Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5292,2,Mod(881,5292)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5292, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5292.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5292.x (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: | \(42.2568327497\) |
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: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 881.1 | ||
Root | \(-0.213160 + 1.71888i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5292.881 |
Dual form | 5292.2.x.a.4409.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) | \(2647\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.43402 | + | 2.48379i | −0.641312 | + | 1.11079i | 0.343828 | + | 0.939033i | \(0.388276\pi\) |
−0.985140 | + | 0.171753i | \(0.945057\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.34941 | + | 1.35643i | −0.708373 | + | 0.408979i | −0.810458 | − | 0.585797i | \(-0.800782\pi\) |
0.102086 | + | 0.994776i | \(0.467448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.18987 | − | 1.84167i | −0.884712 | − | 0.510789i | −0.0125026 | − | 0.999922i | \(-0.503980\pi\) |
−0.872209 | + | 0.489133i | \(0.837313\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.44383 | 1.56286 | 0.781429 | − | 0.623994i | \(-0.214491\pi\) | ||||
0.781429 | + | 0.623994i | \(0.214491\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.16234i | − | 0.725491i | −0.931888 | − | 0.362746i | \(-0.881839\pi\) | ||
0.931888 | − | 0.362746i | \(-0.118161\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.59068 | + | 1.49573i | 0.540195 | + | 0.311882i | 0.745158 | − | 0.666888i | \(-0.232374\pi\) |
−0.204963 | + | 0.978770i | \(0.565707\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.61282 | − | 2.79348i | −0.322563 | − | 0.558696i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.48332 | − | 1.43375i | 0.461142 | − | 0.266240i | −0.251383 | − | 0.967888i | \(-0.580885\pi\) |
0.712524 | + | 0.701648i | \(0.247552\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.26739 | + | 4.77318i | 1.48487 | + | 0.857289i | 0.999852 | − | 0.0172169i | \(-0.00548059\pi\) |
0.485016 | + | 0.874506i | \(0.338814\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.41279 | 0.561059 | 0.280530 | − | 0.959845i | \(-0.409490\pi\) | ||||
0.280530 | + | 0.959845i | \(0.409490\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.794538 | − | 1.37618i | 0.124086 | − | 0.214923i | −0.797289 | − | 0.603597i | \(-0.793733\pi\) |
0.921375 | + | 0.388674i | \(0.127067\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.67828 | − | 8.10302i | −0.713431 | − | 1.23570i | −0.963562 | − | 0.267487i | \(-0.913807\pi\) |
0.250131 | − | 0.968212i | \(-0.419526\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.65372 | + | 9.79254i | 0.824680 | + | 1.42839i | 0.902163 | + | 0.431394i | \(0.141978\pi\) |
−0.0774831 | + | 0.996994i | \(0.524688\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.49899i | − | 0.343263i | −0.985161 | − | 0.171632i | \(-0.945096\pi\) | ||
0.985161 | − | 0.171632i | \(-0.0549039\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.78058i | − | 1.04913i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.33680 | + | 7.51156i | −0.564604 | + | 0.977922i | 0.432483 | + | 0.901642i | \(0.357638\pi\) |
−0.997086 | + | 0.0762801i | \(0.975696\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.566915 | + | 0.327308i | −0.0725860 | + | 0.0419075i | −0.535854 | − | 0.844311i | \(-0.680010\pi\) |
0.463268 | + | 0.886218i | \(0.346677\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.14867 | − | 5.28199i | 1.13475 | − | 0.655150i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.86146 | + | 6.68825i | −0.471752 | + | 0.817099i | −0.999478 | − | 0.0323159i | \(-0.989712\pi\) |
0.527725 | + | 0.849415i | \(0.323045\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.86582i | − | 0.933501i | −0.884389 | − | 0.466750i | \(-0.845425\pi\) | ||
0.884389 | − | 0.466750i | \(-0.154575\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.7905i | 1.49702i | 0.663123 | + | 0.748510i | \(0.269231\pi\) | ||||
−0.663123 | + | 0.748510i | \(0.730769\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.59566 | − | 4.49581i | −0.292034 | − | 0.505819i | 0.682256 | − | 0.731113i | \(-0.260999\pi\) |
−0.974291 | + | 0.225295i | \(0.927666\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.92948 | + | 13.7343i | 0.870373 | + | 1.50753i | 0.861611 | + | 0.507569i | \(0.169456\pi\) |
0.00876173 | + | 0.999962i | \(0.497211\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.24057 | + | 16.0051i | −1.00228 | + | 1.73600i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.29653 | 0.667430 | 0.333715 | − | 0.942674i | \(-0.391698\pi\) | ||||
0.333715 | + | 0.942674i | \(0.391698\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.85460 | + | 4.53486i | 0.805865 | + | 0.465267i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2065 | + | 7.62477i | −1.34092 | + | 0.774178i | −0.986942 | − | 0.161077i | \(-0.948503\pi\) |
−0.353974 | + | 0.935255i | \(0.615170\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.74451 | + | 3.02158i | 0.173585 | + | 0.300658i | 0.939671 | − | 0.342080i | \(-0.111131\pi\) |
−0.766086 | + | 0.642739i | \(0.777798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.89161 | + | 1.66947i | 0.284919 | + | 0.164498i | 0.635648 | − | 0.771979i | \(-0.280733\pi\) |
−0.350729 | + | 0.936477i | \(0.614066\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.58853i | − | 0.346917i | −0.984841 | − | 0.173458i | \(-0.944506\pi\) | ||
0.984841 | − | 0.173458i | \(-0.0554942\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.7935 | −1.32117 | −0.660587 | − | 0.750750i | \(-0.729692\pi\) | ||||
−0.660587 | + | 0.750750i | \(0.729692\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.28607 | + | 3.05191i | 0.497271 | + | 0.287100i | 0.727586 | − | 0.686016i | \(-0.240642\pi\) |
−0.230315 | + | 0.973116i | \(0.573976\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.43018 | + | 4.28981i | −0.692867 | + | 0.400027i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.82019 | + | 3.15267i | −0.165472 | + | 0.286606i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.08895 | −0.455170 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.3819 | −1.18745 | −0.593727 | − | 0.804666i | \(-0.702344\pi\) | ||||
−0.593727 | + | 0.804666i | \(0.702344\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.388964 | − | 0.673705i | 0.0339839 | − | 0.0588619i | −0.848533 | − | 0.529142i | \(-0.822514\pi\) |
0.882517 | + | 0.470280i | \(0.155847\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.3082 | + | 8.26083i | −1.22243 | + | 0.705771i | −0.965435 | − | 0.260642i | \(-0.916066\pi\) |
−0.256995 | + | 0.966413i | \(0.582732\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.91826 | + | 5.72631i | 0.841256 | + | 0.485699i | 0.857691 | − | 0.514165i | \(-0.171898\pi\) |
−0.0164348 | + | 0.999865i | \(0.505232\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.99241 | 0.835607 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.22408i | 0.682973i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.24781 | − | 2.45247i | −0.347994 | − | 0.200914i | 0.315807 | − | 0.948823i | \(-0.397725\pi\) |
−0.663801 | + | 0.747909i | \(0.731058\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.92814 | − | 8.53579i | −0.401047 | − | 0.694633i | 0.592806 | − | 0.805345i | \(-0.298020\pi\) |
−0.993852 | + | 0.110712i | \(0.964687\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.7112 | + | 13.6897i | −1.90453 | + | 1.09958i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.3514 | − | 7.70843i | −1.06556 | − | 0.615200i | −0.138593 | − | 0.990349i | \(-0.544258\pi\) |
−0.926964 | + | 0.375149i | \(0.877591\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.4411 | 0.896133 | 0.448066 | − | 0.894000i | \(-0.352113\pi\) | ||||
0.448066 | + | 0.894000i | \(0.352113\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.49103 | − | 11.2428i | 0.502291 | − | 0.869993i | −0.497706 | − | 0.867346i | \(-0.665824\pi\) |
0.999996 | − | 0.00264735i | \(-0.000842678\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.283528 | + | 0.491084i | 0.0218098 | + | 0.0377757i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.79984 | − | 16.9738i | −0.745068 | − | 1.29050i | −0.950163 | − | 0.311754i | \(-0.899084\pi\) |
0.205095 | − | 0.978742i | \(-0.434250\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.7788i | 1.40360i | 0.712375 | + | 0.701799i | \(0.247619\pi\) | ||||
−0.712375 | + | 0.701799i | \(0.752381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.47775i | 0.332829i | 0.986056 | + | 0.166414i | \(0.0532190\pi\) | ||||
−0.986056 | + | 0.166414i | \(0.946781\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.89400 | + | 8.47666i | −0.359814 | + | 0.623217i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.1392 | + | 8.74061i | −1.10709 | + | 0.639177i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.90050 | + | 3.40665i | −0.426945 | + | 0.246497i | −0.698044 | − | 0.716055i | \(-0.745946\pi\) |
0.271099 | + | 0.962551i | \(0.412613\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.97694 | − | 13.8165i | 0.574193 | − | 0.994531i | −0.421936 | − | 0.906626i | \(-0.638649\pi\) |
0.996129 | − | 0.0879053i | \(-0.0280173\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.9511i | 1.84894i | 0.381254 | + | 0.924470i | \(0.375492\pi\) | ||||
−0.381254 | + | 0.924470i | \(0.624508\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.18358i | 0.225678i | 0.993613 | + | 0.112839i | \(0.0359944\pi\) | ||||
−0.993613 | + | 0.112839i | \(0.964006\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.27876 | + | 3.94693i | 0.159156 | + | 0.275666i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.28950 | + | 7.42963i | 0.296711 | + | 0.513918i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0552411 | + | 0.0956804i | −0.00380295 | + | 0.00658691i | −0.867921 | − | 0.496703i | \(-0.834544\pi\) |
0.864118 | + | 0.503290i | \(0.167877\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 26.8349 | 1.83013 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.5550 | − | 11.8674i | −1.38268 | − | 0.798290i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.3064 | − | 6.52775i | 0.757132 | − | 0.437130i | −0.0711331 | − | 0.997467i | \(-0.522661\pi\) |
0.828265 | + | 0.560336i | \(0.189328\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.63392 | − | 8.02618i | −0.307564 | − | 0.532716i | 0.670265 | − | 0.742122i | \(-0.266180\pi\) |
−0.977829 | + | 0.209406i | \(0.932847\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.6204 | − | 6.70902i | −0.767895 | − | 0.443344i | 0.0642281 | − | 0.997935i | \(-0.479541\pi\) |
−0.832123 | + | 0.554591i | \(0.812875\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 21.1789i | − | 1.38748i | −0.720227 | − | 0.693738i | \(-0.755963\pi\) | ||
0.720227 | − | 0.693738i | \(-0.244037\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −32.4302 | −2.11551 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.73342 | + | 4.46489i | 0.500233 | + | 0.288810i | 0.728810 | − | 0.684716i | \(-0.240074\pi\) |
−0.228577 | + | 0.973526i | \(0.573407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.9430 | + | 9.20469i | −1.02698 | + | 0.592926i | −0.916117 | − | 0.400910i | \(-0.868694\pi\) |
−0.110860 | + | 0.993836i | \(0.535361\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.82401 | + | 10.0875i | −0.370573 | + | 0.641851i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.33194 | 0.399669 | 0.199834 | − | 0.979830i | \(-0.435960\pi\) | ||||
0.199834 | + | 0.979830i | \(0.435960\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.11542 | −0.510212 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.19283 | + | 14.1904i | −0.511054 | + | 0.885172i | 0.488863 | + | 0.872360i | \(0.337412\pi\) |
−0.999918 | + | 0.0128120i | \(0.995922\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.4663 | + | 6.04270i | −0.645377 | + | 0.372609i | −0.786683 | − | 0.617357i | \(-0.788203\pi\) |
0.141306 | + | 0.989966i | \(0.454870\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.20698 | + | 3.58360i | 0.381292 | + | 0.220139i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.3304 | 1.54442 | 0.772212 | − | 0.635365i | \(-0.219150\pi\) | ||||
0.772212 | + | 0.635365i | \(0.219150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.225849i | 0.0137193i | 0.999976 | + | 0.00685967i | \(0.00218352\pi\) | ||||
−0.999976 | + | 0.00685967i | \(0.997816\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.57832 | + | 4.37534i | 0.456990 | + | 0.263843i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.2170 | + | 17.6963i | 0.613878 | + | 1.06327i | 0.990580 | + | 0.136934i | \(0.0437248\pi\) |
−0.376702 | + | 0.926335i | \(0.622942\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.96635 | + | 5.17672i | −0.534887 | + | 0.308817i | −0.743004 | − | 0.669287i | \(-0.766600\pi\) |
0.208117 | + | 0.978104i | \(0.433267\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.8781 | + | 6.85783i | 0.706080 | + | 0.407656i | 0.809608 | − | 0.586971i | \(-0.199680\pi\) |
−0.103528 | + | 0.994627i | \(0.533013\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.5230 | 1.44253 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.21527 | + | 7.30105i | −0.246258 | + | 0.426532i | −0.962485 | − | 0.271336i | \(-0.912535\pi\) |
0.716226 | + | 0.697868i | \(0.245868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.4381 | − | 21.5434i | −0.724175 | − | 1.25431i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.50930 | − | 9.54239i | −0.318611 | − | 0.551851i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.87746i | − | 0.107503i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.34345i | − | 0.304967i | −0.988306 | − | 0.152484i | \(-0.951273\pi\) | ||
0.988306 | − | 0.152484i | \(-0.0487271\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.70867 | + | 8.15565i | −0.267004 | + | 0.462465i | −0.968087 | − | 0.250615i | \(-0.919367\pi\) |
0.701083 | + | 0.713080i | \(0.252700\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.3347 | − | 8.27614i | 0.810245 | − | 0.467795i | −0.0367961 | − | 0.999323i | \(-0.511715\pi\) |
0.847041 | + | 0.531528i | \(0.178382\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.9725 | + | 13.2632i | −1.29026 | + | 0.744934i | −0.978701 | − | 0.205291i | \(-0.934186\pi\) |
−0.311563 | + | 0.950225i | \(0.600853\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.88956 | + | 6.73691i | −0.217773 | + | 0.377194i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 20.3776i | − | 1.13384i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.8811i | 0.659046i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.82000 | + | 15.2767i | 0.484791 | + | 0.839682i | 0.999847 | − | 0.0174739i | \(-0.00556238\pi\) |
−0.515056 | + | 0.857156i | \(0.672229\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0748 | − | 19.1821i | −0.605081 | − | 1.04803i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.31169 | − | 12.6642i | 0.398293 | − | 0.689864i | −0.595222 | − | 0.803561i | \(-0.702936\pi\) |
0.993515 | + | 0.113697i | \(0.0362694\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.8979 | −1.40245 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.05563 | + | 0.609467i | 0.0566691 | + | 0.0327179i | 0.528067 | − | 0.849203i | \(-0.322917\pi\) |
−0.471398 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.6857 | + | 6.16942i | −0.571995 | + | 0.330241i | −0.757946 | − | 0.652318i | \(-0.773797\pi\) |
0.185951 | + | 0.982559i | \(0.440463\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.1484 | + | 19.3097i | 0.593372 | + | 1.02775i | 0.993774 | + | 0.111411i | \(0.0355370\pi\) |
−0.400402 | + | 0.916339i | \(0.631130\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.5371 | + | 11.2797i | 1.03692 | + | 0.598666i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.1035i | 0.638796i | 0.947621 | + | 0.319398i | \(0.103481\pi\) | ||||
−0.947621 | + | 0.319398i | \(0.896519\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.99958 | 0.473662 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.7691 | − | 18.3419i | −1.66287 | − | 0.960058i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7544 | + | 7.36375i | −0.665774 | + | 0.384385i | −0.794473 | − | 0.607299i | \(-0.792253\pi\) |
0.128700 | + | 0.991684i | \(0.458920\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.54279 | − | 7.86834i | 0.235217 | − | 0.407407i | −0.724119 | − | 0.689675i | \(-0.757753\pi\) |
0.959336 | + | 0.282268i | \(0.0910867\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.5620 | −0.543970 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2298 | 1.09050 | 0.545250 | − | 0.838273i | \(-0.316435\pi\) | ||||
0.545250 | + | 0.838273i | \(0.316435\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.35227 | + | 5.80630i | −0.171293 | + | 0.296688i | −0.938872 | − | 0.344266i | \(-0.888128\pi\) |
0.767579 | + | 0.640954i | \(0.221461\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.66661 | + | 3.84897i | −0.338011 | + | 0.195151i | −0.659392 | − | 0.751799i | \(-0.729186\pi\) |
0.321381 | + | 0.946950i | \(0.395853\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.6939 | + | 9.63825i | 0.844249 | + | 0.487427i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.8889 | 0.749141 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.0494341i | 0.00248102i | 0.999999 | + | 0.00124051i | \(0.000394867\pi\) | ||||
−0.999999 | + | 0.00124051i | \(0.999605\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.6039 | + | 10.1636i | 0.879096 | + | 0.507546i | 0.870360 | − | 0.492416i | \(-0.163886\pi\) |
0.00873572 | + | 0.999962i | \(0.497219\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.5813 | − | 30.4517i | −0.875786 | − | 1.51691i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.01803 | + | 4.62921i | −0.397439 | + | 0.229461i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.1144 | + | 6.99428i | 0.599021 | + | 0.345845i | 0.768656 | − | 0.639662i | \(-0.220926\pi\) |
−0.169636 | + | 0.985507i | \(0.554259\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −45.4840 | −2.23272 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.6718 | + | 18.4842i | −0.521353 | + | 0.903010i | 0.478339 | + | 0.878176i | \(0.341239\pi\) |
−0.999692 | + | 0.0248344i | \(0.992094\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.97287 | + | 6.88121i | 0.193626 | + | 0.335370i | 0.946449 | − | 0.322853i | \(-0.104642\pi\) |
−0.752823 | + | 0.658223i | \(0.771309\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.3927 | − | 18.0007i | −0.504121 | − | 0.873163i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.9293i | 1.53798i | 0.639262 | + | 0.768989i | \(0.279240\pi\) | ||||
−0.639262 | + | 0.768989i | \(0.720760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5300i | 0.890493i | 0.895408 | + | 0.445247i | \(0.146884\pi\) | ||||
−0.895408 | + | 0.445247i | \(0.853116\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.73002 | − | 8.19263i | 0.226267 | − | 0.391907i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.80316 | − | 1.04106i | 0.0860603 | − | 0.0496869i | −0.456352 | − | 0.889799i | \(-0.650844\pi\) |
0.542413 | + | 0.840112i | \(0.317511\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.13895 | − | 1.23493i | 0.101625 | − | 0.0586731i | −0.448326 | − | 0.893870i | \(-0.647980\pi\) |
0.549951 | + | 0.835197i | \(0.314646\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.02933 | + | 15.6393i | −0.428031 | + | 0.741372i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.5094i | 1.77018i | 0.465424 | + | 0.885088i | \(0.345902\pi\) | ||||
−0.465424 | + | 0.885088i | \(0.654098\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.31094i | 0.202994i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.92345 | − | 5.06356i | −0.136753 | − | 0.236864i | 0.789513 | − | 0.613734i | \(-0.210333\pi\) |
−0.926266 | + | 0.376871i | \(0.877000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.82830 | − | 6.63081i | −0.178302 | − | 0.308827i | 0.762997 | − | 0.646402i | \(-0.223727\pi\) |
−0.941299 | + | 0.337574i | \(0.890394\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.89449 | − | 8.47751i | 0.227466 | − | 0.393983i | −0.729590 | − | 0.683885i | \(-0.760289\pi\) |
0.957057 | + | 0.289901i | \(0.0936225\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.1612 | 1.30314 | 0.651572 | − | 0.758587i | \(-0.274110\pi\) | ||||
0.651572 | + | 0.758587i | \(0.274110\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.9824 | + | 12.6915i | 1.01075 | + | 0.583557i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.83394 | + | 5.10028i | −0.405329 | + | 0.234017i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.8053 | + | 25.6435i | 0.676470 | + | 1.17168i | 0.976037 | + | 0.217605i | \(0.0698245\pi\) |
−0.299567 | + | 0.954075i | \(0.596842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.8864 | − | 6.28525i | −0.496376 | − | 0.286583i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 43.7362i | − | 1.98596i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.3403 | 1.32953 | 0.664767 | − | 0.747051i | \(-0.268531\pi\) | ||||
0.664767 | + | 0.747051i | \(0.268531\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.63745 | + | 4.98683i | 0.389803 | + | 0.225053i | 0.682075 | − | 0.731283i | \(-0.261078\pi\) |
−0.292272 | + | 0.956335i | \(0.594411\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.0021 | − | 9.23883i | 0.720699 | − | 0.416096i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.79784 | − | 16.9704i | 0.438611 | − | 0.759697i | −0.558971 | − | 0.829187i | \(-0.688804\pi\) |
0.997583 | + | 0.0694898i | \(0.0221371\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.2907 | −0.949304 | −0.474652 | − | 0.880174i | \(-0.657426\pi\) | ||||
−0.474652 | + | 0.880174i | \(0.657426\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0066 | −0.445289 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.8307 | + | 37.8119i | −0.967630 | + | 1.67598i | −0.265252 | + | 0.964179i | \(0.585455\pi\) |
−0.702378 | + | 0.711804i | \(0.747878\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.29324 | + | 4.78810i | −0.365444 | + | 0.210989i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.5658 | − | 15.3378i | −1.16836 | − | 0.674554i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.20087 | 0.227854 | 0.113927 | − | 0.993489i | \(-0.463657\pi\) | ||||
0.113927 | + | 0.993489i | \(0.463657\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.0731i | 1.75227i | 0.482062 | + | 0.876137i | \(0.339888\pi\) | ||||
−0.482062 | + | 0.876137i | \(0.660112\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 53.2737 | + | 30.7576i | 2.32064 | + | 1.33982i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.02557 | − | 12.1686i | −0.305460 | − | 0.529072i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.06895 | + | 2.92656i | −0.219561 | + | 0.126763i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.91317 | + | 5.14602i | 0.385350 | + | 0.222482i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.24192 | 0.354348 | 0.177174 | − | 0.984180i | \(-0.443305\pi\) | ||||
0.177174 | + | 0.984180i | \(0.443305\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.7801 | − | 34.2601i | 0.847285 | − | 1.46754i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.53756 | − | 4.39518i | −0.108498 | − | 0.187925i | 0.806664 | − | 0.591011i | \(-0.201271\pi\) |
−0.915162 | + | 0.403086i | \(0.867938\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.53400 | − | 7.85312i | −0.193155 | − | 0.334554i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 43.4285i | − | 1.84012i | −0.391773 | − | 0.920062i | \(-0.628138\pi\) | ||
0.391773 | − | 0.920062i | \(-0.371862\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.4635i | 1.45765i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.99118 | + | 8.64498i | −0.210353 | + | 0.364343i | −0.951825 | − | 0.306641i | \(-0.900795\pi\) |
0.741472 | + | 0.670984i | \(0.234128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.1606 | + | 8.75300i | −0.637813 | + | 0.368241i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.0597 | + | 8.11739i | −0.589415 | + | 0.340299i | −0.764866 | − | 0.644189i | \(-0.777195\pi\) |
0.175451 | + | 0.984488i | \(0.443862\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.31028 | − | 10.9297i | 0.264077 | − | 0.457395i | −0.703244 | − | 0.710948i | \(-0.748266\pi\) |
0.967321 | + | 0.253553i | \(0.0815994\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 9.64936i | − | 0.402406i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 4.82678i | − | 0.200942i | −0.994940 | − | 0.100471i | \(-0.967965\pi\) | ||
0.994940 | − | 0.100471i | \(-0.0320349\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.38971 | + | 5.87115i | 0.140387 | + | 0.243158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.26032 | − | 9.11114i | −0.217117 | − | 0.376057i | 0.736809 | − | 0.676101i | \(-0.236332\pi\) |
−0.953925 | + | 0.300044i | \(0.902999\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.0944 | − | 26.1443i | 0.621955 | − | 1.07726i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.4685 | 1.21013 | 0.605063 | − | 0.796178i | \(-0.293148\pi\) | ||||
0.605063 | + | 0.796178i | \(0.293148\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.11658 | − | 4.10876i | −0.290776 | − | 0.167879i | 0.347516 | − | 0.937674i | \(-0.387025\pi\) |
−0.638292 | + | 0.769795i | \(0.720359\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.7131 | − | 18.8869i | 1.33439 | − | 0.770413i | 0.348425 | − | 0.937337i | \(-0.386717\pi\) |
0.985970 | + | 0.166924i | \(0.0533833\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.22038 | − | 9.04197i | −0.212239 | − | 0.367608i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.8497 | + | 17.8111i | 1.25215 | + | 0.722929i | 0.971536 | − | 0.236892i | \(-0.0761289\pi\) |
0.280613 | + | 0.959821i | \(0.409462\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 41.6493i | − | 1.68495i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.9319 | −0.966601 | −0.483301 | − | 0.875455i | \(-0.660562\pi\) | ||||
−0.483301 | + | 0.875455i | \(0.660562\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.98622 | + | 1.14675i | 0.0799623 | + | 0.0461663i | 0.539448 | − | 0.842019i | \(-0.318633\pi\) |
−0.459486 | + | 0.888185i | \(0.651966\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.10806 | − | 5.25854i | 0.366084 | − | 0.211359i | −0.305662 | − | 0.952140i | \(-0.598878\pi\) |
0.671746 | + | 0.740781i | \(0.265545\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.3617 | − | 26.6073i | 0.614469 | − | 1.06429i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.9914 | 0.876856 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.02836 | −0.0807477 | −0.0403739 | − | 0.999185i | \(-0.512855\pi\) | ||||
−0.0403739 | + | 0.999185i | \(0.512855\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.1899 | − | 33.2380i | 0.761530 | − | 1.31901i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.7778 | − | 6.22257i | 0.425698 | − | 0.245777i | −0.271814 | − | 0.962350i | \(-0.587624\pi\) |
0.697512 | + | 0.716573i | \(0.254290\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.3358 | − | 7.12209i | −0.486477 | − | 0.280868i | 0.236635 | − | 0.971599i | \(-0.423956\pi\) |
−0.723112 | + | 0.690731i | \(0.757289\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.3820 | −0.801299 | −0.400649 | − | 0.916231i | \(-0.631215\pi\) | ||||
−0.400649 | + | 0.916231i | \(0.631215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 23.5303i | − | 0.923644i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.55335 | + | 4.36093i | 0.295585 | + | 0.170656i | 0.640458 | − | 0.767993i | \(-0.278745\pi\) |
−0.344873 | + | 0.938650i | \(0.612078\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.11556 | + | 1.93221i | 0.0435887 | + | 0.0754978i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.7524 | − | 9.67200i | 0.652581 | − | 0.376768i | −0.136864 | − | 0.990590i | \(-0.543702\pi\) |
0.789444 | + | 0.613822i | \(0.210369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.8948 | − | 18.4145i | −1.24056 | − | 0.716240i | −0.271355 | − | 0.962479i | \(-0.587472\pi\) |
−0.969209 | + | 0.246239i | \(0.920805\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.57801 | 0.332142 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.887942 | − | 1.53796i | 0.0342786 | − | 0.0593723i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.79204 | + | 15.2283i | 0.338908 | + | 0.587006i | 0.984228 | − | 0.176907i | \(-0.0566091\pi\) |
−0.645319 | + | 0.763913i | \(0.723276\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.4146 | + | 35.3590i | 0.784595 | + | 1.35896i | 0.929241 | + | 0.369475i | \(0.120462\pi\) |
−0.144646 | + | 0.989484i | \(0.546204\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.88755i | 0.378337i | 0.981945 | + | 0.189168i | \(0.0605792\pi\) | ||||
−0.981945 | + | 0.189168i | \(0.939421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 47.3847i | − | 1.81048i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.60233 | + | 7.97148i | −0.175335 | + | 0.303689i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.9217 | − | 21.8941i | 1.44261 | − | 0.832891i | 0.444587 | − | 0.895736i | \(-0.353351\pi\) |
0.998023 | + | 0.0628444i | \(0.0200172\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −28.4459 | + | 16.4233i | −1.07902 | + | 0.622970i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.11987 | − | 8.86787i | 0.193929 | − | 0.335894i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 29.6742i | − | 1.12078i | −0.828229 | − | 0.560389i | \(-0.810651\pi\) | ||
0.828229 | − | 0.560389i | \(-0.189349\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 10.7924i | − | 0.407044i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.5269 | − | 40.7498i | −0.883572 | − | 1.53039i | −0.847342 | − | 0.531048i | \(-0.821799\pi\) |
−0.0362296 | − | 0.999343i | \(-0.511535\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.2788 | + | 24.7316i | 0.534745 | + | 0.926206i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.3293 | + | 24.8191i | −0.535885 | + | 0.928180i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.81830 | 0.0678110 | 0.0339055 | − | 0.999425i | \(-0.489205\pi\) | ||||
0.0339055 | + | 0.999425i | \(0.489205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.01029 | − | 4.62474i | −0.297495 | − | 0.171759i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.7854 | − | 12.5778i | 0.807976 | − | 0.466485i | −0.0382766 | − | 0.999267i | \(-0.512187\pi\) |
0.846252 | + | 0.532782i | \(0.178853\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.1460 | − | 52.2145i | −1.11499 | − | 1.93122i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.84543 | + | 2.22016i | 0.142034 | + | 0.0820034i | 0.569333 | − | 0.822107i | \(-0.307201\pi\) |
−0.427299 | + | 0.904110i | \(0.640535\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 20.9512i | − | 0.771747i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.9522 | 0.660381 | 0.330191 | − | 0.943914i | \(-0.392887\pi\) | ||||
0.330191 | + | 0.943914i | \(0.392887\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.3712 | + | 18.1122i | 1.15090 | + | 0.664472i | 0.949106 | − | 0.314956i | \(-0.101990\pi\) |
0.201793 | + | 0.979428i | \(0.435323\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.1829 | − | 7.03378i | 0.446345 | − | 0.257698i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.98210 | + | 10.3613i | −0.218290 | + | 0.378089i | −0.954285 | − | 0.298897i | \(-0.903381\pi\) |
0.735995 | + | 0.676986i | \(0.236714\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.2682 | 1.02878 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.4440 | −1.79707 | −0.898537 | − | 0.438898i | \(-0.855369\pi\) | ||||
−0.898537 | + | 0.438898i | \(0.855369\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.6192 | + | 25.3212i | −0.529945 | + | 0.917892i | 0.469445 | + | 0.882962i | \(0.344454\pi\) |
−0.999390 | + | 0.0349300i | \(0.988879\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.6677 | − | 15.9740i | 0.999023 | − | 0.576786i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.54689 | − | 2.62515i | −0.163965 | − | 0.0946653i | 0.415772 | − | 0.909469i | \(-0.363511\pi\) |
−0.579737 | + | 0.814804i | \(0.696845\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.3657 | −1.12815 | −0.564073 | − | 0.825725i | \(-0.690766\pi\) | ||||
−0.564073 | + | 0.825725i | \(0.690766\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 30.7930i | − | 1.10612i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.35195 | − | 2.51260i | −0.155925 | − | 0.0900233i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.6694 | + | 18.4800i | 0.381782 | + | 0.661266i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 38.2923 | − | 22.1081i | 1.36671 | − | 0.789071i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.59324 | − | 0.919855i | −0.0567927 | − | 0.0327893i | 0.471335 | − | 0.881954i | \(-0.343772\pi\) |
−0.528128 | + | 0.849165i | \(0.677106\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.41118 | 0.0856236 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.39659 | − | 11.0792i | 0.226579 | − | 0.392446i | −0.730213 | − | 0.683219i | \(-0.760579\pi\) |
0.956792 | + | 0.290773i | \(0.0939126\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.4316 | + | 63.1015i | 1.28886 | + | 2.23237i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.3495 | − | 30.0502i | −0.612250 | − | 1.06045i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 14.9206i | − | 0.524582i | −0.964989 | − | 0.262291i | \(-0.915522\pi\) | ||
0.964989 | − | 0.262291i | \(-0.0844780\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.5478i | 1.31848i | 0.751933 | + | 0.659240i | \(0.229122\pi\) | ||||
−0.751933 | + | 0.659240i | \(0.770878\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.4067 | + | 28.4172i | −0.574701 | + | 0.995411i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.6245 | + | 14.7943i | −0.896489 | + | 0.517588i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.88164 | + | 1.66371i | −0.100570 | + | 0.0580640i | −0.549441 | − | 0.835532i | \(-0.685159\pi\) |
0.448872 | + | 0.893596i | \(0.351826\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.4654 | + | 44.1073i | −0.887667 | + | 1.53748i | −0.0450407 | + | 0.998985i | \(0.514342\pi\) |
−0.842626 | + | 0.538499i | \(0.818992\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.9198i | 0.588360i | 0.955750 | + | 0.294180i | \(0.0950465\pi\) | ||||
−0.955750 | + | 0.294180i | \(0.904954\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.37475i | − | 0.186673i | −0.995635 | − | 0.0933364i | \(-0.970247\pi\) | ||
0.995635 | − | 0.0933364i | \(-0.0297532\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.6165 | + | 32.2447i | 0.644251 | + | 1.11588i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.8714 | + | 20.5618i | 0.409846 | + | 0.709874i | 0.994872 | − | 0.101140i | \(-0.0322492\pi\) |
−0.585026 | + | 0.811014i | \(0.698916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.3887 | + | 17.9938i | −0.358232 | + | 0.620477i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.62634 | −0.0559476 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.84146 | + | 5.10462i | 0.303081 | + | 0.174984i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.3810 | + | 5.99345i | −0.355437 | + | 0.205212i | −0.667077 | − | 0.744988i | \(-0.732455\pi\) |
0.311640 | + | 0.950200i | \(0.399122\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.5318 | − | 47.6864i | −0.940467 | − | 1.62894i | −0.764583 | − | 0.644526i | \(-0.777055\pi\) |
−0.175884 | − | 0.984411i | \(-0.556278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.8798 | − | 19.5605i | −1.15596 | − | 0.667395i | −0.205630 | − | 0.978630i | \(-0.565924\pi\) |
−0.950333 | + | 0.311235i | \(0.899258\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.3011i | 1.54207i | 0.636794 | + | 0.771034i | \(0.280260\pi\) | ||||
−0.636794 | + | 0.771034i | \(0.719740\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 56.2126 | 1.91129 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.1965 | + | 7.04166i | 0.413738 | + | 0.238872i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.6351 | − | 14.2231i | 0.834730 | − | 0.481931i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.02825 | − | 3.51304i | 0.0684893 | − | 0.118627i | −0.829747 | − | 0.558139i | \(-0.811515\pi\) |
0.898236 | + | 0.439512i | \(0.144849\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.3727 | −1.83186 | −0.915931 | − | 0.401336i | \(-0.868546\pi\) | ||||
−0.915931 | + | 0.401336i | \(0.868546\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.1175 | 0.777965 | 0.388982 | − | 0.921245i | \(-0.372827\pi\) | ||||
0.388982 | + | 0.921245i | \(0.372827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.7818 | + | 22.1387i | −0.429171 | + | 0.743346i | −0.996800 | − | 0.0799384i | \(-0.974528\pi\) |
0.567629 | + | 0.823285i | \(0.307861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.9674 | − | 17.8790i | 1.03628 | − | 0.598298i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46.6428 | − | 26.9292i | −1.55910 | − | 0.900144i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.3741 | 0.912979 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 16.1031i | − | 0.536472i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.1218 | − | 6.42118i | −0.369702 | − | 0.213447i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5065 | + | 32.0542i | 0.614498 | + | 1.06434i | 0.990472 | + | 0.137712i | \(0.0439748\pi\) |
−0.375974 | + | 0.926630i | \(0.622692\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.16266 | + | 1.82596i | −0.104784 | + | 0.0604969i | −0.551476 | − | 0.834191i | \(-0.685935\pi\) |
0.446692 | + | 0.894688i | \(0.352602\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37.2591 | − | 21.5116i | −1.23310 | − | 0.711929i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.7988 | −1.14791 | −0.573954 | − | 0.818888i | \(-0.694591\pi\) | ||||
−0.573954 | + | 0.818888i | \(0.694591\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.4863 | + | 25.0910i | −0.476822 | + | 0.825879i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.50420 | − | 9.53356i | −0.180977 | − | 0.313461i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.1736 | − | 43.6019i | −0.825917 | − | 1.43053i | −0.901216 | − | 0.433370i | \(-0.857324\pi\) |
0.0752987 | − | 0.997161i | \(-0.476009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 50.1368i | − | 1.63965i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.48087i | 0.211721i | 0.994381 | + | 0.105860i | \(0.0337596\pi\) | ||||
−0.994381 | + | 0.105860i | \(0.966240\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.334024 | − | 0.578547i | 0.0108889 | − | 0.0188601i | −0.860530 | − | 0.509400i | \(-0.829867\pi\) |
0.871418 | + | 0.490540i | \(0.163201\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.11679 | − | 2.37683i | 0.134061 | − | 0.0774003i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50.7461 | + | 29.2983i | −1.64903 | + | 0.952067i | −0.671569 | + | 0.740942i | \(0.734379\pi\) |
−0.977459 | + | 0.211125i | \(0.932287\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.5560 | − | 40.8002i | 0.764661 | − | 1.32443i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 48.3707i | − | 1.56688i | −0.621467 | − | 0.783441i | \(-0.713463\pi\) | ||
0.621467 | − | 0.783441i | \(-0.286537\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 19.5408i | − | 0.632326i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0665 | + | 52.0767i | 0.969887 | + | 1.67989i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.8781 | + | 39.6261i | 0.736474 | + | 1.27561i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.51390 | − | 14.7465i | 0.273788 | − | 0.474216i | −0.696040 | − | 0.718003i | \(-0.745057\pi\) |
0.969829 | + | 0.243787i | \(0.0783898\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.1302 | 0.870651 | 0.435325 | − | 0.900273i | \(-0.356633\pi\) | ||||
0.435325 | + | 0.900273i | \(0.356633\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.49838 | + | 3.17449i | 0.175909 | + | 0.101561i | 0.585369 | − | 0.810767i | \(-0.300950\pi\) |
−0.409460 | + | 0.912328i | \(0.634283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.7931 | + | 8.54080i | −0.472789 | + | 0.272965i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.98300 | − | 17.2911i | −0.318408 | − | 0.551499i | 0.661748 | − | 0.749727i | \(-0.269815\pi\) |
−0.980156 | + | 0.198227i | \(0.936482\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −64.4572 | − | 37.2144i | −2.05378 | − | 1.18575i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 27.9898i | − | 0.890024i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7761 | −0.405845 | −0.202922 | − | 0.979195i | \(-0.565044\pi\) | ||||
−0.202922 | + | 0.979195i | \(0.565044\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.90734 | − | 4.56530i | −0.250679 | − | 0.144730i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.9846 | − | 10.3834i | 0.569579 | − | 0.328847i | −0.187402 | − | 0.982283i | \(-0.560007\pi\) |
0.756981 | + | 0.653436i | \(0.226673\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))