Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,2,Mod(721,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2160.721");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.q (of order \(3\), 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: | \(17.2476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1441.2 | ||
Root | \(-1.62241 - 0.606458i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.1441 |
Dual form | 2160.2.q.k.721.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(1297\) | \(1621\) | \(2081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.714003 | + | 1.23669i | 0.269868 | + | 0.467425i | 0.968828 | − | 0.247736i | \(-0.0796866\pi\) |
−0.698960 | + | 0.715161i | \(0.746353\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.33641 | − | 2.31473i | −0.402943 | − | 0.697918i | 0.591136 | − | 0.806572i | \(-0.298679\pi\) |
−0.994080 | + | 0.108653i | \(0.965346\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.33641 | + | 4.04678i | −0.648004 | + | 1.12238i | 0.335595 | + | 0.942006i | \(0.391063\pi\) |
−0.983599 | + | 0.180370i | \(0.942271\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.67282 | −0.648255 | −0.324127 | − | 0.946013i | \(-0.605071\pi\) | ||||
−0.324127 | + | 0.946013i | \(0.605071\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.67282 | −1.07202 | −0.536010 | − | 0.844212i | \(-0.680069\pi\) | ||||
−0.536010 | + | 0.844212i | \(0.680069\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.95882 | − | 5.12483i | 0.616957 | − | 1.06860i | −0.373081 | − | 0.927799i | \(-0.621699\pi\) |
0.990038 | − | 0.140802i | \(-0.0449680\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.74482 | − | 8.21826i | −0.881090 | − | 1.52609i | −0.850130 | − | 0.526573i | \(-0.823477\pi\) |
−0.0309603 | − | 0.999521i | \(-0.509857\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.48040 | − | 6.02823i | 0.625098 | − | 1.08270i | −0.363424 | − | 0.931624i | \(-0.618392\pi\) |
0.988522 | − | 0.151078i | \(-0.0482743\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.42801 | 0.241377 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.81681 | −0.298682 | −0.149341 | − | 0.988786i | \(-0.547715\pi\) | ||||
−0.149341 | + | 0.988786i | \(0.547715\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.735581 | + | 1.27406i | −0.114879 | + | 0.198975i | −0.917731 | − | 0.397202i | \(-0.869981\pi\) |
0.802853 | + | 0.596177i | \(0.203315\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.235581 | + | 0.408039i | 0.0359258 | + | 0.0622254i | 0.883429 | − | 0.468565i | \(-0.155229\pi\) |
−0.847503 | + | 0.530790i | \(0.821895\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.47842 | − | 6.02480i | −0.507380 | − | 0.878808i | −0.999964 | − | 0.00854274i | \(-0.997281\pi\) |
0.492584 | − | 0.870265i | \(-0.336053\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.48040 | − | 4.29618i | 0.354343 | − | 0.613739i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.14399 | 0.157139 | 0.0785693 | − | 0.996909i | \(-0.474965\pi\) | ||||
0.0785693 | + | 0.996909i | \(0.474965\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.67282 | −0.360403 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.571993 | − | 0.990721i | 0.0744672 | − | 0.128981i | −0.826387 | − | 0.563102i | \(-0.809608\pi\) |
0.900854 | + | 0.434121i | \(0.142941\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.26442 | + | 2.19004i | 0.161892 | + | 0.280406i | 0.935547 | − | 0.353201i | \(-0.114907\pi\) |
−0.773655 | + | 0.633607i | \(0.781574\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.33641 | + | 4.04678i | 0.289796 | + | 0.501942i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.29523 | + | 5.70751i | −0.402577 | + | 0.697283i | −0.994036 | − | 0.109051i | \(-0.965219\pi\) |
0.591459 | + | 0.806335i | \(0.298552\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.8745 | −1.52792 | −0.763960 | − | 0.645263i | \(-0.776748\pi\) | ||||
−0.763960 | + | 0.645263i | \(0.776748\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.71203 | −0.200378 | −0.100189 | − | 0.994968i | \(-0.531945\pi\) | ||||
−0.100189 | + | 0.994968i | \(0.531945\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.90841 | − | 3.30545i | 0.217483 | − | 0.376692i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.143987 | − | 0.249392i | −0.0161998 | − | 0.0280588i | 0.857812 | − | 0.513964i | \(-0.171823\pi\) |
−0.874012 | + | 0.485905i | \(0.838490\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.14201 | + | 3.71007i | 0.235116 | + | 0.407233i | 0.959306 | − | 0.282367i | \(-0.0911196\pi\) |
−0.724190 | + | 0.689600i | \(0.757786\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.33641 | + | 2.31473i | −0.144954 | + | 0.251068i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.67282 | −0.699502 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.33641 | + | 4.04678i | −0.239711 | + | 0.415191i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.91764 | − | 6.78555i | −0.397776 | − | 0.688968i | 0.595675 | − | 0.803225i | \(-0.296885\pi\) |
−0.993451 | + | 0.114257i | \(0.963551\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.10083 | − | 3.63875i | −0.209040 | − | 0.362069i | 0.742372 | − | 0.669988i | \(-0.233701\pi\) |
−0.951413 | + | 0.307919i | \(0.900367\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.908405 | + | 1.57340i | −0.0895078 | + | 0.155032i | −0.907303 | − | 0.420477i | \(-0.861863\pi\) |
0.817795 | + | 0.575509i | \(0.195196\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.9176 | 1.15212 | 0.576061 | − | 0.817407i | \(-0.304589\pi\) | ||||
0.576061 | + | 0.817407i | \(0.304589\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.6521 | −1.59498 | −0.797491 | − | 0.603331i | \(-0.793840\pi\) | ||||
−0.797491 | + | 0.603331i | \(0.793840\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0616 | − | 17.4272i | 0.946518 | − | 1.63942i | 0.193836 | − | 0.981034i | \(-0.437907\pi\) |
0.752682 | − | 0.658384i | \(-0.228760\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.95882 | − | 5.12483i | −0.275911 | − | 0.477893i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.90841 | − | 3.30545i | −0.174943 | − | 0.303011i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.92801 | − | 3.33941i | 0.175273 | − | 0.303582i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.18714 | −0.194078 | −0.0970388 | − | 0.995281i | \(-0.530937\pi\) | ||||
−0.0970388 | + | 0.995281i | \(0.530937\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | − | 5.19615i | 0.262111 | − | 0.453990i | −0.704692 | − | 0.709514i | \(-0.748915\pi\) |
0.966803 | + | 0.255524i | \(0.0822479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.33641 | − | 5.77883i | −0.289304 | − | 0.501089i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.10083 | − | 8.83490i | −0.435793 | − | 0.754816i | 0.561567 | − | 0.827431i | \(-0.310199\pi\) |
−0.997360 | + | 0.0726153i | \(0.976865\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | − | 6.92820i | 0.339276 | − | 0.587643i | −0.645021 | − | 0.764165i | \(-0.723151\pi\) |
0.984297 | + | 0.176522i | \(0.0564848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.4896 | 1.04444 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.48963 | −0.788071 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.0381 | + | 17.3865i | −0.822351 | + | 1.42435i | 0.0815762 | + | 0.996667i | \(0.474005\pi\) |
−0.903927 | + | 0.427687i | \(0.859329\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.51960 | + | 2.63203i | 0.123663 | + | 0.214191i | 0.921210 | − | 0.389066i | \(-0.127202\pi\) |
−0.797546 | + | 0.603258i | \(0.793869\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.48040 | − | 6.02823i | −0.279552 | − | 0.484199i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.100830 | + | 0.174643i | −0.00804714 | + | 0.0139381i | −0.870021 | − | 0.493015i | \(-0.835895\pi\) |
0.861974 | + | 0.506953i | \(0.169228\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.45043 | 0.665987 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.8168 | −1.39552 | −0.697760 | − | 0.716331i | \(-0.745820\pi\) | ||||
−0.697760 | + | 0.716331i | \(0.745820\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.05042 | + | 12.2117i | −0.545578 | + | 0.944968i | 0.452993 | + | 0.891514i | \(0.350356\pi\) |
−0.998570 | + | 0.0534538i | \(0.982977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.41764 | − | 7.65158i | −0.339819 | − | 0.588583i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.18319 | + | 3.78140i | 0.165985 | + | 0.287494i | 0.937005 | − | 0.349317i | \(-0.113586\pi\) |
−0.771020 | + | 0.636811i | \(0.780253\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.714003 | − | 1.23669i | 0.0539736 | − | 0.0934850i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.1625 | −1.13330 | −0.566648 | − | 0.823960i | \(-0.691760\pi\) | ||||
−0.566648 | + | 0.823960i | \(0.691760\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.20166 | 0.237978 | 0.118989 | − | 0.992896i | \(-0.462035\pi\) | ||||
0.118989 | + | 0.992896i | \(0.462035\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.908405 | + | 1.57340i | −0.0667873 | + | 0.115679i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.57199 | + | 6.18687i | 0.261210 | + | 0.452429i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.41877 | + | 2.45738i | 0.102659 | + | 0.177810i | 0.912779 | − | 0.408453i | \(-0.133932\pi\) |
−0.810121 | + | 0.586263i | \(0.800598\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.39409 | − | 16.2710i | 0.676201 | − | 1.17121i | −0.299915 | − | 0.953966i | \(-0.596958\pi\) |
0.976116 | − | 0.217249i | \(-0.0697083\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.83528 | −0.415747 | −0.207873 | − | 0.978156i | \(-0.566654\pi\) | ||||
−0.207873 | + | 0.978156i | \(0.566654\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.0761 | −0.926943 | −0.463472 | − | 0.886112i | \(-0.653396\pi\) | ||||
−0.463472 | + | 0.886112i | \(0.653396\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.77563 | − | 11.7357i | 0.475556 | − | 0.823687i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.735581 | + | 1.27406i | 0.0513752 | + | 0.0889845i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.24482 | + | 10.8163i | 0.431963 | + | 0.748182i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.19243 | − | 7.26149i | 0.288618 | − | 0.499902i | −0.684862 | − | 0.728673i | \(-0.740137\pi\) |
0.973480 | + | 0.228771i | \(0.0734708\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.471163 | 0.0321330 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.94006 | 0.674776 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.24482 | − | 10.8163i | 0.420072 | − | 0.727586i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.58321 | + | 7.93834i | 0.306914 | + | 0.531591i | 0.977686 | − | 0.210073i | \(-0.0673702\pi\) |
−0.670772 | + | 0.741664i | \(0.734037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.33641 | + | 2.31473i | 0.0887008 | + | 0.153634i | 0.906962 | − | 0.421212i | \(-0.138395\pi\) |
−0.818261 | + | 0.574846i | \(0.805062\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.27365 | + | 2.20603i | −0.0841654 | + | 0.145779i | −0.905035 | − | 0.425336i | \(-0.860156\pi\) |
0.820870 | + | 0.571115i | \(0.193489\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.22013 | 0.407494 | 0.203747 | − | 0.979024i | \(-0.434688\pi\) | ||||
0.203747 | + | 0.979024i | \(0.434688\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.95684 | −0.453814 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.06163 | + | 7.03494i | −0.262725 | + | 0.455053i | −0.966965 | − | 0.254909i | \(-0.917954\pi\) |
0.704240 | + | 0.709962i | \(0.251288\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.1821 | + | 22.8320i | 0.849131 | + | 1.47074i | 0.881985 | + | 0.471278i | \(0.156207\pi\) |
−0.0328536 | + | 0.999460i | \(0.510460\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.48040 | − | 4.29618i | −0.158467 | − | 0.274473i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.9176 | − | 18.9099i | 0.694673 | − | 1.20321i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.549569 | −0.0346885 | −0.0173443 | − | 0.999850i | \(-0.505521\pi\) | ||||
−0.0173443 | + | 0.999850i | \(0.505521\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.8168 | −0.994394 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | + | 15.5885i | −0.561405 | + | 0.972381i | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.29721 | − | 2.24683i | −0.0806046 | − | 0.139611i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.94761 | − | 10.3016i | −0.366745 | − | 0.635221i | 0.622309 | − | 0.782771i | \(-0.286195\pi\) |
−0.989055 | + | 0.147550i | \(0.952861\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.571993 | − | 0.990721i | 0.0351373 | − | 0.0608595i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.5737 | −1.74217 | −0.871084 | − | 0.491134i | \(-0.836583\pi\) | ||||
−0.871084 | + | 0.491134i | \(0.836583\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.3641 | 1.41927 | 0.709635 | − | 0.704570i | \(-0.248860\pi\) | ||||
0.709635 | + | 0.704570i | \(0.248860\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.33641 | + | 2.31473i | −0.0805887 | + | 0.139584i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.53807 | + | 13.0563i | 0.452919 | + | 0.784479i | 0.998566 | − | 0.0535366i | \(-0.0170494\pi\) |
−0.545647 | + | 0.838015i | \(0.683716\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.32605 | + | 5.76088i | 0.198415 | + | 0.343665i | 0.948015 | − | 0.318226i | \(-0.103087\pi\) |
−0.749599 | + | 0.661892i | \(0.769754\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.4485 | − | 23.2934i | 0.799428 | − | 1.38465i | −0.120562 | − | 0.992706i | \(-0.538470\pi\) |
0.919989 | − | 0.391943i | \(-0.128197\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.10083 | −0.124008 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.85601 | −0.579765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.19243 | − | 10.7256i | 0.361765 | − | 0.626596i | −0.626486 | − | 0.779433i | \(-0.715507\pi\) |
0.988251 | + | 0.152837i | \(0.0488408\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.571993 | − | 0.990721i | −0.0333027 | − | 0.0576820i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.8260 | + | 23.9474i | 0.799581 | + | 1.38491i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.336412 | + | 0.582682i | −0.0193905 | + | 0.0335853i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.52884 | 0.144801 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.49359 | 0.142317 | 0.0711583 | − | 0.997465i | \(-0.477330\pi\) | ||||
0.0711583 | + | 0.997465i | \(0.477330\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.1101 | − | 20.9752i | 0.686699 | − | 1.18940i | −0.286201 | − | 0.958170i | \(-0.592392\pi\) |
0.972900 | − | 0.231228i | \(-0.0742742\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.5420 | + | 30.3837i | 0.991534 | + | 1.71739i | 0.608219 | + | 0.793770i | \(0.291884\pi\) |
0.383315 | + | 0.923618i | \(0.374782\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.23558 | − | 9.06829i | −0.294060 | − | 0.509326i | 0.680706 | − | 0.732557i | \(-0.261673\pi\) |
−0.974766 | + | 0.223231i | \(0.928340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.6821 | + | 21.9660i | −0.710059 | + | 1.22986i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.4896 | 0.694942 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.67282 | 0.259202 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.96721 | − | 8.60346i | 0.273851 | − | 0.474324i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.38880 | + | 14.5298i | 0.461090 | + | 0.798632i | 0.999016 | − | 0.0443606i | \(-0.0141251\pi\) |
−0.537925 | + | 0.842993i | \(0.680792\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.29523 | + | 5.70751i | 0.180038 | + | 0.311835i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.5905 | − | 23.5394i | 0.740320 | − | 1.28227i | −0.212030 | − | 0.977263i | \(-0.568007\pi\) |
0.952350 | − | 0.305008i | \(-0.0986592\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.6050 | −1.00752 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0801 | 0.922239 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.7829 | − | 20.4086i | 0.632539 | − | 1.09559i | −0.354492 | − | 0.935059i | \(-0.615346\pi\) |
0.987031 | − | 0.160530i | \(-0.0513204\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.35601 | + | 9.27689i | 0.286701 | + | 0.496580i | 0.973020 | − | 0.230720i | \(-0.0741081\pi\) |
−0.686319 | + | 0.727300i | \(0.740775\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.6336 | + | 23.6141i | 0.725644 | + | 1.25685i | 0.958708 | + | 0.284392i | \(0.0917916\pi\) |
−0.233064 | + | 0.972461i | \(0.574875\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.43724 | + | 11.1496i | −0.341653 | + | 0.591761i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.6807 | −0.563707 | −0.281854 | − | 0.959457i | \(-0.590949\pi\) | ||||
−0.281854 | + | 0.959457i | \(0.590949\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.83528 | 0.149225 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.856013 | + | 1.48266i | −0.0448058 | + | 0.0776059i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.23558 | − | 7.33624i | −0.221096 | − | 0.382949i | 0.734045 | − | 0.679100i | \(-0.237630\pi\) |
−0.955141 | + | 0.296152i | \(0.904297\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.816810 | + | 1.41476i | 0.0424067 | + | 0.0734505i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.06163 | + | 8.76700i | −0.262081 | + | 0.453938i | −0.966795 | − | 0.255554i | \(-0.917742\pi\) |
0.704714 | + | 0.709492i | \(0.251075\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 44.3434 | 2.28380 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.9216 | −0.612371 | −0.306186 | − | 0.951972i | \(-0.599053\pi\) | ||||
−0.306186 | + | 0.951972i | \(0.599053\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.90841 | + | 8.50161i | −0.250808 | + | 0.434412i | −0.963748 | − | 0.266813i | \(-0.914030\pi\) |
0.712941 | + | 0.701224i | \(0.247363\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.90841 | − | 3.30545i | −0.0972613 | − | 0.168462i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.61007 | + | 7.98487i | 0.233740 | + | 0.404849i | 0.958906 | − | 0.283725i | \(-0.0915703\pi\) |
−0.725166 | + | 0.688574i | \(0.758237\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.90841 | + | 13.6978i | −0.399945 | + | 0.692725i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.287973 | −0.0144895 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.9793 | −1.15330 | −0.576648 | − | 0.816993i | \(-0.695640\pi\) | ||||
−0.576648 | + | 0.816993i | \(0.695640\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.53279 | + | 9.58307i | −0.276294 | + | 0.478556i | −0.970461 | − | 0.241259i | \(-0.922440\pi\) |
0.694167 | + | 0.719814i | \(0.255773\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.2633 | + | 28.1688i | 0.810132 | + | 1.40319i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.42801 | + | 4.20543i | 0.120352 | + | 0.208455i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.81681 | − | 15.2712i | 0.435963 | − | 0.755110i | −0.561411 | − | 0.827537i | \(-0.689741\pi\) |
0.997374 | + | 0.0724270i | \(0.0230744\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.63362 | 0.0803852 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.28402 | 0.210294 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.5173 | + | 32.0730i | −0.904631 | + | 1.56687i | −0.0832199 | + | 0.996531i | \(0.526520\pi\) |
−0.821411 | + | 0.570336i | \(0.806813\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.52884 | − | 4.38007i | −0.123248 | − | 0.213472i | 0.797799 | − | 0.602924i | \(-0.205998\pi\) |
−0.921047 | + | 0.389452i | \(0.872664\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.33641 | + | 2.31473i | 0.0648255 | + | 0.112281i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.80560 | + | 3.12739i | −0.0873790 | + | 0.151345i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.23030 | −0.251935 | −0.125967 | − | 0.992034i | \(-0.540203\pi\) | ||||
−0.125967 | + | 0.992034i | \(0.540203\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.3434 | 1.65044 | 0.825219 | − | 0.564813i | \(-0.191052\pi\) | ||||
0.825219 | + | 0.564813i | \(0.191052\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.8260 | + | 23.9474i | −0.661389 | + | 1.14556i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.77365 | − | 16.9285i | −0.466471 | − | 0.807952i | 0.532796 | − | 0.846244i | \(-0.321141\pi\) |
−0.999267 | + | 0.0382924i | \(0.987808\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.25208 | − | 9.09686i | −0.249534 | − | 0.432205i | 0.713863 | − | 0.700286i | \(-0.246944\pi\) |
−0.963396 | + | 0.268081i | \(0.913611\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.50000 | − | 2.59808i | 0.0711068 | − | 0.123161i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.8560 | −1.07864 | −0.539321 | − | 0.842100i | \(-0.681319\pi\) | ||||
−0.539321 | + | 0.842100i | \(0.681319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.93216 | 0.185158 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.33641 | + | 5.77883i | −0.156413 | + | 0.270916i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.01319 | + | 12.1472i | 0.328063 | + | 0.568222i | 0.982127 | − | 0.188217i | \(-0.0602708\pi\) |
−0.654064 | + | 0.756439i | \(0.726937\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0513 | − | 20.8734i | −0.561283 | − | 0.972171i | −0.997385 | − | 0.0722736i | \(-0.976975\pi\) |
0.436102 | − | 0.899897i | \(-0.356359\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.9700 | + | 29.3930i | −0.788664 | + | 1.36601i | 0.138121 | + | 0.990415i | \(0.455894\pi\) |
−0.926785 | + | 0.375591i | \(0.877440\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.3720 | −1.26663 | −0.633313 | − | 0.773896i | \(-0.718305\pi\) | ||||
−0.633313 | + | 0.773896i | \(0.718305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.41123 | −0.434570 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.629668 | − | 1.09062i | 0.0289521 | − | 0.0501466i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.33641 | + | 4.04678i | 0.107202 | + | 0.185679i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.61515 | − | 4.52957i | −0.119489 | − | 0.206961i | 0.800076 | − | 0.599898i | \(-0.204792\pi\) |
−0.919565 | + | 0.392937i | \(0.871459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.24482 | − | 7.35224i | 0.193547 | − | 0.335233i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.83528 | −0.355782 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.0185 | 1.08838 | 0.544190 | − | 0.838962i | \(-0.316837\pi\) | ||||
0.544190 | + | 0.838962i | \(0.316837\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.38880 | + | 12.7978i | −0.333452 | + | 0.577556i | −0.983186 | − | 0.182606i | \(-0.941547\pi\) |
0.649734 | + | 0.760161i | \(0.274880\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.6821 | + | 21.9660i | 0.571171 | + | 0.989298i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.19243 | − | 15.9217i | −0.412337 | − | 0.714188i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.4280 | − | 21.5259i | 0.556354 | − | 0.963633i | −0.441443 | − | 0.897289i | \(-0.645533\pi\) |
0.997797 | − | 0.0663440i | \(-0.0211335\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.9154 | 1.73515 | 0.867576 | − | 0.497305i | \(-0.165677\pi\) | ||||
0.867576 | + | 0.497305i | \(0.165677\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.20166 | −0.186971 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.01037 | − | 1.75001i | 0.0447837 | − | 0.0775676i | −0.842765 | − | 0.538282i | \(-0.819073\pi\) |
0.887548 | + | 0.460715i | \(0.152407\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.22239 | − | 2.11725i | −0.0540755 | − | 0.0936615i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.908405 | + | 1.57340i | 0.0400291 | + | 0.0693325i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.29721 | + | 16.1032i | −0.408891 | + | 0.708220i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.0290 | 1.00892 | 0.504460 | − | 0.863435i | \(-0.331692\pi\) | ||||
0.504460 | + | 0.863435i | \(0.331692\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.1170 | 1.79792 | 0.898961 | − | 0.438028i | \(-0.144323\pi\) | ||||
0.898961 | + | 0.438028i | \(0.144323\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.30249 | + | 16.1124i | −0.405223 | + | 0.701867i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.00924 | − | 10.4083i | −0.261271 | − | 0.452535i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.43724 | − | 5.95348i | −0.148883 | − | 0.257874i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.95882 | − | 10.3210i | 0.257622 | − | 0.446215i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.2593 | −0.571120 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.20957 | 0.223977 | 0.111988 | − | 0.993710i | \(-0.464278\pi\) | ||||
0.111988 | + | 0.993710i | \(0.464278\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.32605 | + | 14.4211i | −0.356649 | + | 0.617734i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0204 | + | 34.6764i | 0.856013 | + | 1.48266i | 0.875702 | + | 0.482851i | \(0.160399\pi\) |
−0.0196900 | + | 0.999806i | \(0.506268\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.1717 | + | 38.4025i | 0.944546 | + | 1.63600i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.205614 | − | 0.356133i | 0.00874359 | − | 0.0151443i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.4033 | 0.610288 | 0.305144 | − | 0.952306i | \(-0.401295\pi\) | ||||
0.305144 | + | 0.952306i | \(0.401295\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.20166 | −0.0931203 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.6840 | + | 25.4335i | −0.618858 | + | 1.07189i | 0.370836 | + | 0.928698i | \(0.379071\pi\) |
−0.989694 | + | 0.143196i | \(0.954262\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0616 | − | 17.4272i | −0.423296 | − | 0.733170i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.4033 | + | 40.5357i | 0.981118 | + | 1.69935i | 0.658056 | + | 0.752969i | \(0.271379\pi\) |
0.323062 | + | 0.946378i | \(0.395288\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0000 | − | 17.3205i | 0.418487 | − | 0.724841i | −0.577301 | − | 0.816532i | \(-0.695894\pi\) |
0.995788 | + | 0.0916910i | \(0.0292272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.91764 | −0.246783 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.2386 | 1.17559 | 0.587794 | − | 0.809010i | \(-0.299996\pi\) | ||||
0.587794 | + | 0.809010i | \(0.299996\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.05880 | + | 5.29801i | −0.126901 | + | 0.219798i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.52884 | − | 2.64802i | −0.0633180 | − | 0.109670i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.04118 | − | 15.6598i | −0.373169 | − | 0.646348i | 0.616882 | − | 0.787056i | \(-0.288396\pi\) |
−0.990051 | + | 0.140707i | \(0.955062\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.2633 | + | 28.1688i | −0.670117 | + | 1.16068i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.73840 | 0.317778 | 0.158889 | − | 0.987296i | \(-0.449209\pi\) | ||||
0.158889 | + | 0.987296i | \(0.449209\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.81681 | −0.156474 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.9608 | − | 24.1808i | 0.570423 | − | 0.988001i | −0.426100 | − | 0.904676i | \(-0.640113\pi\) |
0.996522 | − | 0.0833249i | \(-0.0265539\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.2201 | − | 33.2902i | −0.784006 | − | 1.35794i | −0.929591 | − | 0.368592i | \(-0.879840\pi\) |
0.145586 | − | 0.989346i | \(-0.453493\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.92801 | − | 3.33941i | −0.0783846 | − | 0.135766i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.319917 | + | 0.554113i | −0.0129850 | + | 0.0224907i | −0.872445 | − | 0.488712i | \(-0.837467\pi\) |
0.859460 | + | 0.511203i | \(0.170800\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.5081 | 1.31514 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.7467 | 1.72652 | 0.863262 | − | 0.504757i | \(-0.168418\pi\) | ||||
0.863262 | + | 0.504757i | \(0.168418\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.5513 | − | 18.2753i | 0.424778 | − | 0.735737i | −0.571622 | − | 0.820517i | \(-0.693686\pi\) |
0.996400 | + | 0.0847805i | \(0.0270189\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.82605 | − | 11.8231i | −0.274362 | − | 0.475209i | 0.695612 | − | 0.718418i | \(-0.255133\pi\) |
−0.969974 | + | 0.243209i | \(0.921800\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.14201 | + | 3.71007i | 0.0858178 | + | 0.148641i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.85601 | 0.193622 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.2593 | −1.32403 | −0.662017 | − | 0.749489i | \(-0.730299\pi\) | ||||
−0.662017 | + | 0.749489i | \(0.730299\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.09357 | + | 1.89412i | −0.0433971 | + | 0.0751659i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.5905 | + | 20.0753i | 0.459231 | + | 0.795411i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.1429 | + | 22.7641i | 0.519112 | + | 0.899128i | 0.999753 | + | 0.0222106i | \(0.00707044\pi\) |
−0.480642 | + | 0.876917i | \(0.659596\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.2913 | − | 17.8250i | 0.405848 | − | 0.702950i | −0.588571 | − | 0.808445i | \(-0.700309\pi\) |
0.994420 | + | 0.105495i | \(0.0336427\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.2527 | 0.914159 | 0.457079 | − | 0.889426i | \(-0.348896\pi\) | ||||
0.457079 | + | 0.889426i | \(0.348896\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.05767 | −0.120024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.37957 | − | 16.2459i | 0.367051 | − | 0.635751i | −0.622052 | − | 0.782976i | \(-0.713701\pi\) |
0.989103 | + | 0.147225i | \(0.0470342\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.00000 | − | 5.19615i | −0.117220 | − | 0.203030i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.140034 | + | 0.242545i | 0.00545494 | + | 0.00944823i | 0.868740 | − | 0.495268i | \(-0.164930\pi\) |
−0.863285 | + | 0.504717i | \(0.831597\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.8930 | − | 34.4556i | 0.773746 | − | 1.34017i | −0.161750 | − | 0.986832i | \(-0.551714\pi\) |
0.935496 | − | 0.353336i | \(-0.114953\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.67282 | −0.258761 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −56.1562 | −2.17438 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.37957 | − | 5.85358i | 0.130467 | − | 0.225975i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.7644 | − | 29.0368i | −0.646221 | − | 1.11929i | −0.984018 | − | 0.178068i | \(-0.943015\pi\) |
0.337797 | − | 0.941219i | \(-0.390318\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.7437 | + | 23.8048i | 0.528213 | + | 0.914891i | 0.999459 | + | 0.0328897i | \(0.0104710\pi\) |
−0.471246 | + | 0.882002i | \(0.656196\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.59442 | − | 9.68981i | 0.214694 | − | 0.371861i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.5865 | −1.32342 | −0.661708 | − | 0.749762i | \(-0.730168\pi\) | ||||
−0.661708 | + | 0.749762i | \(0.730168\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.2017 | −0.389785 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.67282 | + | 4.62947i | −0.101826 | + | 0.176369i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.3641 | + | 35.2717i | 0.774688 | + | 1.34180i | 0.934970 | + | 0.354727i | \(0.115426\pi\) |
−0.160282 | + | 0.987071i | \(0.551240\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.00000 | − | 6.92820i | −0.151729 | − | 0.262802i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.96608 | − | 3.40535i | 0.0744706 | − | 0.128987i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.4712 | 0.735416 | 0.367708 | − | 0.929941i | \(-0.380143\pi\) | ||||
0.367708 | + | 0.929941i | \(0.380143\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.48963 | 0.320193 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.00000 | − | 5.19615i | 0.112827 | − | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.54316 | − | 13.0651i | −0.283289 | − | 0.490671i | 0.688904 | − | 0.724853i | \(-0.258092\pi\) |
−0.972193 | + | 0.234182i | \(0.924759\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.5957 | − | 35.6729i | −0.771317 | − | 1.33596i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.24482 | − | 10.8163i | 0.233543 | − | 0.404508i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.43196 | −0.127990 | −0.0639952 | − | 0.997950i | \(-0.520384\pi\) | ||||
−0.0639952 | + | 0.997950i | \(0.520384\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.59442 | −0.0966211 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.74482 | + | 8.21826i | −0.176218 | + | 0.305219i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.8857 | − | 30.9789i | −0.663344 | − | 1.14895i | −0.979732 | − | 0.200315i | \(-0.935803\pi\) |
0.316388 | − | 0.948630i | \(-0.397530\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.629668 | − | 1.09062i | −0.0232891 | − | 0.0403379i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0000 | − | 19.0526i | 0.406294 | − | 0.703722i | −0.588177 | − | 0.808732i | \(-0.700154\pi\) |
0.994471 | + | 0.105010i | \(0.0334875\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.6151 | 0.648862 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.08631 | −0.223889 | −0.111944 | − | 0.993714i | \(-0.535708\pi\) | ||||
−0.111944 | + | 0.993714i | \(0.535708\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.7509 | − | 22.0853i | 0.467787 | − | 0.810231i | −0.531536 | − | 0.847036i | \(-0.678385\pi\) |
0.999322 | + | 0.0368054i | \(0.0117182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0381 | + | 17.3865i | 0.367767 | + | 0.636990i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.50924 | + | 14.7384i | 0.310921 | + | 0.538530i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.19638 | + | 15.9286i | −0.335581 | + | 0.581243i | −0.983596 | − | 0.180384i | \(-0.942266\pi\) |
0.648016 | + | 0.761627i | \(0.275599\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.03920 | 0.110608 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.8986 | −1.52283 | −0.761415 | − | 0.648264i | \(-0.775495\pi\) | ||||
−0.761415 | + | 0.648264i | \(0.775495\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.98568 | + | 6.90340i | −0.144481 | + | 0.250248i | −0.929179 | − | 0.369630i | \(-0.879485\pi\) |
0.784698 | + | 0.619878i | \(0.212818\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.8896 | − | 20.5935i | −0.430434 | − | 0.745534i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.67282 | + | 4.62947i | 0.0965101 | + | 0.167160i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.01432 | + | 5.22095i | −0.108699 | + | 0.188272i | −0.915244 | − | 0.402901i | \(-0.868002\pi\) |
0.806544 | + | 0.591174i | \(0.201335\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.4033 | −1.59708 | −0.798538 | − | 0.601944i | \(-0.794393\pi\) | ||||
−0.798538 | + | 0.601944i | \(0.794393\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.96080 | −0.250039 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.43724 | − | 5.95348i | 0.123152 | − | 0.213305i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.2056 | + | 29.8010i | 0.615665 | + | 1.06636i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.100830 | + | 0.174643i | 0.00359879 | + | 0.00623329i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.41877 | − | 14.5817i | 0.300097 | − | 0.519783i | −0.676061 | − | 0.736846i | \(-0.736314\pi\) |
0.976158 | + | 0.217063i | \(0.0696477\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.7361 | 1.02174 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.8168 | −0.419627 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.6860 | + | 28.9010i | −0.591049 | + | 1.02373i | 0.403043 | + | 0.915181i | \(0.367953\pi\) |
−0.994091 | + | 0.108545i | \(0.965381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.29721 | + | 16.1032i | 0.328912 | + | 0.569692i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.28797 | + | 3.96289i | 0.0807408 | + | 0.139847i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.22522 | − | 7.31829i | 0.148919 | − | 0.257936i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.1809 | −1.02595 | −0.512973 | − | 0.858404i | \(-0.671456\pi\) | ||||
−0.512973 | + | 0.858404i | \(0.671456\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.5552 | 0.546217 | 0.273109 | − | 0.961983i | \(-0.411948\pi\) | ||||
0.273109 | + | 0.961983i | \(0.411948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.90841 | + | 15.4298i | −0.312048 | + | 0.540483i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.10083 | − | 1.90669i | −0.0385132 | − | 0.0667068i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.8588 | − | 20.5401i | −0.413876 | − | 0.716855i | 0.581434 | − | 0.813594i | \(-0.302492\pi\) |
−0.995310 | + | 0.0967393i | \(0.969159\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.68404 | − | 16.7732i | 0.337564 | − | 0.584678i | −0.646410 | − | 0.762990i | \(-0.723730\pi\) |
0.983974 | + | 0.178312i | \(0.0570636\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.2241 | 1.81601 | 0.908005 | − | 0.418960i | \(-0.137605\pi\) | ||||
0.908005 | + | 0.418960i | \(0.137605\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.6442 | −0.925391 | −0.462695 | − | 0.886517i | \(-0.653118\pi\) | ||||
−0.462695 | + | 0.886517i | \(0.653118\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.62967 | + | 11.4829i | −0.229704 | + | 0.397860i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.05042 | + | 12.2117i | 0.243990 | + | 0.422603i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.5196 | + | 21.6846i | 0.432225 | + | 0.748635i | 0.997065 | − | 0.0765655i | \(-0.0243954\pi\) |
−0.564840 | + | 0.825201i | \(0.691062\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.5266 | + | 52.8736i | −1.05264 | + | 1.82323i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.83528 | −0.303943 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.50641 | 0.189203 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.37562 | + | 9.31084i | −0.184274 | + | 0.319171i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.43724 | + | 9.41758i | 0.186168 | + | 0.322452i | 0.943969 | − | 0.330033i | \(-0.107060\pi\) |
−0.757802 | + | 0.652485i | \(0.773727\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.29721 | − | 16.1032i | −0.317587 | − | 0.550076i | 0.662397 | − | 0.749153i | \(-0.269539\pi\) |
−0.979984 | + | 0.199077i | \(0.936206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.33246 | + | 4.03994i | −0.0795825 | + | 0.137841i | −0.903070 | − | 0.429494i | \(-0.858692\pi\) |
0.823487 | + | 0.567335i | \(0.192025\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.0594 | −0.955152 | −0.477576 | − | 0.878590i | \(-0.658484\pi\) | ||||
−0.477576 | + | 0.878590i | \(0.658484\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.36638 | 0.148461 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.384851 | + | 0.666581i | −0.0130552 | + | 0.0226122i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.3980 | − | 26.6702i | −0.521743 | − | 0.903685i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.714003 | − | 1.23669i | −0.0241377 | − | 0.0418078i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.3342 | + | 30.0236i | −0.585333 | + | 1.01383i | 0.409501 | + | 0.912310i | \(0.365703\pi\) |
−0.994834 | + | 0.101516i | \(0.967631\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.29854 | 0.178512 | 0.0892561 | − | 0.996009i | \(-0.471551\pi\) | ||||
0.0892561 | + | 0.996009i | \(0.471551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.3025 | 0.346706 | 0.173353 | − | 0.984860i | \(-0.444540\pi\) | ||||
0.173353 | + | 0.984860i | \(0.444540\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.7252 | + | 35.8971i | −0.695885 | + | 1.20531i | 0.273997 | + | 0.961731i | \(0.411654\pi\) |
−0.969882 | + | 0.243577i | \(0.921679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.56163 | − | 2.70482i | −0.0523753 | − | 0.0907167i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.2541 | + | 28.1528i | 0.543921 | + | 0.942099i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.58123 | + | 13.1311i | −0.253413 | + | 0.438923i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −66.0554 | −2.20307 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.05767 | −0.101866 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.60083 | − | 2.77272i | 0.0532134 | − | 0.0921683i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.39606 | − | 14.5424i | −0.278787 | − | 0.482873i | 0.692297 | − | 0.721613i | \(-0.256599\pi\) |
−0.971083 | + | 0.238740i | \(0.923266\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.6768 | − | 32.3491i | −0.618789 | − | 1.07177i | −0.989707 | − | 0.143109i | \(-0.954290\pi\) |
0.370918 | − | 0.928666i | \(-0.379043\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.72522 | − | 9.91636i | 0.189477 | − | 0.328184i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.56804 | 0.282942 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.1316 | −1.22486 | −0.612429 | − | 0.790526i | \(-0.709807\pi\) | ||||
−0.612429 | + | 0.790526i | \(0.709807\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.0801 | − | 52.1003i | 0.990098 | − | 1.71490i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.908405 | + | 1.57340i | 0.0298682 | + | 0.0517332i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.9977 | − | 41.5653i | −0.787340 | − | 1.36371i | −0.927591 | − | 0.373597i | \(-0.878124\pi\) |
0.140251 | − | 0.990116i | \(-0.455209\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.5905 | + | 20.0753i | −0.379862 | + | 0.657941i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.14399 | 0.233633 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0079 | 0.718967 | 0.359483 | − | 0.933151i | \(-0.382953\pi\) | ||||
0.359483 | + | 0.933151i | \(0.382953\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.2921 | − | 35.1470i | 0.661504 | − | 1.14576i | −0.318716 | − | 0.947850i | \(-0.603252\pi\) |
0.980220 | − | 0.197909i | \(-0.0634150\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.35291 | + | 7.53946i | 0.141750 | + | 0.245518i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.1160 | − | 26.1817i | −0.491204 | − | 0.850790i | 0.508745 | − | 0.860917i | \(-0.330110\pi\) |
−0.999949 | + | 0.0101273i | \(0.996776\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | − | 6.92820i | 0.129845 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.50811 | −0.0812455 | −0.0406227 | − | 0.999175i | \(-0.512934\pi\) | ||||
−0.0406227 | + | 0.999175i | \(0.512934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.83754 | 0.0918207 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.28402 | − | 12.6163i | 0.235213 | − | 0.407401i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.72635 | − | 15.1145i | −0.281495 | − | 0.487564i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.39409 | − | 16.2710i | −0.302406 | − | 0.523783i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.8765 | + | 18.8386i | −0.349763 | + | 0.605808i | −0.986207 | − | 0.165515i | \(-0.947071\pi\) |
0.636444 | + | 0.771323i | \(0.280405\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.7512 | 0.730122 | 0.365061 | − | 0.930984i | \(-0.381048\pi\) | ||||
0.365061 | + | 0.930984i | \(0.381048\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.4241 | 0.366238 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.6389 | − | 34.0156i | 0.628304 | − | 1.08825i | −0.359588 | − | 0.933111i | \(-0.617083\pi\) |
0.987892 | − | 0.155143i | \(-0.0495840\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.00924 | − | 6.94420i | −0.128136 | − | 0.221938i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.8949 | − | 29.2629i | −0.538865 | − | 0.933341i | −0.998966 | − | 0.0454743i | \(-0.985520\pi\) |
0.460101 | − | 0.887867i | \(-0.347813\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.91764 | + | 5.05350i | −0.0929638 | + | 0.161018i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.78817 | 0.0886587 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.7983 | 0.755979 | 0.377990 | − | 0.925810i | \(-0.376616\pi\) | ||||
0.377990 | + | 0.925810i | \(0.376616\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.53807 | + | 11.3243i | −0.207271 | + | 0.359004i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.8392 | − | 44.7549i | −0.818337 | − | 1.41740i | −0.906907 | − | 0.421331i | \(-0.861563\pi\) |
0.0885702 | − | 0.996070i | \(-0.471770\pi\) | |||||||
\(998\) | 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 \(a_p\))