Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1685,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.1685");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.bm (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1697.5 | ||
Root | \(-1.61108 - 0.635951i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1697 |
Dual form | 1764.2.bm.a.1685.5 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.127742 | + | 1.72733i | −0.0737520 | + | 0.997277i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.18300 | −0.976269 | −0.488134 | − | 0.872769i | \(-0.662322\pi\) | ||||
−0.488134 | + | 0.872769i | \(0.662322\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.96736 | − | 0.441307i | −0.989121 | − | 0.147102i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.46518i | 0.441770i | 0.975300 | + | 0.220885i | \(0.0708945\pi\) | ||||
−0.975300 | + | 0.220885i | \(0.929106\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.92752 | + | 1.69021i | 0.811948 | + | 0.468779i | 0.847632 | − | 0.530585i | \(-0.178028\pi\) |
−0.0356837 | + | 0.999363i | \(0.511361\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.278862 | − | 3.77077i | 0.0720017 | − | 0.973610i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.32136 | − | 2.28866i | 0.320476 | − | 0.555081i | −0.660110 | − | 0.751169i | \(-0.729491\pi\) |
0.980586 | + | 0.196088i | \(0.0628238\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.87816 | + | 3.97111i | −1.57796 | + | 0.911034i | −0.582813 | + | 0.812606i | \(0.698048\pi\) |
−0.995144 | + | 0.0984279i | \(0.968619\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.00964i | − | 0.836068i | −0.908431 | − | 0.418034i | \(-0.862719\pi\) | ||
0.908431 | − | 0.418034i | \(-0.137281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.234498 | −0.0468996 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.14134 | − | 5.06925i | 0.219651 | − | 0.975578i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.71261 | + | 3.87553i | −1.24650 | + | 0.719667i | −0.970410 | − | 0.241464i | \(-0.922372\pi\) |
−0.276091 | + | 0.961132i | \(0.589039\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.612252 | + | 0.353484i | −0.109964 | + | 0.0634876i | −0.553973 | − | 0.832534i | \(-0.686889\pi\) |
0.444009 | + | 0.896022i | \(0.353556\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.53086 | − | 0.187166i | −0.440567 | − | 0.0325814i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.41738 | + | 2.45498i | 0.233016 | + | 0.403596i | 0.958694 | − | 0.284438i | \(-0.0918071\pi\) |
−0.725678 | + | 0.688034i | \(0.758474\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.29352 | + | 4.84090i | −0.527385 | + | 0.775164i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.74173 | − | 6.48086i | 0.584360 | − | 1.01214i | −0.410595 | − | 0.911818i | \(-0.634679\pi\) |
0.994955 | − | 0.100323i | \(-0.0319876\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.27112 | − | 2.20164i | −0.193844 | − | 0.335748i | 0.752677 | − | 0.658390i | \(-0.228762\pi\) |
−0.946521 | + | 0.322642i | \(0.895429\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.47776 | + | 0.963374i | 0.965648 | + | 0.143611i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.27538 | − | 10.8693i | 0.915358 | − | 1.58545i | 0.108983 | − | 0.994044i | \(-0.465241\pi\) |
0.806376 | − | 0.591403i | \(-0.201426\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.78448 | + | 2.57478i | 0.529933 | + | 0.360541i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.41675 | + | 1.39531i | 0.331966 | + | 0.191661i | 0.656714 | − | 0.754140i | \(-0.271946\pi\) |
−0.324748 | + | 0.945801i | \(0.605279\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.19850i | − | 0.431286i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.98079 | − | 12.3881i | −0.792176 | − | 1.64085i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.71650 | − | 11.6333i | −0.874414 | − | 1.51453i | −0.857385 | − | 0.514675i | \(-0.827913\pi\) |
−0.0170287 | − | 0.999855i | \(-0.505421\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.75061 | − | 3.89747i | −0.864327 | − | 0.499020i | 0.00113176 | − | 0.999999i | \(-0.499640\pi\) |
−0.865459 | + | 0.500980i | \(0.832973\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.39079 | − | 3.68972i | −0.792680 | − | 0.457654i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.92029 | − | 5.05809i | −0.356770 | − | 0.617945i | 0.630649 | − | 0.776068i | \(-0.282789\pi\) |
−0.987419 | + | 0.158124i | \(0.949455\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.92598 | + | 0.512200i | 0.833791 | + | 0.0616616i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.6854i | − | 1.38680i | −0.720554 | − | 0.693398i | \(-0.756113\pi\) | ||
0.720554 | − | 0.693398i | \(-0.243887\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.95924 | + | 2.28587i | 0.463394 | + | 0.267541i | 0.713470 | − | 0.700685i | \(-0.247122\pi\) |
−0.250076 | + | 0.968226i | \(0.580456\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0299553 | − | 0.405056i | 0.00345894 | − | 0.0467719i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.69189 | + | 8.12659i | −0.527879 | + | 0.914312i | 0.471593 | + | 0.881816i | \(0.343679\pi\) |
−0.999472 | + | 0.0324963i | \(0.989654\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.61050 | + | 2.61904i | 0.956722 | + | 0.291004i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.70847 | + | 2.95917i | 0.187529 | + | 0.324811i | 0.944426 | − | 0.328724i | \(-0.106619\pi\) |
−0.756896 | + | 0.653535i | \(0.773285\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.88452 | + | 4.99614i | −0.312871 | + | 0.541908i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.83685 | − | 12.0900i | −0.625776 | − | 1.29618i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.61937 | + | 8.00099i | 0.489653 | + | 0.848103i | 0.999929 | − | 0.0119070i | \(-0.00379021\pi\) |
−0.510276 | + | 0.860010i | \(0.670457\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.532375 | − | 1.10272i | −0.0552047 | − | 0.114347i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.0150 | − | 8.66894i | 1.54051 | − | 0.889414i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.38394 | − | 3.68577i | 0.648191 | − | 0.374233i | −0.139572 | − | 0.990212i | \(-0.544573\pi\) |
0.787763 | + | 0.615979i | \(0.211239\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.646596 | − | 4.34773i | 0.0649853 | − | 0.436964i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.92714 | −0.788780 | −0.394390 | − | 0.918943i | \(-0.629044\pi\) | ||||
−0.394390 | + | 0.918943i | \(0.629044\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.77385i | − | 0.371849i | −0.982564 | − | 0.185924i | \(-0.940472\pi\) | ||
0.982564 | − | 0.185924i | \(-0.0595280\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.88241 | − | 3.97356i | 0.665347 | − | 0.384138i | −0.128964 | − | 0.991649i | \(-0.541165\pi\) |
0.794311 | + | 0.607511i | \(0.207832\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.505142 | − | 0.874932i | 0.0483838 | − | 0.0838033i | −0.840819 | − | 0.541316i | \(-0.817926\pi\) |
0.889203 | + | 0.457513i | \(0.151260\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.42163 | + | 2.13469i | −0.419682 | + | 0.202616i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5557 | − | 6.09431i | −0.992992 | − | 0.573304i | −0.0868250 | − | 0.996224i | \(-0.527672\pi\) |
−0.906167 | + | 0.422919i | \(0.861005\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.75305i | 0.816226i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.94112 | − | 6.30739i | −0.734157 | − | 0.583118i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.85324 | 0.804840 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.7166 | + | 7.29109i | 0.966286 | + | 0.657416i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.4269 | 1.02206 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.79350 | 0.602826 | 0.301413 | − | 0.953494i | \(-0.402542\pi\) | ||||
0.301413 | + | 0.953494i | \(0.402542\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.96535 | − | 1.91441i | 0.349130 | − | 0.168554i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.7358 | −1.20010 | −0.600051 | − | 0.799961i | \(-0.704853\pi\) | ||||
−0.600051 | + | 0.799961i | \(0.704853\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.49155 | + | 11.0662i | −0.214439 | + | 0.952427i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 20.0950i | − | 1.71683i | −0.512954 | − | 0.858416i | \(-0.671449\pi\) | ||
0.512954 | − | 0.858416i | \(-0.328551\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.51403 | + | 4.91558i | 0.722151 | + | 0.416934i | 0.815544 | − | 0.578695i | \(-0.196438\pi\) |
−0.0933930 | + | 0.995629i | \(0.529771\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.9732 | + | 12.2281i | 1.51362 | + | 1.02980i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.47646 | + | 4.28936i | −0.207092 | + | 0.358694i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.6536 | − | 8.46029i | 1.21692 | − | 0.702589i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.0354i | 1.64136i | 0.571386 | + | 0.820682i | \(0.306406\pi\) | ||||
−0.571386 | + | 0.820682i | \(0.693594\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.2337 | −1.80935 | −0.904675 | − | 0.426103i | \(-0.859886\pi\) | ||||
−0.904675 | + | 0.426103i | \(0.859886\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.93094 | + | 6.20815i | −0.398643 | + | 0.501899i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.33655 | − | 0.771657i | 0.107354 | − | 0.0619810i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.95305 | + | 4.01435i | −0.554914 | + | 0.320380i | −0.751102 | − | 0.660187i | \(-0.770477\pi\) |
0.196188 | + | 0.980566i | \(0.437144\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.71889 | + | 3.99629i | −0.215622 | + | 0.316927i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.22604 | − | 10.7838i | −0.487661 | − | 0.844654i | 0.512238 | − | 0.858844i | \(-0.328817\pi\) |
−0.999899 | + | 0.0141893i | \(0.995483\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.52488 | + | 0.408584i | 0.430111 | + | 0.0318082i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.85984 | + | 17.0777i | −0.762978 | + | 1.32152i | 0.178332 | + | 0.983970i | \(0.442930\pi\) |
−0.941309 | + | 0.337546i | \(0.890403\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.786412 | − | 1.36211i | −0.0604933 | − | 0.104777i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.1625 | − | 8.74834i | 1.69481 | − | 0.669002i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.913733 | + | 1.58263i | −0.0694699 | + | 0.120325i | −0.898668 | − | 0.438629i | \(-0.855464\pi\) |
0.829198 | + | 0.558955i | \(0.188797\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20.9526 | − | 10.1156i | 1.57489 | − | 0.760333i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.1182 | − | 6.99645i | −0.905757 | − | 0.522939i | −0.0266934 | − | 0.999644i | \(-0.508498\pi\) |
−0.879064 | + | 0.476705i | \(0.841831\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.3594i | − | 1.21599i | −0.793942 | − | 0.607994i | \(-0.791975\pi\) | ||
0.793942 | − | 0.607994i | \(-0.208025\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.59456 | − | 11.1627i | 0.561406 | − | 0.825170i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.09415 | − | 5.35923i | −0.227486 | − | 0.394018i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.35330 | + | 1.93603i | 0.245218 | + | 0.141577i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.8326 | − | 6.83153i | −0.856173 | − | 0.494312i | 0.00655557 | − | 0.999979i | \(-0.497913\pi\) |
−0.862729 | + | 0.505667i | \(0.831247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.18885 | + | 3.79119i | 0.157557 | + | 0.272896i | 0.933987 | − | 0.357307i | \(-0.116305\pi\) |
−0.776430 | + | 0.630203i | \(0.782972\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.18976 | − | 10.5677i | 0.514869 | − | 0.756768i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.00603i | 0.0716767i | 0.999358 | + | 0.0358384i | \(0.0114101\pi\) | ||||
−0.999358 | + | 0.0358384i | \(0.988590\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.67639 | + | 3.27726i | 0.402388 | + | 0.232319i | 0.687514 | − | 0.726171i | \(-0.258702\pi\) |
−0.285126 | + | 0.958490i | \(0.592035\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.11006 | − | 4.39819i | 0.642574 | − | 0.310224i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.16820 | + | 14.1477i | −0.570492 | + | 0.988121i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.76948 | + | 11.8981i | −0.122987 | + | 0.826972i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.81840 | − | 10.0778i | −0.402467 | − | 0.697094i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.11202 | + | 15.7825i | −0.627297 | + | 1.08651i | 0.360794 | + | 0.932645i | \(0.382506\pi\) |
−0.988092 | + | 0.153866i | \(0.950828\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.1845 | + | 1.49271i | 1.38302 | + | 0.102279i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.77486 | + | 4.80620i | 0.189244 | + | 0.327780i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.45422 | + | 6.54693i | −0.300989 | + | 0.442401i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.73660 | − | 4.46673i | 0.520420 | − | 0.300464i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.71705 | + | 5.03279i | −0.583737 | + | 0.337021i | −0.762617 | − | 0.646850i | \(-0.776086\pi\) |
0.178880 | + | 0.983871i | \(0.442753\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.695841 | + | 0.103486i | 0.0463894 | + | 0.00689904i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.8874 | −1.31998 | −0.659988 | − | 0.751276i | \(-0.729439\pi\) | ||||
−0.659988 | + | 0.751276i | \(0.729439\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 17.7655i | − | 1.17398i | −0.809595 | − | 0.586988i | \(-0.800313\pi\) | ||
0.809595 | − | 0.586988i | \(-0.199687\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.9077 | − | 8.02962i | 0.911124 | − | 0.526038i | 0.0303317 | − | 0.999540i | \(-0.490344\pi\) |
0.880793 | + | 0.473502i | \(0.157010\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.6992 | + | 23.7277i | −0.893636 | + | 1.54782i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.4380 | − | 9.14256i | −0.872890 | − | 0.593873i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.11117 | − | 4.10564i | −0.459983 | − | 0.265572i | 0.252054 | − | 0.967713i | \(-0.418894\pi\) |
−0.712037 | + | 0.702142i | \(0.752227\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.4765i | 1.83433i | 0.398505 | + | 0.917166i | \(0.369529\pi\) | ||||
−0.398505 | + | 0.917166i | \(0.630471\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.62387 | + | 14.5386i | −0.360772 | + | 0.932654i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.8479 | −1.70829 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.32971 | + | 2.57310i | −0.337757 | + | 0.163063i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.656343 | 0.0414280 | 0.0207140 | − | 0.999785i | \(-0.493406\pi\) | ||||
0.0207140 | + | 0.999785i | \(0.493406\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.87486 | 0.369349 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.26153 | − | 5.62075i | −0.517357 | − | 0.351985i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.64084 | 0.476623 | 0.238311 | − | 0.971189i | \(-0.423406\pi\) | ||||
0.238311 | + | 0.971189i | \(0.423406\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.6291 | − | 8.53778i | 1.33880 | − | 0.528475i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.62669i | 0.408619i | 0.978906 | + | 0.204310i | \(0.0654949\pi\) | ||||
−0.978906 | + | 0.204310i | \(0.934505\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.27577 | − | 3.04597i | −0.324088 | − | 0.187112i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.4105 | + | 6.95714i | −0.881907 | + | 0.425770i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.38347 | − | 7.59239i | 0.267265 | − | 0.462916i | −0.700890 | − | 0.713270i | \(-0.747214\pi\) |
0.968154 | + | 0.250354i | \(0.0805469\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.2608 | + | 8.23346i | −0.866280 | + | 0.500147i | −0.866110 | − | 0.499853i | \(-0.833387\pi\) |
−0.000169619 | 1.00000i | \(0.500054\pi\) | ||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 0.343583i | − | 0.0207188i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.7746 | −1.06797 | −0.533987 | − | 0.845493i | \(-0.679307\pi\) | ||||
−0.533987 | + | 0.845493i | \(0.679307\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.97277 | − | 0.778725i | 0.118107 | − | 0.0466210i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.0252 | + | 8.09748i | −0.836676 | + | 0.483055i | −0.856133 | − | 0.516755i | \(-0.827140\pi\) |
0.0194568 | + | 0.999811i | \(0.493806\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.5717 | + | 14.1865i | −1.46063 | + | 0.843298i | −0.999041 | − | 0.0437937i | \(-0.986056\pi\) |
−0.461594 | + | 0.887091i | \(0.652722\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.0561 | + | 27.0434i | 0.773376 | + | 1.60191i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00804 | + | 8.67417i | 0.294590 | + | 0.510246i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.55106 | + | 11.4980i | 0.325409 | + | 0.674027i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.38260 | + | 7.59088i | −0.256034 | + | 0.443464i | −0.965176 | − | 0.261602i | \(-0.915749\pi\) |
0.709142 | + | 0.705066i | \(0.249083\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.6621 | + | 25.3956i | 0.853663 | + | 1.47859i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.42739 | + | 1.67228i | 0.430981 | + | 0.0970353i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.77711 | − | 11.7383i | 0.391931 | − | 0.678844i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.01263 | − | 13.6928i | 0.0581741 | − | 0.786632i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.7366 | + | 8.50818i | 0.843816 | + | 0.487177i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.8497i | 0.733372i | 0.930345 | + | 0.366686i | \(0.119508\pi\) | ||||
−0.930345 | + | 0.366686i | \(0.880492\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.51871 | + | 0.482080i | 0.370836 | + | 0.0274246i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.29671 | + | 5.71007i | 0.186939 | + | 0.323789i | 0.944228 | − | 0.329291i | \(-0.106810\pi\) |
−0.757289 | + | 0.653080i | \(0.773477\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.95711 | + | 1.70729i | 0.167146 | + | 0.0965018i | 0.581239 | − | 0.813733i | \(-0.302568\pi\) |
−0.414093 | + | 0.910234i | \(0.635901\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.8003 | − | 16.0505i | −1.56142 | − | 0.901485i | −0.997114 | − | 0.0759182i | \(-0.975811\pi\) |
−0.564304 | − | 0.825567i | \(-0.690855\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.67836 | − | 9.83521i | −0.317927 | − | 0.550666i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.98449 | + | 12.3958i | 0.334022 | + | 0.691866i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.9890i | 1.16786i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.686498 | − | 0.396350i | −0.0380801 | − | 0.0219855i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.44677 | + | 0.984315i | 0.0800066 | + | 0.0544327i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4416 | − | 25.0137i | 0.793784 | − | 1.37487i | −0.129824 | − | 0.991537i | \(-0.541441\pi\) |
0.923608 | − | 0.383338i | \(-0.125225\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.12249 | − | 7.91032i | −0.171111 | − | 0.433483i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.37501 | + | 11.0418i | 0.348304 | + | 0.603280i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.82568 | − | 8.35833i | 0.262872 | − | 0.455307i | −0.704132 | − | 0.710069i | \(-0.748664\pi\) |
0.967004 | + | 0.254762i | \(0.0819971\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.8753 | − | 17.4546i | 0.644978 | − | 0.948006i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.517919 | − | 0.897063i | −0.0280469 | − | 0.0485787i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.1194 | − | 1.11813i | −0.814004 | − | 0.0601983i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.6758 | − | 6.16367i | 0.573106 | − | 0.330883i | −0.185283 | − | 0.982685i | \(-0.559320\pi\) |
0.758389 | + | 0.651802i | \(0.225987\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.2211 | + | 5.90115i | −0.547123 | + | 0.315881i | −0.747961 | − | 0.663743i | \(-0.768967\pi\) |
0.200838 | + | 0.979624i | \(0.435634\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.9094 | − | 12.9112i | 0.635676 | − | 0.689151i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.1971 | −0.702411 | −0.351205 | − | 0.936298i | \(-0.614228\pi\) | ||||
−0.351205 | + | 0.936298i | \(0.614228\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.5092i | 1.35389i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.22483 | − | 3.01656i | 0.275756 | − | 0.159208i | −0.355745 | − | 0.934583i | \(-0.615773\pi\) |
0.631501 | + | 0.775375i | \(0.282439\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.0394 | − | 38.1733i | 1.15997 | − | 2.00912i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.13093 | + | 15.2925i | −0.0593585 | + | 0.802648i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.64304 | − | 4.99006i | −0.452397 | − | 0.261192i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 17.1767i | − | 0.896618i | −0.893879 | − | 0.448309i | \(-0.852026\pi\) | ||
0.893879 | − | 0.448309i | \(-0.147974\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.9631 | + | 17.5798i | −0.726891 | + | 0.915169i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.71804 | 0.244291 | 0.122146 | − | 0.992512i | \(-0.461023\pi\) | ||||
0.122146 | + | 0.992512i | \(0.461023\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.45970 | + | 19.7381i | −0.0753786 | + | 1.01927i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26.2017 | −1.34946 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.34015 | 0.479771 | 0.239886 | − | 0.970801i | \(-0.422890\pi\) | ||||
0.239886 | + | 0.970801i | \(0.422890\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.867816 | + | 11.7346i | −0.0444596 | + | 0.601184i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.70071 | −0.291293 | −0.145646 | − | 0.989337i | \(-0.546526\pi\) | ||||
−0.145646 | + | 0.989337i | \(0.546526\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.80027 | + | 7.09403i | 0.142346 | + | 0.360610i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 7.66342i | − | 0.388551i | −0.980947 | − | 0.194275i | \(-0.937764\pi\) | ||
0.980947 | − | 0.194275i | \(-0.0622355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.17668 | − | 5.29816i | −0.464085 | − | 0.267939i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.75464 | − | 23.7263i | 0.0885100 | − | 1.19683i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.2424 | − | 17.7404i | 0.515351 | − | 0.892615i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.12810 | − | 0.651310i | 0.0566178 | − | 0.0326883i | −0.471424 | − | 0.881907i | \(-0.656260\pi\) |
0.528042 | + | 0.849218i | \(0.322926\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 9.45443i | − | 0.472132i | −0.971737 | − | 0.236066i | \(-0.924142\pi\) | ||
0.971737 | − | 0.236066i | \(-0.0758581\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.38984 | −0.119047 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.7967 | − | 5.71736i | −0.934018 | − | 0.284098i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.59700 | + | 2.07673i | −0.178296 | + | 0.102940i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.5182 | − | 9.53678i | 0.816771 | − | 0.471563i | −0.0325304 | − | 0.999471i | \(-0.510357\pi\) |
0.849302 | + | 0.527908i | \(0.177023\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 34.7108 | + | 2.56698i | 1.71216 | + | 0.126620i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.72961 | − | 6.45987i | −0.183079 | − | 0.317102i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.57845 | + | 14.0786i | −0.469059 | + | 0.689434i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.20003 | + | 7.27466i | −0.205185 | + | 0.355390i | −0.950192 | − | 0.311666i | \(-0.899113\pi\) |
0.745007 | + | 0.667057i | \(0.232446\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.7178 | + | 34.1522i | 0.960985 | + | 1.66448i | 0.720035 | + | 0.693938i | \(0.244126\pi\) |
0.240951 | + | 0.970537i | \(0.422541\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −23.4180 | + | 29.4837i | −1.13862 | + | 1.43355i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.309855 | + | 0.536685i | −0.0150302 | + | 0.0260331i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.09280 | − | 4.82561i | −0.342444 | − | 0.232983i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.3340 | − | 5.96634i | −0.497772 | − | 0.287389i | 0.230021 | − | 0.973186i | \(-0.426120\pi\) |
−0.727793 | + | 0.685797i | \(0.759454\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.2121i | 0.586875i | 0.955978 | + | 0.293437i | \(0.0947992\pi\) | ||||
−0.955978 | + | 0.293437i | \(0.905201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.7419 | + | 26.3925i | 0.610925 | + | 1.26542i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.9227 | + | 27.5789i | 0.761686 | + | 1.31928i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.4639 | − | 8.35076i | −0.690326 | − | 0.398560i | 0.113408 | − | 0.993548i | \(-0.463823\pi\) |
−0.803734 | + | 0.594989i | \(0.797157\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.2403 | + | 15.1499i | 1.24672 | + | 0.719791i | 0.970453 | − | 0.241291i | \(-0.0775708\pi\) |
0.276262 | + | 0.961082i | \(0.410904\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.0841 | − | 17.4662i | −0.478033 | − | 0.827977i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −34.6078 | − | 2.55936i | −1.63689 | − | 0.121054i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.1253i | 1.42170i | 0.703343 | + | 0.710851i | \(0.251690\pi\) | ||||
−0.703343 | + | 0.710851i | \(0.748310\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.49566 | + | 5.48232i | 0.447133 | + | 0.258152i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.84018 | − | 38.4050i | 0.133443 | − | 1.80442i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.6159 | + | 21.8513i | −0.590146 | + | 1.02216i | 0.404067 | + | 0.914730i | \(0.367596\pi\) |
−0.994212 | + | 0.107433i | \(0.965737\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.0937 | − | 9.31043i | −0.471132 | − | 0.434574i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.3174 | − | 21.3344i | −0.573680 | − | 0.993643i | −0.996184 | − | 0.0872820i | \(-0.972182\pi\) |
0.422503 | − | 0.906361i | \(-0.361151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.33215 | + | 10.9676i | −0.294280 | + | 0.509708i | −0.974817 | − | 0.223006i | \(-0.928413\pi\) |
0.680537 | + | 0.732713i | \(0.261746\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.16218 | + | 2.40724i | 0.0538946 | + | 0.111633i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.4723 | + | 18.1385i | 0.484599 | + | 0.839350i | 0.999843 | − | 0.0176932i | \(-0.00563223\pi\) |
−0.515245 | + | 0.857043i | \(0.672299\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.04592 | − | 12.5230i | −0.278581 | − | 0.577031i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.22581 | − | 1.86242i | 0.148323 | − | 0.0856344i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.61291 | − | 0.931217i | 0.0740056 | − | 0.0427271i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.55562 | − | 5.20692i | −0.300161 | − | 0.238409i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.7705 | −1.45163 | −0.725816 | − | 0.687889i | \(-0.758537\pi\) | ||||
−0.725816 | + | 0.687889i | \(0.758537\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.58267i | 0.436932i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.9362 | + | 8.04605i | −0.632809 | + | 0.365352i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.7821 | + | 30.7995i | −0.805784 | + | 1.39566i | 0.109977 | + | 0.993934i | \(0.464922\pi\) |
−0.915761 | + | 0.401724i | \(0.868411\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.4226 | − | 9.37691i | 0.878320 | − | 0.424038i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.75734 | + | 1.59195i | 0.124437 | + | 0.0718437i | 0.560926 | − | 0.827866i | \(-0.310445\pi\) |
−0.436490 | + | 0.899709i | \(0.643778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.4838i | 0.922544i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.41152 | + | 9.49112i | −0.0634431 | + | 0.426594i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0427 | 1.43443 | 0.717215 | − | 0.696852i | \(-0.245417\pi\) | ||||
0.717215 | + | 0.696852i | \(0.245417\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.2395 | − | 19.2128i | −1.26165 | − | 0.858364i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.6608 | 0.519930 | 0.259965 | − | 0.965618i | \(-0.416289\pi\) | ||||
0.259965 | + | 0.965618i | \(0.416289\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.3050 | 0.770061 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.45327 | − | 1.18440i | 0.108954 | − | 0.0526010i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.8854 | 1.19167 | 0.595836 | − | 0.803106i | \(-0.296821\pi\) | ||||
0.595836 | + | 0.803106i | \(0.296821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.2802 | + | 39.3995i | 0.542185 | + | 1.73953i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.23834i | 0.363024i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.9255 | + | 9.19459i | 0.700402 | + | 0.404378i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.61701 | − | 1.78049i | −0.114874 | − | 0.0781549i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.0385 | − | 29.5116i | 0.746471 | − | 1.29293i | −0.203033 | − | 0.979172i | \(-0.565080\pi\) |
0.949504 | − | 0.313754i | \(-0.101587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.71003 | + | 2.71933i | −0.205955 | + | 0.118908i | −0.599430 | − | 0.800427i | \(-0.704606\pi\) |
0.393475 | + | 0.919335i | \(0.371273\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.86831i | 0.0813850i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.92280 | 0.300991 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.7964 | + | 37.4843i | 0.642111 | + | 1.62668i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.9080 | − | 12.6486i | 0.948940 | − | 0.547871i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.0243 | + | 8.67429i | −0.649558 | + | 0.375022i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.6332 | − | 20.0384i | 0.588316 | − | 0.864722i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.8329 | + | 20.4952i | 0.508737 | + | 0.881158i | 0.999949 | + | 0.0101183i | \(0.00322080\pi\) |
−0.491212 | + | 0.871040i | \(0.663446\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.2582 | + | 2.08979i | 1.21268 | + | 0.0896815i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.10273 | + | 1.90998i | −0.0472356 | + | 0.0818145i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0824 | − | 20.9273i | −0.516606 | − | 0.894788i | −0.999814 | − | 0.0192822i | \(-0.993862\pi\) |
0.483208 | − | 0.875505i | \(-0.339471\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.3115 | + | 14.5443i | 0.781518 | + | 0.620735i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.7803 | − | 53.3130i | 1.31128 | − | 2.27121i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.65243 | − | 4.66003i | 0.409723 | − | 0.197807i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.36315 | + | 4.25111i | 0.311987 | + | 0.180126i | 0.647815 | − | 0.761798i | \(-0.275683\pi\) |
−0.335829 | + | 0.941923i | \(0.609016\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.59381i | − | 0.363480i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.77253 | + | 5.54496i | −0.159276 | + | 0.234108i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.473776 | − | 0.820605i | −0.0199673 | − | 0.0345844i | 0.855869 | − | 0.517192i | \(-0.173023\pi\) |
−0.875836 | + | 0.482608i | \(0.839690\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.0430 | + | 13.3039i | 0.969427 | + | 0.559699i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.7859 | − | 9.11401i | −0.661781 | − | 0.382079i | 0.131175 | − | 0.991359i | \(-0.458125\pi\) |
−0.792955 | + | 0.609280i | \(0.791458\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.12121 | + | 10.6023i | 0.256165 | + | 0.443691i | 0.965211 | − | 0.261471i | \(-0.0842077\pi\) |
−0.709046 | + | 0.705162i | \(0.750874\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.3118 | − | 19.5661i | 0.556110 | − | 0.817385i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.940253i | 0.0392112i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.2500 | + | 5.91784i | 0.426713 | + | 0.246363i | 0.697945 | − | 0.716151i | \(-0.254098\pi\) |
−0.271232 | + | 0.962514i | \(0.587431\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.82827 | + | 3.29657i | −0.283773 | + | 0.137001i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.04439 | + | 3.54098i | −0.0846699 | + | 0.146653i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.3355 | + | 13.7690i | 0.716734 | + | 0.569280i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.57681 | + | 6.19521i | 0.147631 | + | 0.255704i | 0.930351 | − | 0.366669i | \(-0.119502\pi\) |
−0.782721 | + | 0.622373i | \(0.786169\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.80745 | − | 4.86264i | 0.115679 | − | 0.200362i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.73775 | − | 0.128513i | −0.0714815 | − | 0.00528630i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.4811 | + | 23.3500i | 0.553603 | + | 0.958869i | 0.998011 | + | 0.0630442i | \(0.0200809\pi\) |
−0.444408 | + | 0.895825i | \(0.646586\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.38604 | + | 9.38637i | −0.261363 | + | 0.384158i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.5223 | + | 17.6221i | −1.24711 | + | 0.720018i | −0.970532 | − | 0.240974i | \(-0.922533\pi\) |
−0.276576 | + | 0.960992i | \(0.589200\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.39266 | − | 1.95875i | 0.138389 | − | 0.0798991i | −0.429207 | − | 0.903206i | \(-0.641207\pi\) |
0.567596 | + | 0.823307i | \(0.307874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.43340 | + | 16.2979i | 0.261988 | + | 0.663704i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.3266 | −0.785740 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.4772i | − | 0.587613i | −0.955865 | − | 0.293807i | \(-0.905078\pi\) | ||
0.955865 | − | 0.293807i | \(-0.0949222\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.7426 | − | 21.2134i | 1.48645 | − | 0.858201i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.51761 | + | 11.2888i | −0.263244 | + | 0.455952i | −0.967102 | − | 0.254389i | \(-0.918126\pi\) |
0.703858 | + | 0.710341i | \(0.251459\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −23.3944 | − | 15.9165i | −0.943355 | − | 0.641814i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.14491 | − | 1.81571i | −0.126609 | − | 0.0730979i | 0.435358 | − | 0.900258i | \(-0.356622\pi\) |
−0.561967 | + | 0.827160i | \(0.689955\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.4818i | 0.662460i | 0.943550 | + | 0.331230i | \(0.107464\pi\) | ||||
−0.943550 | + | 0.331230i | \(0.892536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.3259 | − | 4.57637i | −0.815649 | − | 0.183643i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.7725 | −0.950901 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.1509 | − | 8.76296i | 0.724878 | − | 0.349959i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.49147 | 0.298704 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.8383 | −1.38689 | −0.693446 | − | 0.720508i | \(-0.743909\pi\) | ||||
−0.693446 | + | 0.720508i | \(0.743909\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.0976 | − | 17.7556i | −1.03729 | − | 0.705721i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.8302 | −0.588520 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.15683 | + | 34.6747i | −0.204001 | + | 1.37171i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 8.37779i | − | 0.330903i | −0.986218 | − | 0.165451i | \(-0.947092\pi\) | ||
0.986218 | − | 0.165451i | \(-0.0529081\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.0021 | − | 10.3935i | −0.709934 | − | 0.409881i | 0.101103 | − | 0.994876i | \(-0.467763\pi\) |
−0.811037 | + | 0.584995i | \(0.801096\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.65637 | + | 4.17915i | −0.340844 | + | 0.164554i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.74770 | − | 8.22325i | 0.186651 | − | 0.323289i | −0.757480 | − | 0.652858i | \(-0.773570\pi\) |
0.944132 | + | 0.329568i | \(0.106903\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.0450 | − | 9.84091i | 0.669073 | − | 0.386290i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 7.67583i | − | 0.300379i | −0.988657 | − | 0.150189i | \(-0.952012\pi\) | ||
0.988657 | − | 0.150189i | \(-0.0479883\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.9853 | 1.17162 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.7397 | − | 8.53025i | −0.418997 | − | 0.332797i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.0493 | − | 21.9678i | 1.48219 | − | 0.855743i | 0.482395 | − | 0.875954i | \(-0.339767\pi\) |
0.999796 | + | 0.0202102i | \(0.00643354\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.1649 | − | 12.7969i | 0.862115 | − | 0.497742i | −0.00260513 | − | 0.999997i | \(-0.500829\pi\) |
0.864720 | + | 0.502254i | \(0.167496\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.72724 | + | 13.9343i | 0.261264 | + | 0.541162i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.5395 | + | 26.9151i | 0.601691 | + | 1.04216i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.57977 | − | 15.7002i | −0.293051 | − | 0.607003i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.71051 | − | 9.89089i | 0.220452 | − | 0.381834i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.64671 | − | 13.2445i | −0.294759 | − | 0.510538i | 0.680170 | − | 0.733055i | \(-0.261906\pi\) |
−0.974929 | + | 0.222517i | \(0.928573\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.267642 | + | 1.18873i | −0.0103016 | + | 0.0457543i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.6459 | + | 39.2238i | −0.870352 | + | 1.50749i | −0.00871898 | + | 0.999962i | \(0.502775\pi\) |
−0.861633 | + | 0.507532i | \(0.830558\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.54047 | − | 34.3523i | 0.0973509 | − | 1.31638i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0891 | − | 13.9079i | −0.921744 | − | 0.532169i | −0.0375529 | − | 0.999295i | \(-0.511956\pi\) |
−0.884191 | + | 0.467126i | \(0.845290\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 43.8674i | 1.67609i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30.6869 | + | 2.26940i | 1.17078 | + | 0.0865831i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.71672 | + | 8.16961i | 0.179693 | + | 0.311237i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.1115 | − | 8.14729i | −0.536828 | − | 0.309938i | 0.206965 | − | 0.978348i | \(-0.433641\pi\) |
−0.743792 | + | 0.668411i | \(0.766975\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.5862 | − | 10.7307i | −0.705013 | − | 0.407040i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.88831 | − | 17.1271i | −0.374546 | − | 0.648733i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.0932 | + | 25.0490i | 0.457408 | + | 0.947439i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 0.393403i | − | 0.0148586i | −0.999972 | − | 0.00742932i | \(-0.997635\pi\) | ||
0.999972 | − | 0.00742932i | \(-0.00236485\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.4980 | − | 11.2572i | −0.735379 | − | 0.424572i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −39.2356 | − | 26.6941i | −1.47770 | − | 1.00536i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.3183 | − | 28.2641i | 0.612846 | − | 1.06148i | −0.377912 | − | 0.925841i | \(-0.623358\pi\) |
0.990758 | − | 0.135639i | \(-0.0433087\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.5089 | − | 22.0440i | 0.656633 | − | 0.826714i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.41734 | + | 2.45491i | 0.0530799 | + | 0.0919372i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.40612 | − | 9.36368i | 0.202178 | − | 0.350182i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.00020 | − | 11.7589i | 0.298773 | − | 0.439144i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.106604 | + | 0.184643i | 0.00397565 | + | 0.00688602i | 0.868006 | − | 0.496553i | \(-0.165401\pi\) |
−0.864031 | + | 0.503439i | \(0.832068\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −49.1884 | − | 3.63765i | −1.82934 | − | 0.135286i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.57409 | − | 0.908804i | 0.0584604 | − | 0.0337521i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.8208 | − | 18.3717i | 1.18017 | − | 0.681370i | 0.224114 | − | 0.974563i | \(-0.428051\pi\) |
0.956053 | + | 0.293193i | \(0.0947180\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.3947 | − | 11.5715i | −0.903507 | − | 0.428574i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.71841 | −0.248489 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.8753i | 0.401689i | 0.979623 | + | 0.200844i | \(0.0643685\pi\) | ||||
−0.979623 | + | 0.200844i | \(0.935631\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.41104 | − | 4.27877i | 0.272989 | − | 0.157610i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.91282 | − | 11.9734i | 0.254292 | − | 0.440447i | −0.710411 | − | 0.703787i | \(-0.751491\pi\) |
0.964703 | + | 0.263340i | \(0.0848242\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.42961 | − | 46.3753i | 0.125990 | − | 1.70364i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.8751 | − | 9.16552i | −0.582403 | − | 0.336250i | 0.179685 | − | 0.983724i | \(-0.442492\pi\) |
−0.762088 | + | 0.647474i | \(0.775825\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 43.7373i | − | 1.60241i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.76377 | − | 9.53488i | −0.137709 | − | 0.348863i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.9417 | −0.727682 | −0.363841 | − | 0.931461i | \(-0.618535\pi\) | ||||
−0.363841 | + | 0.931461i | \(0.618535\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.0838426 | + | 1.13372i | −0.00305540 | + | 0.0413152i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 48.5362 | 1.76641 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.9292 | −1.70567 | −0.852836 | − | 0.522178i | \(-0.825119\pi\) | ||||
−0.852836 | + | 0.522178i | \(0.825119\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.750467 | + | 10.1478i | −0.0272402 | + | 0.368343i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −53.5538 | −1.94132 | −0.970661 | − | 0.240452i | \(-0.922704\pi\) | ||||
−0.970661 | + | 0.240452i | \(0.922704\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.7643 | − | 13.5524i | 0.389183 | − | 0.489988i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 45.4091i | − | 1.63963i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.7306 | − | 20.0517i | −1.25242 | − | 0.723085i | −0.280830 | − | 0.959758i | \(-0.590610\pi\) |
−0.971589 | + | 0.236673i | \(0.923943\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.976058 | + | 13.1983i | −0.0351519 | + | 0.475325i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.82375 | + | 13.5511i | −0.281401 | + | 0.487400i | −0.971730 | − | 0.236095i | \(-0.924132\pi\) |
0.690329 | + | 0.723495i | \(0.257466\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.143572 | − | 0.0828913i | 0.00515726 | − | 0.00297755i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 59.4352i | 2.12949i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.1212 | 0.612645 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.9847 | + | 38.4512i | 0.428297 | + | 1.37413i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.1785 | − | 8.76333i | 0.541745 | − | 0.312777i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.9920 | − | 23.0894i | 1.42556 | − | 0.823048i | 0.428795 | − | 0.903402i | \(-0.358938\pi\) |
0.996766 | + | 0.0803536i | \(0.0256050\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.4465 | − | 0.846508i | −0.407506 | − | 0.0301365i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.1750 | − | 22.8198i | −0.467859 | − | 0.810356i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.93534 | − | 8.72392i | 0.210505 | − | 0.309406i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.9388 | + | 29.3388i | −0.600002 | + | 1.03923i | 0.392818 | + | 0.919616i | \(0.371500\pi\) |
−0.992820 | + | 0.119618i | \(0.961833\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.5840 | − | 28.7244i | −0.586701 | − | 1.01620i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.1765 | − | 25.7804i | −0.359568 | − | 0.910906i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.34922 | + | 5.80102i | −0.118191 | + | 0.204714i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.5546 | + | 8.54158i | 0.441944 | + | 0.300678i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.7873 | + | 19.5071i | 1.18790 | + | 0.685834i | 0.957829 | − | 0.287340i | \(-0.0927711\pi\) |
0.230070 | + | 0.973174i | \(0.426104\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.73397i | − | 0.271577i | −0.990738 | − | 0.135788i | \(-0.956643\pi\) | ||
0.990738 | − | 0.135788i | \(-0.0433567\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.4002 | − | 25.6849i | −0.434895 | − | 0.900807i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.5915 | + | 23.5411i | 0.476088 | + | 0.824609i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.4859 | + | 10.0955i | 0.611755 | + | 0.353197i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.443638 | − | 0.256134i | −0.0154831 | − | 0.00893915i | 0.492238 | − | 0.870460i | \(-0.336179\pi\) |
−0.507722 | + | 0.861521i | \(0.669512\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.1753 | + | 41.8728i | 0.842698 | + | 1.45960i | 0.887606 | + | 0.460604i | \(0.152367\pi\) |
−0.0449080 | + | 0.998991i | \(0.514299\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.593482 | + | 0.0438900i | 0.0206624 | + | 0.00152805i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17.3086i | − | 0.601879i | −0.953643 | − | 0.300940i | \(-0.902700\pi\) | ||
0.953643 | − | 0.300940i | \(-0.0973003\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.0205 | − | 19.0644i | −1.14685 | − | 0.662134i | −0.198733 | − | 0.980054i | \(-0.563683\pi\) |
−0.948118 | + | 0.317919i | \(0.897016\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.27057 | − | 30.7027i | 0.0787652 | − | 1.06507i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.5241 | − | 37.2808i | 0.744871 | − | 1.29015i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.09311 | + | 3.50711i | 0.0377835 | + | 0.121223i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.2026 | − | 26.3317i | −0.524852 | − | 0.909071i | −0.999581 | − | 0.0289389i | \(-0.990787\pi\) |
0.474729 | − | 0.880132i | \(-0.342546\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.5394 | − | 26.9151i | 0.535842 | − | 0.928106i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.1954 | − | 25.2607i | −0.420033 | − | 0.870024i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.71674 | + | 2.97348i | 0.0590577 | + | 0.102291i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.3659 | − | 44.2557i | −0.733276 | − | 1.51885i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.84358 | − | 5.68319i | 0.337434 | − | 0.194817i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.7143 | − | 16.0008i | 0.948919 | − | 0.547858i | 0.0561738 | − | 0.998421i | \(-0.482110\pi\) |
0.892745 | + | 0.450563i | \(0.148777\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −48.3807 | + | 19.0976i | −1.65459 | + | 0.653126i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.1549 | 1.54246 | 0.771230 | − | 0.636556i | \(-0.219642\pi\) | ||||
0.771230 | + | 0.636556i | \(0.219642\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 18.2340i | − | 0.622137i | −0.950388 | − | 0.311068i | \(-0.899313\pi\) | ||
0.950388 | − | 0.311068i | \(-0.100687\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.61966 | − | 3.82186i | 0.225336 | − | 0.130098i | −0.383083 | − | 0.923714i | \(-0.625138\pi\) |
0.608419 | + | 0.793616i | \(0.291804\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.99468 | − | 3.45489i | 0.0678213 | − | 0.117470i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.6229 | + | 7.54249i | −0.530583 | + | 0.256157i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.9069 | − | 6.87448i | −0.403915 | − | 0.233201i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 19.7436i | − | 0.668985i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.5700 | + | 8.11975i | −0.696190 | + | 0.274812i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.0316 | 0.541350 | 0.270675 | − | 0.962671i | \(-0.412753\pi\) | ||||
0.270675 | + | 0.962671i | \(0.412753\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.5521 | − | 8.53988i | −0.423373 | − | 0.288043i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.7532 | 0.833958 | 0.416979 | − | 0.908916i | \(-0.363089\pi\) | ||||
0.416979 | + | 0.908916i | \(0.363089\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.6958 | −0.393595 | −0.196798 | − | 0.980444i | \(-0.563054\pi\) | ||||
−0.196798 | + | 0.980444i | \(0.563054\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −45.7396 | + | 22.0823i | −1.53752 | + | 0.742289i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −55.0859 | −1.84960 | −0.924801 | − | 0.380451i | \(-0.875769\pi\) | ||||
−0.924801 | + | 0.380451i | \(0.875769\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.83737 | + | 12.6160i | −0.128557 | + | 0.422651i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 99.6808i | 3.33569i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.4541 | + | 15.2733i | 0.884262 | + | 0.510529i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.4102 | + | 13.2058i | 0.648089 | + | 0.440929i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.73987 | − | 4.74560i | 0.0913799 | − | 0.158275i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.38677 | − | 3.68741i | 0.212774 | − | 0.122845i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 35.7127i | 1.18713i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.8767 | −0.859220 | −0.429610 | − | 0.903014i | \(-0.641349\pi\) | ||||
−0.429610 | + | 0.903014i | \(0.641349\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.5227 | + | 3.49830i | 0.780199 | + | 0.116031i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.86306 | + | 2.23034i | −0.127989 | + | 0.0738944i | −0.562627 | − | 0.826711i | \(-0.690209\pi\) |
0.434639 | + | 0.900605i | \(0.356876\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.33572 | + | 2.50323i | −0.143491 | + | 0.0828448i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.5790 | + | 24.3682i | −0.548083 | + | 0.805587i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.2352 | − | 36.7805i | −0.700485 | − | 1.21328i | −0.968296 | − | 0.249804i | \(-0.919634\pi\) |
0.267811 | − | 0.963471i | \(-0.413700\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.1958 | − | 1.64145i | −0.731375 | − | 0.0540877i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.7507 | − | 34.2091i | 0.650101 | − | 1.12601i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.332373 | − | 0.575688i | −0.0109284 | − | 0.0189285i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.66543 | + | 11.1984i | −0.0546998 | + | 0.367804i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.72508 | − | 13.3802i | 0.253452 | − | 0.438991i | −0.711022 | − | 0.703170i | \(-0.751767\pi\) |
0.964474 | + | 0.264178i | \(0.0851008\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.2843 | + | 4.96511i | −0.336694 | + | 0.162550i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.32027 | − | 4.22636i | −0.239398 | − | 0.138217i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 46.1410i | − | 1.50736i | −0.657241 | − | 0.753680i | \(-0.728277\pi\) | ||
0.657241 | − | 0.753680i | \(-0.271723\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.32681 | + | 4.88983i | −0.108566 | + | 0.159574i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.5052 | + | 35.5161i | 0.668451 | + | 1.15779i | 0.978337 | + | 0.207017i | \(0.0663756\pi\) |
−0.309886 | + | 0.950774i | \(0.600291\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.9859 | − | 15.0030i | −0.846218 | − | 0.488564i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.50657 | − | 4.91127i | −0.276426 | − | 0.159595i | 0.355378 | − | 0.934723i | \(-0.384352\pi\) |
−0.631804 | + | 0.775128i | \(0.717685\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.72718 | + | 13.3839i | 0.250835 | + | 0.434459i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.2758 | − | 45.9700i | 1.01419 | − | 1.49068i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 17.0826i | − | 0.553359i | −0.960962 | − | 0.276679i | \(-0.910766\pi\) | ||
0.960962 | − | 0.276679i | \(-0.0892340\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.8305 | + | 14.9132i | 0.835855 | + | 0.482581i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.7141 | − | 8.55205i | 0.572614 | − | 0.276449i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.2501 | + | 26.4139i | −0.491939 | + | 0.852063i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.1762 | + | 8.75374i | −0.714617 | + | 0.282085i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.77826 | − | 8.27619i | −0.153818 | − | 0.266420i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.3240 | − | 36.9343i | 0.685735 | − | 1.18773i | −0.287471 | − | 0.957789i | \(-0.592814\pi\) |
0.973205 | − | 0.229938i | \(-0.0738523\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36.2550 | − | 2.68118i | −1.16468 | − | 0.0861318i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.7562 | + | 20.3623i | 0.377275 | + | 0.653459i | 0.990665 | − | 0.136321i | \(-0.0435280\pi\) |
−0.613390 | + | 0.789780i | \(0.710195\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.772323 | − | 1.13518i | 0.0247341 | − | 0.0363549i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.1944 | + | 17.4327i | −0.966003 | + | 0.557722i | −0.898015 | − | 0.439964i | \(-0.854991\pi\) |
−0.0679878 | + | 0.997686i | \(0.521658\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.7229 | + | 6.76824i | −0.374666 | + | 0.216314i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.88505 | + | 2.37332i | −0.0601851 | + | 0.0757742i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.3608 | 0.840780 | 0.420390 | − | 0.907343i | \(-0.361893\pi\) | ||||
0.420390 | + | 0.907343i | \(0.361893\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2.19617i | − | 0.0699757i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.82780 | + | 5.09673i | −0.280708 | + | 0.162067i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.0805213 | − | 0.139467i | 0.00255784 | − | 0.00443031i | −0.864744 | − | 0.502214i | \(-0.832519\pi\) |
0.867301 | + | 0.497783i | \(0.165852\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 41.3621 | + | 28.1408i | 1.31259 | + | 0.893022i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.3916 | − | 7.15427i | −0.392839 | − | 0.226806i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 16.8378i | − | 0.533259i | −0.963799 | − | 0.266629i | \(-0.914090\pi\) | ||
0.963799 | − | 0.266629i | \(-0.0859100\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.0626 | − | 4.38310i | 0.444922 | − | 0.138675i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))