Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(341,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.341");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.w (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: | \(6.03669039281\) |
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 | 341.3 | ||
Root | \(-1.61108 + 0.635951i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.341 |
Dual form | 756.2.w.a.521.3 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(7\) | −1.25859 | + | 2.32722i | −0.475703 | + | 0.879606i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.26889 | + | 0.732592i | 0.382584 | + | 0.220885i | 0.678942 | − | 0.734192i | \(-0.262439\pi\) |
−0.296358 | + | 0.955077i | \(0.595772\pi\) | |||||||
\(12\) | 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 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.32136 | − | 2.28866i | −0.320476 | − | 0.555081i | 0.660110 | − | 0.751169i | \(-0.270509\pi\) |
−0.980586 | + | 0.196088i | \(0.937176\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.87816 | + | 3.97111i | 1.57796 | + | 0.911034i | 0.995144 | + | 0.0984279i | \(0.0313814\pi\) |
0.582813 | + | 0.812606i | \(0.301952\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.47245 | − | 2.00482i | 0.724056 | − | 0.418034i | −0.0921879 | − | 0.995742i | \(-0.529386\pi\) |
0.816244 | + | 0.577708i | \(0.196053\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.117249 | − | 0.203081i | 0.0234498 | − | 0.0406163i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.71261 | − | 3.87553i | 1.24650 | − | 0.719667i | 0.276091 | − | 0.961132i | \(-0.410961\pi\) |
0.970410 | + | 0.241464i | \(0.0776276\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.706968i | − | 0.126975i | −0.997983 | − | 0.0634876i | \(-0.979778\pi\) | ||
0.997983 | − | 0.0634876i | \(-0.0202223\pi\) | |||||||
\(32\) | 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 | −0.725678 | − | 0.688034i | \(-0.758474\pi\) |
0.958694 | + | 0.284438i | \(0.0918071\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.74173 | + | 6.48086i | −0.584360 | + | 1.01214i | 0.410595 | + | 0.911818i | \(0.365321\pi\) |
−0.994955 | + | 0.100323i | \(0.968012\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.5508 | 1.83072 | 0.915358 | − | 0.402640i | \(-0.131907\pi\) | ||||
0.915358 | + | 0.402640i | \(0.131907\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.83190 | − | 5.85803i | −0.547414 | − | 0.836862i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.41675 | − | 1.39531i | 0.331966 | − | 0.191661i | −0.324748 | − | 0.945801i | \(-0.605279\pi\) |
0.656714 | + | 0.754140i | \(0.271946\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.19850i | − | 0.431286i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.4330 | −1.74883 | −0.874414 | − | 0.485180i | \(-0.838754\pi\) | ||||
−0.874414 | + | 0.485180i | \(0.838754\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.79493i | 0.998039i | 0.866591 | + | 0.499020i | \(0.166306\pi\) | ||||
−0.866591 | + | 0.499020i | \(0.833694\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 7.37945i | − | 0.915308i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.84058 | 0.713541 | 0.356770 | − | 0.934192i | \(-0.383878\pi\) | ||||
0.356770 | + | 0.934192i | \(0.383878\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.6854i | 1.38680i | 0.720554 | + | 0.693398i | \(0.243887\pi\) | ||||
−0.720554 | + | 0.693398i | \(0.756113\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.95924 | + | 2.28587i | −0.463394 | + | 0.267541i | −0.713470 | − | 0.700685i | \(-0.752878\pi\) |
0.250076 | + | 0.968226i | \(0.419544\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.30191 | + | 2.03094i | −0.376288 | + | 0.231448i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.38377 | 1.05576 | 0.527879 | − | 0.849320i | \(-0.322988\pi\) | ||||
0.527879 | + | 0.849320i | \(0.322988\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.70847 | − | 2.95917i | −0.187529 | − | 0.324811i | 0.756896 | − | 0.653535i | \(-0.226715\pi\) |
−0.944426 | + | 0.328724i | \(0.893381\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.88452 | + | 4.99614i | −0.312871 | + | 0.541908i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.61937 | + | 8.00099i | −0.489653 | + | 0.848103i | −0.999929 | − | 0.0119070i | \(-0.996210\pi\) |
0.510276 | + | 0.860010i | \(0.329543\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.61803 | + | 4.68571i | −0.798586 | + | 0.491196i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 17.3379i | − | 1.77883i | ||||||
\(96\) | 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 | 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 | −0.652297 | − | 0.757963i | \(-0.726195\pi\) |
0.330267 | + | 0.943888i | \(0.392861\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.88241 | + | 3.97356i | 0.665347 | + | 0.384138i | 0.794311 | − | 0.607511i | \(-0.207832\pi\) |
−0.128964 | + | 0.991649i | \(0.541165\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.505142 | + | 0.874932i | 0.0483838 | + | 0.0838033i | 0.889203 | − | 0.457513i | \(-0.151260\pi\) |
−0.840819 | + | 0.541316i | \(0.817926\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5557 | + | 6.09431i | 0.992992 | + | 0.573304i | 0.906167 | − | 0.422919i | \(-0.138995\pi\) |
0.0868250 | + | 0.996224i | \(0.472328\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.58037 | − | 4.37653i | −0.706873 | − | 0.408113i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.98925 | − | 0.194605i | 0.640703 | − | 0.0178394i | ||||
\(120\) | 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 | ||||||||
\(133\) | −17.8984 | + | 11.0090i | −1.55199 | + | 0.954600i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.4028 | − | 10.0475i | −1.48682 | − | 0.858416i | −0.486933 | − | 0.873439i | \(-0.661884\pi\) |
−0.999887 | + | 0.0150235i | \(0.995218\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | 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 | −0.996424 | − | 0.0844939i | \(-0.973073\pi\) |
−0.425038 | + | 0.905175i | \(0.639739\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | −1.33655 | + | 0.771657i | −0.107354 | + | 0.0619810i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.02869i | − | 0.640759i | −0.947289 | − | 0.320380i | \(-0.896189\pi\) | ||
0.947289 | − | 0.320380i | \(-0.103811\pi\) | |||||||
\(158\) | 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 | −0.999899 | − | 0.0141893i | \(-0.995483\pi\) |
0.512238 | + | 0.858844i | \(0.328817\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.85984 | − | 17.0777i | 0.762978 | − | 1.32152i | −0.178332 | − | 0.983970i | \(-0.557070\pi\) |
0.941309 | − | 0.337546i | \(-0.109597\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.786412 | − | 1.36211i | −0.0604933 | − | 0.104777i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.82747 | −0.138940 | −0.0694699 | − | 0.997584i | \(-0.522131\pi\) | ||||
−0.0694699 | + | 0.997584i | \(0.522131\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.325046 | + | 0.528460i | 0.0245712 | + | 0.0399479i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.1182 | + | 6.99645i | −0.905757 | + | 0.522939i | −0.879064 | − | 0.476705i | \(-0.841831\pi\) |
−0.0266934 | + | 0.999644i | \(0.508498\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.3594i | − | 1.21599i | −0.793942 | − | 0.607994i | \(-0.791975\pi\) | ||
0.793942 | − | 0.607994i | \(-0.208025\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.18830 | −0.454973 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.87206i | − | 0.283153i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 13.6631i | − | 0.988624i | −0.869285 | − | 0.494312i | \(-0.835420\pi\) | ||
0.869285 | − | 0.494312i | \(-0.164580\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.37769 | −0.315113 | −0.157557 | − | 0.987510i | \(-0.550362\pi\) | ||||
−0.157557 | + | 0.987510i | \(0.550362\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.00603i | − | 0.0716767i | −0.999358 | − | 0.0358384i | \(-0.988590\pi\) | ||
0.999358 | − | 0.0358384i | \(-0.0114101\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.67639 | + | 3.27726i | −0.402388 | + | 0.232319i | −0.687514 | − | 0.726171i | \(-0.741298\pi\) |
0.285126 | + | 0.958490i | \(0.407965\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.570774 | + | 20.4994i | 0.0400605 | + | 1.43878i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.3364 | 1.14098 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 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 | ||||||||
\(221\) | − | 8.93345i | − | 0.600929i | ||||||
\(222\) | 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 | 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 | −0.913145 | − | 0.407636i | \(-0.866353\pi\) |
−0.103549 | + | 0.994624i | \(0.533020\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.9077 | + | 8.02962i | 0.911124 | + | 0.526038i | 0.880793 | − | 0.473502i | \(-0.157010\pi\) |
0.0303317 | + | 0.999540i | \(0.490344\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.6992 | − | 23.7277i | −0.893636 | − | 1.54782i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.11117 | + | 4.10564i | 0.459983 | + | 0.265572i | 0.712037 | − | 0.702142i | \(-0.247773\pi\) |
−0.252054 | + | 0.967713i | \(0.581106\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.6614 | − | 14.2382i | −1.58858 | − | 0.917166i | −0.993542 | − | 0.113468i | \(-0.963804\pi\) |
−0.595037 | − | 0.803698i | \(-0.702863\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.89230 | + | 13.6384i | −0.440333 | + | 0.871325i | ||||
\(246\) | 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 | ||||||||
\(259\) | 3.92937 | + | 6.38837i | 0.244159 | + | 0.396954i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.73888 | + | 3.31334i | 0.353874 | + | 0.204310i | 0.666390 | − | 0.745603i | \(-0.267838\pi\) |
−0.312516 | + | 0.949913i | \(0.601172\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.27577 | − | 3.04597i | −0.324088 | − | 0.187112i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.38347 | − | 7.59239i | −0.267265 | − | 0.462916i | 0.700890 | − | 0.713270i | \(-0.252786\pi\) |
−0.968154 | + | 0.250354i | \(0.919453\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.2608 | + | 8.23346i | 0.866280 | + | 0.500147i | 0.866110 | − | 0.499853i | \(-0.166613\pi\) |
0.000169619 | 1.00000i | \(0.499946\pi\) | ||||||||
\(272\) | 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 | ||||||||
\(281\) | 14.0252 | − | 8.09748i | 0.836676 | − | 0.483055i | −0.0194568 | − | 0.999811i | \(-0.506194\pi\) |
0.856133 | + | 0.516755i | \(0.172860\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 28.3729i | − | 1.68660i | −0.537447 | − | 0.843298i | \(-0.680611\pi\) | ||
0.537447 | − | 0.843298i | \(-0.319389\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | 4.38260 | − | 7.59088i | 0.256034 | − | 0.443464i | −0.709142 | − | 0.705066i | \(-0.750917\pi\) |
0.965176 | + | 0.261602i | \(0.0842507\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.6621 | + | 25.3956i | 0.853663 | + | 1.47859i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.5542 | 0.783861 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.72353 | − | 0.187206i | 0.387538 | − | 0.0107904i | ||||
\(302\) | 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 | \(0.119508\pi\) | ||||
−0.930345 | + | 0.366686i | \(0.880492\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.59343 | 0.373879 | 0.186939 | − | 0.982371i | \(-0.440143\pi\) | ||||
0.186939 | + | 0.982371i | \(0.440143\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.41458i | − | 0.193004i | −0.995333 | − | 0.0965018i | \(-0.969235\pi\) | ||
0.995333 | − | 0.0965018i | \(-0.0307654\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 32.1010i | − | 1.80297i | −0.432810 | − | 0.901485i | \(-0.642478\pi\) | ||
0.432810 | − | 0.901485i | \(-0.357522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.3567 | 0.635854 | ||||||||
\(320\) | 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 | ||||||||
\(329\) | −15.7963 | + | 29.2084i | −0.870877 | + | 1.61031i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.8833 | −1.58757 | −0.793784 | − | 0.608199i | \(-0.791892\pi\) | ||||
−0.793784 | + | 0.608199i | \(0.791892\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 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 | ||||||||
\(347\) | − | 12.3273i | − | 0.661766i | −0.943672 | − | 0.330883i | \(-0.892653\pi\) | ||
0.943672 | − | 0.330883i | \(-0.107347\pi\) | |||||||
\(348\) | 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 | ||||||||
\(351\) | 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 | 0.631501 | − | 0.775375i | \(-0.282439\pi\) |
−0.355745 | + | 0.934583i | \(0.615773\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.0394 | + | 38.1733i | 1.15997 | + | 2.00912i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.64304 | + | 4.99006i | 0.452397 | + | 0.261192i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.8755 | + | 8.58836i | 0.776494 | + | 0.448309i | 0.835186 | − | 0.549967i | \(-0.185360\pi\) |
−0.0586924 | + | 0.998276i | \(0.518693\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.205496 | + | 7.38043i | 0.0106688 | + | 0.383173i | ||||
\(372\) | 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 | ||||||||
\(385\) | 7.44361 | + | 4.02560i | 0.379362 | + | 0.205164i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.63671 | − | 3.83171i | −0.336495 | − | 0.194275i | 0.322226 | − | 0.946663i | \(-0.395569\pi\) |
−0.658721 | + | 0.752387i | \(0.728902\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.17668 | − | 5.29816i | −0.464085 | − | 0.267939i | ||||
\(392\) | 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 | 0.471424 | − | 0.881907i | \(-0.343740\pi\) |
−0.528042 | + | 0.849218i | \(0.677074\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.18778 | − | 4.72722i | 0.408878 | − | 0.236066i | −0.281429 | − | 0.959582i | \(-0.590809\pi\) |
0.690308 | + | 0.723516i | \(0.257475\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.19492 | − | 2.06966i | 0.0595233 | − | 0.103097i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.59700 | − | 2.07673i | 0.178296 | − | 0.102940i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0736i | 0.943126i | 0.881832 | + | 0.471563i | \(0.156310\pi\) | ||||
−0.881832 | + | 0.471563i | \(0.843690\pi\) | |||||||
\(410\) | 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 | ||||||||
\(419\) | 4.20003 | − | 7.27466i | 0.205185 | − | 0.355390i | −0.745007 | − | 0.667057i | \(-0.767554\pi\) |
0.950192 | + | 0.311666i | \(0.100887\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.619711 | −0.0300604 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.1405 | − | 9.81063i | −0.877881 | − | 0.474770i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.3340 | + | 5.96634i | −0.497772 | + | 0.287389i | −0.727793 | − | 0.685797i | \(-0.759454\pi\) |
0.230021 | + | 0.973186i | \(0.426120\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.2121i | 0.586875i | 0.955978 | + | 0.293437i | \(0.0947992\pi\) | ||||
−0.955978 | + | 0.293437i | \(0.905201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.8454 | 1.52337 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.7015i | 0.797120i | 0.917142 | + | 0.398560i | \(0.130490\pi\) | ||||
−0.917142 | + | 0.398560i | \(0.869510\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.2997i | 1.43958i | 0.694190 | + | 0.719791i | \(0.255763\pi\) | ||||
−0.694190 | + | 0.719791i | \(0.744237\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.1682 | 0.956065 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 30.1253i | − | 1.42170i | −0.703343 | − | 0.710851i | \(-0.748310\pi\) | ||
0.703343 | − | 0.710851i | \(-0.251690\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.49566 | + | 5.48232i | −0.447133 | + | 0.258152i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.1736 | + | 9.28770i | 0.805110 | + | 0.435414i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.2318 | 1.18029 | 0.590146 | − | 0.807297i | \(-0.299070\pi\) | ||||
0.590146 | + | 0.807297i | \(0.299070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.3174 | + | 21.3344i | 0.573680 | + | 0.993643i | 0.996184 | + | 0.0872820i | \(0.0278181\pi\) |
−0.422503 | + | 0.906361i | \(0.638849\pi\) | |||||||
\(462\) | 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 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.4723 | + | 18.1385i | −0.484599 | + | 0.839350i | −0.999843 | − | 0.0176932i | \(-0.994368\pi\) |
0.515245 | + | 0.857043i | \(0.327701\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.35090 | + | 13.5923i | −0.339433 | + | 0.627635i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 3.72485i | − | 0.171269i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.61291 | − | 0.931217i | 0.0740056 | − | 0.0427271i | ||||
\(476\) | 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 | −0.915761 | − | 0.401724i | \(-0.868411\pi\) |
0.109977 | − | 0.993934i | \(-0.464922\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.75734 | − | 1.59195i | −0.124437 | − | 0.0718437i | 0.436490 | − | 0.899709i | \(-0.356222\pi\) |
−0.560926 | + | 0.827866i | \(0.689555\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.7395 | − | 10.2419i | −0.798947 | − | 0.461272i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −27.1944 | − | 14.7071i | −1.21983 | − | 0.659703i | ||||
\(498\) | 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 | ||||||||
\(511\) | −0.336655 | − | 12.0910i | −0.0148927 | − | 0.534875i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.13461 | + | 4.11917i | 0.314388 | + | 0.181512i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.9255 | + | 9.19459i | 0.700402 | + | 0.404378i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.0385 | − | 29.5116i | −0.746471 | − | 1.29293i | −0.949504 | − | 0.313754i | \(-0.898413\pi\) |
0.203033 | − | 0.979172i | \(-0.434920\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.71003 | + | 2.71933i | 0.205955 | + | 0.118908i | 0.599430 | − | 0.800427i | \(-0.295394\pi\) |
−0.393475 | + | 0.919335i | \(0.628727\pi\) | |||||||
\(524\) | 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 | ||||||||
\(533\) | −21.9080 | + | 12.6486i | −0.948940 | + | 0.547871i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 17.3486i | − | 0.750045i | ||||||
\(536\) | 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 | −0.491212 | − | 0.871040i | \(-0.663446\pi\) |
0.999949 | − | 0.0101183i | \(-0.00322080\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 61.5605 | 2.62257 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.8103 | + | 21.8381i | −0.502226 | + | 0.928650i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.36315 | − | 4.25111i | 0.311987 | − | 0.180126i | −0.335829 | − | 0.941923i | \(-0.609016\pi\) |
0.647815 | + | 0.761798i | \(0.275683\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.59381i | − | 0.363480i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.947553 | −0.0399346 | −0.0199673 | − | 0.999801i | \(-0.506356\pi\) | ||||
−0.0199673 | + | 0.999801i | \(0.506356\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 26.6078i | − | 1.11940i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 18.2280i | − | 0.764158i | −0.924130 | − | 0.382079i | \(-0.875208\pi\) | ||
0.924130 | − | 0.382079i | \(-0.124792\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.2424 | −0.512330 | −0.256165 | − | 0.966633i | \(-0.582459\pi\) | ||||
−0.256165 | + | 0.966633i | \(0.582459\pi\) | |||||||
\(572\) | 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 | −0.697945 | − | 0.716151i | \(-0.745902\pi\) |
0.271232 | + | 0.962514i | \(0.412569\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.03690 | − | 0.251618i | 0.374914 | − | 0.0104389i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.08878 | 0.169340 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.57681 | − | 6.19521i | −0.147631 | − | 0.255704i | 0.782721 | − | 0.622373i | \(-0.213831\pi\) |
−0.930351 | + | 0.366669i | \(0.880498\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.80745 | − | 4.86264i | 0.115679 | − | 0.200362i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.4811 | + | 23.3500i | −0.553603 | + | 0.958869i | 0.444408 | + | 0.895825i | \(0.353414\pi\) |
−0.998011 | + | 0.0630442i | \(0.979919\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.99668 | − | 13.0010i | −0.327832 | − | 0.532990i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.2441i | 1.44004i | 0.693955 | + | 0.720018i | \(0.255867\pi\) | ||||
−0.693955 | + | 0.720018i | \(0.744133\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | 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 | −0.732376 | − | 0.680900i | \(-0.761589\pi\) |
0.223488 | + | 0.974707i | \(0.428256\pi\) | |||||||
\(608\) | 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 | 0.703858 | − | 0.710341i | \(-0.251459\pi\) |
−0.967102 | + | 0.254389i | \(0.918126\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.14491 | + | 1.81571i | 0.126609 | + | 0.0730979i | 0.561967 | − | 0.827160i | \(-0.310045\pi\) |
−0.435358 | + | 0.900258i | \(0.643378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.2737 | − | 8.24091i | −0.573708 | − | 0.331230i | 0.184921 | − | 0.982753i | \(-0.440797\pi\) |
−0.758629 | + | 0.651523i | \(0.774130\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.8062 | − | 20.8203i | −0.513068 | − | 0.834147i | ||||
\(624\) | 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 | ||||||||
\(637\) | −1.31669 | − | 23.6262i | −0.0521692 | − | 0.936105i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.25538 | − | 4.18889i | −0.286570 | − | 0.165451i | 0.349824 | − | 0.936815i | \(-0.386241\pi\) |
−0.636394 | + | 0.771364i | \(0.719575\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.74770 | − | 8.22325i | −0.186651 | − | 0.323289i | 0.757480 | − | 0.652858i | \(-0.226430\pi\) |
−0.944132 | + | 0.329568i | \(0.893097\pi\) | |||||||
\(648\) | 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 | −0.364261 | − | 0.931297i | \(-0.618678\pi\) |
0.624396 | + | 0.781108i | \(0.285345\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.9927 | + | 25.9680i | −0.585811 | + | 1.01465i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.0493 | + | 21.9678i | −1.48219 | + | 0.855743i | −0.999796 | − | 0.0202102i | \(-0.993566\pi\) |
−0.482395 | + | 0.875954i | \(0.660233\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.5938i | 0.995484i | 0.867325 | + | 0.497742i | \(0.165837\pi\) | ||||
−0.867325 | + | 0.497742i | \(0.834163\pi\) | |||||||
\(662\) | 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 | ||||||||
\(671\) | −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 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.2918 | −1.74070 | −0.870352 | − | 0.492430i | \(-0.836109\pi\) | ||||
−0.870352 | + | 0.492430i | \(0.836109\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.542827 | + | 19.4957i | 0.0208318 | + | 0.748177i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0891 | + | 13.9079i | −0.921744 | + | 0.532169i | −0.884191 | − | 0.467126i | \(-0.845290\pi\) |
−0.0375529 | + | 0.999295i | \(0.511956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 43.8674i | 1.67609i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.43345 | 0.359386 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.2946i | 0.619875i | 0.950757 | + | 0.309938i | \(0.100308\pi\) | ||||
−0.950757 | + | 0.309938i | \(0.899692\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 21.4614i | − | 0.814079i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.7766 | 0.749093 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.393403i | 0.0148586i | 0.999972 | + | 0.00742932i | \(0.00236485\pi\) | ||||
−0.999972 | + | 0.00742932i | \(0.997635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.4980 | − | 11.2572i | 0.735379 | − | 0.424572i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.9881 | − | 17.8644i | −0.413250 | − | 0.671862i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.6366 | −1.22569 | −0.612846 | − | 0.790202i | \(-0.709975\pi\) | ||||
−0.612846 | + | 0.790202i | \(0.709975\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 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 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.106604 | + | 0.184643i | −0.00397565 | + | 0.00688602i | −0.868006 | − | 0.496553i | \(-0.834599\pi\) |
0.864031 | + | 0.503439i | \(0.167932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.277900 | − | 9.98081i | −0.0103495 | − | 0.371705i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.81761i | − | 0.0675042i | ||||||
\(726\) | 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 | ||||||||
\(729\) | 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 | −0.315875 | − | 0.948801i | \(-0.602298\pi\) |
0.663748 | + | 0.747956i | \(0.268965\pi\) | |||||||
\(734\) | 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 | 0.964703 | − | 0.263340i | \(-0.0848242\pi\) |
−0.710411 | + | 0.703787i | \(0.751491\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.8751 | + | 9.16552i | 0.582403 | + | 0.336250i | 0.762088 | − | 0.647474i | \(-0.224175\pi\) |
−0.179685 | + | 0.983724i | \(0.557508\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.8776 | + | 21.8687i | 1.38773 | + | 0.801206i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.9095 | + | 11.0158i | −0.654398 | + | 0.402508i | ||||
\(750\) | 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 | ||||||||
\(763\) | −2.67193 | + | 0.0743955i | −0.0967302 | + | 0.00269330i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −39.3254 | − | 22.7045i | −1.41996 | − | 0.819813i | ||||
\(768\) | 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 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.82375 | + | 13.5511i | 0.281401 | + | 0.487400i | 0.971730 | − | 0.236095i | \(-0.0758677\pi\) |
−0.690329 | + | 0.723495i | \(0.742534\pi\) | |||||||
\(774\) | 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 | ||||||||
\(785\) | −15.1785 | + | 8.76333i | −0.541745 | + | 0.312777i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.1788i | 1.64610i | 0.567972 | + | 0.823048i | \(0.307728\pi\) | ||||
−0.567972 | + | 0.823048i | \(0.692272\pi\) | |||||||
\(788\) | 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 | ||||||||
\(797\) | 16.9388 | − | 29.3388i | 0.600002 | − | 1.03923i | −0.392818 | − | 0.919616i | \(-0.628500\pi\) |
0.992820 | − | 0.119618i | \(-0.0381669\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.5840 | − | 28.7244i | −0.586701 | − | 1.01620i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.69844 | −0.236383 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.7257 | − | 12.1329i | 0.695240 | − | 0.427629i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.7873 | − | 19.5071i | 1.18790 | − | 0.685834i | 0.230070 | − | 0.973174i | \(-0.426104\pi\) |
0.957829 | + | 0.287340i | \(0.0927711\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.73397i | − | 0.271577i | −0.990738 | − | 0.135788i | \(-0.956643\pi\) | ||
0.990738 | − | 0.135788i | \(-0.0433567\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.1829 | 0.952177 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 20.1910i | − | 0.706394i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 0.512269i | − | 0.0178783i | −0.999960 | − | 0.00893915i | \(-0.997155\pi\) | ||
0.999960 | − | 0.00893915i | \(-0.00284546\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.3506 | −1.68540 | −0.842698 | − | 0.538387i | \(-0.819034\pi\) | ||||
−0.842698 | + | 0.538387i | \(0.819034\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.3086i | 0.601879i | 0.953643 | + | 0.300940i | \(0.0973003\pi\) | ||||
−0.953643 | + | 0.300940i | \(0.902700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.0205 | − | 19.0644i | 1.14685 | − | 0.662134i | 0.198733 | − | 0.980054i | \(-0.436317\pi\) |
0.948118 | + | 0.317919i | \(0.102984\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.34372 | + | 16.5104i | −0.289093 | + | 0.572053i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −43.0481 | −1.48974 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.2026 | + | 26.3317i | 0.524852 | + | 0.909071i | 0.999581 | + | 0.0289389i | \(0.00921281\pi\) |
−0.474729 | + | 0.880132i | \(0.657454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.5394 | − | 26.9151i | 0.535842 | − | 0.928106i | ||||
\(842\) | 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 | ||||||||
\(851\) | − | 11.3664i | − | 0.389635i | ||||||
\(852\) | 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 | ||||||||
\(855\) | 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 | −0.744587 | − | 0.667526i | \(-0.767353\pi\) |
0.205801 | + | 0.978594i | \(0.434020\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.61966 | + | 3.82186i | 0.225336 | + | 0.130098i | 0.608419 | − | 0.793616i | \(-0.291804\pi\) |
−0.383083 | + | 0.923714i | \(0.625138\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.99468 | + | 3.45489i | 0.0678213 | + | 0.117470i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.9069 | + | 6.87448i | 0.403915 | + | 0.233201i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.0984 | + | 9.87179i | 0.579358 | + | 0.334493i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.3818 | − | 26.5930i | 0.486194 | − | 0.899006i | ||||
\(876\) | 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 | ||||||||
\(889\) | −8.55024 | + | 15.8100i | −0.286766 | + | 0.530249i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 86.3261 | + | 49.8404i | 2.88879 | + | 1.66785i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.4541 | + | 15.2733i | 0.884262 | + | 0.510529i | ||||
\(896\) | 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 | ||||||||
\(911\) | 3.86306 | − | 2.23034i | 0.127989 | − | 0.0738944i | −0.434639 | − | 0.900605i | \(-0.643124\pi\) |
0.562627 | + | 0.826711i | \(0.309791\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 5.00646i | − | 0.165690i | ||||||
\(914\) | 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 | 0.267811 | + | 0.963471i | \(0.413700\pi\) |
−0.968296 | + | 0.249804i | \(0.919634\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 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 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.4502 | 0.506903 | 0.253452 | − | 0.967348i | \(-0.418434\pi\) | ||||
0.253452 | + | 0.967348i | \(0.418434\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.09354 | − | 55.5093i | −0.101387 | − | 1.81925i | ||||
\(932\) | 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 | \(-0.728277\pi\) | ||
0.657241 | − | 0.753680i | \(-0.271723\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.0104 | 1.33690 | 0.668451 | − | 0.743756i | \(-0.266958\pi\) | ||||
0.668451 | + | 0.743756i | \(0.266958\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.0060i | 0.977128i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 9.82254i | − | 0.319190i | −0.987183 | − | 0.159595i | \(-0.948981\pi\) | ||
0.987183 | − | 0.159595i | \(-0.0510188\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.4544 | −0.501670 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.0826i | 0.553359i | 0.960962 | + | 0.276679i | \(0.0892340\pi\) | ||||
−0.960962 | + | 0.276679i | \(0.910766\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.8305 | + | 14.9132i | −0.835855 | + | 0.482581i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.2857 | − | 27.8544i | 1.46235 | − | 0.899466i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.5002 | 0.983877 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.7562 | + | 20.3623i | −0.377275 | + | 0.653459i | −0.990665 | − | 0.136321i | \(-0.956472\pi\) |
0.613390 | + | 0.789780i | \(0.289805\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.1553 | + | 13.6273i | −0.710267 | + | 0.436872i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.8654i | 1.11544i | 0.830028 | + | 0.557722i | \(0.188325\pi\) | ||||
−0.830028 | + | 0.557722i | \(0.811675\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.7229 | + | 6.76824i | −0.374666 | + | 0.216314i | ||||
\(980\) | 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 | 0.867301 | − | 0.497783i | \(-0.165852\pi\) |
−0.864744 | + | 0.502214i | \(0.832519\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.3916 | + | 7.15427i | 0.392839 | + | 0.226806i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.5820 | + | 8.41890i | 0.461816 | + | 0.266629i | 0.712807 | − | 0.701360i | \(-0.247423\pi\) |
−0.250992 | + | 0.967989i | \(0.580757\pi\) | |||||||
\(998\) | 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 \(a_p\))