Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [841,2,Mod(840,841)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(841, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("841.840");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 841 = 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 841.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.71541880999\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 29) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 840.4 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 841.840 |
Dual form | 841.2.b.a.840.1 |
$q$-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 \(\left(\mathbb{Z}/841\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.41421i | 1.70711i | 0.521005 | + | 0.853553i | \(0.325557\pi\) | ||||
−0.521005 | + | 0.853553i | \(0.674443\pi\) | |||||||
\(3\) | − 2.41421i | − 1.39385i | −0.717146 | − | 0.696923i | \(-0.754552\pi\) | ||||
0.717146 | − | 0.696923i | \(-0.245448\pi\) | |||||||
\(4\) | −3.82843 | −1.91421 | ||||||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | 5.82843 | 2.37945 | ||||||||
\(7\) | −2.82843 | −1.06904 | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||||
−0.534522 | + | 0.845154i | \(0.679509\pi\) | |||||||
\(8\) | − 4.41421i | − 1.56066i | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 2.41421i | 0.763441i | ||||||||
\(11\) | 0.414214i | 0.124890i | 0.998048 | + | 0.0624450i | \(0.0198898\pi\) | ||||
−0.998048 | + | 0.0624450i | \(0.980110\pi\) | |||||||
\(12\) | 9.24264i | 2.66812i | ||||||||
\(13\) | 3.82843 | 1.06181 | 0.530907 | − | 0.847430i | \(-0.321851\pi\) | ||||
0.530907 | + | 0.847430i | \(0.321851\pi\) | |||||||
\(14\) | − 6.82843i | − 1.82497i | ||||||||
\(15\) | − 2.41421i | − 0.623347i | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | − 0.828427i | − 0.200923i | −0.994941 | − | 0.100462i | \(-0.967968\pi\) | ||||
0.994941 | − | 0.100462i | \(-0.0320319\pi\) | |||||||
\(18\) | − 6.82843i | − 1.60948i | ||||||||
\(19\) | − 6.00000i | − 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | −3.82843 | −0.856062 | ||||||||
\(21\) | 6.82843i | 1.49008i | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 3.65685 | 0.762507 | 0.381253 | − | 0.924471i | \(-0.375493\pi\) | ||||
0.381253 | + | 0.924471i | \(0.375493\pi\) | |||||||
\(24\) | −10.6569 | −2.17532 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 9.24264i | 1.81263i | ||||||||
\(27\) | − 0.414214i | − 0.0797154i | ||||||||
\(28\) | 10.8284 | 2.04638 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 5.82843 | 1.06412 | ||||||||
\(31\) | − 10.0711i | − 1.80882i | −0.426667 | − | 0.904409i | \(-0.640313\pi\) | ||||
0.426667 | − | 0.904409i | \(-0.359687\pi\) | |||||||
\(32\) | − 1.58579i | − 0.280330i | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | −2.82843 | −0.478091 | ||||||||
\(36\) | 10.8284 | 1.80474 | ||||||||
\(37\) | − 4.00000i | − 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | 14.4853 | 2.34982 | ||||||||
\(39\) | − 9.24264i | − 1.48001i | ||||||||
\(40\) | − 4.41421i | − 0.697948i | ||||||||
\(41\) | − 4.48528i | − 0.700483i | −0.936659 | − | 0.350242i | \(-0.886099\pi\) | ||||
0.936659 | − | 0.350242i | \(-0.113901\pi\) | |||||||
\(42\) | −16.4853 | −2.54373 | ||||||||
\(43\) | − 3.58579i | − 0.546827i | −0.961897 | − | 0.273414i | \(-0.911847\pi\) | ||||
0.961897 | − | 0.273414i | \(-0.0881528\pi\) | |||||||
\(44\) | − 1.58579i | − 0.239066i | ||||||||
\(45\) | −2.82843 | −0.421637 | ||||||||
\(46\) | 8.82843i | 1.30168i | ||||||||
\(47\) | − 3.24264i | − 0.472988i | −0.971633 | − | 0.236494i | \(-0.924002\pi\) | ||||
0.971633 | − | 0.236494i | \(-0.0759983\pi\) | |||||||
\(48\) | − 7.24264i | − 1.04539i | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | − 9.65685i | − 1.36569i | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | −14.6569 | −2.03254 | ||||||||
\(53\) | 9.48528 | 1.30290 | 0.651452 | − | 0.758690i | \(-0.274160\pi\) | ||||
0.651452 | + | 0.758690i | \(0.274160\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.414214i | 0.0558525i | ||||||||
\(56\) | 12.4853i | 1.66842i | ||||||||
\(57\) | −14.4853 | −1.91862 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.65685 | −0.476082 | −0.238041 | − | 0.971255i | \(-0.576505\pi\) | ||||
−0.238041 | + | 0.971255i | \(0.576505\pi\) | |||||||
\(60\) | 9.24264i | 1.19322i | ||||||||
\(61\) | 4.82843i | 0.618217i | 0.951027 | + | 0.309108i | \(0.100031\pi\) | ||||
−0.951027 | + | 0.309108i | \(0.899969\pi\) | |||||||
\(62\) | 24.3137 | 3.08784 | ||||||||
\(63\) | 8.00000 | 1.00791 | ||||||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | 3.82843 | 0.474858 | ||||||||
\(66\) | 2.41421i | 0.297169i | ||||||||
\(67\) | −5.65685 | −0.691095 | −0.345547 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345547 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(68\) | 3.17157i | 0.384610i | ||||||||
\(69\) | − 8.82843i | − 1.06282i | ||||||||
\(70\) | − 6.82843i | − 0.816153i | ||||||||
\(71\) | 8.82843 | 1.04774 | 0.523871 | − | 0.851798i | \(-0.324487\pi\) | ||||
0.523871 | + | 0.851798i | \(0.324487\pi\) | |||||||
\(72\) | 12.4853i | 1.47140i | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | 9.65685 | 1.12259 | ||||||||
\(75\) | 9.65685i | 1.11508i | ||||||||
\(76\) | 22.9706i | 2.63490i | ||||||||
\(77\) | − 1.17157i | − 0.133513i | ||||||||
\(78\) | 22.3137 | 2.52653 | ||||||||
\(79\) | 2.41421i | 0.271620i | 0.990735 | + | 0.135810i | \(0.0433637\pi\) | ||||
−0.990735 | + | 0.135810i | \(0.956636\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 10.8284 | 1.19580 | ||||||||
\(83\) | 7.65685 | 0.840449 | 0.420224 | − | 0.907420i | \(-0.361951\pi\) | ||||
0.420224 | + | 0.907420i | \(0.361951\pi\) | |||||||
\(84\) | − 26.1421i | − 2.85234i | ||||||||
\(85\) | − 0.828427i | − 0.0898555i | ||||||||
\(86\) | 8.65685 | 0.933493 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.82843 | 0.194911 | ||||||||
\(89\) | 12.4853i | 1.32344i | 0.749752 | + | 0.661719i | \(0.230173\pi\) | ||||
−0.749752 | + | 0.661719i | \(0.769827\pi\) | |||||||
\(90\) | − 6.82843i | − 0.719779i | ||||||||
\(91\) | −10.8284 | −1.13513 | ||||||||
\(92\) | −14.0000 | −1.45960 | ||||||||
\(93\) | −24.3137 | −2.52121 | ||||||||
\(94\) | 7.82843 | 0.807441 | ||||||||
\(95\) | − 6.00000i | − 0.615587i | ||||||||
\(96\) | −3.82843 | −0.390737 | ||||||||
\(97\) | 4.48528i | 0.455411i | 0.973730 | + | 0.227706i | \(0.0731224\pi\) | ||||
−0.973730 | + | 0.227706i | \(0.926878\pi\) | |||||||
\(98\) | 2.41421i | 0.243872i | ||||||||
\(99\) | − 1.17157i | − 0.117748i | ||||||||
\(100\) | 15.3137 | 1.53137 | ||||||||
\(101\) | 2.34315i | 0.233152i | 0.993182 | + | 0.116576i | \(0.0371918\pi\) | ||||
−0.993182 | + | 0.116576i | \(0.962808\pi\) | |||||||
\(102\) | − 4.82843i | − 0.478086i | ||||||||
\(103\) | −4.82843 | −0.475759 | −0.237880 | − | 0.971295i | \(-0.576452\pi\) | ||||
−0.237880 | + | 0.971295i | \(0.576452\pi\) | |||||||
\(104\) | − 16.8995i | − 1.65713i | ||||||||
\(105\) | 6.82843i | 0.666386i | ||||||||
\(106\) | 22.8995i | 2.22420i | ||||||||
\(107\) | −14.8284 | −1.43352 | −0.716759 | − | 0.697321i | \(-0.754375\pi\) | ||||
−0.716759 | + | 0.697321i | \(0.754375\pi\) | |||||||
\(108\) | 1.58579i | 0.152592i | ||||||||
\(109\) | −12.6569 | −1.21231 | −0.606153 | − | 0.795348i | \(-0.707288\pi\) | ||||
−0.606153 | + | 0.795348i | \(0.707288\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | −9.65685 | −0.916588 | ||||||||
\(112\) | −8.48528 | −0.801784 | ||||||||
\(113\) | − 13.3137i | − 1.25245i | −0.779643 | − | 0.626224i | \(-0.784599\pi\) | ||||
0.779643 | − | 0.626224i | \(-0.215401\pi\) | |||||||
\(114\) | − 34.9706i | − 3.27529i | ||||||||
\(115\) | 3.65685 | 0.341003 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.8284 | −1.00109 | ||||||||
\(118\) | − 8.82843i | − 0.812723i | ||||||||
\(119\) | 2.34315i | 0.214796i | ||||||||
\(120\) | −10.6569 | −0.972833 | ||||||||
\(121\) | 10.8284 | 0.984402 | ||||||||
\(122\) | −11.6569 | −1.05536 | ||||||||
\(123\) | −10.8284 | −0.976366 | ||||||||
\(124\) | 38.5563i | 3.46246i | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 19.3137i | 1.72060i | ||||||||
\(127\) | 4.34315i | 0.385392i | 0.981259 | + | 0.192696i | \(0.0617231\pi\) | ||||
−0.981259 | + | 0.192696i | \(0.938277\pi\) | |||||||
\(128\) | 20.5563i | 1.81694i | ||||||||
\(129\) | −8.65685 | −0.762194 | ||||||||
\(130\) | 9.24264i | 0.810633i | ||||||||
\(131\) | 21.3137i | 1.86219i | 0.364780 | + | 0.931094i | \(0.381144\pi\) | ||||
−0.364780 | + | 0.931094i | \(0.618856\pi\) | |||||||
\(132\) | −3.82843 | −0.333222 | ||||||||
\(133\) | 16.9706i | 1.47153i | ||||||||
\(134\) | − 13.6569i | − 1.17977i | ||||||||
\(135\) | − 0.414214i | − 0.0356498i | ||||||||
\(136\) | −3.65685 | −0.313573 | ||||||||
\(137\) | − 12.0000i | − 1.02523i | −0.858619 | − | 0.512615i | \(-0.828677\pi\) | ||||
0.858619 | − | 0.512615i | \(-0.171323\pi\) | |||||||
\(138\) | 21.3137 | 1.81434 | ||||||||
\(139\) | 14.0000 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(140\) | 10.8284 | 0.915169 | ||||||||
\(141\) | −7.82843 | −0.659272 | ||||||||
\(142\) | 21.3137i | 1.78861i | ||||||||
\(143\) | 1.58579i | 0.132610i | ||||||||
\(144\) | −8.48528 | −0.707107 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.65685 | −0.799207 | ||||||||
\(147\) | − 2.41421i | − 0.199121i | ||||||||
\(148\) | 15.3137i | 1.25878i | ||||||||
\(149\) | 7.82843 | 0.641330 | 0.320665 | − | 0.947193i | \(-0.396094\pi\) | ||||
0.320665 | + | 0.947193i | \(0.396094\pi\) | |||||||
\(150\) | −23.3137 | −1.90356 | ||||||||
\(151\) | 14.1421 | 1.15087 | 0.575435 | − | 0.817847i | \(-0.304833\pi\) | ||||
0.575435 | + | 0.817847i | \(0.304833\pi\) | |||||||
\(152\) | −26.4853 | −2.14824 | ||||||||
\(153\) | 2.34315i | 0.189432i | ||||||||
\(154\) | 2.82843 | 0.227921 | ||||||||
\(155\) | − 10.0711i | − 0.808928i | ||||||||
\(156\) | 35.3848i | 2.83305i | ||||||||
\(157\) | 8.48528i | 0.677199i | 0.940931 | + | 0.338600i | \(0.109953\pi\) | ||||
−0.940931 | + | 0.338600i | \(0.890047\pi\) | |||||||
\(158\) | −5.82843 | −0.463685 | ||||||||
\(159\) | − 22.8995i | − 1.81605i | ||||||||
\(160\) | − 1.58579i | − 0.125367i | ||||||||
\(161\) | −10.3431 | −0.815154 | ||||||||
\(162\) | − 22.8995i | − 1.79915i | ||||||||
\(163\) | 3.92893i | 0.307738i | 0.988091 | + | 0.153869i | \(0.0491733\pi\) | ||||
−0.988091 | + | 0.153869i | \(0.950827\pi\) | |||||||
\(164\) | 17.1716i | 1.34087i | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | 18.4853i | 1.43474i | ||||||||
\(167\) | 3.17157 | 0.245424 | 0.122712 | − | 0.992442i | \(-0.460841\pi\) | ||||
0.122712 | + | 0.992442i | \(0.460841\pi\) | |||||||
\(168\) | 30.1421 | 2.32552 | ||||||||
\(169\) | 1.65685 | 0.127450 | ||||||||
\(170\) | 2.00000 | 0.153393 | ||||||||
\(171\) | 16.9706i | 1.29777i | ||||||||
\(172\) | 13.7279i | 1.04674i | ||||||||
\(173\) | −12.3431 | −0.938432 | −0.469216 | − | 0.883083i | \(-0.655463\pi\) | ||||
−0.469216 | + | 0.883083i | \(0.655463\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.3137 | 0.855236 | ||||||||
\(176\) | 1.24264i | 0.0936676i | ||||||||
\(177\) | 8.82843i | 0.663585i | ||||||||
\(178\) | −30.1421 | −2.25925 | ||||||||
\(179\) | 6.48528 | 0.484733 | 0.242366 | − | 0.970185i | \(-0.422076\pi\) | ||||
0.242366 | + | 0.970185i | \(0.422076\pi\) | |||||||
\(180\) | 10.8284 | 0.807103 | ||||||||
\(181\) | 8.31371 | 0.617953 | 0.308977 | − | 0.951070i | \(-0.400014\pi\) | ||||
0.308977 | + | 0.951070i | \(0.400014\pi\) | |||||||
\(182\) | − 26.1421i | − 1.93778i | ||||||||
\(183\) | 11.6569 | 0.861699 | ||||||||
\(184\) | − 16.1421i | − 1.19001i | ||||||||
\(185\) | − 4.00000i | − 0.294086i | ||||||||
\(186\) | − 58.6985i | − 4.30398i | ||||||||
\(187\) | 0.343146 | 0.0250933 | ||||||||
\(188\) | 12.4142i | 0.905400i | ||||||||
\(189\) | 1.17157i | 0.0852194i | ||||||||
\(190\) | 14.4853 | 1.05087 | ||||||||
\(191\) | − 25.3137i | − 1.83164i | −0.401594 | − | 0.915818i | \(-0.631544\pi\) | ||||
0.401594 | − | 0.915818i | \(-0.368456\pi\) | |||||||
\(192\) | − 23.7279i | − 1.71242i | ||||||||
\(193\) | 5.17157i | 0.372258i | 0.982525 | + | 0.186129i | \(0.0595942\pi\) | ||||
−0.982525 | + | 0.186129i | \(0.940406\pi\) | |||||||
\(194\) | −10.8284 | −0.777436 | ||||||||
\(195\) | − 9.24264i | − 0.661879i | ||||||||
\(196\) | −3.82843 | −0.273459 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 2.82843 | 0.201008 | ||||||||
\(199\) | −0.485281 | −0.0344007 | −0.0172003 | − | 0.999852i | \(-0.505475\pi\) | ||||
−0.0172003 | + | 0.999852i | \(0.505475\pi\) | |||||||
\(200\) | 17.6569i | 1.24853i | ||||||||
\(201\) | 13.6569i | 0.963280i | ||||||||
\(202\) | −5.65685 | −0.398015 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.65685 | 0.536087 | ||||||||
\(205\) | − 4.48528i | − 0.313266i | ||||||||
\(206\) | − 11.6569i | − 0.812172i | ||||||||
\(207\) | −10.3431 | −0.718898 | ||||||||
\(208\) | 11.4853 | 0.796361 | ||||||||
\(209\) | 2.48528 | 0.171911 | ||||||||
\(210\) | −16.4853 | −1.13759 | ||||||||
\(211\) | − 19.3848i | − 1.33450i | −0.744832 | − | 0.667252i | \(-0.767471\pi\) | ||||
0.744832 | − | 0.667252i | \(-0.232529\pi\) | |||||||
\(212\) | −36.3137 | −2.49404 | ||||||||
\(213\) | − 21.3137i | − 1.46039i | ||||||||
\(214\) | − 35.7990i | − 2.44717i | ||||||||
\(215\) | − 3.58579i | − 0.244549i | ||||||||
\(216\) | −1.82843 | −0.124409 | ||||||||
\(217\) | 28.4853i | 1.93371i | ||||||||
\(218\) | − 30.5563i | − 2.06954i | ||||||||
\(219\) | 9.65685 | 0.652550 | ||||||||
\(220\) | − 1.58579i | − 0.106914i | ||||||||
\(221\) | − 3.17157i | − 0.213343i | ||||||||
\(222\) | − 23.3137i | − 1.56471i | ||||||||
\(223\) | −3.17157 | −0.212384 | −0.106192 | − | 0.994346i | \(-0.533866\pi\) | ||||
−0.106192 | + | 0.994346i | \(0.533866\pi\) | |||||||
\(224\) | 4.48528i | 0.299685i | ||||||||
\(225\) | 11.3137 | 0.754247 | ||||||||
\(226\) | 32.1421 | 2.13806 | ||||||||
\(227\) | −8.14214 | −0.540413 | −0.270206 | − | 0.962802i | \(-0.587092\pi\) | ||||
−0.270206 | + | 0.962802i | \(0.587092\pi\) | |||||||
\(228\) | 55.4558 | 3.67265 | ||||||||
\(229\) | − 3.51472i | − 0.232259i | −0.993234 | − | 0.116130i | \(-0.962951\pi\) | ||||
0.993234 | − | 0.116130i | \(-0.0370488\pi\) | |||||||
\(230\) | 8.82843i | 0.582129i | ||||||||
\(231\) | −2.82843 | −0.186097 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.3137 | 1.19977 | 0.599885 | − | 0.800086i | \(-0.295213\pi\) | ||||
0.599885 | + | 0.800086i | \(0.295213\pi\) | |||||||
\(234\) | − 26.1421i | − 1.70896i | ||||||||
\(235\) | − 3.24264i | − 0.211527i | ||||||||
\(236\) | 14.0000 | 0.911322 | ||||||||
\(237\) | 5.82843 | 0.378597 | ||||||||
\(238\) | −5.65685 | −0.366679 | ||||||||
\(239\) | −19.6569 | −1.27150 | −0.635748 | − | 0.771897i | \(-0.719308\pi\) | ||||
−0.635748 | + | 0.771897i | \(0.719308\pi\) | |||||||
\(240\) | − 7.24264i | − 0.467510i | ||||||||
\(241\) | 18.3137 | 1.17969 | 0.589845 | − | 0.807517i | \(-0.299189\pi\) | ||||
0.589845 | + | 0.807517i | \(0.299189\pi\) | |||||||
\(242\) | 26.1421i | 1.68048i | ||||||||
\(243\) | 21.6569i | 1.38929i | ||||||||
\(244\) | − 18.4853i | − 1.18340i | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | − 26.1421i | − 1.66676i | ||||||||
\(247\) | − 22.9706i | − 1.46158i | ||||||||
\(248\) | −44.4558 | −2.82295 | ||||||||
\(249\) | − 18.4853i | − 1.17146i | ||||||||
\(250\) | − 21.7279i | − 1.37419i | ||||||||
\(251\) | − 20.0711i | − 1.26687i | −0.773794 | − | 0.633437i | \(-0.781643\pi\) | ||||
0.773794 | − | 0.633437i | \(-0.218357\pi\) | |||||||
\(252\) | −30.6274 | −1.92935 | ||||||||
\(253\) | 1.51472i | 0.0952295i | ||||||||
\(254\) | −10.4853 | −0.657905 | ||||||||
\(255\) | −2.00000 | −0.125245 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | −18.1716 | −1.13351 | −0.566756 | − | 0.823886i | \(-0.691802\pi\) | ||||
−0.566756 | + | 0.823886i | \(0.691802\pi\) | |||||||
\(258\) | − 20.8995i | − 1.30115i | ||||||||
\(259\) | 11.3137i | 0.703000i | ||||||||
\(260\) | −14.6569 | −0.908980 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −51.4558 | −3.17895 | ||||||||
\(263\) | − 2.75736i | − 0.170026i | −0.996380 | − | 0.0850130i | \(-0.972907\pi\) | ||||
0.996380 | − | 0.0850130i | \(-0.0270932\pi\) | |||||||
\(264\) | − 4.41421i | − 0.271676i | ||||||||
\(265\) | 9.48528 | 0.582676 | ||||||||
\(266\) | −40.9706 | −2.51207 | ||||||||
\(267\) | 30.1421 | 1.84467 | ||||||||
\(268\) | 21.6569 | 1.32290 | ||||||||
\(269\) | 31.4558i | 1.91790i | 0.283581 | + | 0.958948i | \(0.408478\pi\) | ||||
−0.283581 | + | 0.958948i | \(0.591522\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 16.5563i | 1.00573i | 0.864366 | + | 0.502863i | \(0.167720\pi\) | ||||
−0.864366 | + | 0.502863i | \(0.832280\pi\) | |||||||
\(272\) | − 2.48528i | − 0.150692i | ||||||||
\(273\) | 26.1421i | 1.58219i | ||||||||
\(274\) | 28.9706 | 1.75018 | ||||||||
\(275\) | − 1.65685i | − 0.0999121i | ||||||||
\(276\) | 33.7990i | 2.03446i | ||||||||
\(277\) | −17.3137 | −1.04028 | −0.520140 | − | 0.854081i | \(-0.674120\pi\) | ||||
−0.520140 | + | 0.854081i | \(0.674120\pi\) | |||||||
\(278\) | 33.7990i | 2.02713i | ||||||||
\(279\) | 28.4853i | 1.70537i | ||||||||
\(280\) | 12.4853i | 0.746138i | ||||||||
\(281\) | 31.9706 | 1.90720 | 0.953602 | − | 0.301070i | \(-0.0973439\pi\) | ||||
0.953602 | + | 0.301070i | \(0.0973439\pi\) | |||||||
\(282\) | − 18.8995i | − 1.12545i | ||||||||
\(283\) | −11.6569 | −0.692928 | −0.346464 | − | 0.938063i | \(-0.612618\pi\) | ||||
−0.346464 | + | 0.938063i | \(0.612618\pi\) | |||||||
\(284\) | −33.7990 | −2.00560 | ||||||||
\(285\) | −14.4853 | −0.858034 | ||||||||
\(286\) | −3.82843 | −0.226380 | ||||||||
\(287\) | 12.6863i | 0.748848i | ||||||||
\(288\) | 4.48528i | 0.264298i | ||||||||
\(289\) | 16.3137 | 0.959630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.8284 | 0.634774 | ||||||||
\(292\) | − 15.3137i | − 0.896167i | ||||||||
\(293\) | − 7.65685i | − 0.447318i | −0.974667 | − | 0.223659i | \(-0.928200\pi\) | ||||
0.974667 | − | 0.223659i | \(-0.0718002\pi\) | |||||||
\(294\) | 5.82843 | 0.339921 | ||||||||
\(295\) | −3.65685 | −0.212910 | ||||||||
\(296\) | −17.6569 | −1.02628 | ||||||||
\(297\) | 0.171573 | 0.00995567 | ||||||||
\(298\) | 18.8995i | 1.09482i | ||||||||
\(299\) | 14.0000 | 0.809641 | ||||||||
\(300\) | − 36.9706i | − 2.13450i | ||||||||
\(301\) | 10.1421i | 0.584583i | ||||||||
\(302\) | 34.1421i | 1.96466i | ||||||||
\(303\) | 5.65685 | 0.324978 | ||||||||
\(304\) | − 18.0000i | − 1.03237i | ||||||||
\(305\) | 4.82843i | 0.276475i | ||||||||
\(306\) | −5.65685 | −0.323381 | ||||||||
\(307\) | − 2.89949i | − 0.165483i | −0.996571 | − | 0.0827415i | \(-0.973632\pi\) | ||||
0.996571 | − | 0.0827415i | \(-0.0263676\pi\) | |||||||
\(308\) | 4.48528i | 0.255573i | ||||||||
\(309\) | 11.6569i | 0.663135i | ||||||||
\(310\) | 24.3137 | 1.38093 | ||||||||
\(311\) | − 2.68629i | − 0.152326i | −0.997095 | − | 0.0761628i | \(-0.975733\pi\) | ||||
0.997095 | − | 0.0761628i | \(-0.0242669\pi\) | |||||||
\(312\) | −40.7990 | −2.30979 | ||||||||
\(313\) | 9.82843 | 0.555536 | 0.277768 | − | 0.960648i | \(-0.410405\pi\) | ||||
0.277768 | + | 0.960648i | \(0.410405\pi\) | |||||||
\(314\) | −20.4853 | −1.15605 | ||||||||
\(315\) | 8.00000 | 0.450749 | ||||||||
\(316\) | − 9.24264i | − 0.519939i | ||||||||
\(317\) | − 31.4558i | − 1.76674i | −0.468680 | − | 0.883368i | \(-0.655270\pi\) | ||||
0.468680 | − | 0.883368i | \(-0.344730\pi\) | |||||||
\(318\) | 55.2843 | 3.10019 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 9.82843 | 0.549426 | ||||||||
\(321\) | 35.7990i | 1.99810i | ||||||||
\(322\) | − 24.9706i | − 1.39156i | ||||||||
\(323\) | −4.97056 | −0.276570 | ||||||||
\(324\) | 36.3137 | 2.01743 | ||||||||
\(325\) | −15.3137 | −0.849452 | ||||||||
\(326\) | −9.48528 | −0.525341 | ||||||||
\(327\) | 30.5563i | 1.68977i | ||||||||
\(328\) | −19.7990 | −1.09322 | ||||||||
\(329\) | 9.17157i | 0.505645i | ||||||||
\(330\) | 2.41421i | 0.132898i | ||||||||
\(331\) | − 2.41421i | − 0.132697i | −0.997797 | − | 0.0663486i | \(-0.978865\pi\) | ||||
0.997797 | − | 0.0663486i | \(-0.0211349\pi\) | |||||||
\(332\) | −29.3137 | −1.60880 | ||||||||
\(333\) | 11.3137i | 0.619987i | ||||||||
\(334\) | 7.65685i | 0.418964i | ||||||||
\(335\) | −5.65685 | −0.309067 | ||||||||
\(336\) | 20.4853i | 1.11756i | ||||||||
\(337\) | 21.7990i | 1.18747i | 0.804662 | + | 0.593733i | \(0.202347\pi\) | ||||
−0.804662 | + | 0.593733i | \(0.797653\pi\) | |||||||
\(338\) | 4.00000i | 0.217571i | ||||||||
\(339\) | −32.1421 | −1.74572 | ||||||||
\(340\) | 3.17157i | 0.172003i | ||||||||
\(341\) | 4.17157 | 0.225903 | ||||||||
\(342\) | −40.9706 | −2.21543 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | −15.8284 | −0.853412 | ||||||||
\(345\) | − 8.82843i | − 0.475307i | ||||||||
\(346\) | − 29.7990i | − 1.60200i | ||||||||
\(347\) | −2.48528 | −0.133417 | −0.0667084 | − | 0.997773i | \(-0.521250\pi\) | ||||
−0.0667084 | + | 0.997773i | \(0.521250\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.14214 | −0.275252 | −0.137626 | − | 0.990484i | \(-0.543947\pi\) | ||||
−0.137626 | + | 0.990484i | \(0.543947\pi\) | |||||||
\(350\) | 27.3137i | 1.45998i | ||||||||
\(351\) | − 1.58579i | − 0.0846430i | ||||||||
\(352\) | 0.656854 | 0.0350104 | ||||||||
\(353\) | −26.9706 | −1.43550 | −0.717749 | − | 0.696302i | \(-0.754828\pi\) | ||||
−0.717749 | + | 0.696302i | \(0.754828\pi\) | |||||||
\(354\) | −21.3137 | −1.13281 | ||||||||
\(355\) | 8.82843 | 0.468564 | ||||||||
\(356\) | − 47.7990i | − 2.53334i | ||||||||
\(357\) | 5.65685 | 0.299392 | ||||||||
\(358\) | 15.6569i | 0.827490i | ||||||||
\(359\) | − 3.92893i | − 0.207361i | −0.994611 | − | 0.103681i | \(-0.966938\pi\) | ||||
0.994611 | − | 0.103681i | \(-0.0330620\pi\) | |||||||
\(360\) | 12.4853i | 0.658032i | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 20.0711i | 1.05491i | ||||||||
\(363\) | − 26.1421i | − 1.37211i | ||||||||
\(364\) | 41.4558 | 2.17288 | ||||||||
\(365\) | 4.00000i | 0.209370i | ||||||||
\(366\) | 28.1421i | 1.47101i | ||||||||
\(367\) | − 18.0000i | − 0.939592i | −0.882775 | − | 0.469796i | \(-0.844327\pi\) | ||||
0.882775 | − | 0.469796i | \(-0.155673\pi\) | |||||||
\(368\) | 10.9706 | 0.571880 | ||||||||
\(369\) | 12.6863i | 0.660422i | ||||||||
\(370\) | 9.65685 | 0.502036 | ||||||||
\(371\) | −26.8284 | −1.39286 | ||||||||
\(372\) | 93.0833 | 4.82614 | ||||||||
\(373\) | −26.3137 | −1.36247 | −0.681236 | − | 0.732064i | \(-0.738557\pi\) | ||||
−0.681236 | + | 0.732064i | \(0.738557\pi\) | |||||||
\(374\) | 0.828427i | 0.0428369i | ||||||||
\(375\) | 21.7279i | 1.12203i | ||||||||
\(376\) | −14.3137 | −0.738173 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.82843 | −0.145479 | ||||||||
\(379\) | 6.97056i | 0.358054i | 0.983844 | + | 0.179027i | \(0.0572949\pi\) | ||||
−0.983844 | + | 0.179027i | \(0.942705\pi\) | |||||||
\(380\) | 22.9706i | 1.17837i | ||||||||
\(381\) | 10.4853 | 0.537177 | ||||||||
\(382\) | 61.1127 | 3.12680 | ||||||||
\(383\) | 3.51472 | 0.179594 | 0.0897969 | − | 0.995960i | \(-0.471378\pi\) | ||||
0.0897969 | + | 0.995960i | \(0.471378\pi\) | |||||||
\(384\) | 49.6274 | 2.53254 | ||||||||
\(385\) | − 1.17157i | − 0.0597089i | ||||||||
\(386\) | −12.4853 | −0.635484 | ||||||||
\(387\) | 10.1421i | 0.515554i | ||||||||
\(388\) | − 17.1716i | − 0.871755i | ||||||||
\(389\) | 3.02944i | 0.153599i | 0.997047 | + | 0.0767993i | \(0.0244701\pi\) | ||||
−0.997047 | + | 0.0767993i | \(0.975530\pi\) | |||||||
\(390\) | 22.3137 | 1.12990 | ||||||||
\(391\) | − 3.02944i | − 0.153205i | ||||||||
\(392\) | − 4.41421i | − 0.222951i | ||||||||
\(393\) | 51.4558 | 2.59560 | ||||||||
\(394\) | 4.82843i | 0.243253i | ||||||||
\(395\) | 2.41421i | 0.121472i | ||||||||
\(396\) | 4.48528i | 0.225394i | ||||||||
\(397\) | 19.3431 | 0.970805 | 0.485402 | − | 0.874291i | \(-0.338673\pi\) | ||||
0.485402 | + | 0.874291i | \(0.338673\pi\) | |||||||
\(398\) | − 1.17157i | − 0.0587256i | ||||||||
\(399\) | 40.9706 | 2.05109 | ||||||||
\(400\) | −12.0000 | −0.600000 | ||||||||
\(401\) | −18.6569 | −0.931679 | −0.465839 | − | 0.884869i | \(-0.654248\pi\) | ||||
−0.465839 | + | 0.884869i | \(0.654248\pi\) | |||||||
\(402\) | −32.9706 | −1.64442 | ||||||||
\(403\) | − 38.5563i | − 1.92063i | ||||||||
\(404\) | − 8.97056i | − 0.446302i | ||||||||
\(405\) | −9.48528 | −0.471327 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.65685 | 0.0821272 | ||||||||
\(408\) | 8.82843i | 0.437072i | ||||||||
\(409\) | 18.9706i | 0.938034i | 0.883189 | + | 0.469017i | \(0.155392\pi\) | ||||
−0.883189 | + | 0.469017i | \(0.844608\pi\) | |||||||
\(410\) | 10.8284 | 0.534778 | ||||||||
\(411\) | −28.9706 | −1.42901 | ||||||||
\(412\) | 18.4853 | 0.910704 | ||||||||
\(413\) | 10.3431 | 0.508953 | ||||||||
\(414\) | − 24.9706i | − 1.22724i | ||||||||
\(415\) | 7.65685 | 0.375860 | ||||||||
\(416\) | − 6.07107i | − 0.297659i | ||||||||
\(417\) | − 33.7990i | − 1.65514i | ||||||||
\(418\) | 6.00000i | 0.293470i | ||||||||
\(419\) | 9.51472 | 0.464824 | 0.232412 | − | 0.972617i | \(-0.425338\pi\) | ||||
0.232412 | + | 0.972617i | \(0.425338\pi\) | |||||||
\(420\) | − 26.1421i | − 1.27561i | ||||||||
\(421\) | 37.1127i | 1.80876i | 0.426726 | + | 0.904381i | \(0.359667\pi\) | ||||
−0.426726 | + | 0.904381i | \(0.640333\pi\) | |||||||
\(422\) | 46.7990 | 2.27814 | ||||||||
\(423\) | 9.17157i | 0.445937i | ||||||||
\(424\) | − 41.8701i | − 2.03339i | ||||||||
\(425\) | 3.31371i | 0.160738i | ||||||||
\(426\) | 51.4558 | 2.49304 | ||||||||
\(427\) | − 13.6569i | − 0.660901i | ||||||||
\(428\) | 56.7696 | 2.74406 | ||||||||
\(429\) | 3.82843 | 0.184838 | ||||||||
\(430\) | 8.65685 | 0.417471 | ||||||||
\(431\) | 19.6569 | 0.946837 | 0.473419 | − | 0.880838i | \(-0.343020\pi\) | ||||
0.473419 | + | 0.880838i | \(0.343020\pi\) | |||||||
\(432\) | − 1.24264i | − 0.0597866i | ||||||||
\(433\) | 30.6274i | 1.47186i | 0.677058 | + | 0.735930i | \(0.263255\pi\) | ||||
−0.677058 | + | 0.735930i | \(0.736745\pi\) | |||||||
\(434\) | −68.7696 | −3.30104 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 48.4558 | 2.32061 | ||||||||
\(437\) | − 21.9411i | − 1.04959i | ||||||||
\(438\) | 23.3137i | 1.11397i | ||||||||
\(439\) | 0.343146 | 0.0163775 | 0.00818873 | − | 0.999966i | \(-0.497393\pi\) | ||||
0.00818873 | + | 0.999966i | \(0.497393\pi\) | |||||||
\(440\) | 1.82843 | 0.0871668 | ||||||||
\(441\) | −2.82843 | −0.134687 | ||||||||
\(442\) | 7.65685 | 0.364199 | ||||||||
\(443\) | − 24.3431i | − 1.15658i | −0.815832 | − | 0.578289i | \(-0.803721\pi\) | ||||
0.815832 | − | 0.578289i | \(-0.196279\pi\) | |||||||
\(444\) | 36.9706 | 1.75455 | ||||||||
\(445\) | 12.4853i | 0.591859i | ||||||||
\(446\) | − 7.65685i | − 0.362563i | ||||||||
\(447\) | − 18.8995i | − 0.893915i | ||||||||
\(448\) | −27.7990 | −1.31338 | ||||||||
\(449\) | 34.9706i | 1.65036i | 0.564868 | + | 0.825181i | \(0.308927\pi\) | ||||
−0.564868 | + | 0.825181i | \(0.691073\pi\) | |||||||
\(450\) | 27.3137i | 1.28758i | ||||||||
\(451\) | 1.85786 | 0.0874834 | ||||||||
\(452\) | 50.9706i | 2.39745i | ||||||||
\(453\) | − 34.1421i | − 1.60414i | ||||||||
\(454\) | − 19.6569i | − 0.922542i | ||||||||
\(455\) | −10.8284 | −0.507644 | ||||||||
\(456\) | 63.9411i | 2.99432i | ||||||||
\(457\) | −1.02944 | −0.0481550 | −0.0240775 | − | 0.999710i | \(-0.507665\pi\) | ||||
−0.0240775 | + | 0.999710i | \(0.507665\pi\) | |||||||
\(458\) | 8.48528 | 0.396491 | ||||||||
\(459\) | −0.343146 | −0.0160167 | ||||||||
\(460\) | −14.0000 | −0.652753 | ||||||||
\(461\) | 14.0000i | 0.652045i | 0.945362 | + | 0.326023i | \(0.105709\pi\) | ||||
−0.945362 | + | 0.326023i | \(0.894291\pi\) | |||||||
\(462\) | − 6.82843i | − 0.317687i | ||||||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24.3137 | −1.12752 | ||||||||
\(466\) | 44.2132i | 2.04814i | ||||||||
\(467\) | 38.3553i | 1.77487i | 0.460930 | + | 0.887437i | \(0.347516\pi\) | ||||
−0.460930 | + | 0.887437i | \(0.652484\pi\) | |||||||
\(468\) | 41.4558 | 1.91630 | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 7.82843 | 0.361098 | ||||||||
\(471\) | 20.4853 | 0.943912 | ||||||||
\(472\) | 16.1421i | 0.743002i | ||||||||
\(473\) | 1.48528 | 0.0682933 | ||||||||
\(474\) | 14.0711i | 0.646306i | ||||||||
\(475\) | 24.0000i | 1.10120i | ||||||||
\(476\) | − 8.97056i | − 0.411165i | ||||||||
\(477\) | −26.8284 | −1.22839 | ||||||||
\(478\) | − 47.4558i | − 2.17058i | ||||||||
\(479\) | 6.89949i | 0.315246i | 0.987499 | + | 0.157623i | \(0.0503831\pi\) | ||||
−0.987499 | + | 0.157623i | \(0.949617\pi\) | |||||||
\(480\) | −3.82843 | −0.174743 | ||||||||
\(481\) | − 15.3137i | − 0.698245i | ||||||||
\(482\) | 44.2132i | 2.01386i | ||||||||
\(483\) | 24.9706i | 1.13620i | ||||||||
\(484\) | −41.4558 | −1.88436 | ||||||||
\(485\) | 4.48528i | 0.203666i | ||||||||
\(486\) | −52.2843 | −2.37166 | ||||||||
\(487\) | −11.5147 | −0.521782 | −0.260891 | − | 0.965368i | \(-0.584016\pi\) | ||||
−0.260891 | + | 0.965368i | \(0.584016\pi\) | |||||||
\(488\) | 21.3137 | 0.964826 | ||||||||
\(489\) | 9.48528 | 0.428939 | ||||||||
\(490\) | 2.41421i | 0.109063i | ||||||||
\(491\) | − 21.2426i | − 0.958667i | −0.877633 | − | 0.479333i | \(-0.840878\pi\) | ||||
0.877633 | − | 0.479333i | \(-0.159122\pi\) | |||||||
\(492\) | 41.4558 | 1.86897 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 55.4558 | 2.49508 | ||||||||
\(495\) | − 1.17157i | − 0.0526583i | ||||||||
\(496\) | − 30.2132i | − 1.35661i | ||||||||
\(497\) | −24.9706 | −1.12008 | ||||||||
\(498\) | 44.6274 | 1.99980 | ||||||||
\(499\) | −18.9706 | −0.849239 | −0.424620 | − | 0.905372i | \(-0.639592\pi\) | ||||
−0.424620 | + | 0.905372i | \(0.639592\pi\) | |||||||
\(500\) | 34.4558 | 1.54091 | ||||||||
\(501\) | − 7.65685i | − 0.342083i | ||||||||
\(502\) | 48.4558 | 2.16269 | ||||||||
\(503\) | 0.272078i | 0.0121314i | 0.999982 | + | 0.00606568i | \(0.00193078\pi\) | ||||
−0.999982 | + | 0.00606568i | \(0.998069\pi\) | |||||||
\(504\) | − 35.3137i | − 1.57300i | ||||||||
\(505\) | 2.34315i | 0.104269i | ||||||||
\(506\) | −3.65685 | −0.162567 | ||||||||
\(507\) | − 4.00000i | − 0.177646i | ||||||||
\(508\) | − 16.6274i | − 0.737722i | ||||||||
\(509\) | −10.5147 | −0.466057 | −0.233028 | − | 0.972470i | \(-0.574863\pi\) | ||||
−0.233028 | + | 0.972470i | \(0.574863\pi\) | |||||||
\(510\) | − 4.82843i | − 0.213806i | ||||||||
\(511\) | − 11.3137i | − 0.500489i | ||||||||
\(512\) | − 31.2426i | − 1.38074i | ||||||||
\(513\) | −2.48528 | −0.109728 | ||||||||
\(514\) | − 43.8701i | − 1.93503i | ||||||||
\(515\) | −4.82843 | −0.212766 | ||||||||
\(516\) | 33.1421 | 1.45900 | ||||||||
\(517\) | 1.34315 | 0.0590715 | ||||||||
\(518\) | −27.3137 | −1.20010 | ||||||||
\(519\) | 29.7990i | 1.30803i | ||||||||
\(520\) | − 16.8995i | − 0.741092i | ||||||||
\(521\) | 29.1421 | 1.27674 | 0.638370 | − | 0.769730i | \(-0.279609\pi\) | ||||
0.638370 | + | 0.769730i | \(0.279609\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.68629 | 0.204917 | 0.102459 | − | 0.994737i | \(-0.467329\pi\) | ||||
0.102459 | + | 0.994737i | \(0.467329\pi\) | |||||||
\(524\) | − 81.5980i | − 3.56462i | ||||||||
\(525\) | − 27.3137i | − 1.19207i | ||||||||
\(526\) | 6.65685 | 0.290253 | ||||||||
\(527\) | −8.34315 | −0.363433 | ||||||||
\(528\) | 3.00000 | 0.130558 | ||||||||
\(529\) | −9.62742 | −0.418583 | ||||||||
\(530\) | 22.8995i | 0.994690i | ||||||||
\(531\) | 10.3431 | 0.448854 | ||||||||
\(532\) | − 64.9706i | − 2.81683i | ||||||||
\(533\) | − 17.1716i | − 0.743783i | ||||||||
\(534\) | 72.7696i | 3.14905i | ||||||||
\(535\) | −14.8284 | −0.641089 | ||||||||
\(536\) | 24.9706i | 1.07856i | ||||||||
\(537\) | − 15.6569i | − 0.675643i | ||||||||
\(538\) | −75.9411 | −3.27405 | ||||||||
\(539\) | 0.414214i | 0.0178414i | ||||||||
\(540\) | 1.58579i | 0.0682414i | ||||||||
\(541\) | 10.3431i | 0.444687i | 0.974968 | + | 0.222343i | \(0.0713706\pi\) | ||||
−0.974968 | + | 0.222343i | \(0.928629\pi\) | |||||||
\(542\) | −39.9706 | −1.71688 | ||||||||
\(543\) | − 20.0711i | − 0.861332i | ||||||||
\(544\) | −1.31371 | −0.0563248 | ||||||||
\(545\) | −12.6569 | −0.542160 | ||||||||
\(546\) | −63.1127 | −2.70097 | ||||||||
\(547\) | 35.7990 | 1.53065 | 0.765327 | − | 0.643641i | \(-0.222577\pi\) | ||||
0.765327 | + | 0.643641i | \(0.222577\pi\) | |||||||
\(548\) | 45.9411i | 1.96251i | ||||||||
\(549\) | − 13.6569i | − 0.582860i | ||||||||
\(550\) | 4.00000 | 0.170561 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −38.9706 | −1.65870 | ||||||||
\(553\) | − 6.82843i | − 0.290374i | ||||||||
\(554\) | − 41.7990i | − 1.77587i | ||||||||
\(555\) | −9.65685 | −0.409911 | ||||||||
\(556\) | −53.5980 | −2.27306 | ||||||||
\(557\) | 17.3137 | 0.733605 | 0.366803 | − | 0.930299i | \(-0.380452\pi\) | ||||
0.366803 | + | 0.930299i | \(0.380452\pi\) | |||||||
\(558\) | −68.7696 | −2.91125 | ||||||||
\(559\) | − 13.7279i | − 0.580629i | ||||||||
\(560\) | −8.48528 | −0.358569 | ||||||||
\(561\) | − 0.828427i | − 0.0349762i | ||||||||
\(562\) | 77.1838i | 3.25580i | ||||||||
\(563\) | − 0.757359i | − 0.0319189i | −0.999873 | − | 0.0159594i | \(-0.994920\pi\) | ||||
0.999873 | − | 0.0159594i | \(-0.00508026\pi\) | |||||||
\(564\) | 29.9706 | 1.26199 | ||||||||
\(565\) | − 13.3137i | − 0.560112i | ||||||||
\(566\) | − 28.1421i | − 1.18290i | ||||||||
\(567\) | 26.8284 | 1.12669 | ||||||||
\(568\) | − 38.9706i | − 1.63517i | ||||||||
\(569\) | − 39.6569i | − 1.66250i | −0.555897 | − | 0.831251i | \(-0.687625\pi\) | ||||
0.555897 | − | 0.831251i | \(-0.312375\pi\) | |||||||
\(570\) | − 34.9706i | − 1.46476i | ||||||||
\(571\) | 14.6274 | 0.612138 | 0.306069 | − | 0.952009i | \(-0.400986\pi\) | ||||
0.306069 | + | 0.952009i | \(0.400986\pi\) | |||||||
\(572\) | − 6.07107i | − 0.253844i | ||||||||
\(573\) | −61.1127 | −2.55302 | ||||||||
\(574\) | −30.6274 | −1.27836 | ||||||||
\(575\) | −14.6274 | −0.610005 | ||||||||
\(576\) | −27.7990 | −1.15829 | ||||||||
\(577\) | − 29.7990i | − 1.24055i | −0.784385 | − | 0.620274i | \(-0.787021\pi\) | ||||
0.784385 | − | 0.620274i | \(-0.212979\pi\) | |||||||
\(578\) | 39.3848i | 1.63819i | ||||||||
\(579\) | 12.4853 | 0.518871 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.6569 | −0.898478 | ||||||||
\(582\) | 26.1421i | 1.08363i | ||||||||
\(583\) | 3.92893i | 0.162720i | ||||||||
\(584\) | 17.6569 | 0.730646 | ||||||||
\(585\) | −10.8284 | −0.447700 | ||||||||
\(586\) | 18.4853 | 0.763620 | ||||||||
\(587\) | 7.65685 | 0.316032 | 0.158016 | − | 0.987437i | \(-0.449490\pi\) | ||||
0.158016 | + | 0.987437i | \(0.449490\pi\) | |||||||
\(588\) | 9.24264i | 0.381160i | ||||||||
\(589\) | −60.4264 | −2.48983 | ||||||||
\(590\) | − 8.82843i | − 0.363461i | ||||||||
\(591\) | − 4.82843i | − 0.198615i | ||||||||
\(592\) | − 12.0000i | − 0.493197i | ||||||||
\(593\) | 19.4853 | 0.800165 | 0.400082 | − | 0.916479i | \(-0.368982\pi\) | ||||
0.400082 | + | 0.916479i | \(0.368982\pi\) | |||||||
\(594\) | 0.414214i | 0.0169954i | ||||||||
\(595\) | 2.34315i | 0.0960596i | ||||||||
\(596\) | −29.9706 | −1.22764 | ||||||||
\(597\) | 1.17157i | 0.0479493i | ||||||||
\(598\) | 33.7990i | 1.38214i | ||||||||
\(599\) | − 9.87006i | − 0.403280i | −0.979460 | − | 0.201640i | \(-0.935373\pi\) | ||||
0.979460 | − | 0.201640i | \(-0.0646270\pi\) | |||||||
\(600\) | 42.6274 | 1.74026 | ||||||||
\(601\) | 17.1716i | 0.700443i | 0.936667 | + | 0.350222i | \(0.113894\pi\) | ||||
−0.936667 | + | 0.350222i | \(0.886106\pi\) | |||||||
\(602\) | −24.4853 | −0.997946 | ||||||||
\(603\) | 16.0000 | 0.651570 | ||||||||
\(604\) | −54.1421 | −2.20301 | ||||||||
\(605\) | 10.8284 | 0.440238 | ||||||||
\(606\) | 13.6569i | 0.554772i | ||||||||
\(607\) | − 7.72792i | − 0.313667i | −0.987625 | − | 0.156833i | \(-0.949871\pi\) | ||||
0.987625 | − | 0.156833i | \(-0.0501286\pi\) | |||||||
\(608\) | −9.51472 | −0.385873 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.6569 | −0.471972 | ||||||||
\(611\) | − 12.4142i | − 0.502225i | ||||||||
\(612\) | − 8.97056i | − 0.362614i | ||||||||
\(613\) | 9.00000 | 0.363507 | 0.181753 | − | 0.983344i | \(-0.441823\pi\) | ||||
0.181753 | + | 0.983344i | \(0.441823\pi\) | |||||||
\(614\) | 7.00000 | 0.282497 | ||||||||
\(615\) | −10.8284 | −0.436644 | ||||||||
\(616\) | −5.17157 | −0.208369 | ||||||||
\(617\) | 0.686292i | 0.0276291i | 0.999905 | + | 0.0138145i | \(0.00439744\pi\) | ||||
−0.999905 | + | 0.0138145i | \(0.995603\pi\) | |||||||
\(618\) | −28.1421 | −1.13204 | ||||||||
\(619\) | 33.5858i | 1.34993i | 0.737851 | + | 0.674963i | \(0.235841\pi\) | ||||
−0.737851 | + | 0.674963i | \(0.764159\pi\) | |||||||
\(620\) | 38.5563i | 1.54846i | ||||||||
\(621\) | − 1.51472i | − 0.0607836i | ||||||||
\(622\) | 6.48528 | 0.260036 | ||||||||
\(623\) | − 35.3137i | − 1.41481i | ||||||||
\(624\) | − 27.7279i | − 1.11001i | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 23.7279i | 0.948358i | ||||||||
\(627\) | − 6.00000i | − 0.239617i | ||||||||
\(628\) | − 32.4853i | − 1.29630i | ||||||||
\(629\) | −3.31371 | −0.132126 | ||||||||
\(630\) | 19.3137i | 0.769477i | ||||||||
\(631\) | 36.8284 | 1.46612 | 0.733058 | − | 0.680166i | \(-0.238092\pi\) | ||||
0.733058 | + | 0.680166i | \(0.238092\pi\) | |||||||
\(632\) | 10.6569 | 0.423907 | ||||||||
\(633\) | −46.7990 | −1.86009 | ||||||||
\(634\) | 75.9411 | 3.01601 | ||||||||
\(635\) | 4.34315i | 0.172352i | ||||||||
\(636\) | 87.6690i | 3.47630i | ||||||||
\(637\) | 3.82843 | 0.151688 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.9706 | −0.987820 | ||||||||
\(640\) | 20.5563i | 0.812561i | ||||||||
\(641\) | − 17.7990i | − 0.703018i | −0.936185 | − | 0.351509i | \(-0.885669\pi\) | ||||
0.936185 | − | 0.351509i | \(-0.114331\pi\) | |||||||
\(642\) | −86.4264 | −3.41098 | ||||||||
\(643\) | −32.4853 | −1.28109 | −0.640547 | − | 0.767919i | \(-0.721292\pi\) | ||||
−0.640547 | + | 0.767919i | \(0.721292\pi\) | |||||||
\(644\) | 39.5980 | 1.56038 | ||||||||
\(645\) | −8.65685 | −0.340863 | ||||||||
\(646\) | − 12.0000i | − 0.472134i | ||||||||
\(647\) | −39.6569 | −1.55907 | −0.779536 | − | 0.626358i | \(-0.784545\pi\) | ||||
−0.779536 | + | 0.626358i | \(0.784545\pi\) | |||||||
\(648\) | 41.8701i | 1.64481i | ||||||||
\(649\) | − 1.51472i | − 0.0594579i | ||||||||
\(650\) | − 36.9706i | − 1.45010i | ||||||||
\(651\) | 68.7696 | 2.69529 | ||||||||
\(652\) | − 15.0416i | − 0.589076i | ||||||||
\(653\) | − 30.1421i | − 1.17955i | −0.807567 | − | 0.589776i | \(-0.799216\pi\) | ||||
0.807567 | − | 0.589776i | \(-0.200784\pi\) | |||||||
\(654\) | −73.7696 | −2.88462 | ||||||||
\(655\) | 21.3137i | 0.832796i | ||||||||
\(656\) | − 13.4558i | − 0.525362i | ||||||||
\(657\) | − 11.3137i | − 0.441390i | ||||||||
\(658\) | −22.1421 | −0.863190 | ||||||||
\(659\) | − 14.4142i | − 0.561498i | −0.959781 | − | 0.280749i | \(-0.909417\pi\) | ||||
0.959781 | − | 0.280749i | \(-0.0905829\pi\) | |||||||
\(660\) | −3.82843 | −0.149021 | ||||||||
\(661\) | 33.3137 | 1.29575 | 0.647877 | − | 0.761745i | \(-0.275657\pi\) | ||||
0.647877 | + | 0.761745i | \(0.275657\pi\) | |||||||
\(662\) | 5.82843 | 0.226528 | ||||||||
\(663\) | −7.65685 | −0.297368 | ||||||||
\(664\) | − 33.7990i | − 1.31166i | ||||||||
\(665\) | 16.9706i | 0.658090i | ||||||||
\(666\) | −27.3137 | −1.05838 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −12.1421 | −0.469793 | ||||||||
\(669\) | 7.65685i | 0.296031i | ||||||||
\(670\) | − 13.6569i | − 0.527610i | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 10.8284 | 0.417716 | ||||||||
\(673\) | 21.6274 | 0.833676 | 0.416838 | − | 0.908981i | \(-0.363138\pi\) | ||||
0.416838 | + | 0.908981i | \(0.363138\pi\) | |||||||
\(674\) | −52.6274 | −2.02713 | ||||||||
\(675\) | 1.65685i | 0.0637723i | ||||||||
\(676\) | −6.34315 | −0.243967 | ||||||||
\(677\) | − 22.0000i | − 0.845529i | −0.906240 | − | 0.422764i | \(-0.861060\pi\) | ||||
0.906240 | − | 0.422764i | \(-0.138940\pi\) | |||||||
\(678\) | − 77.5980i | − 2.98013i | ||||||||
\(679\) | − 12.6863i | − 0.486855i | ||||||||
\(680\) | −3.65685 | −0.140234 | ||||||||
\(681\) | 19.6569i | 0.753252i | ||||||||
\(682\) | 10.0711i | 0.385641i | ||||||||
\(683\) | 20.9706 | 0.802416 | 0.401208 | − | 0.915987i | \(-0.368590\pi\) | ||||
0.401208 | + | 0.915987i | \(0.368590\pi\) | |||||||
\(684\) | − 64.9706i | − 2.48421i | ||||||||
\(685\) | − 12.0000i | − 0.458496i | ||||||||
\(686\) | 40.9706i | 1.56426i | ||||||||
\(687\) | −8.48528 | −0.323734 | ||||||||
\(688\) | − 10.7574i | − 0.410120i | ||||||||
\(689\) | 36.3137 | 1.38344 | ||||||||
\(690\) | 21.3137 | 0.811399 | ||||||||
\(691\) | 48.0000 | 1.82601 | 0.913003 | − | 0.407953i | \(-0.133757\pi\) | ||||
0.913003 | + | 0.407953i | \(0.133757\pi\) | |||||||
\(692\) | 47.2548 | 1.79636 | ||||||||
\(693\) | 3.31371i | 0.125877i | ||||||||
\(694\) | − 6.00000i | − 0.227757i | ||||||||
\(695\) | 14.0000 | 0.531050 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.71573 | −0.140743 | ||||||||
\(698\) | − 12.4142i | − 0.469885i | ||||||||
\(699\) | − 44.2132i | − 1.67230i | ||||||||
\(700\) | −43.3137 | −1.63710 | ||||||||
\(701\) | 40.1127 | 1.51504 | 0.757518 | − | 0.652814i | \(-0.226412\pi\) | ||||
0.757518 | + | 0.652814i | \(0.226412\pi\) | |||||||
\(702\) | 3.82843 | 0.144495 | ||||||||
\(703\) | −24.0000 | −0.905177 | ||||||||
\(704\) | 4.07107i | 0.153434i | ||||||||
\(705\) | −7.82843 | −0.294836 | ||||||||
\(706\) | − 65.1127i | − 2.45055i | ||||||||
\(707\) | − 6.62742i | − 0.249250i | ||||||||
\(708\) | − 33.7990i | − 1.27024i | ||||||||
\(709\) | −29.1421 | −1.09446 | −0.547228 | − | 0.836984i | \(-0.684317\pi\) | ||||
−0.547228 | + | 0.836984i | \(0.684317\pi\) | |||||||
\(710\) | 21.3137i | 0.799889i | ||||||||
\(711\) | − 6.82843i | − 0.256086i | ||||||||
\(712\) | 55.1127 | 2.06544 | ||||||||
\(713\) | − 36.8284i | − 1.37924i | ||||||||
\(714\) | 13.6569i | 0.511095i | ||||||||
\(715\) | 1.58579i | 0.0593051i | ||||||||
\(716\) | −24.8284 | −0.927882 | ||||||||
\(717\) | 47.4558i | 1.77227i | ||||||||
\(718\) | 9.48528 | 0.353988 | ||||||||
\(719\) | −20.1421 | −0.751175 | −0.375587 | − | 0.926787i | \(-0.622559\pi\) | ||||
−0.375587 | + | 0.926787i | \(0.622559\pi\) | |||||||
\(720\) | −8.48528 | −0.316228 | ||||||||
\(721\) | 13.6569 | 0.508608 | ||||||||
\(722\) | − 41.0416i | − 1.52741i | ||||||||
\(723\) | − 44.2132i | − 1.64431i | ||||||||
\(724\) | −31.8284 | −1.18289 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 63.1127 | 2.34233 | ||||||||
\(727\) | − 1.31371i | − 0.0487228i | −0.999703 | − | 0.0243614i | \(-0.992245\pi\) | ||||
0.999703 | − | 0.0243614i | \(-0.00775523\pi\) | |||||||
\(728\) | 47.7990i | 1.77155i | ||||||||
\(729\) | 23.8284 | 0.882534 | ||||||||
\(730\) | −9.65685 | −0.357416 | ||||||||
\(731\) | −2.97056 | −0.109870 | ||||||||
\(732\) | −44.6274 | −1.64948 | ||||||||
\(733\) | − 41.2548i | − 1.52378i | −0.647705 | − | 0.761891i | \(-0.724271\pi\) | ||||
0.647705 | − | 0.761891i | \(-0.275729\pi\) | |||||||
\(734\) | 43.4558 | 1.60398 | ||||||||
\(735\) | − 2.41421i | − 0.0890496i | ||||||||
\(736\) | − 5.79899i | − 0.213754i | ||||||||
\(737\) | − 2.34315i | − 0.0863109i | ||||||||
\(738\) | −30.6274 | −1.12741 | ||||||||
\(739\) | − 4.07107i | − 0.149757i | −0.997193 | − | 0.0748783i | \(-0.976143\pi\) | ||||
0.997193 | − | 0.0748783i | \(-0.0238568\pi\) | |||||||
\(740\) | 15.3137i | 0.562943i | ||||||||
\(741\) | −55.4558 | −2.03722 | ||||||||
\(742\) | − 64.7696i | − 2.37777i | ||||||||
\(743\) | 23.6569i | 0.867886i | 0.900940 | + | 0.433943i | \(0.142878\pi\) | ||||
−0.900940 | + | 0.433943i | \(0.857122\pi\) | |||||||
\(744\) | 107.326i | 3.93476i | ||||||||
\(745\) | 7.82843 | 0.286811 | ||||||||
\(746\) | − 63.5269i | − 2.32589i | ||||||||
\(747\) | −21.6569 | −0.792383 | ||||||||
\(748\) | −1.31371 | −0.0480339 | ||||||||
\(749\) | 41.9411 | 1.53250 | ||||||||
\(750\) | −52.4558 | −1.91542 | ||||||||
\(751\) | 25.3137i | 0.923710i | 0.886955 | + | 0.461855i | \(0.152816\pi\) | ||||
−0.886955 | + | 0.461855i | \(0.847184\pi\) | |||||||
\(752\) | − 9.72792i | − 0.354741i | ||||||||
\(753\) | −48.4558 | −1.76583 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.1421 | 0.514685 | ||||||||
\(756\) | − 4.48528i | − 0.163128i | ||||||||
\(757\) | − 25.5147i | − 0.927348i | −0.886006 | − | 0.463674i | \(-0.846531\pi\) | ||||
0.886006 | − | 0.463674i | \(-0.153469\pi\) | |||||||
\(758\) | −16.8284 | −0.611236 | ||||||||
\(759\) | 3.65685 | 0.132735 | ||||||||
\(760\) | −26.4853 | −0.960722 | ||||||||
\(761\) | 45.5980 | 1.65293 | 0.826463 | − | 0.562991i | \(-0.190350\pi\) | ||||
0.826463 | + | 0.562991i | \(0.190350\pi\) | |||||||
\(762\) | 25.3137i | 0.917019i | ||||||||
\(763\) | 35.7990 | 1.29601 | ||||||||
\(764\) | 96.9117i | 3.50614i | ||||||||
\(765\) | 2.34315i | 0.0847166i | ||||||||
\(766\) | 8.48528i | 0.306586i | ||||||||
\(767\) | −14.0000 | −0.505511 | ||||||||
\(768\) | 72.3553i | 2.61090i | ||||||||
\(769\) | − 49.1127i | − 1.77105i | −0.464592 | − | 0.885525i | \(-0.653799\pi\) | ||||
0.464592 | − | 0.885525i | \(-0.346201\pi\) | |||||||
\(770\) | 2.82843 | 0.101929 | ||||||||
\(771\) | 43.8701i | 1.57994i | ||||||||
\(772\) | − 19.7990i | − 0.712581i | ||||||||
\(773\) | 19.5147i | 0.701896i | 0.936395 | + | 0.350948i | \(0.114141\pi\) | ||||
−0.936395 | + | 0.350948i | \(0.885859\pi\) | |||||||
\(774\) | −24.4853 | −0.880105 | ||||||||
\(775\) | 40.2843i | 1.44705i | ||||||||
\(776\) | 19.7990 | 0.710742 | ||||||||
\(777\) | 27.3137 | 0.979874 | ||||||||
\(778\) | −7.31371 | −0.262209 | ||||||||
\(779\) | −26.9117 | −0.964211 | ||||||||
\(780\) | 35.3848i | 1.26698i | ||||||||
\(781\) | 3.65685i | 0.130853i | ||||||||
\(782\) | 7.31371 | 0.261538 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 8.48528i | 0.302853i | ||||||||
\(786\) | 124.225i | 4.43097i | ||||||||
\(787\) | 54.0833 | 1.92786 | 0.963930 | − | 0.266156i | \(-0.0857536\pi\) | ||||
0.963930 | + | 0.266156i | \(0.0857536\pi\) | |||||||
\(788\) | −7.65685 | −0.272764 | ||||||||
\(789\) | −6.65685 | −0.236990 | ||||||||
\(790\) | −5.82843 | −0.207366 | ||||||||
\(791\) | 37.6569i | 1.33892i | ||||||||
\(792\) | −5.17157 | −0.183764 | ||||||||
\(793\) | 18.4853i | 0.656432i | ||||||||
\(794\) | 46.6985i | 1.65727i | ||||||||
\(795\) | − 22.8995i | − 0.812161i | ||||||||
\(796\) | 1.85786 | 0.0658503 | ||||||||
\(797\) | − 51.7401i | − 1.83273i | −0.400345 | − | 0.916364i | \(-0.631110\pi\) | ||||
0.400345 | − | 0.916364i | \(-0.368890\pi\) | |||||||
\(798\) | 98.9117i | 3.50144i | ||||||||
\(799\) | −2.68629 | −0.0950342 | ||||||||
\(800\) | 6.34315i | 0.224264i | ||||||||
\(801\) | − 35.3137i | − 1.24775i | ||||||||
\(802\) | − 45.0416i | − 1.59048i | ||||||||
\(803\) | −1.65685 | −0.0584691 | ||||||||
\(804\) | − 52.2843i | − 1.84392i | ||||||||
\(805\) | −10.3431 | −0.364548 | ||||||||
\(806\) | 93.0833 | 3.27872 | ||||||||
\(807\) | 75.9411 | 2.67325 | ||||||||
\(808\) | 10.3431 | 0.363871 | ||||||||
\(809\) | 36.2843i | 1.27569i | 0.770166 | + | 0.637844i | \(0.220173\pi\) | ||||
−0.770166 | + | 0.637844i | \(0.779827\pi\) | |||||||
\(810\) | − 22.8995i | − 0.804606i | ||||||||
\(811\) | −10.8284 | −0.380238 | −0.190119 | − | 0.981761i | \(-0.560887\pi\) | ||||
−0.190119 | + | 0.981761i | \(0.560887\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39.9706 | 1.40183 | ||||||||
\(814\) | 4.00000i | 0.140200i | ||||||||
\(815\) | 3.92893i | 0.137624i | ||||||||
\(816\) | −6.00000 | −0.210042 | ||||||||
\(817\) | −21.5147 | −0.752705 | ||||||||
\(818\) | −45.7990 | −1.60132 | ||||||||
\(819\) | 30.6274 | 1.07021 | ||||||||
\(820\) | 17.1716i | 0.599657i | ||||||||
\(821\) | 1.48528 | 0.0518367 | 0.0259183 | − | 0.999664i | \(-0.491749\pi\) | ||||
0.0259183 | + | 0.999664i | \(0.491749\pi\) | |||||||
\(822\) | − 69.9411i | − 2.43948i | ||||||||
\(823\) | 54.2843i | 1.89223i | 0.323830 | + | 0.946115i | \(0.395029\pi\) | ||||
−0.323830 | + | 0.946115i | \(0.604971\pi\) | |||||||
\(824\) | 21.3137i | 0.742498i | ||||||||
\(825\) | −4.00000 | −0.139262 | ||||||||
\(826\) | 24.9706i | 0.868837i | ||||||||
\(827\) | 32.8995i | 1.14403i | 0.820244 | + | 0.572014i | \(0.193838\pi\) | ||||
−0.820244 | + | 0.572014i | \(0.806162\pi\) | |||||||
\(828\) | 39.5980 | 1.37612 | ||||||||
\(829\) | 29.7990i | 1.03496i | 0.855695 | + | 0.517481i | \(0.173130\pi\) | ||||
−0.855695 | + | 0.517481i | \(0.826870\pi\) | |||||||
\(830\) | 18.4853i | 0.641633i | ||||||||
\(831\) | 41.7990i | 1.44999i | ||||||||
\(832\) | 37.6274 | 1.30450 | ||||||||
\(833\) | − 0.828427i | − 0.0287033i | ||||||||
\(834\) | 81.5980 | 2.82551 | ||||||||
\(835\) | 3.17157 | 0.109757 | ||||||||
\(836\) | −9.51472 | −0.329073 | ||||||||
\(837\) | −4.17157 | −0.144191 | ||||||||
\(838\) | 22.9706i | 0.793505i | ||||||||
\(839\) | − 7.92893i | − 0.273737i | −0.990589 | − | 0.136869i | \(-0.956296\pi\) | ||||
0.990589 | − | 0.136869i | \(-0.0437038\pi\) | |||||||
\(840\) | 30.1421 | 1.04000 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | −89.5980 | −3.08775 | ||||||||
\(843\) | − 77.1838i | − 2.65835i | ||||||||
\(844\) | 74.2132i | 2.55452i | ||||||||
\(845\) | 1.65685 | 0.0569975 | ||||||||
\(846\) | −22.1421 | −0.761262 | ||||||||
\(847\) | −30.6274 | −1.05237 | ||||||||
\(848\) | 28.4558 | 0.977178 | ||||||||
\(849\) | 28.1421i | 0.965836i | ||||||||
\(850\) | −8.00000 | −0.274398 | ||||||||
\(851\) | − 14.6274i | − 0.501421i | ||||||||
\(852\) | 81.5980i | 2.79550i | ||||||||
\(853\) | − 22.9706i | − 0.786497i | −0.919432 | − | 0.393249i | \(-0.871351\pi\) | ||||
0.919432 | − | 0.393249i | \(-0.128649\pi\) | |||||||
\(854\) | 32.9706 | 1.12823 | ||||||||
\(855\) | 16.9706i | 0.580381i | ||||||||
\(856\) | 65.4558i | 2.23723i | ||||||||
\(857\) | −6.17157 | −0.210817 | −0.105408 | − | 0.994429i | \(-0.533615\pi\) | ||||
−0.105408 | + | 0.994429i | \(0.533615\pi\) | |||||||
\(858\) | 9.24264i | 0.315539i | ||||||||
\(859\) | 19.7279i | 0.673108i | 0.941664 | + | 0.336554i | \(0.109261\pi\) | ||||
−0.941664 | + | 0.336554i | \(0.890739\pi\) | |||||||
\(860\) | 13.7279i | 0.468118i | ||||||||
\(861\) | 30.6274 | 1.04378 | ||||||||
\(862\) | 47.4558i | 1.61635i | ||||||||
\(863\) | −17.1127 | −0.582523 | −0.291262 | − | 0.956643i | \(-0.594075\pi\) | ||||
−0.291262 | + | 0.956643i | \(0.594075\pi\) | |||||||
\(864\) | −0.656854 | −0.0223466 | ||||||||
\(865\) | −12.3431 | −0.419680 | ||||||||
\(866\) | −73.9411 | −2.51262 | ||||||||
\(867\) | − 39.3848i | − 1.33758i | ||||||||
\(868\) | − 109.054i | − 3.70153i | ||||||||
\(869\) | −1.00000 | −0.0339227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.6569 | −0.733815 | ||||||||
\(872\) | 55.8701i | 1.89200i | ||||||||
\(873\) | − 12.6863i | − 0.429366i | ||||||||
\(874\) | 52.9706 | 1.79176 | ||||||||
\(875\) | 25.4558 | 0.860565 | ||||||||
\(876\) | −36.9706 | −1.24912 | ||||||||
\(877\) | −37.1421 | −1.25420 | −0.627100 | − | 0.778938i | \(-0.715758\pi\) | ||||
−0.627100 | + | 0.778938i | \(0.715758\pi\) | |||||||
\(878\) | 0.828427i | 0.0279581i | ||||||||
\(879\) | −18.4853 | −0.623493 | ||||||||
\(880\) | 1.24264i | 0.0418894i | ||||||||
\(881\) | − 14.0000i | − 0.471672i | −0.971793 | − | 0.235836i | \(-0.924217\pi\) | ||||
0.971793 | − | 0.235836i | \(-0.0757828\pi\) | |||||||
\(882\) | − 6.82843i | − 0.229925i | ||||||||
\(883\) | −38.4264 | −1.29315 | −0.646576 | − | 0.762850i | \(-0.723800\pi\) | ||||
−0.646576 | + | 0.762850i | \(0.723800\pi\) | |||||||
\(884\) | 12.1421i | 0.408384i | ||||||||
\(885\) | 8.82843i | 0.296764i | ||||||||
\(886\) | 58.7696 | 1.97440 | ||||||||
\(887\) | − 17.1005i | − 0.574179i | −0.957904 | − | 0.287089i | \(-0.907312\pi\) | ||||
0.957904 | − | 0.287089i | \(-0.0926877\pi\) | |||||||
\(888\) | 42.6274i | 1.43048i | ||||||||
\(889\) | − 12.2843i | − 0.412001i | ||||||||
\(890\) | −30.1421 | −1.01037 | ||||||||
\(891\) | − 3.92893i | − 0.131624i | ||||||||
\(892\) | 12.1421 | 0.406549 | ||||||||
\(893\) | −19.4558 | −0.651065 | ||||||||
\(894\) | 45.6274 | 1.52601 | ||||||||
\(895\) | 6.48528 | 0.216779 | ||||||||
\(896\) | − 58.1421i | − 1.94239i | ||||||||
\(897\) | − 33.7990i | − 1.12852i | ||||||||
\(898\) | −84.4264 | −2.81735 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −43.3137 | −1.44379 | ||||||||
\(901\) | − 7.85786i | − 0.261783i | ||||||||
\(902\) | 4.48528i | 0.149344i | ||||||||
\(903\) | 24.4853 | 0.814819 | ||||||||
\(904\) | −58.7696 | −1.95465 | ||||||||
\(905\) | 8.31371 | 0.276357 | ||||||||
\(906\) | 82.4264 | 2.73843 | ||||||||
\(907\) | 22.2843i | 0.739937i | 0.929044 | + | 0.369969i | \(0.120632\pi\) | ||||
−0.929044 | + | 0.369969i | \(0.879368\pi\) | |||||||
\(908\) | 31.1716 | 1.03446 | ||||||||
\(909\) | − 6.62742i | − 0.219818i | ||||||||
\(910\) | − 26.1421i | − 0.866603i | ||||||||
\(911\) | − 15.4437i | − 0.511671i | −0.966720 | − | 0.255835i | \(-0.917649\pi\) | ||||
0.966720 | − | 0.255835i | \(-0.0823505\pi\) | |||||||
\(912\) | −43.4558 | −1.43897 | ||||||||
\(913\) | 3.17157i | 0.104964i | ||||||||
\(914\) | − 2.48528i | − 0.0822058i | ||||||||
\(915\) | 11.6569 | 0.385364 | ||||||||
\(916\) | 13.4558i | 0.444594i | ||||||||
\(917\) | − 60.2843i | − 1.99076i | ||||||||
\(918\) | − 0.828427i | − 0.0273422i | ||||||||
\(919\) | 8.14214 | 0.268584 | 0.134292 | − | 0.990942i | \(-0.457124\pi\) | ||||
0.134292 | + | 0.990942i | \(0.457124\pi\) | |||||||
\(920\) | − 16.1421i | − 0.532190i | ||||||||
\(921\) | −7.00000 | −0.230658 | ||||||||
\(922\) | −33.7990 | −1.11311 | ||||||||
\(923\) | 33.7990 | 1.11251 | ||||||||
\(924\) | 10.8284 | 0.356229 | ||||||||
\(925\) | 16.0000i | 0.526077i | ||||||||
\(926\) | 62.7696i | 2.06274i | ||||||||
\(927\) | 13.6569 | 0.448550 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.6863 | 0.613077 | 0.306539 | − | 0.951858i | \(-0.400829\pi\) | ||||
0.306539 | + | 0.951858i | \(0.400829\pi\) | |||||||
\(930\) | − 58.6985i | − 1.92480i | ||||||||
\(931\) | − 6.00000i | − 0.196642i | ||||||||
\(932\) | −70.1127 | −2.29662 | ||||||||
\(933\) | −6.48528 | −0.212319 | ||||||||
\(934\) | −92.5980 | −3.02990 | ||||||||
\(935\) | 0.343146 | 0.0112221 | ||||||||
\(936\) | 47.7990i | 1.56236i | ||||||||
\(937\) | 16.6274 | 0.543194 | 0.271597 | − | 0.962411i | \(-0.412448\pi\) | ||||
0.271597 | + | 0.962411i | \(0.412448\pi\) | |||||||
\(938\) | 38.6274i | 1.26123i | ||||||||
\(939\) | − 23.7279i | − 0.774331i | ||||||||
\(940\) | 12.4142i | 0.404907i | ||||||||
\(941\) | 56.5980 | 1.84504 | 0.922521 | − | 0.385948i | \(-0.126125\pi\) | ||||
0.922521 | + | 0.385948i | \(0.126125\pi\) | |||||||
\(942\) | 49.4558i | 1.61136i | ||||||||
\(943\) | − 16.4020i | − 0.534123i | ||||||||
\(944\) | −10.9706 | −0.357061 | ||||||||
\(945\) | 1.17157i | 0.0381113i | ||||||||
\(946\) | 3.58579i | 0.116584i | ||||||||
\(947\) | − 2.61522i | − 0.0849834i | −0.999097 | − | 0.0424917i | \(-0.986470\pi\) | ||||
0.999097 | − | 0.0424917i | \(-0.0135296\pi\) | |||||||
\(948\) | −22.3137 | −0.724716 | ||||||||
\(949\) | 15.3137i | 0.497104i | ||||||||
\(950\) | −57.9411 | −1.87986 | ||||||||
\(951\) | −75.9411 | −2.46256 | ||||||||
\(952\) | 10.3431 | 0.335223 | ||||||||
\(953\) | −35.6274 | −1.15409 | −0.577043 | − | 0.816714i | \(-0.695793\pi\) | ||||
−0.577043 | + | 0.816714i | \(0.695793\pi\) | |||||||
\(954\) | − 64.7696i | − 2.09699i | ||||||||
\(955\) | − 25.3137i | − 0.819132i | ||||||||
\(956\) | 75.2548 | 2.43392 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.6569 | −0.538159 | ||||||||
\(959\) | 33.9411i | 1.09602i | ||||||||
\(960\) | − 23.7279i | − 0.765815i | ||||||||
\(961\) | −70.4264 | −2.27182 | ||||||||
\(962\) | 36.9706 | 1.19198 | ||||||||
\(963\) | 41.9411 | 1.35153 | ||||||||
\(964\) | −70.1127 | −2.25818 | ||||||||
\(965\) | 5.17157i | 0.166479i | ||||||||
\(966\) | −60.2843 | −1.93961 | ||||||||
\(967\) | − 35.2426i | − 1.13333i | −0.823949 | − | 0.566663i | \(-0.808234\pi\) | ||||
0.823949 | − | 0.566663i | \(-0.191766\pi\) | |||||||
\(968\) | − 47.7990i | − 1.53632i | ||||||||
\(969\) | 12.0000i | 0.385496i | ||||||||
\(970\) | −10.8284 | −0.347680 | ||||||||
\(971\) | 15.6569i | 0.502452i | 0.967928 | + | 0.251226i | \(0.0808338\pi\) | ||||
−0.967928 | + | 0.251226i | \(0.919166\pi\) | |||||||
\(972\) | − 82.9117i | − 2.65939i | ||||||||
\(973\) | −39.5980 | −1.26945 | ||||||||
\(974\) | − 27.7990i | − 0.890737i | ||||||||
\(975\) | 36.9706i | 1.18401i | ||||||||
\(976\) | 14.4853i | 0.463663i | ||||||||
\(977\) | 36.1716 | 1.15723 | 0.578616 | − | 0.815600i | \(-0.303593\pi\) | ||||
0.578616 | + | 0.815600i | \(0.303593\pi\) | |||||||
\(978\) | 22.8995i | 0.732245i | ||||||||
\(979\) | −5.17157 | −0.165284 | ||||||||
\(980\) | −3.82843 | −0.122295 | ||||||||
\(981\) | 35.7990 | 1.14297 | ||||||||
\(982\) | 51.2843 | 1.63655 | ||||||||
\(983\) | − 21.8701i | − 0.697547i | −0.937207 | − | 0.348773i | \(-0.886598\pi\) | ||||
0.937207 | − | 0.348773i | \(-0.113402\pi\) | |||||||
\(984\) | 47.7990i | 1.52378i | ||||||||
\(985\) | 2.00000 | 0.0637253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.1421 | 0.704792 | ||||||||
\(988\) | 87.9411i | 2.79778i | ||||||||
\(989\) | − 13.1127i | − 0.416960i | ||||||||
\(990\) | 2.82843 | 0.0898933 | ||||||||
\(991\) | 12.8284 | 0.407508 | 0.203754 | − | 0.979022i | \(-0.434686\pi\) | ||||
0.203754 | + | 0.979022i | \(0.434686\pi\) | |||||||
\(992\) | −15.9706 | −0.507066 | ||||||||
\(993\) | −5.82843 | −0.184960 | ||||||||
\(994\) | − 60.2843i | − 1.91210i | ||||||||
\(995\) | −0.485281 | −0.0153845 | ||||||||
\(996\) | 70.7696i | 2.24242i | ||||||||
\(997\) | − 28.2843i | − 0.895772i | −0.894091 | − | 0.447886i | \(-0.852177\pi\) | ||||
0.894091 | − | 0.447886i | \(-0.147823\pi\) | |||||||
\(998\) | − 45.7990i | − 1.44974i | ||||||||
\(999\) | −1.65685 | −0.0524205 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))