Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(337,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.b (of order \(2\), degree \(1\), 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: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.337 |
Dual form | 1014.2.b.e.337.4 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 3.73205i | − 1.66902i | −0.550990 | − | 0.834512i | \(-0.685750\pi\) | ||||
0.550990 | − | 0.834512i | \(-0.314250\pi\) | |||||||
\(6\) | − 1.00000i | − 0.408248i | ||||||||
\(7\) | − 2.73205i | − 1.03262i | −0.856402 | − | 0.516309i | \(-0.827306\pi\) | ||||
0.856402 | − | 0.516309i | \(-0.172694\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.73205 | −1.18018 | ||||||||
\(11\) | 1.26795i | 0.382301i | 0.981561 | + | 0.191151i | \(0.0612219\pi\) | ||||
−0.981561 | + | 0.191151i | \(0.938778\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.73205 | −0.730171 | ||||||||
\(15\) | − 3.73205i | − 0.963611i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.73205 | 1.39023 | 0.695113 | − | 0.718900i | \(-0.255354\pi\) | ||||
0.695113 | + | 0.718900i | \(0.255354\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | − 4.73205i | − 1.08561i | −0.839860 | − | 0.542803i | \(-0.817363\pi\) | ||||
0.839860 | − | 0.542803i | \(-0.182637\pi\) | |||||||
\(20\) | 3.73205i | 0.834512i | ||||||||
\(21\) | − 2.73205i | − 0.596182i | ||||||||
\(22\) | 1.26795 | 0.270328 | ||||||||
\(23\) | −4.19615 | −0.874958 | −0.437479 | − | 0.899229i | \(-0.644129\pi\) | ||||
−0.437479 | + | 0.899229i | \(0.644129\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −8.92820 | −1.78564 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.73205i | 0.516309i | ||||||||
\(29\) | −4.46410 | −0.828963 | −0.414481 | − | 0.910058i | \(-0.636037\pi\) | ||||
−0.414481 | + | 0.910058i | \(0.636037\pi\) | |||||||
\(30\) | −3.73205 | −0.681376 | ||||||||
\(31\) | − 1.46410i | − 0.262960i | −0.991319 | − | 0.131480i | \(-0.958027\pi\) | ||||
0.991319 | − | 0.131480i | \(-0.0419730\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 1.26795i | 0.220722i | ||||||||
\(34\) | − 5.73205i | − 0.983039i | ||||||||
\(35\) | −10.1962 | −1.72346 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 3.53590i | 0.581298i | 0.956830 | + | 0.290649i | \(0.0938712\pi\) | ||||
−0.956830 | + | 0.290649i | \(0.906129\pi\) | |||||||
\(38\) | −4.73205 | −0.767640 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.73205 | 0.590089 | ||||||||
\(41\) | 9.39230i | 1.46683i | 0.679780 | + | 0.733416i | \(0.262075\pi\) | ||||
−0.679780 | + | 0.733416i | \(0.737925\pi\) | |||||||
\(42\) | −2.73205 | −0.421565 | ||||||||
\(43\) | 9.66025 | 1.47317 | 0.736587 | − | 0.676342i | \(-0.236436\pi\) | ||||
0.736587 | + | 0.676342i | \(0.236436\pi\) | |||||||
\(44\) | − 1.26795i | − 0.191151i | ||||||||
\(45\) | − 3.73205i | − 0.556341i | ||||||||
\(46\) | 4.19615i | 0.618689i | ||||||||
\(47\) | 2.19615i | 0.320342i | 0.987089 | + | 0.160171i | \(0.0512045\pi\) | ||||
−0.987089 | + | 0.160171i | \(0.948795\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −0.464102 | −0.0663002 | ||||||||
\(50\) | 8.92820i | 1.26264i | ||||||||
\(51\) | 5.73205 | 0.802648 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.46410 | −0.887913 | −0.443956 | − | 0.896048i | \(-0.646425\pi\) | ||||
−0.443956 | + | 0.896048i | \(0.646425\pi\) | |||||||
\(54\) | − 1.00000i | − 0.136083i | ||||||||
\(55\) | 4.73205 | 0.638070 | ||||||||
\(56\) | 2.73205 | 0.365086 | ||||||||
\(57\) | − 4.73205i | − 0.626775i | ||||||||
\(58\) | 4.46410i | 0.586165i | ||||||||
\(59\) | 8.00000i | 1.04151i | 0.853706 | + | 0.520756i | \(0.174350\pi\) | ||||
−0.853706 | + | 0.520756i | \(0.825650\pi\) | |||||||
\(60\) | 3.73205i | 0.481806i | ||||||||
\(61\) | −9.19615 | −1.17745 | −0.588723 | − | 0.808335i | \(-0.700369\pi\) | ||||
−0.588723 | + | 0.808335i | \(0.700369\pi\) | |||||||
\(62\) | −1.46410 | −0.185941 | ||||||||
\(63\) | − 2.73205i | − 0.344206i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.26795 | 0.156074 | ||||||||
\(67\) | − 13.1244i | − 1.60340i | −0.597730 | − | 0.801698i | \(-0.703930\pi\) | ||||
0.597730 | − | 0.801698i | \(-0.296070\pi\) | |||||||
\(68\) | −5.73205 | −0.695113 | ||||||||
\(69\) | −4.19615 | −0.505157 | ||||||||
\(70\) | 10.1962i | 1.21867i | ||||||||
\(71\) | − 4.73205i | − 0.561591i | −0.959768 | − | 0.280796i | \(-0.909402\pi\) | ||||
0.959768 | − | 0.280796i | \(-0.0905983\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − 6.26795i | − 0.733608i | −0.930298 | − | 0.366804i | \(-0.880452\pi\) | ||||
0.930298 | − | 0.366804i | \(-0.119548\pi\) | |||||||
\(74\) | 3.53590 | 0.411040 | ||||||||
\(75\) | −8.92820 | −1.03094 | ||||||||
\(76\) | 4.73205i | 0.542803i | ||||||||
\(77\) | 3.46410 | 0.394771 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.53590 | −0.285311 | −0.142655 | − | 0.989772i | \(-0.545564\pi\) | ||||
−0.142655 | + | 0.989772i | \(0.545564\pi\) | |||||||
\(80\) | − 3.73205i | − 0.417256i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.39230 | 1.03721 | ||||||||
\(83\) | 0.196152i | 0.0215305i | 0.999942 | + | 0.0107653i | \(0.00342676\pi\) | ||||
−0.999942 | + | 0.0107653i | \(0.996573\pi\) | |||||||
\(84\) | 2.73205i | 0.298091i | ||||||||
\(85\) | − 21.3923i | − 2.32032i | ||||||||
\(86\) | − 9.66025i | − 1.04169i | ||||||||
\(87\) | −4.46410 | −0.478602 | ||||||||
\(88\) | −1.26795 | −0.135164 | ||||||||
\(89\) | − 9.46410i | − 1.00319i | −0.865102 | − | 0.501596i | \(-0.832746\pi\) | ||||
0.865102 | − | 0.501596i | \(-0.167254\pi\) | |||||||
\(90\) | −3.73205 | −0.393393 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.19615 | 0.437479 | ||||||||
\(93\) | − 1.46410i | − 0.151820i | ||||||||
\(94\) | 2.19615 | 0.226516 | ||||||||
\(95\) | −17.6603 | −1.81190 | ||||||||
\(96\) | − 1.00000i | − 0.102062i | ||||||||
\(97\) | 6.00000i | 0.609208i | 0.952479 | + | 0.304604i | \(0.0985241\pi\) | ||||
−0.952479 | + | 0.304604i | \(0.901476\pi\) | |||||||
\(98\) | 0.464102i | 0.0468813i | ||||||||
\(99\) | 1.26795i | 0.127434i | ||||||||
\(100\) | 8.92820 | 0.892820 | ||||||||
\(101\) | −1.92820 | −0.191863 | −0.0959317 | − | 0.995388i | \(-0.530583\pi\) | ||||
−0.0959317 | + | 0.995388i | \(0.530583\pi\) | |||||||
\(102\) | − 5.73205i | − 0.567558i | ||||||||
\(103\) | 15.2679 | 1.50440 | 0.752198 | − | 0.658937i | \(-0.228994\pi\) | ||||
0.752198 | + | 0.658937i | \(0.228994\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.1962 | −0.995043 | ||||||||
\(106\) | 6.46410i | 0.627849i | ||||||||
\(107\) | 10.1962 | 0.985699 | 0.492850 | − | 0.870114i | \(-0.335955\pi\) | ||||
0.492850 | + | 0.870114i | \(0.335955\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | − 1.46410i | − 0.140236i | −0.997539 | − | 0.0701178i | \(-0.977662\pi\) | ||||
0.997539 | − | 0.0701178i | \(-0.0223375\pi\) | |||||||
\(110\) | − 4.73205i | − 0.451183i | ||||||||
\(111\) | 3.53590i | 0.335613i | ||||||||
\(112\) | − 2.73205i | − 0.258155i | ||||||||
\(113\) | −1.33975 | −0.126033 | −0.0630163 | − | 0.998012i | \(-0.520072\pi\) | ||||
−0.0630163 | + | 0.998012i | \(0.520072\pi\) | |||||||
\(114\) | −4.73205 | −0.443197 | ||||||||
\(115\) | 15.6603i | 1.46033i | ||||||||
\(116\) | 4.46410 | 0.414481 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.00000 | 0.736460 | ||||||||
\(119\) | − 15.6603i | − 1.43557i | ||||||||
\(120\) | 3.73205 | 0.340688 | ||||||||
\(121\) | 9.39230 | 0.853846 | ||||||||
\(122\) | 9.19615i | 0.832581i | ||||||||
\(123\) | 9.39230i | 0.846876i | ||||||||
\(124\) | 1.46410i | 0.131480i | ||||||||
\(125\) | 14.6603i | 1.31125i | ||||||||
\(126\) | −2.73205 | −0.243390 | ||||||||
\(127\) | 9.85641 | 0.874615 | 0.437307 | − | 0.899312i | \(-0.355932\pi\) | ||||
0.437307 | + | 0.899312i | \(0.355932\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 9.66025 | 0.850538 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.53590 | 0.571044 | 0.285522 | − | 0.958372i | \(-0.407833\pi\) | ||||
0.285522 | + | 0.958372i | \(0.407833\pi\) | |||||||
\(132\) | − 1.26795i | − 0.110361i | ||||||||
\(133\) | −12.9282 | −1.12102 | ||||||||
\(134\) | −13.1244 | −1.13377 | ||||||||
\(135\) | − 3.73205i | − 0.321204i | ||||||||
\(136\) | 5.73205i | 0.491519i | ||||||||
\(137\) | 11.9282i | 1.01910i | 0.860442 | + | 0.509548i | \(0.170187\pi\) | ||||
−0.860442 | + | 0.509548i | \(0.829813\pi\) | |||||||
\(138\) | 4.19615i | 0.357200i | ||||||||
\(139\) | 17.8564 | 1.51456 | 0.757280 | − | 0.653090i | \(-0.226528\pi\) | ||||
0.757280 | + | 0.653090i | \(0.226528\pi\) | |||||||
\(140\) | 10.1962 | 0.861732 | ||||||||
\(141\) | 2.19615i | 0.184949i | ||||||||
\(142\) | −4.73205 | −0.397105 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 16.6603i | 1.38356i | ||||||||
\(146\) | −6.26795 | −0.518739 | ||||||||
\(147\) | −0.464102 | −0.0382785 | ||||||||
\(148\) | − 3.53590i | − 0.290649i | ||||||||
\(149\) | − 13.1962i | − 1.08107i | −0.841321 | − | 0.540535i | \(-0.818222\pi\) | ||||
0.841321 | − | 0.540535i | \(-0.181778\pi\) | |||||||
\(150\) | 8.92820i | 0.728985i | ||||||||
\(151\) | 6.73205i | 0.547847i | 0.961752 | + | 0.273923i | \(0.0883214\pi\) | ||||
−0.961752 | + | 0.273923i | \(0.911679\pi\) | |||||||
\(152\) | 4.73205 | 0.383820 | ||||||||
\(153\) | 5.73205 | 0.463409 | ||||||||
\(154\) | − 3.46410i | − 0.279145i | ||||||||
\(155\) | −5.46410 | −0.438887 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.58846 | 0.605625 | 0.302812 | − | 0.953050i | \(-0.402074\pi\) | ||||
0.302812 | + | 0.953050i | \(0.402074\pi\) | |||||||
\(158\) | 2.53590i | 0.201745i | ||||||||
\(159\) | −6.46410 | −0.512637 | ||||||||
\(160\) | −3.73205 | −0.295045 | ||||||||
\(161\) | 11.4641i | 0.903498i | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | − 13.4641i | − 1.05459i | −0.849682 | − | 0.527295i | \(-0.823206\pi\) | ||||
0.849682 | − | 0.527295i | \(-0.176794\pi\) | |||||||
\(164\) | − 9.39230i | − 0.733416i | ||||||||
\(165\) | 4.73205 | 0.368390 | ||||||||
\(166\) | 0.196152 | 0.0152244 | ||||||||
\(167\) | − 9.46410i | − 0.732354i | −0.930545 | − | 0.366177i | \(-0.880666\pi\) | ||||
0.930545 | − | 0.366177i | \(-0.119334\pi\) | |||||||
\(168\) | 2.73205 | 0.210782 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −21.3923 | −1.64071 | ||||||||
\(171\) | − 4.73205i | − 0.361869i | ||||||||
\(172\) | −9.66025 | −0.736587 | ||||||||
\(173\) | −4.39230 | −0.333941 | −0.166970 | − | 0.985962i | \(-0.553398\pi\) | ||||
−0.166970 | + | 0.985962i | \(0.553398\pi\) | |||||||
\(174\) | 4.46410i | 0.338423i | ||||||||
\(175\) | 24.3923i | 1.84388i | ||||||||
\(176\) | 1.26795i | 0.0955753i | ||||||||
\(177\) | 8.00000i | 0.601317i | ||||||||
\(178\) | −9.46410 | −0.709364 | ||||||||
\(179\) | 16.0526 | 1.19982 | 0.599912 | − | 0.800066i | \(-0.295202\pi\) | ||||
0.599912 | + | 0.800066i | \(0.295202\pi\) | |||||||
\(180\) | 3.73205i | 0.278171i | ||||||||
\(181\) | −19.1962 | −1.42684 | −0.713419 | − | 0.700737i | \(-0.752855\pi\) | ||||
−0.713419 | + | 0.700737i | \(0.752855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.19615 | −0.679799 | ||||||||
\(184\) | − 4.19615i | − 0.309344i | ||||||||
\(185\) | 13.1962 | 0.970200 | ||||||||
\(186\) | −1.46410 | −0.107353 | ||||||||
\(187\) | 7.26795i | 0.531485i | ||||||||
\(188\) | − 2.19615i | − 0.160171i | ||||||||
\(189\) | − 2.73205i | − 0.198727i | ||||||||
\(190\) | 17.6603i | 1.28121i | ||||||||
\(191\) | −6.92820 | −0.501307 | −0.250654 | − | 0.968077i | \(-0.580646\pi\) | ||||
−0.250654 | + | 0.968077i | \(0.580646\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | − 11.7321i | − 0.844491i | −0.906481 | − | 0.422246i | \(-0.861242\pi\) | ||||
0.906481 | − | 0.422246i | \(-0.138758\pi\) | |||||||
\(194\) | 6.00000 | 0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.464102 | 0.0331501 | ||||||||
\(197\) | 17.8564i | 1.27222i | 0.771600 | + | 0.636108i | \(0.219457\pi\) | ||||
−0.771600 | + | 0.636108i | \(0.780543\pi\) | |||||||
\(198\) | 1.26795 | 0.0901092 | ||||||||
\(199\) | 14.1962 | 1.00634 | 0.503169 | − | 0.864188i | \(-0.332167\pi\) | ||||
0.503169 | + | 0.864188i | \(0.332167\pi\) | |||||||
\(200\) | − 8.92820i | − 0.631319i | ||||||||
\(201\) | − 13.1244i | − 0.925721i | ||||||||
\(202\) | 1.92820i | 0.135668i | ||||||||
\(203\) | 12.1962i | 0.856002i | ||||||||
\(204\) | −5.73205 | −0.401324 | ||||||||
\(205\) | 35.0526 | 2.44818 | ||||||||
\(206\) | − 15.2679i | − 1.06377i | ||||||||
\(207\) | −4.19615 | −0.291653 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 10.1962i | 0.703601i | ||||||||
\(211\) | 16.3923 | 1.12849 | 0.564246 | − | 0.825606i | \(-0.309167\pi\) | ||||
0.564246 | + | 0.825606i | \(0.309167\pi\) | |||||||
\(212\) | 6.46410 | 0.443956 | ||||||||
\(213\) | − 4.73205i | − 0.324235i | ||||||||
\(214\) | − 10.1962i | − 0.696995i | ||||||||
\(215\) | − 36.0526i | − 2.45876i | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | −1.46410 | −0.0991615 | ||||||||
\(219\) | − 6.26795i | − 0.423549i | ||||||||
\(220\) | −4.73205 | −0.319035 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.53590 | 0.237314 | ||||||||
\(223\) | 26.9282i | 1.80325i | 0.432523 | + | 0.901623i | \(0.357623\pi\) | ||||
−0.432523 | + | 0.901623i | \(0.642377\pi\) | |||||||
\(224\) | −2.73205 | −0.182543 | ||||||||
\(225\) | −8.92820 | −0.595214 | ||||||||
\(226\) | 1.33975i | 0.0891186i | ||||||||
\(227\) | 12.1962i | 0.809487i | 0.914430 | + | 0.404744i | \(0.132639\pi\) | ||||
−0.914430 | + | 0.404744i | \(0.867361\pi\) | |||||||
\(228\) | 4.73205i | 0.313388i | ||||||||
\(229\) | − 11.8564i | − 0.783493i | −0.920073 | − | 0.391747i | \(-0.871871\pi\) | ||||
0.920073 | − | 0.391747i | \(-0.128129\pi\) | |||||||
\(230\) | 15.6603 | 1.03261 | ||||||||
\(231\) | 3.46410 | 0.227921 | ||||||||
\(232\) | − 4.46410i | − 0.293083i | ||||||||
\(233\) | 7.85641 | 0.514690 | 0.257345 | − | 0.966320i | \(-0.417152\pi\) | ||||
0.257345 | + | 0.966320i | \(0.417152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.19615 | 0.534658 | ||||||||
\(236\) | − 8.00000i | − 0.520756i | ||||||||
\(237\) | −2.53590 | −0.164724 | ||||||||
\(238\) | −15.6603 | −1.01510 | ||||||||
\(239\) | − 7.66025i | − 0.495501i | −0.968824 | − | 0.247750i | \(-0.920309\pi\) | ||||
0.968824 | − | 0.247750i | \(-0.0796913\pi\) | |||||||
\(240\) | − 3.73205i | − 0.240903i | ||||||||
\(241\) | 13.5885i | 0.875309i | 0.899143 | + | 0.437655i | \(0.144191\pi\) | ||||
−0.899143 | + | 0.437655i | \(0.855809\pi\) | |||||||
\(242\) | − 9.39230i | − 0.603760i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 9.19615 | 0.588723 | ||||||||
\(245\) | 1.73205i | 0.110657i | ||||||||
\(246\) | 9.39230 | 0.598831 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.46410 | 0.0929705 | ||||||||
\(249\) | 0.196152i | 0.0124307i | ||||||||
\(250\) | 14.6603 | 0.927196 | ||||||||
\(251\) | −13.4641 | −0.849847 | −0.424923 | − | 0.905229i | \(-0.639699\pi\) | ||||
−0.424923 | + | 0.905229i | \(0.639699\pi\) | |||||||
\(252\) | 2.73205i | 0.172103i | ||||||||
\(253\) | − 5.32051i | − 0.334497i | ||||||||
\(254\) | − 9.85641i | − 0.618446i | ||||||||
\(255\) | − 21.3923i | − 1.33964i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.33975 | −0.582597 | −0.291299 | − | 0.956632i | \(-0.594087\pi\) | ||||
−0.291299 | + | 0.956632i | \(0.594087\pi\) | |||||||
\(258\) | − 9.66025i | − 0.601421i | ||||||||
\(259\) | 9.66025 | 0.600259 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.46410 | −0.276321 | ||||||||
\(262\) | − 6.53590i | − 0.403789i | ||||||||
\(263\) | −10.0526 | −0.619867 | −0.309934 | − | 0.950758i | \(-0.600307\pi\) | ||||
−0.309934 | + | 0.950758i | \(0.600307\pi\) | |||||||
\(264\) | −1.26795 | −0.0780369 | ||||||||
\(265\) | 24.1244i | 1.48195i | ||||||||
\(266\) | 12.9282i | 0.792679i | ||||||||
\(267\) | − 9.46410i | − 0.579194i | ||||||||
\(268\) | 13.1244i | 0.801698i | ||||||||
\(269\) | 5.46410 | 0.333152 | 0.166576 | − | 0.986029i | \(-0.446729\pi\) | ||||
0.166576 | + | 0.986029i | \(0.446729\pi\) | |||||||
\(270\) | −3.73205 | −0.227125 | ||||||||
\(271\) | − 21.8564i | − 1.32768i | −0.747874 | − | 0.663841i | \(-0.768925\pi\) | ||||
0.747874 | − | 0.663841i | \(-0.231075\pi\) | |||||||
\(272\) | 5.73205 | 0.347557 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.9282 | 0.720609 | ||||||||
\(275\) | − 11.3205i | − 0.682652i | ||||||||
\(276\) | 4.19615 | 0.252579 | ||||||||
\(277\) | 5.73205 | 0.344406 | 0.172203 | − | 0.985062i | \(-0.444912\pi\) | ||||
0.172203 | + | 0.985062i | \(0.444912\pi\) | |||||||
\(278\) | − 17.8564i | − 1.07096i | ||||||||
\(279\) | − 1.46410i | − 0.0876535i | ||||||||
\(280\) | − 10.1962i | − 0.609337i | ||||||||
\(281\) | 12.3205i | 0.734980i | 0.930027 | + | 0.367490i | \(0.119783\pi\) | ||||
−0.930027 | + | 0.367490i | \(0.880217\pi\) | |||||||
\(282\) | 2.19615 | 0.130779 | ||||||||
\(283\) | −25.6603 | −1.52534 | −0.762672 | − | 0.646786i | \(-0.776113\pi\) | ||||
−0.762672 | + | 0.646786i | \(0.776113\pi\) | |||||||
\(284\) | 4.73205i | 0.280796i | ||||||||
\(285\) | −17.6603 | −1.04610 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.6603 | 1.51468 | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | 15.8564 | 0.932730 | ||||||||
\(290\) | 16.6603 | 0.978324 | ||||||||
\(291\) | 6.00000i | 0.351726i | ||||||||
\(292\) | 6.26795i | 0.366804i | ||||||||
\(293\) | 30.5167i | 1.78280i | 0.453215 | + | 0.891401i | \(0.350277\pi\) | ||||
−0.453215 | + | 0.891401i | \(0.649723\pi\) | |||||||
\(294\) | 0.464102i | 0.0270670i | ||||||||
\(295\) | 29.8564 | 1.73831 | ||||||||
\(296\) | −3.53590 | −0.205520 | ||||||||
\(297\) | 1.26795i | 0.0735739i | ||||||||
\(298\) | −13.1962 | −0.764433 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 8.92820 | 0.515470 | ||||||||
\(301\) | − 26.3923i | − 1.52123i | ||||||||
\(302\) | 6.73205 | 0.387386 | ||||||||
\(303\) | −1.92820 | −0.110772 | ||||||||
\(304\) | − 4.73205i | − 0.271402i | ||||||||
\(305\) | 34.3205i | 1.96519i | ||||||||
\(306\) | − 5.73205i | − 0.327680i | ||||||||
\(307\) | − 22.5885i | − 1.28919i | −0.764524 | − | 0.644596i | \(-0.777026\pi\) | ||||
0.764524 | − | 0.644596i | \(-0.222974\pi\) | |||||||
\(308\) | −3.46410 | −0.197386 | ||||||||
\(309\) | 15.2679 | 0.868563 | ||||||||
\(310\) | 5.46410i | 0.310340i | ||||||||
\(311\) | 1.66025 | 0.0941444 | 0.0470722 | − | 0.998891i | \(-0.485011\pi\) | ||||
0.0470722 | + | 0.998891i | \(0.485011\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.53590 | 0.369431 | 0.184715 | − | 0.982792i | \(-0.440864\pi\) | ||||
0.184715 | + | 0.982792i | \(0.440864\pi\) | |||||||
\(314\) | − 7.58846i | − 0.428241i | ||||||||
\(315\) | −10.1962 | −0.574488 | ||||||||
\(316\) | 2.53590 | 0.142655 | ||||||||
\(317\) | − 20.6603i | − 1.16040i | −0.814476 | − | 0.580198i | \(-0.802975\pi\) | ||||
0.814476 | − | 0.580198i | \(-0.197025\pi\) | |||||||
\(318\) | 6.46410i | 0.362489i | ||||||||
\(319\) | − 5.66025i | − 0.316913i | ||||||||
\(320\) | 3.73205i | 0.208628i | ||||||||
\(321\) | 10.1962 | 0.569094 | ||||||||
\(322\) | 11.4641 | 0.638869 | ||||||||
\(323\) | − 27.1244i | − 1.50924i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13.4641 | −0.745708 | ||||||||
\(327\) | − 1.46410i | − 0.0809650i | ||||||||
\(328\) | −9.39230 | −0.518603 | ||||||||
\(329\) | 6.00000 | 0.330791 | ||||||||
\(330\) | − 4.73205i | − 0.260491i | ||||||||
\(331\) | − 20.0000i | − 1.09930i | −0.835395 | − | 0.549650i | \(-0.814761\pi\) | ||||
0.835395 | − | 0.549650i | \(-0.185239\pi\) | |||||||
\(332\) | − 0.196152i | − 0.0107653i | ||||||||
\(333\) | 3.53590i | 0.193766i | ||||||||
\(334\) | −9.46410 | −0.517853 | ||||||||
\(335\) | −48.9808 | −2.67610 | ||||||||
\(336\) | − 2.73205i | − 0.149046i | ||||||||
\(337\) | 20.8564 | 1.13612 | 0.568060 | − | 0.822987i | \(-0.307694\pi\) | ||||
0.568060 | + | 0.822987i | \(0.307694\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.33975 | −0.0727650 | ||||||||
\(340\) | 21.3923i | 1.16016i | ||||||||
\(341\) | 1.85641 | 0.100530 | ||||||||
\(342\) | −4.73205 | −0.255880 | ||||||||
\(343\) | − 17.8564i | − 0.964155i | ||||||||
\(344\) | 9.66025i | 0.520846i | ||||||||
\(345\) | 15.6603i | 0.843120i | ||||||||
\(346\) | 4.39230i | 0.236132i | ||||||||
\(347\) | 33.1244 | 1.77821 | 0.889104 | − | 0.457705i | \(-0.151328\pi\) | ||||
0.889104 | + | 0.457705i | \(0.151328\pi\) | |||||||
\(348\) | 4.46410 | 0.239301 | ||||||||
\(349\) | 15.3205i | 0.820088i | 0.912066 | + | 0.410044i | \(0.134487\pi\) | ||||
−0.912066 | + | 0.410044i | \(0.865513\pi\) | |||||||
\(350\) | 24.3923 | 1.30382 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.26795 | 0.0675819 | ||||||||
\(353\) | 21.7846i | 1.15948i | 0.814802 | + | 0.579739i | \(0.196845\pi\) | ||||
−0.814802 | + | 0.579739i | \(0.803155\pi\) | |||||||
\(354\) | 8.00000 | 0.425195 | ||||||||
\(355\) | −17.6603 | −0.937309 | ||||||||
\(356\) | 9.46410i | 0.501596i | ||||||||
\(357\) | − 15.6603i | − 0.828829i | ||||||||
\(358\) | − 16.0526i | − 0.848404i | ||||||||
\(359\) | − 1.12436i | − 0.0593412i | −0.999560 | − | 0.0296706i | \(-0.990554\pi\) | ||||
0.999560 | − | 0.0296706i | \(-0.00944584\pi\) | |||||||
\(360\) | 3.73205 | 0.196696 | ||||||||
\(361\) | −3.39230 | −0.178542 | ||||||||
\(362\) | 19.1962i | 1.00893i | ||||||||
\(363\) | 9.39230 | 0.492968 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.3923 | −1.22441 | ||||||||
\(366\) | 9.19615i | 0.480691i | ||||||||
\(367\) | −11.2679 | −0.588182 | −0.294091 | − | 0.955777i | \(-0.595017\pi\) | ||||
−0.294091 | + | 0.955777i | \(0.595017\pi\) | |||||||
\(368\) | −4.19615 | −0.218740 | ||||||||
\(369\) | 9.39230i | 0.488944i | ||||||||
\(370\) | − 13.1962i | − 0.686035i | ||||||||
\(371\) | 17.6603i | 0.916875i | ||||||||
\(372\) | 1.46410i | 0.0759101i | ||||||||
\(373\) | −13.7321 | −0.711019 | −0.355509 | − | 0.934673i | \(-0.615693\pi\) | ||||
−0.355509 | + | 0.934673i | \(0.615693\pi\) | |||||||
\(374\) | 7.26795 | 0.375817 | ||||||||
\(375\) | 14.6603i | 0.757052i | ||||||||
\(376\) | −2.19615 | −0.113258 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.73205 | −0.140522 | ||||||||
\(379\) | 5.46410i | 0.280672i | 0.990104 | + | 0.140336i | \(0.0448183\pi\) | ||||
−0.990104 | + | 0.140336i | \(0.955182\pi\) | |||||||
\(380\) | 17.6603 | 0.905952 | ||||||||
\(381\) | 9.85641 | 0.504959 | ||||||||
\(382\) | 6.92820i | 0.354478i | ||||||||
\(383\) | 1.46410i | 0.0748121i | 0.999300 | + | 0.0374060i | \(0.0119095\pi\) | ||||
−0.999300 | + | 0.0374060i | \(0.988091\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | − 12.9282i | − 0.658882i | ||||||||
\(386\) | −11.7321 | −0.597146 | ||||||||
\(387\) | 9.66025 | 0.491058 | ||||||||
\(388\) | − 6.00000i | − 0.304604i | ||||||||
\(389\) | −11.7846 | −0.597503 | −0.298752 | − | 0.954331i | \(-0.596570\pi\) | ||||
−0.298752 | + | 0.954331i | \(0.596570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0526 | −1.21639 | ||||||||
\(392\) | − 0.464102i | − 0.0234407i | ||||||||
\(393\) | 6.53590 | 0.329692 | ||||||||
\(394\) | 17.8564 | 0.899593 | ||||||||
\(395\) | 9.46410i | 0.476191i | ||||||||
\(396\) | − 1.26795i | − 0.0637168i | ||||||||
\(397\) | 20.3923i | 1.02346i | 0.859146 | + | 0.511730i | \(0.170995\pi\) | ||||
−0.859146 | + | 0.511730i | \(0.829005\pi\) | |||||||
\(398\) | − 14.1962i | − 0.711589i | ||||||||
\(399\) | −12.9282 | −0.647220 | ||||||||
\(400\) | −8.92820 | −0.446410 | ||||||||
\(401\) | 8.07180i | 0.403086i | 0.979480 | + | 0.201543i | \(0.0645956\pi\) | ||||
−0.979480 | + | 0.201543i | \(0.935404\pi\) | |||||||
\(402\) | −13.1244 | −0.654583 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.92820 | 0.0959317 | ||||||||
\(405\) | − 3.73205i | − 0.185447i | ||||||||
\(406\) | 12.1962 | 0.605285 | ||||||||
\(407\) | −4.48334 | −0.222231 | ||||||||
\(408\) | 5.73205i | 0.283779i | ||||||||
\(409\) | − 17.7321i | − 0.876793i | −0.898782 | − | 0.438397i | \(-0.855546\pi\) | ||||
0.898782 | − | 0.438397i | \(-0.144454\pi\) | |||||||
\(410\) | − 35.0526i | − 1.73112i | ||||||||
\(411\) | 11.9282i | 0.588375i | ||||||||
\(412\) | −15.2679 | −0.752198 | ||||||||
\(413\) | 21.8564 | 1.07548 | ||||||||
\(414\) | 4.19615i | 0.206230i | ||||||||
\(415\) | 0.732051 | 0.0359350 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.8564 | 0.874432 | ||||||||
\(418\) | − 6.00000i | − 0.293470i | ||||||||
\(419\) | −17.4641 | −0.853177 | −0.426589 | − | 0.904446i | \(-0.640285\pi\) | ||||
−0.426589 | + | 0.904446i | \(0.640285\pi\) | |||||||
\(420\) | 10.1962 | 0.497521 | ||||||||
\(421\) | 22.7128i | 1.10695i | 0.832864 | + | 0.553477i | \(0.186699\pi\) | ||||
−0.832864 | + | 0.553477i | \(0.813301\pi\) | |||||||
\(422\) | − 16.3923i | − 0.797965i | ||||||||
\(423\) | 2.19615i | 0.106781i | ||||||||
\(424\) | − 6.46410i | − 0.313925i | ||||||||
\(425\) | −51.1769 | −2.48244 | ||||||||
\(426\) | −4.73205 | −0.229269 | ||||||||
\(427\) | 25.1244i | 1.21585i | ||||||||
\(428\) | −10.1962 | −0.492850 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −36.0526 | −1.73861 | ||||||||
\(431\) | − 13.1244i | − 0.632178i | −0.948730 | − | 0.316089i | \(-0.897630\pi\) | ||||
0.948730 | − | 0.316089i | \(-0.102370\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −12.8564 | −0.617839 | −0.308920 | − | 0.951088i | \(-0.599967\pi\) | ||||
−0.308920 | + | 0.951088i | \(0.599967\pi\) | |||||||
\(434\) | 4.00000i | 0.192006i | ||||||||
\(435\) | 16.6603i | 0.798798i | ||||||||
\(436\) | 1.46410i | 0.0701178i | ||||||||
\(437\) | 19.8564i | 0.949861i | ||||||||
\(438\) | −6.26795 | −0.299494 | ||||||||
\(439\) | 0.339746 | 0.0162152 | 0.00810760 | − | 0.999967i | \(-0.497419\pi\) | ||||
0.00810760 | + | 0.999967i | \(0.497419\pi\) | |||||||
\(440\) | 4.73205i | 0.225592i | ||||||||
\(441\) | −0.464102 | −0.0221001 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.6077 | 0.741544 | 0.370772 | − | 0.928724i | \(-0.379093\pi\) | ||||
0.370772 | + | 0.928724i | \(0.379093\pi\) | |||||||
\(444\) | − 3.53590i | − 0.167806i | ||||||||
\(445\) | −35.3205 | −1.67435 | ||||||||
\(446\) | 26.9282 | 1.27509 | ||||||||
\(447\) | − 13.1962i | − 0.624157i | ||||||||
\(448\) | 2.73205i | 0.129077i | ||||||||
\(449\) | 11.3205i | 0.534248i | 0.963662 | + | 0.267124i | \(0.0860733\pi\) | ||||
−0.963662 | + | 0.267124i | \(0.913927\pi\) | |||||||
\(450\) | 8.92820i | 0.420880i | ||||||||
\(451\) | −11.9090 | −0.560771 | ||||||||
\(452\) | 1.33975 | 0.0630163 | ||||||||
\(453\) | 6.73205i | 0.316299i | ||||||||
\(454\) | 12.1962 | 0.572394 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.73205 | 0.221599 | ||||||||
\(457\) | − 1.33975i | − 0.0626707i | −0.999509 | − | 0.0313353i | \(-0.990024\pi\) | ||||
0.999509 | − | 0.0313353i | \(-0.00997598\pi\) | |||||||
\(458\) | −11.8564 | −0.554013 | ||||||||
\(459\) | 5.73205 | 0.267549 | ||||||||
\(460\) | − 15.6603i | − 0.730163i | ||||||||
\(461\) | − 22.2679i | − 1.03712i | −0.855041 | − | 0.518561i | \(-0.826468\pi\) | ||||
0.855041 | − | 0.518561i | \(-0.173532\pi\) | |||||||
\(462\) | − 3.46410i | − 0.161165i | ||||||||
\(463\) | 10.0526i | 0.467182i | 0.972335 | + | 0.233591i | \(0.0750477\pi\) | ||||
−0.972335 | + | 0.233591i | \(0.924952\pi\) | |||||||
\(464\) | −4.46410 | −0.207241 | ||||||||
\(465\) | −5.46410 | −0.253392 | ||||||||
\(466\) | − 7.85641i | − 0.363941i | ||||||||
\(467\) | −18.5885 | −0.860171 | −0.430086 | − | 0.902788i | \(-0.641517\pi\) | ||||
−0.430086 | + | 0.902788i | \(0.641517\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −35.8564 | −1.65570 | ||||||||
\(470\) | − 8.19615i | − 0.378060i | ||||||||
\(471\) | 7.58846 | 0.349658 | ||||||||
\(472\) | −8.00000 | −0.368230 | ||||||||
\(473\) | 12.2487i | 0.563196i | ||||||||
\(474\) | 2.53590i | 0.116478i | ||||||||
\(475\) | 42.2487i | 1.93850i | ||||||||
\(476\) | 15.6603i | 0.717787i | ||||||||
\(477\) | −6.46410 | −0.295971 | ||||||||
\(478\) | −7.66025 | −0.350372 | ||||||||
\(479\) | 33.4641i | 1.52901i | 0.644616 | + | 0.764507i | \(0.277017\pi\) | ||||
−0.644616 | + | 0.764507i | \(0.722983\pi\) | |||||||
\(480\) | −3.73205 | −0.170344 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 13.5885 | 0.618937 | ||||||||
\(483\) | 11.4641i | 0.521635i | ||||||||
\(484\) | −9.39230 | −0.426923 | ||||||||
\(485\) | 22.3923 | 1.01678 | ||||||||
\(486\) | − 1.00000i | − 0.0453609i | ||||||||
\(487\) | 3.12436i | 0.141578i | 0.997491 | + | 0.0707890i | \(0.0225517\pi\) | ||||
−0.997491 | + | 0.0707890i | \(0.977448\pi\) | |||||||
\(488\) | − 9.19615i | − 0.416290i | ||||||||
\(489\) | − 13.4641i | − 0.608868i | ||||||||
\(490\) | 1.73205 | 0.0782461 | ||||||||
\(491\) | −8.73205 | −0.394072 | −0.197036 | − | 0.980396i | \(-0.563132\pi\) | ||||
−0.197036 | + | 0.980396i | \(0.563132\pi\) | |||||||
\(492\) | − 9.39230i | − 0.423438i | ||||||||
\(493\) | −25.5885 | −1.15245 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.73205 | 0.212690 | ||||||||
\(496\) | − 1.46410i | − 0.0657401i | ||||||||
\(497\) | −12.9282 | −0.579909 | ||||||||
\(498\) | 0.196152 | 0.00878980 | ||||||||
\(499\) | − 32.0000i | − 1.43252i | −0.697835 | − | 0.716258i | \(-0.745853\pi\) | ||||
0.697835 | − | 0.716258i | \(-0.254147\pi\) | |||||||
\(500\) | − 14.6603i | − 0.655626i | ||||||||
\(501\) | − 9.46410i | − 0.422825i | ||||||||
\(502\) | 13.4641i | 0.600932i | ||||||||
\(503\) | 40.9808 | 1.82724 | 0.913621 | − | 0.406567i | \(-0.133274\pi\) | ||||
0.913621 | + | 0.406567i | \(0.133274\pi\) | |||||||
\(504\) | 2.73205 | 0.121695 | ||||||||
\(505\) | 7.19615i | 0.320225i | ||||||||
\(506\) | −5.32051 | −0.236525 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.85641 | −0.437307 | ||||||||
\(509\) | − 13.7321i | − 0.608662i | −0.952566 | − | 0.304331i | \(-0.901567\pi\) | ||||
0.952566 | − | 0.304331i | \(-0.0984330\pi\) | |||||||
\(510\) | −21.3923 | −0.947267 | ||||||||
\(511\) | −17.1244 | −0.757537 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 4.73205i | − 0.208925i | ||||||||
\(514\) | 9.33975i | 0.411959i | ||||||||
\(515\) | − 56.9808i | − 2.51087i | ||||||||
\(516\) | −9.66025 | −0.425269 | ||||||||
\(517\) | −2.78461 | −0.122467 | ||||||||
\(518\) | − 9.66025i | − 0.424447i | ||||||||
\(519\) | −4.39230 | −0.192801 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.4449 | 1.81573 | 0.907866 | − | 0.419260i | \(-0.137710\pi\) | ||||
0.907866 | + | 0.419260i | \(0.137710\pi\) | |||||||
\(522\) | 4.46410i | 0.195388i | ||||||||
\(523\) | −22.4449 | −0.981445 | −0.490723 | − | 0.871316i | \(-0.663267\pi\) | ||||
−0.490723 | + | 0.871316i | \(0.663267\pi\) | |||||||
\(524\) | −6.53590 | −0.285522 | ||||||||
\(525\) | 24.3923i | 1.06457i | ||||||||
\(526\) | 10.0526i | 0.438312i | ||||||||
\(527\) | − 8.39230i | − 0.365575i | ||||||||
\(528\) | 1.26795i | 0.0551804i | ||||||||
\(529\) | −5.39230 | −0.234448 | ||||||||
\(530\) | 24.1244 | 1.04790 | ||||||||
\(531\) | 8.00000i | 0.347170i | ||||||||
\(532\) | 12.9282 | 0.560509 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −9.46410 | −0.409552 | ||||||||
\(535\) | − 38.0526i | − 1.64516i | ||||||||
\(536\) | 13.1244 | 0.566886 | ||||||||
\(537\) | 16.0526 | 0.692719 | ||||||||
\(538\) | − 5.46410i | − 0.235574i | ||||||||
\(539\) | − 0.588457i | − 0.0253466i | ||||||||
\(540\) | 3.73205i | 0.160602i | ||||||||
\(541\) | 5.67949i | 0.244180i | 0.992519 | + | 0.122090i | \(0.0389597\pi\) | ||||
−0.992519 | + | 0.122090i | \(0.961040\pi\) | |||||||
\(542\) | −21.8564 | −0.938813 | ||||||||
\(543\) | −19.1962 | −0.823786 | ||||||||
\(544\) | − 5.73205i | − 0.245760i | ||||||||
\(545\) | −5.46410 | −0.234056 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.19615 | −0.179415 | −0.0897073 | − | 0.995968i | \(-0.528593\pi\) | ||||
−0.0897073 | + | 0.995968i | \(0.528593\pi\) | |||||||
\(548\) | − 11.9282i | − 0.509548i | ||||||||
\(549\) | −9.19615 | −0.392482 | ||||||||
\(550\) | −11.3205 | −0.482708 | ||||||||
\(551\) | 21.1244i | 0.899928i | ||||||||
\(552\) | − 4.19615i | − 0.178600i | ||||||||
\(553\) | 6.92820i | 0.294617i | ||||||||
\(554\) | − 5.73205i | − 0.243532i | ||||||||
\(555\) | 13.1962 | 0.560145 | ||||||||
\(556\) | −17.8564 | −0.757280 | ||||||||
\(557\) | 42.3731i | 1.79540i | 0.440603 | + | 0.897702i | \(0.354765\pi\) | ||||
−0.440603 | + | 0.897702i | \(0.645235\pi\) | |||||||
\(558\) | −1.46410 | −0.0619804 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −10.1962 | −0.430866 | ||||||||
\(561\) | 7.26795i | 0.306853i | ||||||||
\(562\) | 12.3205 | 0.519709 | ||||||||
\(563\) | −34.9282 | −1.47205 | −0.736024 | − | 0.676955i | \(-0.763299\pi\) | ||||
−0.736024 | + | 0.676955i | \(0.763299\pi\) | |||||||
\(564\) | − 2.19615i | − 0.0924747i | ||||||||
\(565\) | 5.00000i | 0.210352i | ||||||||
\(566\) | 25.6603i | 1.07858i | ||||||||
\(567\) | − 2.73205i | − 0.114735i | ||||||||
\(568\) | 4.73205 | 0.198552 | ||||||||
\(569\) | −30.6410 | −1.28454 | −0.642269 | − | 0.766479i | \(-0.722007\pi\) | ||||
−0.642269 | + | 0.766479i | \(0.722007\pi\) | |||||||
\(570\) | 17.6603i | 0.739707i | ||||||||
\(571\) | −14.0526 | −0.588081 | −0.294041 | − | 0.955793i | \(-0.595000\pi\) | ||||
−0.294041 | + | 0.955793i | \(0.595000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.92820 | −0.289430 | ||||||||
\(574\) | − 25.6603i | − 1.07104i | ||||||||
\(575\) | 37.4641 | 1.56236 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 3.73205i | − 0.155367i | −0.996978 | − | 0.0776837i | \(-0.975248\pi\) | ||||
0.996978 | − | 0.0776837i | \(-0.0247524\pi\) | |||||||
\(578\) | − 15.8564i | − 0.659540i | ||||||||
\(579\) | − 11.7321i | − 0.487567i | ||||||||
\(580\) | − 16.6603i | − 0.691779i | ||||||||
\(581\) | 0.535898 | 0.0222328 | ||||||||
\(582\) | 6.00000 | 0.248708 | ||||||||
\(583\) | − 8.19615i | − 0.339450i | ||||||||
\(584\) | 6.26795 | 0.259370 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.5167 | 1.26063 | ||||||||
\(587\) | − 16.0000i | − 0.660391i | −0.943913 | − | 0.330195i | \(-0.892885\pi\) | ||||
0.943913 | − | 0.330195i | \(-0.107115\pi\) | |||||||
\(588\) | 0.464102 | 0.0191392 | ||||||||
\(589\) | −6.92820 | −0.285472 | ||||||||
\(590\) | − 29.8564i | − 1.22917i | ||||||||
\(591\) | 17.8564i | 0.734514i | ||||||||
\(592\) | 3.53590i | 0.145325i | ||||||||
\(593\) | − 9.14359i | − 0.375482i | −0.982219 | − | 0.187741i | \(-0.939883\pi\) | ||||
0.982219 | − | 0.187741i | \(-0.0601166\pi\) | |||||||
\(594\) | 1.26795 | 0.0520246 | ||||||||
\(595\) | −58.4449 | −2.39601 | ||||||||
\(596\) | 13.1962i | 0.540535i | ||||||||
\(597\) | 14.1962 | 0.581010 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.53590 | −0.103614 | −0.0518070 | − | 0.998657i | \(-0.516498\pi\) | ||||
−0.0518070 | + | 0.998657i | \(0.516498\pi\) | |||||||
\(600\) | − 8.92820i | − 0.364492i | ||||||||
\(601\) | 7.92820 | 0.323398 | 0.161699 | − | 0.986840i | \(-0.448303\pi\) | ||||
0.161699 | + | 0.986840i | \(0.448303\pi\) | |||||||
\(602\) | −26.3923 | −1.07567 | ||||||||
\(603\) | − 13.1244i | − 0.534465i | ||||||||
\(604\) | − 6.73205i | − 0.273923i | ||||||||
\(605\) | − 35.0526i | − 1.42509i | ||||||||
\(606\) | 1.92820i | 0.0783279i | ||||||||
\(607\) | −40.7846 | −1.65540 | −0.827698 | − | 0.561174i | \(-0.810350\pi\) | ||||
−0.827698 | + | 0.561174i | \(0.810350\pi\) | |||||||
\(608\) | −4.73205 | −0.191910 | ||||||||
\(609\) | 12.1962i | 0.494213i | ||||||||
\(610\) | 34.3205 | 1.38960 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.73205 | −0.231704 | ||||||||
\(613\) | 9.39230i | 0.379352i | 0.981847 | + | 0.189676i | \(0.0607437\pi\) | ||||
−0.981847 | + | 0.189676i | \(0.939256\pi\) | |||||||
\(614\) | −22.5885 | −0.911596 | ||||||||
\(615\) | 35.0526 | 1.41346 | ||||||||
\(616\) | 3.46410i | 0.139573i | ||||||||
\(617\) | 13.2487i | 0.533373i | 0.963783 | + | 0.266687i | \(0.0859288\pi\) | ||||
−0.963783 | + | 0.266687i | \(0.914071\pi\) | |||||||
\(618\) | − 15.2679i | − 0.614167i | ||||||||
\(619\) | 17.4641i | 0.701942i | 0.936386 | + | 0.350971i | \(0.114148\pi\) | ||||
−0.936386 | + | 0.350971i | \(0.885852\pi\) | |||||||
\(620\) | 5.46410 | 0.219444 | ||||||||
\(621\) | −4.19615 | −0.168386 | ||||||||
\(622\) | − 1.66025i | − 0.0665701i | ||||||||
\(623\) | −25.8564 | −1.03592 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | − 6.53590i | − 0.261227i | ||||||||
\(627\) | 6.00000 | 0.239617 | ||||||||
\(628\) | −7.58846 | −0.302812 | ||||||||
\(629\) | 20.2679i | 0.808136i | ||||||||
\(630\) | 10.1962i | 0.406224i | ||||||||
\(631\) | − 7.71281i | − 0.307042i | −0.988145 | − | 0.153521i | \(-0.950939\pi\) | ||||
0.988145 | − | 0.153521i | \(-0.0490613\pi\) | |||||||
\(632\) | − 2.53590i | − 0.100873i | ||||||||
\(633\) | 16.3923 | 0.651536 | ||||||||
\(634\) | −20.6603 | −0.820524 | ||||||||
\(635\) | − 36.7846i | − 1.45975i | ||||||||
\(636\) | 6.46410 | 0.256318 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.66025 | −0.224092 | ||||||||
\(639\) | − 4.73205i | − 0.187197i | ||||||||
\(640\) | 3.73205 | 0.147522 | ||||||||
\(641\) | 25.9808 | 1.02618 | 0.513089 | − | 0.858335i | \(-0.328501\pi\) | ||||
0.513089 | + | 0.858335i | \(0.328501\pi\) | |||||||
\(642\) | − 10.1962i | − 0.402410i | ||||||||
\(643\) | 13.8564i | 0.546443i | 0.961951 | + | 0.273222i | \(0.0880892\pi\) | ||||
−0.961951 | + | 0.273222i | \(0.911911\pi\) | |||||||
\(644\) | − 11.4641i | − 0.451749i | ||||||||
\(645\) | − 36.0526i | − 1.41957i | ||||||||
\(646\) | −27.1244 | −1.06719 | ||||||||
\(647\) | 22.2487 | 0.874687 | 0.437344 | − | 0.899295i | \(-0.355919\pi\) | ||||
0.437344 | + | 0.899295i | \(0.355919\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −10.1436 | −0.398171 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00000 | −0.156772 | ||||||||
\(652\) | 13.4641i | 0.527295i | ||||||||
\(653\) | −17.4641 | −0.683423 | −0.341712 | − | 0.939805i | \(-0.611007\pi\) | ||||
−0.341712 | + | 0.939805i | \(0.611007\pi\) | |||||||
\(654\) | −1.46410 | −0.0572509 | ||||||||
\(655\) | − 24.3923i | − 0.953086i | ||||||||
\(656\) | 9.39230i | 0.366708i | ||||||||
\(657\) | − 6.26795i | − 0.244536i | ||||||||
\(658\) | − 6.00000i | − 0.233904i | ||||||||
\(659\) | −10.2487 | −0.399233 | −0.199617 | − | 0.979874i | \(-0.563970\pi\) | ||||
−0.199617 | + | 0.979874i | \(0.563970\pi\) | |||||||
\(660\) | −4.73205 | −0.184195 | ||||||||
\(661\) | 11.3923i | 0.443109i | 0.975148 | + | 0.221555i | \(0.0711131\pi\) | ||||
−0.975148 | + | 0.221555i | \(0.928887\pi\) | |||||||
\(662\) | −20.0000 | −0.777322 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.196152 | −0.00761219 | ||||||||
\(665\) | 48.2487i | 1.87100i | ||||||||
\(666\) | 3.53590 | 0.137013 | ||||||||
\(667\) | 18.7321 | 0.725308 | ||||||||
\(668\) | 9.46410i | 0.366177i | ||||||||
\(669\) | 26.9282i | 1.04110i | ||||||||
\(670\) | 48.9808i | 1.89229i | ||||||||
\(671\) | − 11.6603i | − 0.450139i | ||||||||
\(672\) | −2.73205 | −0.105391 | ||||||||
\(673\) | −27.9282 | −1.07655 | −0.538277 | − | 0.842768i | \(-0.680924\pi\) | ||||
−0.538277 | + | 0.842768i | \(0.680924\pi\) | |||||||
\(674\) | − 20.8564i | − 0.803359i | ||||||||
\(675\) | −8.92820 | −0.343647 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.4641 | −1.74733 | −0.873664 | − | 0.486530i | \(-0.838262\pi\) | ||||
−0.873664 | + | 0.486530i | \(0.838262\pi\) | |||||||
\(678\) | 1.33975i | 0.0514526i | ||||||||
\(679\) | 16.3923 | 0.629079 | ||||||||
\(680\) | 21.3923 | 0.820357 | ||||||||
\(681\) | 12.1962i | 0.467358i | ||||||||
\(682\) | − 1.85641i | − 0.0710855i | ||||||||
\(683\) | − 10.1436i | − 0.388134i | −0.980988 | − | 0.194067i | \(-0.937832\pi\) | ||||
0.980988 | − | 0.194067i | \(-0.0621679\pi\) | |||||||
\(684\) | 4.73205i | 0.180934i | ||||||||
\(685\) | 44.5167 | 1.70089 | ||||||||
\(686\) | −17.8564 | −0.681761 | ||||||||
\(687\) | − 11.8564i | − 0.452350i | ||||||||
\(688\) | 9.66025 | 0.368294 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 15.6603 | 0.596176 | ||||||||
\(691\) | − 43.6603i | − 1.66091i | −0.557082 | − | 0.830457i | \(-0.688079\pi\) | ||||
0.557082 | − | 0.830457i | \(-0.311921\pi\) | |||||||
\(692\) | 4.39230 | 0.166970 | ||||||||
\(693\) | 3.46410 | 0.131590 | ||||||||
\(694\) | − 33.1244i | − 1.25738i | ||||||||
\(695\) | − 66.6410i | − 2.52784i | ||||||||
\(696\) | − 4.46410i | − 0.169211i | ||||||||
\(697\) | 53.8372i | 2.03923i | ||||||||
\(698\) | 15.3205 | 0.579890 | ||||||||
\(699\) | 7.85641 | 0.297157 | ||||||||
\(700\) | − 24.3923i | − 0.921942i | ||||||||
\(701\) | 3.32051 | 0.125414 | 0.0627069 | − | 0.998032i | \(-0.480027\pi\) | ||||
0.0627069 | + | 0.998032i | \(0.480027\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.7321 | 0.631061 | ||||||||
\(704\) | − 1.26795i | − 0.0477876i | ||||||||
\(705\) | 8.19615 | 0.308685 | ||||||||
\(706\) | 21.7846 | 0.819875 | ||||||||
\(707\) | 5.26795i | 0.198122i | ||||||||
\(708\) | − 8.00000i | − 0.300658i | ||||||||
\(709\) | 13.1436i | 0.493618i | 0.969064 | + | 0.246809i | \(0.0793820\pi\) | ||||
−0.969064 | + | 0.246809i | \(0.920618\pi\) | |||||||
\(710\) | 17.6603i | 0.662778i | ||||||||
\(711\) | −2.53590 | −0.0951036 | ||||||||
\(712\) | 9.46410 | 0.354682 | ||||||||
\(713\) | 6.14359i | 0.230079i | ||||||||
\(714\) | −15.6603 | −0.586070 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.0526 | −0.599912 | ||||||||
\(717\) | − 7.66025i | − 0.286077i | ||||||||
\(718\) | −1.12436 | −0.0419606 | ||||||||
\(719\) | 29.4641 | 1.09883 | 0.549413 | − | 0.835551i | \(-0.314851\pi\) | ||||
0.549413 | + | 0.835551i | \(0.314851\pi\) | |||||||
\(720\) | − 3.73205i | − 0.139085i | ||||||||
\(721\) | − 41.7128i | − 1.55347i | ||||||||
\(722\) | 3.39230i | 0.126249i | ||||||||
\(723\) | 13.5885i | 0.505360i | ||||||||
\(724\) | 19.1962 | 0.713419 | ||||||||
\(725\) | 39.8564 | 1.48023 | ||||||||
\(726\) | − 9.39230i | − 0.348581i | ||||||||
\(727\) | 30.9808 | 1.14901 | 0.574506 | − | 0.818500i | \(-0.305194\pi\) | ||||
0.574506 | + | 0.818500i | \(0.305194\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 23.3923i | 0.865788i | ||||||||
\(731\) | 55.3731 | 2.04805 | ||||||||
\(732\) | 9.19615 | 0.339900 | ||||||||
\(733\) | − 19.0000i | − 0.701781i | −0.936416 | − | 0.350891i | \(-0.885879\pi\) | ||||
0.936416 | − | 0.350891i | \(-0.114121\pi\) | |||||||
\(734\) | 11.2679i | 0.415908i | ||||||||
\(735\) | 1.73205i | 0.0638877i | ||||||||
\(736\) | 4.19615i | 0.154672i | ||||||||
\(737\) | 16.6410 | 0.612980 | ||||||||
\(738\) | 9.39230 | 0.345736 | ||||||||
\(739\) | 2.92820i | 0.107716i | 0.998549 | + | 0.0538578i | \(0.0171518\pi\) | ||||
−0.998549 | + | 0.0538578i | \(0.982848\pi\) | |||||||
\(740\) | −13.1962 | −0.485100 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.6603 | 0.648328 | ||||||||
\(743\) | 48.3923i | 1.77534i | 0.460479 | + | 0.887671i | \(0.347678\pi\) | ||||
−0.460479 | + | 0.887671i | \(0.652322\pi\) | |||||||
\(744\) | 1.46410 | 0.0536766 | ||||||||
\(745\) | −49.2487 | −1.80433 | ||||||||
\(746\) | 13.7321i | 0.502766i | ||||||||
\(747\) | 0.196152i | 0.00717684i | ||||||||
\(748\) | − 7.26795i | − 0.265743i | ||||||||
\(749\) | − 27.8564i | − 1.01785i | ||||||||
\(750\) | 14.6603 | 0.535317 | ||||||||
\(751\) | 49.9090 | 1.82120 | 0.910602 | − | 0.413284i | \(-0.135618\pi\) | ||||
0.910602 | + | 0.413284i | \(0.135618\pi\) | |||||||
\(752\) | 2.19615i | 0.0800854i | ||||||||
\(753\) | −13.4641 | −0.490659 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.1244 | 0.914369 | ||||||||
\(756\) | 2.73205i | 0.0993637i | ||||||||
\(757\) | 20.9282 | 0.760648 | 0.380324 | − | 0.924853i | \(-0.375812\pi\) | ||||
0.380324 | + | 0.924853i | \(0.375812\pi\) | |||||||
\(758\) | 5.46410 | 0.198465 | ||||||||
\(759\) | − 5.32051i | − 0.193122i | ||||||||
\(760\) | − 17.6603i | − 0.640605i | ||||||||
\(761\) | 11.3205i | 0.410368i | 0.978723 | + | 0.205184i | \(0.0657793\pi\) | ||||
−0.978723 | + | 0.205184i | \(0.934221\pi\) | |||||||
\(762\) | − 9.85641i | − 0.357060i | ||||||||
\(763\) | −4.00000 | −0.144810 | ||||||||
\(764\) | 6.92820 | 0.250654 | ||||||||
\(765\) | − 21.3923i | − 0.773440i | ||||||||
\(766\) | 1.46410 | 0.0529001 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 43.8564i | 1.58150i | 0.612138 | + | 0.790751i | \(0.290310\pi\) | ||||
−0.612138 | + | 0.790751i | \(0.709690\pi\) | |||||||
\(770\) | −12.9282 | −0.465900 | ||||||||
\(771\) | −9.33975 | −0.336363 | ||||||||
\(772\) | 11.7321i | 0.422246i | ||||||||
\(773\) | 48.9282i | 1.75983i | 0.475136 | + | 0.879913i | \(0.342399\pi\) | ||||
−0.475136 | + | 0.879913i | \(0.657601\pi\) | |||||||
\(774\) | − 9.66025i | − 0.347231i | ||||||||
\(775\) | 13.0718i | 0.469553i | ||||||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | 9.66025 | 0.346560 | ||||||||
\(778\) | 11.7846i | 0.422499i | ||||||||
\(779\) | 44.4449 | 1.59240 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | 24.0526i | 0.860118i | ||||||||
\(783\) | −4.46410 | −0.159534 | ||||||||
\(784\) | −0.464102 | −0.0165751 | ||||||||
\(785\) | − 28.3205i | − 1.01080i | ||||||||
\(786\) | − 6.53590i | − 0.233128i | ||||||||
\(787\) | 4.67949i | 0.166806i | 0.996516 | + | 0.0834029i | \(0.0265789\pi\) | ||||
−0.996516 | + | 0.0834029i | \(0.973421\pi\) | |||||||
\(788\) | − 17.8564i | − 0.636108i | ||||||||
\(789\) | −10.0526 | −0.357881 | ||||||||
\(790\) | 9.46410 | 0.336718 | ||||||||
\(791\) | 3.66025i | 0.130144i | ||||||||
\(792\) | −1.26795 | −0.0450546 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 20.3923 | 0.723696 | ||||||||
\(795\) | 24.1244i | 0.855603i | ||||||||
\(796\) | −14.1962 | −0.503169 | ||||||||
\(797\) | 34.0000 | 1.20434 | 0.602171 | − | 0.798367i | \(-0.294303\pi\) | ||||
0.602171 | + | 0.798367i | \(0.294303\pi\) | |||||||
\(798\) | 12.9282i | 0.457653i | ||||||||
\(799\) | 12.5885i | 0.445348i | ||||||||
\(800\) | 8.92820i | 0.315660i | ||||||||
\(801\) | − 9.46410i | − 0.334398i | ||||||||
\(802\) | 8.07180 | 0.285025 | ||||||||
\(803\) | 7.94744 | 0.280459 | ||||||||
\(804\) | 13.1244i | 0.462860i | ||||||||
\(805\) | 42.7846 | 1.50796 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.46410 | 0.192345 | ||||||||
\(808\) | − 1.92820i | − 0.0678340i | ||||||||
\(809\) | −53.5885 | −1.88407 | −0.942035 | − | 0.335515i | \(-0.891090\pi\) | ||||
−0.942035 | + | 0.335515i | \(0.891090\pi\) | |||||||
\(810\) | −3.73205 | −0.131131 | ||||||||
\(811\) | − 17.1769i | − 0.603163i | −0.953440 | − | 0.301582i | \(-0.902485\pi\) | ||||
0.953440 | − | 0.301582i | \(-0.0975145\pi\) | |||||||
\(812\) | − 12.1962i | − 0.428001i | ||||||||
\(813\) | − 21.8564i | − 0.766538i | ||||||||
\(814\) | 4.48334i | 0.157141i | ||||||||
\(815\) | −50.2487 | −1.76014 | ||||||||
\(816\) | 5.73205 | 0.200662 | ||||||||
\(817\) | − 45.7128i | − 1.59929i | ||||||||
\(818\) | −17.7321 | −0.619987 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −35.0526 | −1.22409 | ||||||||
\(821\) | 0.928203i | 0.0323945i | 0.999869 | + | 0.0161973i | \(0.00515597\pi\) | ||||
−0.999869 | + | 0.0161973i | \(0.994844\pi\) | |||||||
\(822\) | 11.9282 | 0.416044 | ||||||||
\(823\) | −41.5692 | −1.44901 | −0.724506 | − | 0.689269i | \(-0.757932\pi\) | ||||
−0.724506 | + | 0.689269i | \(0.757932\pi\) | |||||||
\(824\) | 15.2679i | 0.531884i | ||||||||
\(825\) | − 11.3205i | − 0.394130i | ||||||||
\(826\) | − 21.8564i | − 0.760482i | ||||||||
\(827\) | 26.5359i | 0.922744i | 0.887207 | + | 0.461372i | \(0.152643\pi\) | ||||
−0.887207 | + | 0.461372i | \(0.847357\pi\) | |||||||
\(828\) | 4.19615 | 0.145826 | ||||||||
\(829\) | 12.1244 | 0.421096 | 0.210548 | − | 0.977583i | \(-0.432475\pi\) | ||||
0.210548 | + | 0.977583i | \(0.432475\pi\) | |||||||
\(830\) | − 0.732051i | − 0.0254099i | ||||||||
\(831\) | 5.73205 | 0.198843 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.66025 | −0.0921723 | ||||||||
\(834\) | − 17.8564i | − 0.618317i | ||||||||
\(835\) | −35.3205 | −1.22232 | ||||||||
\(836\) | −6.00000 | −0.207514 | ||||||||
\(837\) | − 1.46410i | − 0.0506068i | ||||||||
\(838\) | 17.4641i | 0.603287i | ||||||||
\(839\) | 41.8564i | 1.44504i | 0.691348 | + | 0.722522i | \(0.257017\pi\) | ||||
−0.691348 | + | 0.722522i | \(0.742983\pi\) | |||||||
\(840\) | − 10.1962i | − 0.351801i | ||||||||
\(841\) | −9.07180 | −0.312821 | ||||||||
\(842\) | 22.7128 | 0.782735 | ||||||||
\(843\) | 12.3205i | 0.424341i | ||||||||
\(844\) | −16.3923 | −0.564246 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.19615 | 0.0755053 | ||||||||
\(847\) | − 25.6603i | − 0.881697i | ||||||||
\(848\) | −6.46410 | −0.221978 | ||||||||
\(849\) | −25.6603 | −0.880658 | ||||||||
\(850\) | 51.1769i | 1.75535i | ||||||||
\(851\) | − 14.8372i | − 0.508612i | ||||||||
\(852\) | 4.73205i | 0.162117i | ||||||||
\(853\) | − 54.1769i | − 1.85498i | −0.373845 | − | 0.927491i | \(-0.621961\pi\) | ||||
0.373845 | − | 0.927491i | \(-0.378039\pi\) | |||||||
\(854\) | 25.1244 | 0.859738 | ||||||||
\(855\) | −17.6603 | −0.603968 | ||||||||
\(856\) | 10.1962i | 0.348497i | ||||||||
\(857\) | −39.4449 | −1.34741 | −0.673705 | − | 0.739000i | \(-0.735298\pi\) | ||||
−0.673705 | + | 0.739000i | \(0.735298\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.1244 | −1.60786 | −0.803931 | − | 0.594722i | \(-0.797262\pi\) | ||||
−0.803931 | + | 0.594722i | \(0.797262\pi\) | |||||||
\(860\) | 36.0526i | 1.22938i | ||||||||
\(861\) | 25.6603 | 0.874499 | ||||||||
\(862\) | −13.1244 | −0.447017 | ||||||||
\(863\) | 17.1244i | 0.582920i | 0.956583 | + | 0.291460i | \(0.0941410\pi\) | ||||
−0.956583 | + | 0.291460i | \(0.905859\pi\) | |||||||
\(864\) | − 1.00000i | − 0.0340207i | ||||||||
\(865\) | 16.3923i | 0.557355i | ||||||||
\(866\) | 12.8564i | 0.436878i | ||||||||
\(867\) | 15.8564 | 0.538512 | ||||||||
\(868\) | 4.00000 | 0.135769 | ||||||||
\(869\) | − 3.21539i | − 0.109075i | ||||||||
\(870\) | 16.6603 | 0.564836 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.46410 | 0.0495807 | ||||||||
\(873\) | 6.00000i | 0.203069i | ||||||||
\(874\) | 19.8564 | 0.671653 | ||||||||
\(875\) | 40.0526 | 1.35402 | ||||||||
\(876\) | 6.26795i | 0.211774i | ||||||||
\(877\) | − 23.9282i | − 0.807998i | −0.914759 | − | 0.403999i | \(-0.867620\pi\) | ||||
0.914759 | − | 0.403999i | \(-0.132380\pi\) | |||||||
\(878\) | − 0.339746i | − 0.0114659i | ||||||||
\(879\) | 30.5167i | 1.02930i | ||||||||
\(880\) | 4.73205 | 0.159517 | ||||||||
\(881\) | 27.8372 | 0.937858 | 0.468929 | − | 0.883236i | \(-0.344640\pi\) | ||||
0.468929 | + | 0.883236i | \(0.344640\pi\) | |||||||
\(882\) | 0.464102i | 0.0156271i | ||||||||
\(883\) | −42.9282 | −1.44465 | −0.722325 | − | 0.691554i | \(-0.756926\pi\) | ||||
−0.722325 | + | 0.691554i | \(0.756926\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 29.8564 | 1.00361 | ||||||||
\(886\) | − 15.6077i | − 0.524351i | ||||||||
\(887\) | 37.8564 | 1.27109 | 0.635547 | − | 0.772062i | \(-0.280775\pi\) | ||||
0.635547 | + | 0.772062i | \(0.280775\pi\) | |||||||
\(888\) | −3.53590 | −0.118657 | ||||||||
\(889\) | − 26.9282i | − 0.903143i | ||||||||
\(890\) | 35.3205i | 1.18395i | ||||||||
\(891\) | 1.26795i | 0.0424779i | ||||||||
\(892\) | − 26.9282i | − 0.901623i | ||||||||
\(893\) | 10.3923 | 0.347765 | ||||||||
\(894\) | −13.1962 | −0.441345 | ||||||||
\(895\) | − 59.9090i | − 2.00254i | ||||||||
\(896\) | 2.73205 | 0.0912714 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.3205 | 0.377770 | ||||||||
\(899\) | 6.53590i | 0.217984i | ||||||||
\(900\) | 8.92820 | 0.297607 | ||||||||
\(901\) | −37.0526 | −1.23440 | ||||||||
\(902\) | 11.9090i | 0.396525i | ||||||||
\(903\) | − 26.3923i | − 0.878281i | ||||||||
\(904\) | − 1.33975i | − 0.0445593i | ||||||||
\(905\) | 71.6410i | 2.38143i | ||||||||
\(906\) | 6.73205 | 0.223657 | ||||||||
\(907\) | −36.3923 | −1.20839 | −0.604193 | − | 0.796838i | \(-0.706505\pi\) | ||||
−0.604193 | + | 0.796838i | \(0.706505\pi\) | |||||||
\(908\) | − 12.1962i | − 0.404744i | ||||||||
\(909\) | −1.92820 | −0.0639545 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.53590 | −0.0840181 | −0.0420090 | − | 0.999117i | \(-0.513376\pi\) | ||||
−0.0420090 | + | 0.999117i | \(0.513376\pi\) | |||||||
\(912\) | − 4.73205i | − 0.156694i | ||||||||
\(913\) | −0.248711 | −0.00823114 | ||||||||
\(914\) | −1.33975 | −0.0443149 | ||||||||
\(915\) | 34.3205i | 1.13460i | ||||||||
\(916\) | 11.8564i | 0.391747i | ||||||||
\(917\) | − 17.8564i | − 0.589670i | ||||||||
\(918\) | − 5.73205i | − 0.189186i | ||||||||
\(919\) | 45.9615 | 1.51613 | 0.758065 | − | 0.652179i | \(-0.226145\pi\) | ||||
0.758065 | + | 0.652179i | \(0.226145\pi\) | |||||||
\(920\) | −15.6603 | −0.516303 | ||||||||
\(921\) | − 22.5885i | − 0.744315i | ||||||||
\(922\) | −22.2679 | −0.733356 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.46410 | −0.113961 | ||||||||
\(925\) | − 31.5692i | − 1.03799i | ||||||||
\(926\) | 10.0526 | 0.330348 | ||||||||
\(927\) | 15.2679 | 0.501465 | ||||||||
\(928\) | 4.46410i | 0.146541i | ||||||||
\(929\) | 39.2487i | 1.28771i | 0.765148 | + | 0.643854i | \(0.222666\pi\) | ||||
−0.765148 | + | 0.643854i | \(0.777334\pi\) | |||||||
\(930\) | 5.46410i | 0.179175i | ||||||||
\(931\) | 2.19615i | 0.0719760i | ||||||||
\(932\) | −7.85641 | −0.257345 | ||||||||
\(933\) | 1.66025 | 0.0543543 | ||||||||
\(934\) | 18.5885i | 0.608233i | ||||||||
\(935\) | 27.1244 | 0.887061 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.24871 | −0.171468 | −0.0857340 | − | 0.996318i | \(-0.527324\pi\) | ||||
−0.0857340 | + | 0.996318i | \(0.527324\pi\) | |||||||
\(938\) | 35.8564i | 1.17075i | ||||||||
\(939\) | 6.53590 | 0.213291 | ||||||||
\(940\) | −8.19615 | −0.267329 | ||||||||
\(941\) | − 12.6410i | − 0.412085i | −0.978543 | − | 0.206043i | \(-0.933941\pi\) | ||||
0.978543 | − | 0.206043i | \(-0.0660586\pi\) | |||||||
\(942\) | − 7.58846i | − 0.247245i | ||||||||
\(943\) | − 39.4115i | − 1.28342i | ||||||||
\(944\) | 8.00000i | 0.260378i | ||||||||
\(945\) | −10.1962 | −0.331681 | ||||||||
\(946\) | 12.2487 | 0.398240 | ||||||||
\(947\) | 21.0718i | 0.684741i | 0.939565 | + | 0.342371i | \(0.111230\pi\) | ||||
−0.939565 | + | 0.342371i | \(0.888770\pi\) | |||||||
\(948\) | 2.53590 | 0.0823622 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 42.2487 | 1.37073 | ||||||||
\(951\) | − 20.6603i | − 0.669955i | ||||||||
\(952\) | 15.6603 | 0.507552 | ||||||||
\(953\) | −41.5692 | −1.34656 | −0.673280 | − | 0.739388i | \(-0.735115\pi\) | ||||
−0.673280 | + | 0.739388i | \(0.735115\pi\) | |||||||
\(954\) | 6.46410i | 0.209283i | ||||||||
\(955\) | 25.8564i | 0.836694i | ||||||||
\(956\) | 7.66025i | 0.247750i | ||||||||
\(957\) | − 5.66025i | − 0.182970i | ||||||||
\(958\) | 33.4641 | 1.08118 | ||||||||
\(959\) | 32.5885 | 1.05234 | ||||||||
\(960\) | 3.73205i | 0.120451i | ||||||||
\(961\) | 28.8564 | 0.930852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.1962 | 0.328566 | ||||||||
\(964\) | − 13.5885i | − 0.437655i | ||||||||
\(965\) | −43.7846 | −1.40948 | ||||||||
\(966\) | 11.4641 | 0.368851 | ||||||||
\(967\) | 43.1244i | 1.38679i | 0.720560 | + | 0.693393i | \(0.243885\pi\) | ||||
−0.720560 | + | 0.693393i | \(0.756115\pi\) | |||||||
\(968\) | 9.39230i | 0.301880i | ||||||||
\(969\) | − 27.1244i | − 0.871360i | ||||||||
\(970\) | − 22.3923i | − 0.718974i | ||||||||
\(971\) | 30.2487 | 0.970727 | 0.485364 | − | 0.874312i | \(-0.338687\pi\) | ||||
0.485364 | + | 0.874312i | \(0.338687\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | − 48.7846i | − 1.56396i | ||||||||
\(974\) | 3.12436 | 0.100111 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.19615 | −0.294362 | ||||||||
\(977\) | − 45.9282i | − 1.46937i | −0.678407 | − | 0.734687i | \(-0.737329\pi\) | ||||
0.678407 | − | 0.734687i | \(-0.262671\pi\) | |||||||
\(978\) | −13.4641 | −0.430534 | ||||||||
\(979\) | 12.0000 | 0.383522 | ||||||||
\(980\) | − 1.73205i | − 0.0553283i | ||||||||
\(981\) | − 1.46410i | − 0.0467452i | ||||||||
\(982\) | 8.73205i | 0.278651i | ||||||||
\(983\) | 20.7846i | 0.662926i | 0.943468 | + | 0.331463i | \(0.107542\pi\) | ||||
−0.943468 | + | 0.331463i | \(0.892458\pi\) | |||||||
\(984\) | −9.39230 | −0.299416 | ||||||||
\(985\) | 66.6410 | 2.12336 | ||||||||
\(986\) | 25.5885i | 0.814902i | ||||||||
\(987\) | 6.00000 | 0.190982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −40.5359 | −1.28897 | ||||||||
\(990\) | − 4.73205i | − 0.150394i | ||||||||
\(991\) | 22.5885 | 0.717546 | 0.358773 | − | 0.933425i | \(-0.383195\pi\) | ||||
0.358773 | + | 0.933425i | \(0.383195\pi\) | |||||||
\(992\) | −1.46410 | −0.0464853 | ||||||||
\(993\) | − 20.0000i | − 0.634681i | ||||||||
\(994\) | 12.9282i | 0.410058i | ||||||||
\(995\) | − 52.9808i | − 1.67960i | ||||||||
\(996\) | − 0.196152i | − 0.00621533i | ||||||||
\(997\) | 21.3397 | 0.675837 | 0.337918 | − | 0.941175i | \(-0.390277\pi\) | ||||
0.337918 | + | 0.941175i | \(0.390277\pi\) | |||||||
\(998\) | −32.0000 | −1.01294 | ||||||||
\(999\) | 3.53590i | 0.111871i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))