Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [88,2,Mod(19,88)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(88, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("88.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 88 = 2^{3} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 88.k (of order \(10\), degree \(4\), 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: | \(0.702683537787\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.64000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 51.2 | ||
Root | \(0.831254 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 88.51 |
Dual form | 88.2.k.a.19.2 |
$q$-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 \(\left(\mathbb{Z}/88\mathbb{Z}\right)^\times\).
\(n\) | \(23\) | \(45\) | \(57\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{7}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.831254 | − | 1.14412i | 0.587785 | − | 0.809017i | ||||
\(3\) | 0.0137431 | − | 0.0422971i | 0.00793461 | − | 0.0244202i | −0.947011 | − | 0.321202i | \(-0.895913\pi\) |
0.954945 | + | 0.296781i | \(0.0959133\pi\) | |||||||
\(4\) | −0.618034 | − | 1.90211i | −0.309017 | − | 0.951057i | ||||
\(5\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(6\) | −0.0369690 | − | 0.0508834i | −0.0150925 | − | 0.0207731i | ||||
\(7\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(8\) | −2.68999 | − | 0.874032i | −0.951057 | − | 0.309017i | ||||
\(9\) | 2.42545 | + | 1.76219i | 0.808484 | + | 0.587398i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.27205 | + | 2.41615i | −0.685048 | + | 0.728498i | ||||
\(12\) | −0.0889475 | −0.0256769 | ||||||||
\(13\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.23607 | + | 2.35114i | −0.809017 | + | 0.587785i | ||||
\(17\) | 2.32662 | + | 3.20231i | 0.564287 | + | 0.776675i | 0.991864 | − | 0.127304i | \(-0.0406325\pi\) |
−0.427576 | + | 0.903979i | \(0.640633\pi\) | |||||||
\(18\) | 4.03233 | − | 1.31018i | 0.950429 | − | 0.308813i | ||||
\(19\) | −4.30278 | − | 1.39806i | −0.987125 | − | 0.320736i | −0.229416 | − | 0.973329i | \(-0.573682\pi\) |
−0.757709 | + | 0.652592i | \(0.773682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.875728 | + | 4.60794i | 0.186706 | + | 0.982416i | ||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | −0.0739380 | + | 0.101767i | −0.0150925 | + | 0.0207731i | ||||
\(25\) | 1.54508 | − | 4.75528i | 0.309017 | − | 0.951057i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.215809 | − | 0.156794i | 0.0415325 | − | 0.0301751i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(32\) | 5.65685i | 1.00000i | ||||||||
\(33\) | 0.0709711 | + | 0.129307i | 0.0123545 | + | 0.0225094i | ||||
\(34\) | 5.59785 | 0.960023 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.85288 | − | 5.70258i | 0.308813 | − | 0.950429i | ||||
\(37\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(38\) | −5.17625 | + | 3.76077i | −0.839699 | + | 0.610077i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.0591 | − | 3.91824i | −1.88332 | − | 0.611926i | −0.984994 | − | 0.172588i | \(-0.944787\pi\) |
−0.898322 | − | 0.439338i | \(-0.855213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 12.7426i | − | 1.94323i | −0.236575 | − | 0.971613i | \(-0.576025\pi\) | ||
0.236575 | − | 0.971613i | \(-0.423975\pi\) | |||||||
\(44\) | 6.00000 | + | 2.82843i | 0.904534 | + | 0.426401i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(48\) | 0.0549726 | + | 0.169188i | 0.00793461 | + | 0.0244202i | ||||
\(49\) | 5.66312 | − | 4.11450i | 0.809017 | − | 0.587785i | ||||
\(50\) | −4.15627 | − | 5.72061i | −0.587785 | − | 0.809017i | ||||
\(51\) | 0.167423 | − | 0.0543992i | 0.0234440 | − | 0.00761741i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(54\) | − | 0.377248i | − | 0.0513369i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.118267 | + | 0.162781i | −0.0156649 | + | 0.0215609i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.58332 | + | 11.0283i | 0.466509 | + | 1.43577i | 0.857075 | + | 0.515191i | \(0.172279\pi\) |
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.47214 | + | 4.70228i | 0.809017 | + | 0.587785i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.206938 | + | 0.0262869i | 0.0254722 | + | 0.00323569i | ||||
\(67\) | 12.3962 | 1.51444 | 0.757220 | − | 0.653160i | \(-0.226557\pi\) | ||||
0.757220 | + | 0.653160i | \(0.226557\pi\) | |||||||
\(68\) | 4.65323 | − | 6.40462i | 0.564287 | − | 0.776675i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(72\) | −4.98423 | − | 6.86021i | −0.587398 | − | 0.808484i | ||||
\(73\) | −11.9395 | + | 3.87937i | −1.39741 | + | 0.454046i | −0.908352 | − | 0.418206i | \(-0.862659\pi\) |
−0.489057 | + | 0.872252i | \(0.662659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.179900 | − | 0.130705i | −0.0207731 | − | 0.0150925i | ||||
\(76\) | 9.04842i | 1.03792i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.77565 | + | 8.54258i | 0.308406 | + | 0.949176i | ||||
\(82\) | −14.5071 | + | 10.5400i | −1.60204 | + | 1.16395i | ||||
\(83\) | 7.56384 | + | 10.4107i | 0.830240 | + | 1.14273i | 0.987878 | + | 0.155230i | \(0.0496119\pi\) |
−0.157639 | + | 0.987497i | \(0.550388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.5791 | − | 10.5923i | −1.57210 | − | 1.14220i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.22359 | − | 4.51360i | 0.876638 | − | 0.481151i | ||||
\(89\) | −17.8873 | −1.89605 | −0.948026 | − | 0.318192i | \(-0.896924\pi\) | ||||
−0.948026 | + | 0.318192i | \(0.896924\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.239268 | + | 0.0777430i | 0.0244202 | + | 0.00793461i | ||||
\(97\) | 14.6151 | + | 10.6185i | 1.48394 | + | 1.07814i | 0.976262 | + | 0.216592i | \(0.0694942\pi\) |
0.507673 | + | 0.861550i | \(0.330506\pi\) | |||||||
\(98\) | − | 9.89949i | − | 1.00000i | ||||||
\(99\) | −9.76847 | + | 1.85647i | −0.981768 | + | 0.186583i | ||||
\(100\) | −10.0000 | −1.00000 | ||||||||
\(101\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(102\) | 0.0769320 | − | 0.236772i | 0.00761741 | − | 0.0234440i | ||||
\(103\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.8797 | + | 3.85993i | 1.14845 | + | 0.373154i | 0.820559 | − | 0.571562i | \(-0.193662\pi\) |
0.327891 | + | 0.944716i | \(0.393662\pi\) | |||||||
\(108\) | −0.431618 | − | 0.313589i | −0.0415325 | − | 0.0301751i | ||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.60617 | − | 4.94328i | 0.151096 | − | 0.465024i | −0.846649 | − | 0.532152i | \(-0.821383\pi\) |
0.997744 | + | 0.0671276i | \(0.0213835\pi\) | |||||||
\(114\) | 0.0879314 | + | 0.270625i | 0.00823553 | + | 0.0253464i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.5964 | + | 5.06758i | 1.43577 | + | 0.466509i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.675596 | − | 10.9792i | −0.0614178 | − | 0.998112i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.331460 | + | 0.456216i | −0.0298868 | + | 0.0411356i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(128\) | 10.7600 | − | 3.49613i | 0.951057 | − | 0.309017i | ||||
\(129\) | −0.538974 | − | 0.175123i | −0.0474540 | − | 0.0154187i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 21.4892i | − | 1.87752i | −0.344574 | − | 0.938759i | \(-0.611977\pi\) | ||
0.344574 | − | 0.938759i | \(-0.388023\pi\) | |||||||
\(132\) | 0.202093 | − | 0.214911i | 0.0175899 | − | 0.0187056i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10.3044 | − | 14.1828i | 0.890165 | − | 1.22521i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.45966 | − | 10.6477i | −0.296663 | − | 0.913036i | ||||
\(137\) | 14.6870 | − | 10.6707i | 1.25480 | − | 0.911664i | 0.256307 | − | 0.966595i | \(-0.417494\pi\) |
0.998490 | + | 0.0549317i | \(0.0174941\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.06998 | + | 2.62210i | −0.684487 | + | 0.222403i | −0.630559 | − | 0.776142i | \(-0.717174\pi\) |
−0.0539282 | + | 0.998545i | \(0.517174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −11.9921 | −0.999341 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.48626 | + | 16.8850i | −0.454046 | + | 1.39741i | ||||
\(147\) | −0.0962020 | − | 0.296079i | −0.00793461 | − | 0.0244202i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(150\) | −0.299085 | + | 0.0971787i | −0.0244202 | + | 0.00793461i | ||||
\(151\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(152\) | 10.3525 | + | 7.52153i | 0.839699 | + | 0.610077i | ||||
\(153\) | 11.8670i | 0.959390i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 12.0810 | + | 3.92537i | 0.949176 | + | 0.308406i | ||||
\(163\) | −19.0863 | − | 13.8670i | −1.49495 | − | 1.08615i | −0.972339 | − | 0.233575i | \(-0.924958\pi\) |
−0.522612 | − | 0.852570i | \(-0.675042\pi\) | |||||||
\(164\) | 25.3594i | 1.98024i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 18.1986 | 1.41249 | ||||||||
\(167\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.01722 | − | 12.3637i | −0.309017 | − | 0.951057i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.97253 | − | 10.9732i | −0.609675 | − | 0.839145i | ||||
\(172\) | −24.2378 | + | 7.87535i | −1.84812 | + | 0.600490i | ||||
\(173\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.67178 | − | 13.1607i | 0.126015 | − | 0.992028i | ||||
\(177\) | 0.515712 | 0.0387633 | ||||||||
\(178\) | −14.8689 | + | 20.4653i | −1.11447 | + | 1.53394i | ||||
\(179\) | −7.53762 | + | 23.1984i | −0.563388 | + | 1.73393i | 0.109303 | + | 0.994008i | \(0.465138\pi\) |
−0.672692 | + | 0.739923i | \(0.734862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.0235 | − | 1.65435i | −0.952370 | − | 0.120978i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(192\) | 0.287840 | − | 0.209128i | 0.0207731 | − | 0.0150925i | ||||
\(193\) | 9.97505 | + | 13.7295i | 0.718020 | + | 0.988269i | 0.999587 | + | 0.0287278i | \(0.00914559\pi\) |
−0.281568 | + | 0.959541i | \(0.590854\pi\) | |||||||
\(194\) | 24.2977 | − | 7.89479i | 1.74447 | − | 0.566813i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.3262 | − | 8.22899i | −0.809017 | − | 0.587785i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | −5.99604 | + | 12.7195i | −0.426120 | + | 0.903938i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | −8.31254 | + | 11.4412i | −0.587785 | + | 0.809017i | ||||
\(201\) | 0.170363 | − | 0.524324i | 0.0120165 | − | 0.0369829i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.206947 | − | 0.284838i | −0.0144892 | − | 0.0199426i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.1540 | − | 7.21972i | 0.909884 | − | 0.499398i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.26809 | + | 10.0037i | −0.500356 | + | 0.688681i | −0.982256 | − | 0.187545i | \(-0.939947\pi\) |
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.2912 | − | 10.3832i | 0.976930 | − | 0.709781i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.717568 | + | 0.233152i | −0.0488243 | + | 0.0158640i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.558319i | 0.0377277i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.1273 | − | 8.81097i | 0.808484 | − | 0.587398i | ||||
\(226\) | −4.32058 | − | 5.94677i | −0.287401 | − | 0.395573i | ||||
\(227\) | 27.9665 | − | 9.08687i | 1.85620 | − | 0.603117i | 0.860617 | − | 0.509252i | \(-0.170078\pi\) |
0.995585 | − | 0.0938647i | \(-0.0299221\pi\) | |||||||
\(228\) | 0.382722 | + | 0.124354i | 0.0253464 | + | 0.00823553i | ||||
\(229\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.67475 | + | 10.5634i | −0.502790 | + | 0.692031i | −0.982683 | − | 0.185296i | \(-0.940675\pi\) |
0.479893 | + | 0.877327i | \(0.340675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 18.7625 | − | 13.6318i | 1.22134 | − | 0.887352i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.9717i | 1.93064i | 0.261061 | + | 0.965322i | \(0.415928\pi\) | ||||
−0.261061 | + | 0.965322i | \(0.584072\pi\) | |||||||
\(242\) | −13.1232 | − | 8.35357i | −0.843590 | − | 0.536988i | ||||
\(243\) | 1.19974 | 0.0769631 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.246439 | + | 0.758462i | 0.0157124 | + | 0.0483578i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.544295 | − | 0.176852i | 0.0344933 | − | 0.0112075i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.85410 | − | 3.52671i | −0.306388 | − | 0.222604i | 0.423957 | − | 0.905682i | \(-0.360641\pi\) |
−0.730345 | + | 0.683078i | \(0.760641\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.94427 | − | 15.2169i | 0.309017 | − | 0.951057i | ||||
\(257\) | −5.44503 | − | 16.7581i | −0.339651 | − | 1.04534i | −0.964385 | − | 0.264502i | \(-0.914792\pi\) |
0.624734 | − | 0.780838i | \(-0.285208\pi\) | |||||||
\(258\) | −0.648387 | + | 0.471081i | −0.0403668 | + | 0.0293282i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.5863 | − | 17.8630i | −1.51894 | − | 1.10358i | ||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | −0.0778938 | − | 0.409865i | −0.00479403 | − | 0.0252254i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.245828 | + | 0.756581i | −0.0150444 | + | 0.0463020i | ||||
\(268\) | −7.66129 | − | 23.5790i | −0.467987 | − | 1.44032i | ||||
\(269\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(272\) | −15.0582 | − | 4.89270i | −0.913036 | − | 0.296663i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 25.6739i | − | 1.55101i | ||||||
\(275\) | 7.97899 | + | 14.5374i | 0.481151 | + | 0.876638i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(278\) | −3.70820 | + | 11.4127i | −0.222403 | + | 0.684487i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.23112 | − | 9.95279i | −0.431373 | − | 0.593734i | 0.536895 | − | 0.843649i | \(-0.319597\pi\) |
−0.968268 | + | 0.249916i | \(0.919597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.2099 | + | 7.86629i | 1.43913 | + | 0.467602i | 0.921627 | − | 0.388078i | \(-0.126861\pi\) |
0.517505 | + | 0.855680i | \(0.326861\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −9.96847 | + | 13.7204i | −0.587398 | + | 0.808484i | ||||
\(289\) | 0.411629 | − | 1.26686i | 0.0242135 | − | 0.0745214i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.649987 | − | 0.472243i | 0.0381029 | − | 0.0276834i | ||||
\(292\) | 14.7580 | + | 20.3126i | 0.863647 | + | 1.18871i | ||||
\(293\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(294\) | −0.418720 | − | 0.136050i | −0.0244202 | − | 0.00793461i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.111489 | + | 0.877672i | −0.00646925 | + | 0.0509277i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.137431 | + | 0.422971i | −0.00793461 | + | 0.0244202i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 17.2111 | − | 5.59223i | 0.987125 | − | 0.320736i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 13.5773 | + | 9.86449i | 0.776163 | + | 0.563915i | ||||
\(307\) | 13.1200i | 0.748796i | 0.927268 | + | 0.374398i | \(0.122151\pi\) | ||||
−0.927268 | + | 0.374398i | \(0.877849\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.6150 | + | 17.1573i | −1.33480 | + | 0.969788i | −0.335181 | + | 0.942154i | \(0.608798\pi\) |
−0.999618 | + | 0.0276348i | \(0.991202\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.326528 | − | 0.449427i | 0.0182250 | − | 0.0250846i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.53390 | − | 17.0316i | −0.307914 | − | 0.947663i | ||||
\(324\) | 14.5335 | − | 10.5592i | 0.807417 | − | 0.586623i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −31.7311 | + | 10.3100i | −1.75742 | + | 0.571021i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 29.0143 | + | 21.0801i | 1.60204 | + | 1.16395i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.9970 | 1.97857 | 0.989287 | − | 0.145981i | \(-0.0466339\pi\) | ||||
0.989287 | + | 0.145981i | \(0.0466339\pi\) | |||||||
\(332\) | 15.1277 | − | 20.8215i | 0.830240 | − | 1.14273i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.68807 | + | 0.873408i | −0.146429 | + | 0.0475775i | −0.381314 | − | 0.924445i | \(-0.624528\pi\) |
0.234886 | + | 0.972023i | \(0.424528\pi\) | |||||||
\(338\) | −17.4850 | − | 5.68121i | −0.951057 | − | 0.309017i | ||||
\(339\) | −0.187012 | − | 0.135872i | −0.0101571 | − | 0.00737958i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −19.1819 | −1.03724 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.1374 | + | 34.2775i | −0.600490 | + | 1.84812i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.32456 | − | 4.57586i | −0.178472 | − | 0.245645i | 0.710404 | − | 0.703795i | \(-0.248512\pi\) |
−0.888875 | + | 0.458149i | \(0.848512\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −13.6678 | − | 12.8526i | −0.728498 | − | 0.685048i | ||||
\(353\) | −30.7905 | −1.63881 | −0.819405 | − | 0.573214i | \(-0.805696\pi\) | ||||
−0.819405 | + | 0.573214i | \(0.805696\pi\) | |||||||
\(354\) | 0.428688 | − | 0.590038i | 0.0227845 | − | 0.0313602i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.0550 | + | 34.0237i | 0.585912 | + | 1.80325i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.2762 | + | 27.9077i | 1.07163 | + | 1.47497i | ||||
\(359\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.18802 | + | 0.863144i | 0.0625272 | + | 0.0454286i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.473674 | − | 0.122314i | −0.0248614 | − | 0.00641980i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.3441 | − | 30.7540i | −1.16319 | − | 1.60099i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | −12.7186 | + | 13.5253i | −0.657662 | + | 0.699374i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.9063 | + | 21.0017i | −1.48482 | + | 1.07878i | −0.508853 | + | 0.860853i | \(0.669930\pi\) |
−0.975964 | + | 0.217930i | \(0.930070\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(384\) | − | 0.503163i | − | 0.0256769i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.0000 | 1.22157 | ||||||||
\(387\) | 22.4549 | − | 30.9065i | 1.14145 | − | 1.57107i | ||||
\(388\) | 11.1649 | − | 34.3621i | 0.566813 | − | 1.74447i | ||||
\(389\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −18.8300 | + | 6.11822i | −0.951057 | + | 0.309017i | ||||
\(393\) | −0.908929 | − | 0.295329i | −0.0458494 | − | 0.0148974i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.56847 | + | 17.4334i | 0.480834 | + | 0.876060i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.18034 | + | 19.0211i | 0.309017 | + | 0.951057i | ||||
\(401\) | −14.9029 | + | 10.8276i | −0.744216 | + | 0.540704i | −0.894029 | − | 0.448010i | \(-0.852133\pi\) |
0.149813 | + | 0.988714i | \(0.452133\pi\) | |||||||
\(402\) | −0.458276 | − | 0.630762i | −0.0228567 | − | 0.0314596i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.497915 | −0.0246504 | ||||||||
\(409\) | 19.9501 | − | 27.4589i | 0.986469 | − | 1.35776i | 0.0531978 | − | 0.998584i | \(-0.483059\pi\) |
0.933271 | − | 0.359174i | \(-0.116941\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.249495 | − | 0.767868i | −0.0123067 | − | 0.0378761i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.377372i | 0.0184800i | ||||||||
\(418\) | 2.67410 | − | 21.0513i | 0.130795 | − | 1.02965i | ||||
\(419\) | −36.1749 | −1.76726 | −0.883630 | − | 0.468186i | \(-0.844908\pi\) | ||||
−0.883630 | + | 0.468186i | \(0.844908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(422\) | 5.40380 | + | 16.6312i | 0.263053 | + | 0.809593i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.8227 | − | 6.11587i | 0.913036 | − | 0.296663i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 24.9820i | − | 1.20755i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(432\) | −0.329727 | + | 1.01479i | −0.0158640 | + | 0.0488243i | ||||
\(433\) | −1.35885 | − | 4.18210i | −0.0653020 | − | 0.200979i | 0.913082 | − | 0.407777i | \(-0.133696\pi\) |
−0.978384 | + | 0.206798i | \(0.933696\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0.638786 | + | 0.464105i | 0.0305224 | + | 0.0221758i | ||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.9862 | 0.999341 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.0137 | − | 33.8968i | 0.523279 | − | 1.61049i | −0.244416 | − | 0.969670i | \(-0.578596\pi\) |
0.767695 | − | 0.640816i | \(-0.221404\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.14750 | − | 4.46642i | −0.290118 | − | 0.210783i | 0.433200 | − | 0.901298i | \(-0.357384\pi\) |
−0.723319 | + | 0.690514i | \(0.757384\pi\) | |||||||
\(450\) | − | 21.1992i | − | 0.999341i | ||||||
\(451\) | 36.8659 | − | 20.2342i | 1.73595 | − | 0.952792i | ||||
\(452\) | −10.3953 | −0.488956 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.8508 | − | 39.5506i | 0.603117 | − | 1.85620i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.460415 | − | 0.334511i | 0.0215609 | − | 0.0156649i | ||||
\(457\) | 7.15719 | + | 9.85102i | 0.334799 | + | 0.460811i | 0.942913 | − | 0.333038i | \(-0.108074\pi\) |
−0.608114 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.00421 | + | 0.326287i | 0.0468725 | + | 0.0152298i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.70615 | + | 17.5617i | 0.264332 | + | 0.813531i | ||||
\(467\) | −24.2705 | + | 17.6336i | −1.12311 | + | 0.815984i | −0.984677 | − | 0.174389i | \(-0.944205\pi\) |
−0.138428 | + | 0.990372i | \(0.544205\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 32.7981i | − | 1.50965i | ||||||
\(473\) | 30.7881 | + | 28.9518i | 1.41564 | + | 1.33120i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.2963 | + | 18.3008i | −0.610077 | + | 0.839699i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 34.2913 | + | 24.9141i | 1.56192 | + | 1.13480i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −20.4662 | + | 8.07060i | −0.930282 | + | 0.366845i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.997285 | − | 1.37265i | 0.0452378 | − | 0.0622645i | ||||
\(487\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.848838 | + | 0.616717i | −0.0383858 | + | 0.0278889i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.5975 | + | 4.09316i | −0.568515 | + | 0.184722i | −0.579149 | − | 0.815222i | \(-0.696615\pi\) |
0.0106338 | + | 0.999943i | \(0.496615\pi\) | |||||||
\(492\) | 1.07263 | + | 0.348518i | 0.0483578 | + | 0.0157124i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.250107 | − | 0.769749i | 0.0112075 | − | 0.0344933i | ||||
\(499\) | 11.2061 | + | 34.4890i | 0.501656 | + | 1.54394i | 0.806321 | + | 0.591479i | \(0.201456\pi\) |
−0.304664 | + | 0.952460i | \(0.598544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.06998 | + | 2.62210i | −0.360181 | + | 0.117030i | ||||
\(503\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.578159 | −0.0256769 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −13.3001 | − | 18.3060i | −0.587785 | − | 0.809017i | ||||
\(513\) | −1.14779 | + | 0.372938i | −0.0506760 | + | 0.0164656i | ||||
\(514\) | −23.6995 | − | 7.70043i | −1.04534 | − | 0.339651i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.13342i | 0.0498961i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.7271 | + | 39.1700i | 0.557585 | + | 1.71607i | 0.689017 | + | 0.724745i | \(0.258042\pi\) |
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.6190 | − | 22.8740i | −0.726696 | − | 1.00021i | −0.999275 | − | 0.0380781i | \(-0.987876\pi\) |
0.272578 | − | 0.962134i | \(-0.412124\pi\) | |||||||
\(524\) | −40.8748 | + | 13.2810i | −1.78563 | + | 0.580185i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.533685 | − | 0.251582i | −0.0232257 | − | 0.0109487i | ||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.7429 | + | 33.0632i | −0.466201 | + | 1.43482i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.661276 | + | 0.910169i | 0.0286162 | + | 0.0393868i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −33.3458 | − | 10.8347i | −1.44032 | − | 0.467987i | ||||
\(537\) | 0.877634 | + | 0.637639i | 0.0378727 | + | 0.0275161i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.92562 | + | 23.0313i | −0.126015 | + | 0.992028i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18.1150 | + | 13.1613i | −0.776675 | + | 0.564287i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.1012 | − | 14.3293i | −1.88563 | − | 0.612678i | −0.983409 | − | 0.181402i | \(-0.941936\pi\) |
−0.902220 | − | 0.431276i | \(-0.858064\pi\) | |||||||
\(548\) | −29.3741 | − | 21.3415i | −1.25480 | − | 0.911664i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 23.2651 | + | 2.95532i | 0.992028 | + | 0.126015i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.97505 | + | 13.7295i | 0.423036 | + | 0.582259i | ||||
\(557\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.248957 | + | 0.528118i | −0.0105110 | + | 0.0222972i | ||||
\(562\) | −17.3981 | −0.733895 | ||||||||
\(563\) | 7.12022 | − | 9.80014i | 0.300081 | − | 0.413027i | −0.632175 | − | 0.774826i | \(-0.717837\pi\) |
0.932256 | + | 0.361799i | \(0.117837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 29.1246 | − | 21.1603i | 1.22420 | − | 0.889432i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 44.6394 | + | 14.5042i | 1.87138 | + | 0.608048i | 0.991015 | + | 0.133753i | \(0.0427029\pi\) |
0.880366 | + | 0.474295i | \(0.157297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.4264i | 1.77549i | 0.460336 | + | 0.887745i | \(0.347729\pi\) | ||||
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.41152 | + | 22.8103i | 0.308813 | + | 0.950429i | ||||
\(577\) | −34.6150 | + | 25.1493i | −1.44104 | + | 1.04698i | −0.453218 | + | 0.891400i | \(0.649724\pi\) |
−0.987824 | + | 0.155579i | \(0.950276\pi\) | |||||||
\(578\) | −1.10728 | − | 1.52404i | −0.0460567 | − | 0.0633917i | ||||
\(579\) | 0.717805 | − | 0.233229i | 0.0298310 | − | 0.00969266i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 1.13622i | − | 0.0470978i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 35.5078 | 1.46932 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.7043 | − | 45.2551i | −0.606910 | − | 1.86788i | −0.483087 | − | 0.875573i | \(-0.660484\pi\) |
−0.123823 | − | 0.992304i | \(-0.539516\pi\) | |||||||
\(588\) | −0.503720 | + | 0.365974i | −0.0207731 | + | 0.0150925i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 31.1035i | − | 1.27727i | −0.769510 | − | 0.638634i | \(-0.779500\pi\) | ||
0.769510 | − | 0.638634i | \(-0.220500\pi\) | |||||||
\(594\) | 0.911489 | + | 0.857126i | 0.0373988 | + | 0.0351683i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(600\) | 0.369690 | + | 0.508834i | 0.0150925 | + | 0.0207731i | ||||
\(601\) | 12.6573 | − | 4.11260i | 0.516301 | − | 0.167756i | −0.0392649 | − | 0.999229i | \(-0.512502\pi\) |
0.555566 | + | 0.831472i | \(0.312502\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.0664 | + | 21.8445i | 1.22440 | + | 0.889578i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(608\) | 7.90861 | − | 24.3402i | 0.320736 | − | 0.987125i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 22.5724 | − | 7.33421i | 0.912434 | − | 0.296468i | ||||
\(613\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(614\) | 15.0108 | + | 10.9060i | 0.605789 | + | 0.440131i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.3894 | 1.14291 | 0.571457 | − | 0.820632i | \(-0.306378\pi\) | ||||
0.571457 | + | 0.820632i | \(0.306378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.9516 | − | 46.0163i | 0.600955 | − | 1.84955i | 0.0784409 | − | 0.996919i | \(-0.475006\pi\) |
0.522514 | − | 0.852631i | \(-0.324994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.2254 | − | 14.6946i | −0.809017 | − | 0.587785i | ||||
\(626\) | 41.2806i | 1.64990i | ||||||||
\(627\) | −0.124595 | − | 0.655599i | −0.00497584 | − | 0.0261821i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.323239 | + | 0.444901i | 0.0128476 | + | 0.0176832i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.36257 | − | 16.5043i | 0.211809 | − | 0.651880i | −0.787556 | − | 0.616243i | \(-0.788654\pi\) |
0.999365 | − | 0.0356372i | \(-0.0113461\pi\) | |||||||
\(642\) | −0.242772 | − | 0.747176i | −0.00958145 | − | 0.0294887i | ||||
\(643\) | 28.6904 | − | 20.8448i | 1.13144 | − | 0.822039i | 0.145537 | − | 0.989353i | \(-0.453509\pi\) |
0.985904 | + | 0.167313i | \(0.0535092\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.0863 | − | 7.82611i | −0.947663 | − | 0.307914i | ||||
\(647\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(648\) | − | 25.4055i | − | 0.998023i | ||||||
\(649\) | −34.7876 | − | 16.3990i | −1.36553 | − | 0.643718i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.5806 | + | 44.8745i | −0.571021 | + | 1.75742i | ||||
\(653\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 48.2364 | − | 15.6730i | 1.88332 | − | 0.611926i | ||||
\(657\) | −35.7948 | − | 11.6304i | −1.39649 | − | 0.453746i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2.26047i | − | 0.0880555i | −0.999030 | − | 0.0440278i | \(-0.985981\pi\) | ||
0.999030 | − | 0.0440278i | \(-0.0140190\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 29.9227 | − | 41.1850i | 1.16298 | − | 1.60070i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.2474 | − | 34.6159i | −0.436483 | − | 1.34336i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.65721 | − | 5.03371i | 0.140975 | − | 0.194035i | −0.732691 | − | 0.680561i | \(-0.761736\pi\) |
0.873666 | + | 0.486526i | \(0.161736\pi\) | |||||||
\(674\) | −1.23518 | + | 3.80151i | −0.0475775 | + | 0.146429i | ||||
\(675\) | −0.412159 | − | 1.26849i | −0.0158640 | − | 0.0488243i | ||||
\(676\) | −21.0344 | + | 15.2824i | −0.809017 | + | 0.587785i | ||||
\(677\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(678\) | −0.310909 | + | 0.101021i | −0.0119404 | + | 0.00387967i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1.30778i | − | 0.0501144i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.0000 | −1.60709 | −0.803543 | − | 0.595247i | \(-0.797054\pi\) | ||||
−0.803543 | + | 0.595247i | \(0.797054\pi\) | |||||||
\(684\) | −15.9451 | + | 21.9465i | −0.609675 | + | 0.839145i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 29.9596 | + | 41.2359i | 1.14220 | + | 1.57210i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.08626 | − | 5.87501i | −0.307616 | − | 0.223496i | 0.423257 | − | 0.906010i | \(-0.360887\pi\) |
−0.730873 | + | 0.682514i | \(0.760887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.99890 | −0.303634 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.5095 | − | 47.7333i | −0.587463 | − | 1.80803i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.341325 | + | 0.469794i | 0.0129101 | + | 0.0177692i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −26.0664 | + | 4.95386i | −0.982416 | + | 0.186706i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −25.5947 | + | 35.2281i | −0.963269 | + | 1.32583i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.318727 | − | 0.980942i | −0.0119785 | − | 0.0368661i | ||||
\(709\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 48.1168 | + | 15.6341i | 1.80325 | + | 0.585912i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 48.7845 | 1.82316 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.97509 | − | 0.641744i | 0.0735051 | − | 0.0238833i | ||||
\(723\) | 1.26771 | + | 0.411905i | 0.0471468 | + | 0.0153189i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.533685 | + | 0.440268i | −0.0198069 | + | 0.0163399i | ||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.31047 | + | 25.5770i | −0.307795 | + | 0.947296i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.8057 | − | 29.6471i | 1.50925 | − | 1.09654i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −28.1648 | + | 29.9512i | −1.03746 | + | 1.10327i | ||||
\(738\) | −53.7599 | −1.97893 | ||||||||
\(739\) | 11.3004 | − | 15.5537i | 0.415693 | − | 0.572152i | −0.548902 | − | 0.835886i | \(-0.684954\pi\) |
0.964595 | + | 0.263734i | \(0.0849541\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 38.5797i | 1.41156i | ||||||||
\(748\) | 4.90219 | + | 25.7945i | 0.179242 | + | 0.943142i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.215880 | + | 0.156846i | −0.00786711 | + | 0.00571579i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(758\) | 50.5301i | 1.83534i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.2419 | + | 44.3772i | −1.16877 | + | 1.60867i | −0.497475 | + | 0.867479i | \(0.665739\pi\) |
−0.671293 | + | 0.741192i | \(0.734261\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.575680 | − | 0.418256i | −0.0207731 | − | 0.0150925i | ||||
\(769\) | − | 50.9117i | − | 1.83592i | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||
0.396670 | − | 0.917961i | \(-0.370166\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.783649 | −0.0282224 | ||||||||
\(772\) | 19.9501 | − | 27.4589i | 0.718020 | − | 0.988269i | ||||
\(773\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(774\) | −16.6951 | − | 51.3823i | −0.600094 | − | 1.84690i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −30.0336 | − | 41.3377i | −1.07814 | − | 1.48394i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 46.4097 | + | 33.7186i | 1.66280 | + | 1.20810i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.65248 | + | 26.6296i | −0.309017 | + | 0.951057i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.09344 | + | 0.794433i | −0.0390018 | + | 0.0283365i | ||||
\(787\) | 32.5745 | + | 44.8350i | 1.16116 | + | 1.59820i | 0.706877 | + | 0.707336i | \(0.250103\pi\) |
0.454280 | + | 0.890859i | \(0.349897\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 27.8997 | + | 3.54405i | 0.991374 | + | 0.125932i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 26.8999 | + | 8.74032i | 0.951057 | + | 0.309017i | ||||
\(801\) | −43.3848 | − | 31.5209i | −1.53293 | − | 1.11374i | ||||
\(802\) | 26.0512i | 0.919901i | ||||||||
\(803\) | 17.7539 | − | 37.6617i | 0.626522 | − | 1.32905i | ||||
\(804\) | −1.10261 | −0.0388862 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.6290 | + | 18.7587i | 0.479169 | + | 0.659519i | 0.978345 | − | 0.206981i | \(-0.0663639\pi\) |
−0.499176 | + | 0.866501i | \(0.666364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.4011 | − | 3.70445i | −0.400347 | − | 0.130081i | 0.101921 | − | 0.994792i | \(-0.467501\pi\) |
−0.502268 | + | 0.864712i | \(0.667501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.413893 | + | 0.569675i | −0.0144892 | + | 0.0199426i | ||||
\(817\) | −17.8149 | + | 54.8285i | −0.623264 | + | 1.91821i | ||||
\(818\) | −14.8328 | − | 45.6507i | −0.518617 | − | 1.59614i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(822\) | −1.08593 | − | 0.352840i | −0.0378761 | − | 0.0123067i | ||||
\(823\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.724545 | − | 0.137698i | 0.0252254 | − | 0.00479403i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.5907 | + | 36.5990i | −0.924650 | + | 1.27267i | 0.0372604 | + | 0.999306i | \(0.488137\pi\) |
−0.961910 | + | 0.273366i | \(0.911863\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.3518 | + | 8.56222i | 0.913036 | + | 0.296663i | ||||
\(834\) | 0.431760 | + | 0.313692i | 0.0149506 | + | 0.0108623i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −21.8624 | − | 20.5584i | −0.756126 | − | 0.711029i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −30.0705 | + | 41.3885i | −1.03877 | + | 1.42974i | ||||
\(839\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.4615 | − | 17.0458i | 0.809017 | − | 0.587785i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.520352 | + | 0.169073i | −0.0179219 | + | 0.00582317i | ||||
\(844\) | 23.5200 | + | 7.64212i | 0.809593 | + | 0.263053i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.665442 | − | 0.915902i | 0.0228379 | − | 0.0314337i | ||||
\(850\) | 8.64915 | − | 26.6193i | 0.296663 | − | 0.913036i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −28.5825 | − | 20.7664i | −0.976930 | − | 0.709781i | ||||
\(857\) | − | 13.4344i | − | 0.458912i | −0.973319 | − | 0.229456i | \(-0.926305\pi\) | ||
0.973319 | − | 0.229456i | \(-0.0736947\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.9930 | 0.886869 | 0.443434 | − | 0.896307i | \(-0.353760\pi\) | ||||
0.443434 | + | 0.896307i | \(0.353760\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(864\) | 0.886963 | + | 1.22080i | 0.0301751 | + | 0.0415325i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.91438 | − | 1.92170i | −0.200979 | − | 0.0653020i | ||||
\(867\) | −0.0479275 | − | 0.0348214i | −0.00162770 | − | 0.00118260i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.7363 | + | 51.5091i | 0.566439 | + | 1.74332i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.06199 | − | 0.345060i | 0.0358812 | − | 0.0116585i | ||||
\(877\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.6878 | 0.629610 | 0.314805 | − | 0.949156i | \(-0.398061\pi\) | ||||
0.314805 | + | 0.949156i | \(0.398061\pi\) | |||||||
\(882\) | 17.4448 | − | 24.0107i | 0.587398 | − | 0.808484i | ||||
\(883\) | −11.2886 | + | 34.7428i | −0.379892 | + | 1.16919i | 0.560227 | + | 0.828339i | \(0.310714\pi\) |
−0.940119 | + | 0.340848i | \(0.889286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.6269 | − | 40.7779i | −0.995335 | − | 1.36996i | ||||
\(887\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.9466 | − | 12.7028i | −0.902745 | − | 0.425558i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.2203 | + | 3.32076i | −0.341055 | + | 0.110815i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −24.2545 | − | 17.6219i | −0.808484 | − | 0.587398i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 7.49452 | − | 58.9989i | 0.249540 | − | 1.96445i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.64117 | + | 11.8935i | −0.287401 | + | 0.395573i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.2013 | − | 35.0203i | 1.60050 | − | 1.16283i | 0.713943 | − | 0.700204i | \(-0.246908\pi\) |
0.886554 | − | 0.462625i | \(-0.153092\pi\) | |||||||
\(908\) | −34.5685 | − | 47.5795i | −1.14720 | − | 1.57898i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(912\) | − | 0.804834i | − | 0.0266507i | ||||||
\(913\) | −42.3394 | − | 5.37829i | −1.40123 | − | 0.177995i | ||||
\(914\) | 17.2202 | 0.569594 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.20807 | − | 0.877711i | 0.0398721 | − | 0.0289688i | ||||
\(919\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.554936 | + | 0.180310i | 0.0182858 | + | 0.00594140i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.2625 | − | 25.6197i | 1.15693 | − | 0.840555i | 0.167539 | − | 0.985865i | \(-0.446418\pi\) |
0.989386 | + | 0.145310i | \(0.0464179\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.1195 | + | 9.78640i | −0.987125 | + | 0.320736i | ||||
\(932\) | 24.8360 | + | 8.06971i | 0.813531 | + | 0.264332i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 42.4264i | 1.38823i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.2540 | − | 38.8882i | 0.923016 | − | 1.27042i | −0.0395055 | − | 0.999219i | \(-0.512578\pi\) |
0.962522 | − | 0.271204i | \(-0.0874217\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.401159 | + | 1.23464i | 0.0130913 | + | 0.0402910i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −37.5250 | − | 27.2635i | −1.22134 | − | 0.887352i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 58.7171 | − | 11.1590i | 1.90906 | − | 0.362812i | ||||
\(947\) | −60.3804 | −1.96210 | −0.981050 | − | 0.193757i | \(-0.937933\pi\) | ||||
−0.981050 | + | 0.193757i | \(0.937933\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 9.88576 | + | 30.4252i | 0.320736 | + | 0.987125i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.3413 | − | 3.68501i | 0.367381 | − | 0.119369i | −0.119508 | − | 0.992833i | \(-0.538132\pi\) |
0.486889 | + | 0.873464i | \(0.338132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.57953 | + | 29.4828i | 0.309017 | + | 0.951057i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.0116 | + | 30.2963i | 0.709313 | + | 0.976285i | ||||
\(964\) | 57.0095 | − | 18.5235i | 1.83615 | − | 0.596602i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(968\) | −7.77885 | + | 30.1246i | −0.250022 | + | 0.968240i | ||||
\(969\) | −0.796439 | −0.0255853 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.6869 | − | 51.3571i | 0.535509 | − | 1.64813i | −0.207039 | − | 0.978333i | \(-0.566383\pi\) |
0.742547 | − | 0.669793i | \(-0.233617\pi\) | |||||||
\(972\) | −0.741478 | − | 2.28203i | −0.0237829 | − | 0.0731963i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.85410 | − | 3.52671i | −0.155296 | − | 0.112829i | 0.507423 | − | 0.861697i | \(-0.330598\pi\) |
−0.662720 | + | 0.748867i | \(0.730598\pi\) | |||||||
\(978\) | 1.48382i | 0.0474474i | ||||||||
\(979\) | 40.6409 | − | 43.2185i | 1.29889 | − | 1.38127i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.78861 | + | 17.8155i | −0.184722 | + | 0.568515i | ||||
\(983\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(984\) | 1.29037 | − | 0.937511i | 0.0411356 | − | 0.0298868i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.494712 | − | 1.52257i | 0.0156992 | − | 0.0483172i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.672785 | − | 0.926009i | −0.0213180 | − | 0.0293417i | ||||
\(997\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(998\) | 48.7748 | + | 15.8479i | 1.54394 | + | 0.501656i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))