Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(161,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.f (of order \(10\), degree \(4\), 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: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.228765625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 5x^{5} + x^{4} + 15x^{3} - 18x^{2} - 27x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 233.2 | ||
Root | \(-0.570223 - 1.63550i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.233 |
Dual form | 363.2.f.c.215.2 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) |
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 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(3\) | 0.570223 | + | 1.63550i | 0.329218 | + | 0.944254i | ||||
\(4\) | 1.61803 | + | 1.17557i | 0.809017 | + | 0.587785i | ||||
\(5\) | −3.15430 | + | 1.02489i | −1.41064 | + | 0.458346i | −0.912617 | − | 0.408815i | \(-0.865942\pi\) |
−0.498027 | + | 0.867161i | \(0.665942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.34969 | + | 1.86519i | −0.783230 | + | 0.621732i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | + | 3.31662i | −0.288675 | + | 0.957427i | ||||
\(13\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.47486 | − | 4.57442i | −0.897205 | − | 1.18111i | ||||
\(16\) | 1.23607 | + | 3.80423i | 0.309017 | + | 0.951057i | ||||
\(17\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(20\) | −6.30860 | − | 2.04979i | −1.41064 | − | 0.458346i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.31662i | 0.691564i | 0.938315 | + | 0.345782i | \(0.112386\pi\) | ||||
−0.938315 | + | 0.345782i | \(0.887614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.85410 | − | 3.52671i | 0.970820 | − | 0.705342i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.39037 | − | 2.77933i | −0.844926 | − | 0.534883i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.54508 | − | 4.75528i | 0.277505 | − | 0.854074i | −0.711040 | − | 0.703151i | \(-0.751776\pi\) |
0.988546 | − | 0.150923i | \(-0.0482244\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.99455 | + | 0.255720i | −0.999091 | + | 0.0426201i | ||||
\(37\) | 5.66312 | + | 4.11450i | 0.931011 | + | 0.676419i | 0.946240 | − | 0.323465i | \(-0.104848\pi\) |
−0.0152291 | + | 0.999884i | \(0.504848\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.50000 | − | 8.29156i | 0.819892 | − | 1.23603i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.89893 | + | 5.36641i | 0.568717 | + | 0.782772i | 0.992402 | − | 0.123038i | \(-0.0392637\pi\) |
−0.423685 | + | 0.905810i | \(0.639264\pi\) | |||||||
\(48\) | −5.51696 | + | 4.19084i | −0.796305 | + | 0.604896i | ||||
\(49\) | 2.16312 | + | 6.65740i | 0.309017 | + | 0.951057i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.6172 | + | 4.09957i | 1.73310 | + | 0.563120i | 0.993892 | − | 0.110353i | \(-0.0351982\pi\) |
0.739212 | + | 0.673473i | \(0.235198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.94946 | − | 2.68321i | 0.253798 | − | 0.349324i | −0.663039 | − | 0.748585i | \(-0.730733\pi\) |
0.916837 | + | 0.399262i | \(0.130733\pi\) | |||||||
\(60\) | −0.244889 | − | 11.4865i | −0.0316151 | − | 1.48290i | ||||
\(61\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.47214 | + | 7.60845i | −0.309017 | + | 0.951057i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.0000 | −1.58820 | −0.794101 | − | 0.607785i | \(-0.792058\pi\) | ||||
−0.794101 | + | 0.607785i | \(0.792058\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.42433 | + | 1.89122i | −0.653012 | + | 0.227676i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.7715 | − | 5.12447i | 1.87173 | − | 0.608162i | 0.880855 | − | 0.473386i | \(-0.156968\pi\) |
0.990876 | − | 0.134777i | \(-0.0430317\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.53584 | + | 5.92785i | 0.985634 | + | 0.684489i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(80\) | −7.79785 | − | 10.7328i | −0.871826 | − | 1.19997i | ||||
\(81\) | 2.04210 | − | 8.76526i | 0.226900 | − | 0.973918i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 16.5831i | − | 1.75781i | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||
0.476999 | − | 0.878904i | \(-0.341725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.89893 | + | 5.36641i | −0.406491 | + | 0.559487i | ||||
\(93\) | 8.65829 | − | 0.184592i | 0.897822 | − | 0.0191413i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.25329 | − | 16.1680i | 0.533391 | − | 1.64161i | −0.213710 | − | 0.976897i | \(-0.568555\pi\) |
0.747101 | − | 0.664711i | \(-0.231445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.0000 | 1.20000 | ||||||||
\(101\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.23607 | + | 2.35114i | 0.318859 | + | 0.231665i | 0.735689 | − | 0.677320i | \(-0.236859\pi\) |
−0.416829 | + | 0.908985i | \(0.636859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(108\) | −3.83646 | − | 9.65824i | −0.369163 | − | 0.929364i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.50000 | + | 11.6082i | −0.332205 | + | 1.10180i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.94946 | − | 2.68321i | −0.183390 | − | 0.252415i | 0.707417 | − | 0.706796i | \(-0.249860\pi\) |
−0.890807 | + | 0.454382i | \(0.849860\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.39919 | − | 10.4616i | −0.316976 | − | 0.975551i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.09017 | − | 5.87785i | 0.726519 | − | 0.527847i | ||||
\(125\) | −1.94946 | + | 2.68321i | −0.174365 | + | 0.239993i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.6970 | + | 4.26719i | 1.43705 | + | 0.367261i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22.0801 | + | 7.17425i | −1.88643 | + | 0.612938i | −0.903613 | + | 0.428350i | \(0.859095\pi\) |
−0.982816 | + | 0.184588i | \(0.940905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.55348 | + | 9.43673i | −0.551903 | + | 0.794716i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −10.0000 | − | 6.63325i | −0.833333 | − | 0.552771i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.65468 | + | 7.33397i | −0.796305 | + | 0.604896i | ||||
\(148\) | 4.32624 | + | 13.3148i | 0.355615 | + | 1.09447i | ||||
\(149\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.5831i | 1.33199i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.6074 | + | 13.5191i | −1.48503 | + | 1.07894i | −0.509140 | + | 0.860684i | \(0.670036\pi\) |
−0.975892 | + | 0.218255i | \(0.929964\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.489779 | + | 22.9730i | 0.0388420 | + | 1.82188i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.94427 | + | 15.2169i | −0.387265 | + | 1.19188i | 0.547558 | + | 0.836768i | \(0.315557\pi\) |
−0.934824 | + | 0.355112i | \(0.884443\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5172 | − | 7.64121i | −0.809017 | − | 0.587785i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.50000 | + | 1.65831i | 0.413405 | + | 0.124646i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.74732 | + | 13.4160i | 0.728549 | + | 1.00276i | 0.999196 | + | 0.0400827i | \(0.0127621\pi\) |
−0.270648 | + | 0.962678i | \(0.587238\pi\) | |||||||
\(180\) | 18.6465 | − | 6.95039i | 1.38983 | − | 0.518052i | ||||
\(181\) | −7.72542 | − | 23.7764i | −0.574226 | − | 1.76729i | −0.638799 | − | 0.769374i | \(-0.720568\pi\) |
0.0645725 | − | 0.997913i | \(-0.479432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −22.0801 | − | 7.17425i | −1.62336 | − | 0.527462i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 13.2665i | 0.967559i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6462 | − | 18.7824i | 0.987407 | − | 1.35905i | 0.0546656 | − | 0.998505i | \(-0.482591\pi\) |
0.932742 | − | 0.360545i | \(-0.117409\pi\) | |||||||
\(192\) | −13.8533 | + | 0.295348i | −0.999773 | + | 0.0213149i | ||||
\(193\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.32624 | + | 13.3148i | −0.309017 | + | 0.951057i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0000 | 1.41776 | 0.708881 | − | 0.705328i | \(-0.249200\pi\) | ||||
0.708881 | + | 0.705328i | \(0.249200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.41290 | − | 21.2614i | −0.522866 | − | 1.49967i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.18615 | − | 7.79304i | −0.429967 | − | 0.541654i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(212\) | 15.5957 | + | 21.4656i | 1.07112 | + | 1.47427i | ||||
\(213\) | 17.3743 | + | 22.8721i | 1.19047 | + | 1.56717i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.809017 | − | 0.587785i | 0.0541758 | − | 0.0393610i | −0.560368 | − | 0.828244i | \(-0.689340\pi\) |
0.614544 | + | 0.788883i | \(0.289340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.82764 | + | 17.3405i | −0.321843 | + | 1.15604i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.54508 | − | 4.75528i | 0.102102 | − | 0.314238i | −0.886937 | − | 0.461890i | \(-0.847172\pi\) |
0.989039 | + | 0.147652i | \(0.0471715\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.7984 | − | 12.9313i | −1.16104 | − | 0.843543i | ||||
\(236\) | 6.30860 | − | 2.04979i | 0.410655 | − | 0.133430i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(240\) | 13.1070 | − | 18.8735i | 0.846051 | − | 1.21828i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5000 | − | 1.65831i | 0.994325 | − | 0.106381i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.6462 | − | 18.7824i | −0.871826 | − | 1.19997i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.7715 | − | 5.12447i | −0.995488 | − | 0.323453i | −0.234427 | − | 0.972134i | \(-0.575321\pi\) |
−0.761061 | + | 0.648680i | \(0.775321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9443 | + | 9.40456i | −0.809017 | + | 0.587785i | ||||
\(257\) | −15.5957 | + | 21.4656i | −0.972833 | + | 1.33899i | −0.0322308 | + | 0.999480i | \(0.510261\pi\) |
−0.940603 | + | 0.339510i | \(0.889739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −44.0000 | −2.70290 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.1216 | − | 9.45608i | 1.65982 | − | 0.578703i | ||||
\(268\) | −21.0344 | − | 15.2824i | −1.28488 | − | 0.933522i | ||||
\(269\) | −12.6172 | + | 4.09957i | −0.769284 | + | 0.249955i | −0.667258 | − | 0.744826i | \(-0.732532\pi\) |
−0.102025 | + | 0.994782i | \(0.532532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.0000 | − | 3.31662i | −0.662122 | − | 0.199637i | ||||
\(277\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.23905 | + | 14.0553i | 0.313654 | + | 0.841471i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(284\) | 31.5430 | + | 10.2489i | 1.87173 | + | 0.608162i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7533 | − | 9.99235i | 0.809017 | − | 0.587785i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.4382 | − | 0.627614i | 1.72570 | − | 0.0367914i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.39919 | + | 10.4616i | −0.197908 | + | 0.609099i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 6.84268 | + | 19.6259i | 0.395062 | + | 1.13310i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.00000 | + | 6.63325i | −0.113776 | + | 0.377352i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.4946 | − | 26.8321i | −1.10544 | − | 1.52151i | −0.827970 | − | 0.560772i | \(-0.810505\pi\) |
−0.277469 | − | 0.960735i | \(-0.589495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.87132 | − | 18.0701i | −0.331867 | − | 1.02138i | −0.968245 | − | 0.250004i | \(-0.919568\pi\) |
0.636378 | − | 0.771377i | \(-0.280432\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.0801 | + | 7.17425i | 1.24014 | + | 0.402946i | 0.854378 | − | 0.519652i | \(-0.173938\pi\) |
0.385763 | + | 0.922598i | \(0.373938\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 26.5330i | − | 1.48324i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 13.6084 | − | 11.7819i | 0.756021 | − | 0.654548i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.0000 | 1.92377 | 0.961887 | − | 0.273447i | \(-0.0881639\pi\) | ||||
0.961887 | + | 0.273447i | \(0.0881639\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.9809 | + | 0.895022i | −1.14975 | + | 0.0490469i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 41.0059 | − | 13.3236i | 2.24039 | − | 0.727947i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.27674 | − | 4.71836i | 0.177968 | − | 0.256266i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.1716 | − | 11.5248i | 0.816814 | − | 0.620475i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 36.4829i | − | 1.94179i | −0.239511 | − | 0.970894i | \(-0.576987\pi\) | ||
0.239511 | − | 0.970894i | \(-0.423013\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −44.4959 | + | 32.3282i | −2.36160 | + | 1.71580i | ||||
\(356\) | 19.4946 | − | 26.8321i | 1.03321 | − | 1.42210i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.87132 | − | 18.0701i | 0.309017 | − | 0.951057i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.9336 | + | 21.7481i | 1.56252 | + | 1.13524i | 0.933903 | + | 0.357526i | \(0.116380\pi\) |
0.628620 | + | 0.777713i | \(0.283620\pi\) | |||||||
\(368\) | −12.6172 | + | 4.09957i | −0.657717 | + | 0.213705i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 14.2264 | + | 9.87975i | 0.737605 | + | 0.512241i | ||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.50000 | − | 1.65831i | −0.284019 | − | 0.0856349i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.72542 | − | 23.7764i | −0.396828 | − | 1.22131i | −0.927528 | − | 0.373753i | \(-0.878071\pi\) |
0.530700 | − | 0.847560i | \(-0.321929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.15430 | + | 1.02489i | 0.161177 | + | 0.0523696i | 0.388494 | − | 0.921451i | \(-0.372995\pi\) |
−0.227317 | + | 0.973821i | \(0.572995\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 27.5066 | − | 19.9847i | 1.39643 | − | 1.01457i | ||||
\(389\) | −21.4441 | + | 29.5153i | −1.08726 | + | 1.49648i | −0.235988 | + | 0.971756i | \(0.575833\pi\) |
−0.851270 | + | 0.524727i | \(0.824167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.4164 | + | 14.1068i | 0.970820 | + | 0.705342i | ||||
\(401\) | 25.2344 | − | 8.19915i | 1.26014 | − | 0.409446i | 0.398599 | − | 0.917125i | \(-0.369497\pi\) |
0.861546 | + | 0.507679i | \(0.169497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.54207 | + | 29.7412i | 0.126317 | + | 1.47785i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.3240 | − | 32.0210i | −1.19982 | − | 1.57948i | ||||
\(412\) | 2.47214 | + | 7.60845i | 0.121793 | + | 0.374842i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.1662i | 1.62028i | 0.586238 | + | 0.810139i | \(0.300608\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.09017 | − | 5.87785i | 0.394291 | − | 0.286469i | −0.372921 | − | 0.927863i | \(-0.621644\pi\) |
0.767211 | + | 0.641394i | \(0.221644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.1707 | − | 5.33715i | −0.932110 | − | 0.259501i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(432\) | 5.14642 | − | 20.1374i | 0.247607 | − | 0.968860i | ||||
\(433\) | −23.4615 | − | 17.0458i | −1.12749 | − | 0.819168i | −0.142160 | − | 0.989844i | \(-0.545405\pi\) |
−0.985327 | + | 0.170676i | \(0.945405\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.5000 | − | 11.6082i | −0.833333 | − | 0.552771i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.4441 | + | 29.5153i | 1.01884 | + | 1.40231i | 0.913014 | + | 0.407928i | \(0.133748\pi\) |
0.105825 | + | 0.994385i | \(0.466252\pi\) | |||||||
\(444\) | −19.3094 | + | 14.6679i | −0.916382 | + | 0.696110i | ||||
\(445\) | 16.9959 | + | 52.3081i | 0.805685 | + | 2.47964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.7715 | − | 5.12447i | −0.744303 | − | 0.241839i | −0.0877747 | − | 0.996140i | \(-0.527976\pi\) |
−0.656528 | + | 0.754302i | \(0.727976\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 6.63325i | − | 0.312002i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.79837 | − | 20.9232i | 0.316976 | − | 0.975551i | ||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.0000 | −1.44069 | −0.720346 | − | 0.693615i | \(-0.756017\pi\) | ||||
−0.720346 | + | 0.693615i | \(0.756017\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −27.1216 | + | 9.45608i | −1.25774 | + | 0.438515i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −41.0059 | + | 13.3236i | −1.89753 | + | 0.616543i | −0.927313 | + | 0.374286i | \(0.877888\pi\) |
−0.970212 | + | 0.242257i | \(0.922112\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −32.7207 | − | 22.7234i | −1.50769 | − | 1.04704i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −37.2930 | + | 13.9008i | −1.70753 | + | 0.636473i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 56.3826i | 2.56020i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.7877 | − | 25.2748i | 1.57638 | − | 1.14531i | 0.655683 | − | 0.755036i | \(-0.272381\pi\) |
0.920699 | − | 0.390273i | \(-0.127619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −27.7065 | + | 0.590695i | −1.25293 | + | 0.0267122i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0000 | 0.898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.3607 | + | 23.5114i | 1.44866 | + | 1.05252i | 0.986141 | + | 0.165907i | \(0.0530552\pi\) |
0.462522 | + | 0.886608i | \(0.346945\pi\) | |||||||
\(500\) | −6.30860 | + | 2.04979i | −0.282129 | + | 0.0916693i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.50000 | − | 21.5581i | 0.288675 | − | 0.957427i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.94946 | − | 2.68321i | −0.0864084 | − | 0.118931i | 0.763624 | − | 0.645661i | \(-0.223418\pi\) |
−0.850033 | + | 0.526730i | \(0.823418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.6172 | − | 4.09957i | −0.555980 | − | 0.180649i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.3430 | − | 34.8817i | 1.11030 | − | 1.52819i | 0.289321 | − | 0.957232i | \(-0.406570\pi\) |
0.820977 | − | 0.570962i | \(-0.193430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.0000 | 0.521739 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.424064 | + | 9.94083i | 0.0184028 | + | 0.431395i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.3837 | + | 23.5918i | −0.707009 | + | 1.01806i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 22.0000 | + | 26.5330i | 0.946729 | + | 1.14180i | ||||
\(541\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 34.4810 | − | 26.1928i | 1.47972 | − | 1.12404i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(548\) | −44.1602 | − | 14.3485i | −1.88643 | − | 0.612938i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.857113 | − | 40.2028i | −0.0363824 | − | 1.70651i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(564\) | −21.6973 | + | 7.56486i | −0.913621 | + | 0.318538i | ||||
\(565\) | 8.89919 | + | 6.46564i | 0.374392 | + | 0.272011i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38.5000 | + | 11.6082i | 1.60836 | + | 0.484939i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.6968 | + | 16.0992i | 0.487789 | + | 0.671385i | ||||
\(576\) | −8.38249 | − | 22.4885i | −0.349270 | − | 0.937022i | ||||
\(577\) | 14.5238 | + | 44.6997i | 0.604634 | + | 1.86087i | 0.499290 | + | 0.866435i | \(0.333594\pi\) |
0.105344 | + | 0.994436i | \(0.466406\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.89893 | + | 5.36641i | −0.160926 | + | 0.221496i | −0.881864 | − | 0.471504i | \(-0.843711\pi\) |
0.720938 | + | 0.693000i | \(0.243711\pi\) | |||||||
\(588\) | −24.2432 | + | 0.516858i | −0.999773 | + | 0.0213149i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.65248 | + | 26.6296i | −0.355615 | + | 1.09447i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.4045 | + | 32.7099i | 0.466754 | + | 1.33873i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.5430 | + | 10.2489i | −1.28881 | + | 0.418760i | −0.871675 | − | 0.490084i | \(-0.836966\pi\) |
−0.417136 | + | 0.908844i | \(0.636966\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.5460 | − | 24.2475i | 1.24393 | − | 0.987436i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 26.5330i | − | 1.06818i | −0.845428 | − | 0.534089i | \(-0.820655\pi\) | ||
0.845428 | − | 0.534089i | \(-0.179345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.809017 | − | 0.587785i | 0.0325171 | − | 0.0236251i | −0.571408 | − | 0.820666i | \(-0.693603\pi\) |
0.603925 | + | 0.797041i | \(0.293603\pi\) | |||||||
\(620\) | −19.4946 | + | 26.8321i | −0.782923 | + | 1.07760i | ||||
\(621\) | 9.21800 | − | 14.5612i | 0.369906 | − | 0.584321i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.87132 | + | 18.0701i | −0.234853 | + | 0.722803i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −46.0000 | −1.83560 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.66312 | + | 4.11450i | 0.225445 | + | 0.163796i | 0.694774 | − | 0.719228i | \(-0.255504\pi\) |
−0.469329 | + | 0.883023i | \(0.655504\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −26.2139 | + | 37.7469i | −1.03945 | + | 1.49676i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.5000 | + | 41.4578i | −1.08788 | + | 1.64005i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.6462 | − | 18.7824i | −0.538994 | − | 0.741862i | 0.449474 | − | 0.893294i | \(-0.351612\pi\) |
−0.988468 | + | 0.151432i | \(0.951612\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.6697 | + | 38.9933i | 0.499644 | + | 1.53775i | 0.809592 | + | 0.586993i | \(0.199688\pi\) |
−0.309948 | + | 0.950753i | \(0.600312\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.0059 | + | 13.3236i | 1.61211 | + | 0.523805i | 0.970061 | − | 0.242861i | \(-0.0780858\pi\) |
0.642046 | + | 0.766666i | \(0.278086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −25.8885 | + | 18.8091i | −1.01387 | + | 0.736622i | ||||
\(653\) | 1.94946 | − | 2.68321i | 0.0762884 | − | 0.105002i | −0.769167 | − | 0.639047i | \(-0.779329\pi\) |
0.845456 | + | 0.534045i | \(0.179329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.0000 | −0.505641 | −0.252821 | − | 0.967513i | \(-0.581358\pi\) | ||||
−0.252821 | + | 0.967513i | \(0.581358\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.42264 | + | 0.987975i | 0.0550025 | + | 0.0381973i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −31.1132 | + | 1.99239i | −1.19755 | + | 0.0766871i | ||||
\(676\) | −8.03444 | − | 24.7275i | −0.309017 | − | 0.951057i | ||||
\(677\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 46.4327i | − | 1.77670i | −0.459167 | − | 0.888350i | \(-0.651852\pi\) | ||
0.459167 | − | 0.888350i | \(-0.348148\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 62.2943 | − | 45.2595i | 2.38014 | − | 1.72928i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.65829 | − | 0.184592i | 0.330334 | − | 0.00704263i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.25329 | − | 16.1680i | 0.199845 | − | 0.615058i | −0.800041 | − | 0.599945i | \(-0.795189\pi\) |
0.999886 | − | 0.0151132i | \(-0.00481087\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.0000 | − | 36.4829i | 0.414284 | − | 1.37402i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.94972 | + | 9.14884i | 0.261187 | + | 0.343835i | ||||
\(709\) | −5.87132 | − | 18.0701i | −0.220502 | − | 0.678636i | −0.998717 | − | 0.0506378i | \(-0.983875\pi\) |
0.778215 | − | 0.627998i | \(-0.216125\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.7715 | + | 5.12447i | 0.590647 | + | 0.191913i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 33.1662i | 1.23948i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.74732 | + | 13.4160i | −0.363514 | + | 0.500333i | −0.951123 | − | 0.308811i | \(-0.900069\pi\) |
0.587610 | + | 0.809144i | \(0.300069\pi\) | |||||||
\(720\) | 38.3414 | + | 10.6743i | 1.42890 | + | 0.397808i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.4508 | − | 47.5528i | 0.574226 | − | 1.76729i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 53.0000 | 1.96566 | 0.982831 | − | 0.184510i | \(-0.0590699\pi\) | ||||
0.982831 | + | 0.184510i | \(0.0590699\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.5506 | + | 24.4046i | 0.427801 | + | 0.903873i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.9372 | − | 33.0285i | 0.846051 | − | 1.21828i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(740\) | −27.2925 | − | 37.5649i | −1.00329 | − | 1.38091i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.6074 | + | 13.5191i | −0.678993 | + | 0.493318i | −0.873024 | − | 0.487678i | \(-0.837844\pi\) |
0.194030 | + | 0.980996i | \(0.437844\pi\) | |||||||
\(752\) | −15.5957 | + | 21.4656i | −0.568717 | + | 0.782772i | ||||
\(753\) | −0.612223 | − | 28.7163i | −0.0223107 | − | 1.04648i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.7426 | − | 36.1401i | 0.426794 | − | 1.31354i | −0.474473 | − | 0.880270i | \(-0.657361\pi\) |
0.901266 | − | 0.433266i | \(-0.142639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 44.1602 | − | 14.3485i | 1.59766 | − | 0.519111i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −22.7622 | − | 15.8076i | −0.821362 | − | 0.570408i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.0000 | − | 13.2665i | −1.58462 | − | 0.477781i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.79785 | − | 10.7328i | −0.280469 | − | 0.386033i | 0.645420 | − | 0.763828i | \(-0.276682\pi\) |
−0.925889 | + | 0.377795i | \(0.876682\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.27051 | − | 28.5317i | −0.333007 | − | 1.02489i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −22.6525 | + | 16.4580i | −0.809017 | + | 0.587785i | ||||
\(785\) | 44.8377 | − | 61.7137i | 1.60032 | − | 2.20266i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −25.0898 | − | 71.9618i | −0.889844 | − | 2.55222i | ||||
\(796\) | 32.3607 | + | 23.5114i | 1.14699 | + | 0.833340i | ||||
\(797\) | 53.6231 | − | 17.4232i | 1.89943 | − | 0.617161i | 0.933294 | − | 0.359113i | \(-0.116921\pi\) |
0.966132 | − | 0.258048i | \(-0.0830794\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 30.9308 | + | 38.9652i | 1.09288 | + | 1.37677i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 13.0000 | − | 43.1161i | 0.458475 | − | 1.52059i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.8994 | − | 18.2977i | −0.489284 | − | 0.644109i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 53.0660i | − | 1.85882i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.1418 | + | 46.6018i | −0.527811 | + | 1.62444i | 0.230878 | + | 0.972983i | \(0.425840\pi\) |
−0.758689 | + | 0.651453i | \(0.774160\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(828\) | −0.848129 | − | 19.8817i | −0.0294745 | − | 0.690936i | ||||
\(829\) | −23.4615 | − | 17.0458i | −0.814851 | − | 0.592024i | 0.100382 | − | 0.994949i | \(-0.467994\pi\) |
−0.915233 | + | 0.402925i | \(0.867994\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.0000 | + | 16.5831i | −0.691301 | + | 0.573197i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.4441 | + | 29.5153i | 0.740332 | + | 1.01898i | 0.998599 | + | 0.0529065i | \(0.0168485\pi\) |
−0.258267 | + | 0.966074i | \(0.583151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.96149 | − | 27.5806i | −0.309017 | − | 0.951057i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 41.0059 | + | 13.3236i | 1.41064 | + | 0.458346i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 53.0660i | 1.82229i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.6462 | + | 18.7824i | −0.467787 | + | 0.643854i | ||||
\(852\) | 1.22445 | + | 57.4326i | 0.0419488 | + | 1.96761i | ||||
\(853\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.0000 | −1.05771 | −0.528853 | − | 0.848713i | \(-0.677378\pi\) | ||||
−0.528853 | + | 0.848713i | \(0.677378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.1602 | − | 14.3485i | 1.50323 | − | 0.488429i | 0.562272 | − | 0.826953i | \(-0.309928\pi\) |
0.940958 | + | 0.338524i | \(0.109928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.1849 | + | 16.7956i | 0.821362 | + | 0.570408i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.8128 | + | 47.7881i | 0.602871 | + | 1.61738i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 16.5831i | − | 0.558700i | −0.960189 | − | 0.279350i | \(-0.909881\pi\) | ||
0.960189 | − | 0.279350i | \(-0.0901189\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.3050 | + | 32.9160i | −1.52463 | + | 1.10771i | −0.565503 | + | 0.824747i | \(0.691318\pi\) |
−0.959130 | + | 0.282964i | \(0.908682\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.0482 | + | 0.406103i | −0.640299 | + | 0.0136510i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.00000 | 0.0669650 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44.4959 | − | 32.3282i | −1.48734 | − | 1.08061i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −28.1963 | + | 22.3823i | −0.939877 | + | 0.746078i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 48.7366 | + | 67.0801i | 1.62006 | + | 2.22982i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.47214 | + | 7.60845i | 0.0820859 | + | 0.252635i | 0.983674 | − | 0.179962i | \(-0.0575975\pi\) |
−0.901588 | + | 0.432597i | \(0.857597\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.30860 | − | 2.04979i | −0.209013 | − | 0.0679125i | 0.202639 | − | 0.979253i | \(-0.435048\pi\) |
−0.411652 | + | 0.911341i | \(0.635048\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.09017 | − | 5.87785i | 0.267307 | − | 0.194210i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.0000 | 1.38095 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.9891 | + | 0.511441i | −0.393774 | + | 0.0167979i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.4688 | + | 16.3983i | −1.65583 | + | 0.538011i | −0.979991 | − | 0.199042i | \(-0.936217\pi\) |
−0.675835 | + | 0.737053i | \(0.736217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.7674 | − | 47.1836i | 1.07276 | − | 1.54472i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.2056 | − | 19.9065i | 0.855186 | − | 0.649624i | ||||
\(940\) | −13.5967 | − | 41.8465i | −0.443477 | − | 1.36488i | ||||
\(941\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 12.6172 | + | 4.09957i | 0.410655 | + | 0.133430i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.2164i | 0.754431i | 0.926126 | + | 0.377215i | \(0.123118\pi\) | ||||
−0.926126 | + | 0.377215i | \(0.876882\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.857113 | + | 40.2028i | 0.0277938 | + | 1.30367i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.7943 | + | 73.2314i | −0.769966 | + | 2.36971i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 43.3946 | − | 15.1297i | 1.40055 | − | 0.488310i | ||||
\(961\) | 4.85410 | + | 3.52671i | 0.156584 | + | 0.113765i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.3430 | − | 34.8817i | −0.813296 | − | 1.11941i | −0.990806 | − | 0.135287i | \(-0.956804\pi\) |
0.177510 | − | 0.984119i | \(-0.443196\pi\) | |||||||
\(972\) | 27.0290 | + | 15.5381i | 0.866955 | + | 0.498386i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −53.6231 | − | 17.4232i | −1.71555 | − | 0.557417i | −0.724311 | − | 0.689473i | \(-0.757842\pi\) |
−0.991242 | + | 0.132056i | \(0.957842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 46.4327i | − | 1.48324i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.4441 | + | 29.5153i | −0.683960 | + | 0.941391i | −0.999973 | − | 0.00736431i | \(-0.997656\pi\) |
0.316012 | + | 0.948755i | \(0.397656\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.9578 | + | 57.2423i | 0.633342 | + | 1.81653i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −63.0860 | + | 20.4979i | −1.99996 | + | 0.649826i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.4276 | − | 33.8038i | −0.424831 | − | 1.06951i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))