Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(1781,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.1781");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.t (of order \(6\), degree \(2\), 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: | \(18.1100711784\) |
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: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1781.3 | ||
Root | \(-1.61108 + 0.635951i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.1781 |
Dual form | 2268.2.t.a.2105.3 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.09150 | − | 1.89054i | −0.488134 | − | 0.845473i | 0.511773 | − | 0.859121i | \(-0.328989\pi\) |
−0.999907 | + | 0.0136476i | \(0.995656\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.38614 | + | 2.25358i | −0.523910 | + | 0.851774i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.26889 | − | 0.732592i | −0.382584 | − | 0.220885i | 0.296358 | − | 0.955077i | \(-0.404228\pi\) |
−0.678942 | + | 0.734192i | \(0.737561\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.38041i | 0.937557i | 0.883316 | + | 0.468779i | \(0.155306\pi\) | ||||
−0.883316 | + | 0.468779i | \(0.844694\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.32136 | + | 2.28866i | −0.320476 | + | 0.555081i | −0.980586 | − | 0.196088i | \(-0.937176\pi\) |
0.660110 | + | 0.751169i | \(0.270509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.87816 | − | 3.97111i | 1.57796 | − | 0.911034i | 0.582813 | − | 0.812606i | \(-0.301952\pi\) |
0.995144 | − | 0.0984279i | \(-0.0313814\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.47245 | + | 2.00482i | −0.724056 | + | 0.418034i | −0.816244 | − | 0.577708i | \(-0.803947\pi\) |
0.0921879 | + | 0.995742i | \(0.470614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.117249 | − | 0.203081i | 0.0234498 | − | 0.0406163i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.75105i | − | 1.43933i | −0.694319 | − | 0.719667i | \(-0.744294\pi\) | ||
0.694319 | − | 0.719667i | \(-0.255706\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.612252 | − | 0.353484i | −0.109964 | − | 0.0634876i | 0.444009 | − | 0.896022i | \(-0.353556\pi\) |
−0.553973 | + | 0.832534i | \(0.686889\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.77345 | + | 0.160752i | 0.975890 | + | 0.0271721i | ||||
\(36\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.48345 | 1.16872 | 0.584360 | − | 0.811495i | \(-0.301346\pi\) | ||||
0.584360 | + | 0.811495i | \(0.301346\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.54224 | 0.387688 | 0.193844 | − | 0.981032i | \(-0.437904\pi\) | ||||
0.193844 | + | 0.981032i | \(0.437904\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.27538 | − | 10.8693i | −0.915358 | − | 1.58545i | −0.806376 | − | 0.591403i | \(-0.798574\pi\) |
−0.108983 | − | 0.994044i | \(-0.534759\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.15726 | − | 6.24754i | −0.451036 | − | 0.892506i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 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 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.71650 | − | 11.6333i | 0.874414 | − | 1.51453i | 0.0170287 | − | 0.999855i | \(-0.494579\pi\) |
0.857385 | − | 0.514675i | \(-0.172087\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.75061 | + | 3.89747i | −0.864327 | + | 0.499020i | −0.865459 | − | 0.500980i | \(-0.832973\pi\) |
0.00113176 | + | 0.999999i | \(0.499640\pi\) | |||||||
\(62\) | 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 | −0.987419 | − | 0.158124i | \(-0.949455\pi\) |
0.630649 | + | 0.776068i | \(0.282789\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | 0.250076 | − | 0.968226i | \(-0.419544\pi\) |
−0.713470 | + | 0.700685i | \(0.752878\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.40980 | − | 1.84407i | 0.388583 | − | 0.210151i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.69189 | − | 8.12659i | −0.527879 | − | 0.914312i | −0.999472 | − | 0.0324963i | \(-0.989654\pi\) |
0.471593 | − | 0.881816i | \(-0.343679\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.41695 | 0.375059 | 0.187529 | − | 0.982259i | \(-0.439952\pi\) | ||||
0.187529 | + | 0.982259i | \(0.439952\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.76905 | 0.625741 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.61937 | − | 8.00099i | −0.489653 | − | 0.848103i | 0.510276 | − | 0.860010i | \(-0.329543\pi\) |
−0.999929 | + | 0.0119070i | \(0.996210\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.61803 | − | 4.68571i | −0.798586 | − | 0.491196i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.0150 | − | 8.66894i | −1.54051 | − | 0.889414i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7.37154i | − | 0.748467i | −0.927335 | − | 0.374233i | \(-0.877906\pi\) | ||
0.927335 | − | 0.374233i | \(-0.122094\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.96357 | + | 6.86510i | −0.394390 | + | 0.683103i | −0.993023 | − | 0.117920i | \(-0.962377\pi\) |
0.598633 | + | 0.801023i | \(0.295711\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.26825 | − | 1.88693i | 0.322031 | − | 0.185924i | −0.330267 | − | 0.943888i | \(-0.607139\pi\) |
0.652297 | + | 0.757963i | \(0.273805\pi\) | |||||||
\(104\) | 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 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.1886i | 1.14661i | 0.819342 | + | 0.573304i | \(0.194339\pi\) | ||||
−0.819342 | + | 0.573304i | \(0.805661\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.58037 | + | 4.37653i | 0.706873 | + | 0.408113i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.32609 | − | 6.15017i | −0.304902 | − | 0.563785i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.42662 | − | 7.66713i | −0.402420 | − | 0.697012i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.86790 | − | 11.8956i | −0.600051 | − | 1.03932i | −0.992813 | − | 0.119679i | \(-0.961813\pi\) |
0.392761 | − | 0.919640i | \(-0.371520\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.584850 | + | 21.0050i | −0.0507130 | + | 1.82136i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.4028 | + | 10.0475i | 1.48682 | + | 0.858416i | 0.999887 | − | 0.0150235i | \(-0.00478229\pi\) |
0.486933 | + | 0.873439i | \(0.338116\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.83116i | 0.833868i | 0.908937 | + | 0.416934i | \(0.136895\pi\) | ||||
−0.908937 | + | 0.416934i | \(0.863105\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 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 | ||||||||
\(149\) | 17.3512 | − | 10.0177i | 1.42146 | − | 0.820682i | 0.425038 | − | 0.905175i | \(-0.360261\pi\) |
0.996424 | + | 0.0844939i | \(0.0269274\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.1168 | − | 19.2549i | 0.904675 | − | 1.56694i | 0.0833218 | − | 0.996523i | \(-0.473447\pi\) |
0.821353 | − | 0.570420i | \(-0.193220\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.54331i | 0.123962i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.95305 | − | 4.01435i | −0.554914 | − | 0.320380i | 0.196188 | − | 0.980566i | \(-0.437144\pi\) |
−0.751102 | + | 0.660187i | \(0.770477\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.295263 | − | 10.6044i | 0.0232700 | − | 0.835744i | ||||
\(162\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.7197 | −1.52596 | −0.762978 | − | 0.646425i | \(-0.776263\pi\) | ||||
−0.762978 | + | 0.646425i | \(0.776263\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.57282 | 0.120987 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.913733 | + | 1.58263i | 0.0694699 | + | 0.120325i | 0.898668 | − | 0.438629i | \(-0.144536\pi\) |
−0.829198 | + | 0.558955i | \(0.811203\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.295137 | + | 0.545728i | 0.0223103 | + | 0.0412532i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 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 | \(0.208025\pi\) | ||||
−0.793942 | + | 0.607994i | \(0.791975\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | \(-0.502087\pi\) |
0.862729 | + | 0.505667i | \(0.168753\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.18885 | − | 3.79119i | 0.157557 | − | 0.272896i | −0.776430 | − | 0.630203i | \(-0.782972\pi\) |
0.933987 | + | 0.357307i | \(0.116305\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 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 | 0.285126 | − | 0.958490i | \(-0.407965\pi\) |
−0.687514 | + | 0.726171i | \(0.741298\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.4676 | + | 10.7440i | 1.22599 | + | 0.754082i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.16820 | − | 14.1477i | −0.570492 | − | 0.988121i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.6368 | −0.804934 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2240 | 1.25459 | 0.627297 | − | 0.778780i | \(-0.284161\pi\) | ||||
0.627297 | + | 0.778780i | \(0.284161\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.77486 | − | 4.80620i | −0.189244 | − | 0.327780i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.64527 | − | 0.889784i | 0.111688 | − | 0.0604024i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.73660 | − | 4.46673i | −0.520420 | − | 0.300464i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0656i | 0.674041i | 0.941497 | + | 0.337021i | \(0.109419\pi\) | ||||
−0.941497 | + | 0.337021i | \(0.890581\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.94372 | + | 17.2230i | −0.659988 | + | 1.14313i | 0.320630 | + | 0.947204i | \(0.396105\pi\) |
−0.980618 | + | 0.195928i | \(0.937228\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.3854 | − | 8.88275i | 1.01669 | − | 0.586988i | 0.103549 | − | 0.994624i | \(-0.466980\pi\) |
0.913145 | + | 0.407636i | \(0.133647\pi\) | |||||||
\(230\) | 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 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.21127i | 0.531143i | 0.964091 | + | 0.265572i | \(0.0855607\pi\) | ||||
−0.964091 | + | 0.265572i | \(0.914439\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.6614 | + | 14.2382i | 1.58858 | + | 0.917166i | 0.993542 | + | 0.113468i | \(0.0361959\pi\) |
0.595037 | + | 0.803698i | \(0.297137\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.36505 | + | 12.7881i | −0.534423 | + | 0.817002i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.4240 | + | 23.2510i | 0.854147 | + | 1.47943i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.656343 | −0.0414280 | −0.0207140 | − | 0.999785i | \(-0.506594\pi\) | ||||
−0.0207140 | + | 0.999785i | \(0.506594\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.87486 | 0.369349 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.82042 | + | 6.61716i | 0.238311 | + | 0.412767i | 0.960230 | − | 0.279211i | \(-0.0900728\pi\) |
−0.721918 | + | 0.691978i | \(0.756739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.49718 | − | 0.208747i | −0.465852 | − | 0.0129709i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.73888 | − | 3.31334i | −0.353874 | − | 0.204310i | 0.312516 | − | 0.949913i | \(-0.398828\pi\) |
−0.666390 | + | 0.745603i | \(0.732162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6.09194i | − | 0.374225i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.38347 | + | 7.59239i | −0.267265 | + | 0.462916i | −0.968154 | − | 0.250354i | \(-0.919453\pi\) |
0.700890 | + | 0.713270i | \(0.252786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.2608 | − | 8.23346i | 0.866280 | − | 0.500147i | 0.000169619 | − | 1.00000i | \(-0.499946\pi\) |
0.866110 | + | 0.499853i | \(0.166613\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.297551 | + | 0.171791i | −0.0179430 | + | 0.0103594i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.88732 | − | 15.3933i | 0.533987 | − | 0.924893i | −0.465225 | − | 0.885193i | \(-0.654026\pi\) |
0.999212 | − | 0.0397001i | \(-0.0126402\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 16.1950i | − | 0.966111i | −0.875590 | − | 0.483055i | \(-0.839527\pi\) | ||
0.875590 | − | 0.483055i | \(-0.160473\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.5717 | − | 14.1865i | −1.46063 | − | 0.843298i | −0.461594 | − | 0.887091i | \(-0.652722\pi\) |
−0.999041 | + | 0.0437937i | \(0.986056\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.3731 | + | 16.8646i | −0.612304 | + | 0.995484i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00804 | + | 8.67417i | 0.294590 | + | 0.510246i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.76520 | −0.512068 | −0.256034 | − | 0.966668i | \(-0.582416\pi\) | ||||
−0.256034 | + | 0.966668i | \(0.582416\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.3243 | −1.70733 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.77711 | − | 11.7383i | −0.391931 | − | 0.678844i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.52389 | + | 5.72914i | −0.203114 | + | 0.330222i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.7366 | + | 8.50818i | 0.843816 | + | 0.487177i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.8497i | − | 0.733372i | −0.930345 | − | 0.366686i | \(-0.880492\pi\) | ||
0.930345 | − | 0.366686i | \(-0.119508\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.29671 | + | 5.71007i | −0.186939 | + | 0.323789i | −0.944228 | − | 0.329291i | \(-0.893190\pi\) |
0.757289 | + | 0.653080i | \(0.226523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.95711 | − | 1.70729i | 0.167146 | − | 0.0965018i | −0.414093 | − | 0.910234i | \(-0.635901\pi\) |
0.581239 | + | 0.813733i | \(0.302568\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.8003 | − | 16.0505i | 1.56142 | − | 0.901485i | 0.564304 | − | 0.825567i | \(-0.309145\pi\) |
0.997114 | − | 0.0759182i | \(-0.0241888\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.67836 | + | 9.83521i | −0.317927 | + | 0.550666i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.9890i | 1.16786i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.686498 | + | 0.396350i | 0.0380801 | + | 0.0219855i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.1933 | + | 0.924216i | 1.83001 | + | 0.0509537i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4416 | + | 25.0137i | 0.793784 | + | 1.37487i | 0.923608 | + | 0.383338i | \(0.125225\pi\) |
−0.129824 | + | 0.991537i | \(0.541441\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.7500 | 0.696608 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.65137 | −0.525743 | −0.262872 | − | 0.964831i | \(-0.584670\pi\) | ||||
−0.262872 | + | 0.964831i | \(0.584670\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.517919 | + | 0.897063i | 0.0280469 | + | 0.0485787i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4557 | + | 1.54481i | 0.996515 | + | 0.0834117i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.6758 | − | 6.16367i | −0.573106 | − | 0.330883i | 0.185283 | − | 0.982685i | \(-0.440680\pi\) |
−0.758389 | + | 0.651802i | \(0.774013\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.8023i | 0.631763i | 0.948799 | + | 0.315881i | \(0.102300\pi\) | ||||
−0.948799 | + | 0.315881i | \(0.897700\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.59855 | + | 11.4290i | −0.351205 | + | 0.608305i | −0.986461 | − | 0.163997i | \(-0.947561\pi\) |
0.635256 | + | 0.772302i | \(0.280895\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.0916 | + | 12.7546i | −1.17250 | + | 0.676943i | ||||
\(356\) | 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 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.98012i | 0.522384i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.8755 | − | 8.58836i | −0.776494 | − | 0.448309i | 0.0586924 | − | 0.998276i | \(-0.481307\pi\) |
−0.835186 | + | 0.549967i | \(0.814640\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.49439 | + | 3.51225i | −0.337172 | + | 0.182347i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.35902 | − | 4.08595i | −0.122146 | − | 0.211562i | 0.798468 | − | 0.602037i | \(-0.205644\pi\) |
−0.920614 | + | 0.390475i | \(0.872311\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.85036 | − | 4.93696i | −0.145646 | − | 0.252267i | 0.783968 | − | 0.620802i | \(-0.213193\pi\) |
−0.929614 | + | 0.368535i | \(0.879860\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.20808 | − | 4.43356i | −0.367358 | − | 0.225955i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.63671 | + | 3.83171i | 0.336495 | + | 0.194275i | 0.658721 | − | 0.752387i | \(-0.271098\pi\) |
−0.322226 | + | 0.946663i | \(0.604431\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.5963i | − | 0.535879i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.2424 | + | 17.7404i | −0.515351 | + | 0.892615i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.12810 | + | 0.651310i | −0.0566178 | + | 0.0326883i | −0.528042 | − | 0.849218i | \(-0.677074\pi\) |
0.471424 | + | 0.881907i | \(0.343740\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.18778 | + | 4.72722i | −0.408878 | + | 0.236066i | −0.690308 | − | 0.723516i | \(-0.742525\pi\) |
0.281429 | + | 0.959582i | \(0.409191\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.19492 | − | 2.06966i | 0.0595233 | − | 0.103097i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4.15345i | − | 0.205879i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.5182 | + | 9.53678i | 0.816771 | + | 0.471563i | 0.849302 | − | 0.527908i | \(-0.177023\pi\) |
−0.0325304 | + | 0.999471i | \(0.510357\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.9067 | + | 31.2615i | 0.831922 | + | 1.53828i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.72961 | − | 6.45987i | −0.183079 | − | 0.317102i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.40005 | −0.410369 | −0.205185 | − | 0.978723i | \(-0.565780\pi\) | ||||
−0.205185 | + | 0.978723i | \(0.565780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.4355 | −1.92197 | −0.960985 | − | 0.276599i | \(-0.910792\pi\) | ||||
−0.960985 | + | 0.276599i | \(0.910792\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.309855 | + | 0.536685i | 0.0150302 | + | 0.0260331i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.574005 | − | 20.6155i | 0.0277781 | − | 0.997652i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(-0.905201\pi\) | ||
0.955978 | − | 0.293437i | \(-0.0947992\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.9227 | + | 27.5789i | −0.761686 | + | 1.31928i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.4639 | + | 8.35076i | −0.690326 | + | 0.398560i | −0.803734 | − | 0.594989i | \(-0.797157\pi\) |
0.113408 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.2403 | + | 15.1499i | −1.24672 | + | 0.719791i | −0.970453 | − | 0.241291i | \(-0.922429\pi\) |
−0.276262 | + | 0.961082i | \(0.589096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.0841 | + | 17.4662i | −0.478033 | + | 0.827977i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 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 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.543409 | + | 19.5166i | −0.0254754 | + | 0.914953i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.6159 | − | 21.8513i | −0.590146 | − | 1.02216i | −0.994212 | − | 0.107433i | \(-0.965737\pi\) |
0.404067 | − | 0.914730i | \(-0.367596\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.6349 | −1.14736 | −0.573680 | − | 0.819079i | \(-0.694485\pi\) | ||||
−0.573680 | + | 0.819079i | \(0.694485\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.6643 | 0.588560 | 0.294280 | − | 0.955719i | \(-0.404920\pi\) | ||||
0.294280 | + | 0.955719i | \(0.404920\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.4723 | − | 18.1385i | −0.484599 | − | 0.839350i | 0.515245 | − | 0.857043i | \(-0.327701\pi\) |
−0.999843 | + | 0.0176932i | \(0.994368\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.35090 | − | 13.5923i | −0.339433 | − | 0.627635i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.22581 | − | 1.86242i | −0.148323 | − | 0.0856344i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.86243i | − | 0.0854543i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.8852 | + | 27.5141i | −0.725816 | + | 1.25715i | 0.232822 | + | 0.972519i | \(0.425204\pi\) |
−0.958637 | + | 0.284630i | \(0.908129\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.29884 | + | 4.79134i | −0.378394 | + | 0.218466i | ||||
\(482\) | 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 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.18390i | − | 0.143687i | −0.997416 | − | 0.0718437i | \(-0.977112\pi\) | ||
0.997416 | − | 0.0718437i | \(-0.0228883\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.7395 | + | 10.2419i | 0.798947 | + | 0.461272i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 26.3339 | + | 16.1975i | 1.18124 | + | 0.726557i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.0214 | − | 27.7498i | −0.717215 | − | 1.24225i | −0.962099 | − | 0.272700i | \(-0.912083\pi\) |
0.244884 | − | 0.969552i | \(-0.421250\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.6608 | −0.519930 | −0.259965 | − | 0.965618i | \(-0.583711\pi\) | ||||
−0.259965 | + | 0.965618i | \(0.583711\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.3050 | 0.770061 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.4427 | + | 23.2834i | 0.595836 | + | 1.03202i | 0.993428 | + | 0.114457i | \(0.0365127\pi\) |
−0.397592 | + | 0.917562i | \(0.630154\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.6394 | − | 5.75395i | 0.470661 | − | 0.254540i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.13461 | − | 4.11917i | −0.314388 | − | 0.181512i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.3892i | 0.808755i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.0385 | + | 29.5116i | −0.746471 | + | 1.29293i | 0.203033 | + | 0.979172i | \(0.434920\pi\) |
−0.949504 | + | 0.313754i | \(0.898413\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.71003 | − | 2.71933i | 0.205955 | − | 0.118908i | −0.393475 | − | 0.919335i | \(-0.628727\pi\) |
0.599430 | + | 0.800427i | \(0.295394\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.61801 | − | 0.934157i | 0.0704815 | − | 0.0406925i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.46140 | + | 5.99532i | −0.150496 | + | 0.260666i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.2971i | 1.09574i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.0243 | − | 8.67429i | −0.649558 | − | 0.375022i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.570698 | + | 10.2404i | −0.0245817 | + | 0.441085i | ||||
\(540\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.20545 | −0.0944713 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.1648 | 1.03321 | 0.516606 | − | 0.856223i | \(-0.327195\pi\) | ||||
0.516606 | + | 0.856223i | \(0.327195\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.7803 | − | 53.3130i | −1.31128 | − | 2.27121i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.8175 | + | 0.691004i | 1.05535 | + | 0.0293845i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 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 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.473776 | − | 0.820605i | 0.0199673 | − | 0.0345844i | −0.855869 | − | 0.517192i | \(-0.826977\pi\) |
0.875836 | + | 0.482608i | \(0.160310\pi\) | |||||||
\(564\) | 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 | \(-0.541875\pi\) |
0.792955 | + | 0.609280i | \(0.208542\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.12121 | − | 10.6023i | 0.256165 | − | 0.443691i | −0.709046 | − | 0.705162i | \(-0.750874\pi\) |
0.965211 | + | 0.261471i | \(0.0842077\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.940253i | 0.0392112i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.2500 | − | 5.91784i | −0.426713 | − | 0.246363i | 0.271232 | − | 0.962514i | \(-0.412569\pi\) |
−0.697945 | + | 0.716151i | \(0.745902\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.73636 | + | 7.70037i | −0.196497 | + | 0.319465i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.04439 | − | 3.54098i | −0.0846699 | − | 0.146653i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.15361 | 0.295261 | 0.147631 | − | 0.989043i | \(-0.452835\pi\) | ||||
0.147631 | + | 0.989043i | \(0.452835\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.61489 | −0.231358 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.4811 | − | 23.3500i | −0.553603 | − | 0.958869i | −0.998011 | − | 0.0630442i | \(-0.979919\pi\) |
0.444408 | − | 0.895825i | \(-0.353414\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.99668 | + | 13.0010i | −0.327832 | + | 0.532990i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.5223 | + | 17.6221i | 1.24711 | + | 0.720018i | 0.970532 | − | 0.240974i | \(-0.0774668\pi\) |
0.276576 | + | 0.960992i | \(0.410800\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.91750i | − | 0.159798i | −0.996803 | − | 0.0798991i | \(-0.974540\pi\) | ||
0.996803 | − | 0.0798991i | \(-0.0254598\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.66332 | + | 16.7374i | −0.392870 | + | 0.680470i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.5377 | − | 7.23862i | 0.508888 | − | 0.293807i | −0.223488 | − | 0.974707i | \(-0.571744\pi\) |
0.732376 | + | 0.680900i | \(0.238411\pi\) | |||||||
\(608\) | 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 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.63143i | 0.146196i | 0.997325 | + | 0.0730979i | \(0.0232886\pi\) | ||||
−0.997325 | + | 0.0730979i | \(0.976711\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.2737 | + | 8.24091i | 0.573708 | + | 0.331230i | 0.758629 | − | 0.651523i | \(-0.225870\pi\) |
−0.184921 | + | 0.982753i | \(0.559203\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.4340 | + | 0.680325i | 0.978926 | + | 0.0272567i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.8863 | + | 20.5876i | 0.475450 | + | 0.823504i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.41512 | − | 12.8434i | −0.294260 | − | 0.509673i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.1192 | − | 10.6728i | 0.836775 | − | 0.422873i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.25538 | + | 4.18889i | 0.286570 | + | 0.165451i | 0.636394 | − | 0.771364i | \(-0.280425\pi\) |
−0.349824 | + | 0.936815i | \(0.613759\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 20.7870i | − | 0.819761i | −0.912139 | − | 0.409881i | \(-0.865570\pi\) | ||
0.912139 | − | 0.409881i | \(-0.134430\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.74770 | + | 8.22325i | −0.186651 | + | 0.323289i | −0.944132 | − | 0.329568i | \(-0.893097\pi\) |
0.757480 | + | 0.652858i | \(0.226430\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.0450 | + | 9.84091i | −0.669073 | + | 0.386290i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.64747 | + | 3.83792i | −0.260136 | + | 0.150189i | −0.624396 | − | 0.781108i | \(-0.714655\pi\) |
0.364261 | + | 0.931297i | \(0.381322\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.9927 | + | 25.9680i | −0.585811 | + | 1.01465i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.9356i | 1.71149i | 0.517400 | + | 0.855743i | \(0.326900\pi\) | ||||
−0.517400 | + | 0.855743i | \(0.673100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.1649 | + | 12.7969i | 0.862115 | + | 0.497742i | 0.864720 | − | 0.502254i | \(-0.167496\pi\) |
−0.00260513 | + | 0.999997i | \(0.500829\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 40.3490 | − | 21.8213i | 1.56467 | − | 0.846193i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.5395 | + | 26.9151i | 0.601691 | + | 1.04216i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.4210 | 0.440903 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.2934 | 0.589518 | 0.294759 | − | 0.955572i | \(-0.404761\pi\) | ||||
0.294759 | + | 0.955572i | \(0.404761\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.6459 | + | 39.2238i | 0.870352 | + | 1.50749i | 0.861633 | + | 0.507532i | \(0.169442\pi\) |
0.00871898 | + | 0.999962i | \(0.497225\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.6124 | + | 10.2180i | 0.637524 | + | 0.392129i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.71672 | + | 8.16961i | −0.179693 | + | 0.311237i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.1115 | + | 8.14729i | −0.536828 | + | 0.309938i | −0.743792 | − | 0.668411i | \(-0.766975\pi\) |
0.206965 | + | 0.978348i | \(0.433641\pi\) | |||||||
\(692\) | 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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 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 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.97702 | − | 18.4482i | −0.375225 | − | 0.693816i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.3183 | + | 28.2641i | 0.612846 | + | 1.06148i | 0.990758 | + | 0.135639i | \(0.0433087\pi\) |
−0.377912 | + | 0.925841i | \(0.623358\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.83469 | 0.106160 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.8122 | −0.404355 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.106604 | − | 0.184643i | −0.00397565 | − | 0.00688602i | 0.864031 | − | 0.503439i | \(-0.167932\pi\) |
−0.868006 | + | 0.496553i | \(0.834599\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.277900 | + | 9.98081i | −0.0103495 | + | 0.371705i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.57409 | − | 0.908804i | −0.0584604 | − | 0.0337521i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 36.7435i | − | 1.36274i | −0.731939 | − | 0.681370i | \(-0.761385\pi\) | ||
0.731939 | − | 0.681370i | \(-0.238615\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.35920 | + | 5.81831i | −0.124245 | + | 0.215198i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.41829 | + | 5.43765i | −0.347873 | + | 0.200844i | −0.663748 | − | 0.747956i | \(-0.731035\pi\) |
0.315875 | + | 0.948801i | \(0.397702\pi\) | |||||||
\(734\) | 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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.3310i | 0.672501i | 0.941773 | + | 0.336250i | \(0.109159\pi\) | ||||
−0.941773 | + | 0.336250i | \(0.890841\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.8776 | − | 21.8687i | −1.38773 | − | 0.801206i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.585212 | + | 21.0180i | −0.0213832 | + | 0.767979i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.97084 | + | 17.2700i | 0.363841 | + | 0.630191i | 0.988589 | − | 0.150635i | \(-0.0481318\pi\) |
−0.624748 | + | 0.780826i | \(0.714798\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.7769 | − | 46.3789i | −0.970661 | − | 1.68123i | −0.693568 | − | 0.720391i | \(-0.743962\pi\) |
−0.277093 | − | 0.960843i | \(-0.589371\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.27153 | + | 2.35115i | 0.0460326 | + | 0.0851175i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.3254 | + | 22.7045i | 1.41996 | + | 0.819813i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 40.1035i | − | 1.44617i | −0.690760 | − | 0.723085i | \(-0.742724\pi\) | ||
0.690760 | − | 0.723085i | \(-0.257276\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.82375 | − | 13.5511i | 0.281401 | − | 0.487400i | −0.690329 | − | 0.723495i | \(-0.742534\pi\) |
0.971730 | + | 0.236095i | \(0.0758677\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.143572 | + | 0.0828913i | −0.00515726 | + | 0.00297755i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 51.4724 | − | 29.7176i | 1.84419 | − | 1.06474i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.56060 | + | 14.8274i | −0.306322 | + | 0.530566i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.5267i | 0.625553i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.9920 | + | 23.0894i | 1.42556 | + | 0.823048i | 0.996766 | − | 0.0803536i | \(-0.0256050\pi\) |
0.428795 | + | 0.903402i | \(0.358938\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.4680 | − | 16.8951i | −0.976651 | − | 0.600720i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.1750 | − | 22.8198i | −0.467859 | − | 0.810356i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.8775 | −1.20000 | −0.600002 | − | 0.799998i | \(-0.704834\pi\) | ||||
−0.600002 | + | 0.799998i | \(0.704834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.1680 | 1.17340 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.34922 | + | 5.80102i | 0.118191 | + | 0.204714i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.3703 | + | 11.0165i | −0.717958 | + | 0.388281i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 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 | \(0.0433567\pi\) | ||||
−0.990738 | + | 0.135788i | \(0.956643\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | \(-0.663821\pi\) |
0.507722 | + | 0.861521i | \(0.330488\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.1753 | − | 41.8728i | 0.842698 | − | 1.45960i | −0.0449080 | − | 0.998991i | \(-0.514299\pi\) |
0.887606 | − | 0.460604i | \(-0.152367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 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 | 0.948118 | − | 0.317919i | \(-0.102984\pi\) |
0.198733 | + | 0.980054i | \(0.436317\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.4703 | + | 1.02935i | 0.639959 | + | 0.0356649i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.5241 | + | 37.2808i | 0.744871 | + | 1.29015i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.4052 | −1.04970 | −0.524852 | − | 0.851193i | \(-0.675879\pi\) | ||||
−0.524852 | + | 0.851193i | \(0.675879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31.0789 | −1.07168 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.71674 | − | 2.97348i | −0.0590577 | − | 0.102291i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.4144 | + | 0.651937i | 0.804528 | + | 0.0224008i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.84358 | − | 5.68319i | −0.337434 | − | 0.194817i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 32.0017i | − | 1.09572i | −0.836571 | − | 0.547858i | \(-0.815443\pi\) | ||
0.836571 | − | 0.547858i | \(-0.184557\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.5774 | − | 39.1053i | 0.771230 | − | 1.33581i | −0.165659 | − | 0.986183i | \(-0.552975\pi\) |
0.936889 | − | 0.349627i | \(-0.113692\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.7911 | − | 9.11701i | 0.538786 | − | 0.311068i | −0.205801 | − | 0.978594i | \(-0.565980\pi\) |
0.744587 | + | 0.667526i | \(0.232647\pi\) | |||||||
\(860\) | 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 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.7490i | 0.466401i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.0984 | − | 9.87179i | −0.579358 | − | 0.334493i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.8393 | − | 25.7515i | 0.535465 | − | 0.870560i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.01581 | − | 13.8838i | −0.270675 | − | 0.468822i | 0.698360 | − | 0.715747i | \(-0.253913\pi\) |
−0.969035 | + | 0.246924i | \(0.920580\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.7532 | −0.833958 | −0.416979 | − | 0.908916i | \(-0.636911\pi\) | ||||
−0.416979 | + | 0.908916i | \(0.636911\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.6958 | −0.393595 | −0.196798 | − | 0.980444i | \(-0.563054\pi\) | ||||
−0.196798 | + | 0.980444i | \(0.563054\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.5429 | − | 47.7058i | −0.924801 | − | 1.60180i | −0.791880 | − | 0.610676i | \(-0.790898\pi\) |
−0.132921 | − | 0.991127i | \(-0.542436\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.41671 | + | 15.3097i | −0.315826 | + | 0.513471i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −86.3261 | − | 49.8404i | −2.88879 | − | 1.66785i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.5465i | 1.02106i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||||||
\(905\) | 30.9281 | − | 17.8563i | 1.02808 | − | 0.593565i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.9383 | − | 22.4098i | 0.429610 | − | 0.744107i | −0.567228 | − | 0.823560i | \(-0.691984\pi\) |
0.996839 | + | 0.0794540i | \(0.0253177\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.46068i | − | 0.147789i | −0.997266 | − | 0.0738944i | \(-0.976457\pi\) | ||
0.997266 | − | 0.0738944i | \(-0.0235428\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.33572 | − | 2.50323i | −0.143491 | − | 0.0828448i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.3274 | + | 1.01148i | 1.19964 | + | 0.0334020i | ||||
\(918\) | 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 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.5013 | 1.30020 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.664747 | 0.0218567 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.72508 | − | 13.3802i | −0.253452 | − | 0.438991i | 0.711022 | − | 0.703170i | \(-0.248233\pi\) |
−0.964474 | + | 0.264178i | \(0.914899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −46.5257 | − | 30.4338i | −1.52482 | − | 0.997426i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.32027 | − | 4.22636i | −0.239398 | − | 0.138217i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.1410i | 1.50736i | 0.657241 | + | 0.753680i | \(0.271723\pi\) | ||||
−0.657241 | + | 0.753680i | \(0.728277\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.5052 | + | 35.5161i | −0.668451 | + | 1.15779i | 0.309886 | + | 0.950774i | \(0.399709\pi\) |
−0.978337 | + | 0.207017i | \(0.933624\pi\) | |||||||
\(942\) | 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 | \(-0.615648\pi\) |
0.631804 | + | 0.775128i | \(0.282315\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.72718 | − | 13.3839i | 0.250835 | − | 0.434459i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 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 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46.7655 | + | 25.2914i | −1.51014 | + | 0.816701i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.2501 | − | 26.4139i | −0.491939 | − | 0.852063i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.55652 | −0.307635 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.6481 | −1.37147 | −0.685735 | − | 0.727852i | \(-0.740519\pi\) | ||||
−0.685735 | + | 0.727852i | \(0.740519\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.7562 | − | 20.3623i | −0.377275 | − | 0.653459i | 0.613390 | − | 0.789780i | \(-0.289805\pi\) |
−0.990665 | + | 0.136321i | \(0.956472\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.1553 | − | 13.6273i | −0.710267 | − | 0.436872i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.1944 | + | 17.4327i | 0.966003 | + | 0.557722i | 0.898015 | − | 0.439964i | \(-0.145009\pi\) |
0.0679878 | + | 0.997686i | \(0.478342\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.5365i | 0.432627i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.1804 | − | 22.8292i | 0.420390 | − | 0.728137i | −0.575587 | − | 0.817740i | \(-0.695227\pi\) |
0.995978 | + | 0.0896033i | \(0.0285599\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.90194 | − | 1.09808i | 0.0606008 | − | 0.0349879i | ||||
\(986\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.3085i | 0.453611i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.5820 | − | 8.41890i | −0.461816 | − | 0.266629i | 0.250992 | − | 0.967989i | \(-0.419243\pi\) |
−0.712807 | + | 0.701360i | \(0.752577\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))