84671i | −0.108552 | + | 0.188018i | −0.915184 | − | 0.403037i | \(-0.867955\pi\) |
0.806632 | + | 0.591054i | \(0.201288\pi\) | |||||||
\(968\) | 18.3810 | − | 10.6123i | 0.590789 | − | 0.341092i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.39218 | + | 9.33953i | −0.173133 | + | 0.299874i | ||||
\(971\) | −3.20362 | + | 5.54883i | −0.102809 | + | 0.178070i | −0.912841 | − | 0.408315i | \(-0.866116\pi\) |
0.810032 | + | 0.586386i | \(0.199450\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −16.8720 | + | 9.74105i | −0.540613 | + | 0.312123i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.99970i | 0.288073i | ||||||||
\(977\) | 13.5987i | 0.435062i | 0.976053 | + | 0.217531i | \(0.0698004\pi\) | ||||
−0.976053 | + | 0.217531i | \(0.930200\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.70793 | − | 3.29547i | 0.182426 | − | 0.105324i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.2443 | + | 17.7437i | −0.326910 | + | 0.566224i | ||||
\(983\) | −11.3849 | + | 19.7192i | −0.363122 | + | 0.628946i | −0.988473 | − | 0.151398i | \(-0.951623\pi\) |
0.625351 | + | 0.780344i | \(0.284956\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.1497 | + | 12.7882i | −0.705749 | + | 0.407464i | ||||
\(986\) | −3.67528 | + | 6.36577i | −0.117045 | + | 0.202728i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.979729 | + | 1.69694i | 0.0311693 | + | 0.0539869i | ||||
\(989\) | −11.2066 | − | 6.47011i | −0.356348 | − | 0.205738i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.4953 | + | 23.3745i | 0.428691 | + | 0.742515i | 0.996757 | − | 0.0804680i | \(-0.0256415\pi\) |
−0.568066 | + | 0.822983i | \(0.692308\pi\) | |||||||
\(992\) | −8.37019 | −0.265754 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 56.0869 | + | 32.3818i | 1.77807 | + | 1.02657i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.7263 | + | 9.65694i | 0.529728 | + | 0.305838i | 0.740906 | − | 0.671609i | \(-0.234397\pi\) |
−0.211178 | + | 0.977448i | \(0.567730\pi\) | |||||||
\(998\) | −8.87845 | + | 5.12598i | −0.281043 | + | 0.162260i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))