Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(161,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.f (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.228765625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 5x^{5} + x^{4} + 15x^{3} - 18x^{2} - 27x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 161.2 | ||
Root | \(-1.73166 - 0.0369185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.161 |
Dual form | 363.2.f.c.239.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(3\) | 1.73166 | + | 0.0369185i | 0.999773 | + | 0.0213149i | ||||
\(4\) | −0.618034 | − | 1.90211i | −0.309017 | − | 0.951057i | ||||
\(5\) | 1.94946 | + | 2.68321i | 0.871826 | + | 1.19997i | 0.978618 | + | 0.205685i | \(0.0659421\pi\) |
−0.106792 | + | 0.994281i | \(0.534058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.99727 | + | 0.127860i | 0.999091 | + | 0.0426201i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | − | 3.31662i | −0.288675 | − | 0.957427i | ||||
\(13\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.27674 | + | 4.71836i | 0.846051 | + | 1.21828i | ||||
\(16\) | −3.23607 | + | 2.35114i | −0.809017 | + | 0.587785i | ||||
\(17\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(20\) | 3.89893 | − | 5.36641i | 0.871826 | − | 1.19997i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.31662i | − | 0.691564i | −0.938315 | − | 0.345782i | \(-0.887614\pi\) | ||
0.938315 | − | 0.345782i | \(-0.112386\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.85410 | + | 5.70634i | −0.370820 | + | 1.14127i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.18553 | + | 0.332065i | 0.997956 | + | 0.0639059i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.04508 | − | 2.93893i | −0.726519 | − | 0.527847i | 0.161942 | − | 0.986800i | \(-0.448224\pi\) |
−0.888460 | + | 0.458954i | \(0.848224\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.60921 | − | 5.78018i | −0.268202 | − | 0.963363i | ||||
\(37\) | −2.16312 | − | 6.65740i | −0.355615 | − | 1.09447i | −0.955652 | − | 0.294497i | \(-0.904848\pi\) |
0.600038 | − | 0.799972i | \(-0.295152\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.50000 | + | 8.29156i | 0.819892 | + | 1.23603i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.30860 | + | 2.04979i | 0.920203 | + | 0.298992i | 0.730550 | − | 0.682859i | \(-0.239264\pi\) |
0.189653 | + | 0.981851i | \(0.439264\pi\) | |||||||
\(48\) | −5.69056 | + | 3.95190i | −0.821362 | + | 0.570408i | ||||
\(49\) | −5.66312 | + | 4.11450i | −0.809017 | + | 0.587785i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.79785 | + | 10.7328i | −1.07112 | + | 1.47427i | −0.202178 | + | 0.979349i | \(0.564802\pi\) |
−0.868940 | + | 0.494918i | \(0.835198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.15430 | − | 1.02489i | 0.410655 | − | 0.133430i | −0.0964021 | − | 0.995342i | \(-0.530733\pi\) |
0.507057 | + | 0.861913i | \(0.330733\pi\) | |||||||
\(60\) | 6.94972 | − | 9.14884i | 0.897205 | − | 1.18111i | ||||
\(61\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.47214 | + | 4.70228i | 0.809017 | + | 0.587785i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.0000 | −1.58820 | −0.794101 | − | 0.607785i | \(-0.792058\pi\) | ||||
−0.794101 | + | 0.607785i | \(0.792058\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.122445 | − | 5.74326i | 0.0147406 | − | 0.691407i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.74732 | − | 13.4160i | −1.15679 | − | 1.59219i | −0.722416 | − | 0.691459i | \(-0.756968\pi\) |
−0.434378 | − | 0.900731i | \(-0.643032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.42134 | + | 9.81297i | −0.395062 | + | 1.13310i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(80\) | −12.6172 | − | 4.09957i | −1.41064 | − | 0.458346i | ||||
\(81\) | 8.96730 | + | 0.766464i | 0.996367 | + | 0.0851627i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.5831i | 1.75781i | 0.476999 | + | 0.878904i | \(0.341725\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.30860 | + | 2.04979i | −0.657717 | + | 0.213705i | ||||
\(93\) | −6.89620 | − | 5.23855i | −0.715103 | − | 0.543212i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.7533 | − | 9.99235i | −1.39643 | − | 1.01457i | −0.995124 | − | 0.0986273i | \(-0.968555\pi\) |
−0.401310 | − | 0.915942i | \(-0.631445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.0000 | 1.20000 | ||||||||
\(101\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.23607 | − | 3.80423i | −0.121793 | − | 0.374842i | 0.871510 | − | 0.490378i | \(-0.163141\pi\) |
−0.993303 | + | 0.115536i | \(0.963141\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(108\) | −2.57321 | − | 10.0687i | −0.247607 | − | 0.968860i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.50000 | − | 11.6082i | −0.332205 | − | 1.10180i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.15430 | − | 1.02489i | −0.296731 | − | 0.0964139i | 0.156868 | − | 0.987620i | \(-0.449860\pi\) |
−0.453599 | + | 0.891206i | \(0.649860\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.89919 | − | 6.46564i | 0.829853 | − | 0.602924i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.09017 | + | 9.51057i | −0.277505 | + | 0.854074i | ||||
\(125\) | −3.15430 | + | 1.02489i | −0.282129 | + | 0.0916693i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.21800 | + | 14.5612i | 0.793359 | + | 1.25323i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.6462 | + | 18.7824i | 1.16588 | + | 1.60469i | 0.686617 | + | 0.727019i | \(0.259095\pi\) |
0.479260 | + | 0.877673i | \(0.340905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.8487 | + | 3.78243i | 0.913621 | + | 0.318538i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −10.0000 | + | 6.63325i | −0.833333 | + | 0.552771i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.95848 | + | 6.91582i | −0.821362 | + | 0.570408i | ||||
\(148\) | −11.3262 | + | 8.22899i | −0.931011 | + | 0.676419i | ||||
\(149\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 16.5831i | − | 1.33199i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.10739 | − | 21.8743i | 0.567232 | − | 1.74576i | −0.0939948 | − | 0.995573i | \(-0.529964\pi\) |
0.661226 | − | 0.750186i | \(-0.270036\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.8994 | + | 18.2977i | −1.10230 | + | 1.45110i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.9443 | + | 9.40456i | 1.01387 | + | 0.736622i | 0.965018 | − | 0.262184i | \(-0.0844426\pi\) |
0.0488556 | + | 0.998806i | \(0.484443\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.01722 | + | 12.3637i | 0.309017 | + | 0.951057i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.50000 | − | 1.65831i | 0.413405 | − | 0.124646i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.7715 | + | 5.12447i | 1.17882 | + | 0.383021i | 0.831927 | − | 0.554885i | \(-0.187238\pi\) |
0.346890 | + | 0.937906i | \(0.387238\pi\) | |||||||
\(180\) | 12.3723 | − | 15.5861i | 0.922177 | − | 1.16172i | ||||
\(181\) | 20.2254 | − | 14.6946i | 1.50334 | − | 1.09224i | 0.534318 | − | 0.845283i | \(-0.320568\pi\) |
0.969026 | − | 0.246960i | \(-0.0794316\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.6462 | − | 18.7824i | 1.00329 | − | 1.38091i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 13.2665i | − | 0.967559i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.0801 | − | 7.17425i | 1.59766 | − | 0.519111i | 0.631132 | − | 0.775676i | \(-0.282591\pi\) |
0.966527 | + | 0.256565i | \(0.0825907\pi\) | |||||||
\(192\) | 11.0339 | + | 8.38168i | 0.796305 | + | 0.604896i | ||||
\(193\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.3262 | + | 8.22899i | 0.809017 | + | 0.587785i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0000 | 1.41776 | 0.708881 | − | 0.705328i | \(-0.249200\pi\) | ||||
0.708881 | + | 0.705328i | \(0.249200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −22.5115 | − | 0.479940i | −1.58784 | − | 0.0338524i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.424064 | − | 9.94083i | 0.0294745 | − | 0.690936i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(212\) | 25.2344 | + | 8.19915i | 1.73310 | + | 0.563120i | ||||
\(213\) | −16.3837 | − | 23.5918i | −1.12259 | − | 1.61648i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.309017 | + | 0.951057i | −0.0206933 | + | 0.0636875i | −0.960870 | − | 0.277000i | \(-0.910660\pi\) |
0.940177 | + | 0.340687i | \(0.110660\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.28687 | + | 16.8664i | −0.419124 | + | 1.12443i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.04508 | − | 2.93893i | −0.267307 | − | 0.194210i | 0.446055 | − | 0.895005i | \(-0.352828\pi\) |
−0.713362 | + | 0.700796i | \(0.752828\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.79837 | + | 20.9232i | 0.443477 | + | 1.36488i | ||||
\(236\) | −3.89893 | − | 5.36641i | −0.253798 | − | 0.349324i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(240\) | −21.6973 | − | 7.56486i | −1.40055 | − | 0.488310i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5000 | + | 1.65831i | 0.994325 | + | 0.106381i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −22.0801 | − | 7.17425i | −1.41064 | − | 0.458346i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.74732 | − | 13.4160i | 0.615245 | − | 0.846812i | −0.381751 | − | 0.924265i | \(-0.624679\pi\) |
0.996996 | + | 0.0774530i | \(0.0246788\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.94427 | − | 15.2169i | 0.309017 | − | 0.951057i | ||||
\(257\) | −25.2344 | + | 8.19915i | −1.57408 | + | 0.511449i | −0.960522 | − | 0.278203i | \(-0.910261\pi\) |
−0.613555 | + | 0.789652i | \(0.710261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −44.0000 | −2.70290 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.612223 | + | 28.7163i | −0.0374675 | + | 1.75741i | ||||
\(268\) | 8.03444 | + | 24.7275i | 0.490782 | + | 1.51047i | ||||
\(269\) | 7.79785 | + | 10.7328i | 0.475443 | + | 0.654392i | 0.977621 | − | 0.210373i | \(-0.0674677\pi\) |
−0.502178 | + | 0.864764i | \(0.667468\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.0000 | + | 3.31662i | −0.662122 | + | 0.199637i | ||||
\(277\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.7485 | − | 9.32597i | −0.703362 | − | 0.558331i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(284\) | −19.4946 | + | 26.8321i | −1.15679 | + | 1.59219i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.25329 | + | 16.1680i | −0.309017 | + | 0.951057i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.4471 | − | 17.8111i | −1.37449 | − | 1.04410i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.89919 | + | 6.46564i | 0.518131 | + | 0.376444i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 20.7799 | + | 0.443021i | 1.19973 | + | 0.0255779i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.00000 | − | 6.63325i | −0.113776 | − | 0.377352i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.5430 | − | 10.2489i | −1.78864 | − | 0.581164i | −0.789183 | − | 0.614159i | \(-0.789495\pi\) |
−0.999456 | + | 0.0329949i | \(0.989495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.3713 | − | 11.1679i | 0.868839 | − | 0.631248i | −0.0614365 | − | 0.998111i | \(-0.519568\pi\) |
0.930275 | + | 0.366863i | \(0.119568\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.6462 | + | 18.7824i | −0.766449 | + | 1.05493i | 0.230201 | + | 0.973143i | \(0.426062\pi\) |
−0.996650 | + | 0.0817838i | \(0.973938\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 26.5330i | 1.48324i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −4.08420 | − | 17.5305i | −0.226900 | − | 0.973918i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.0000 | 1.92377 | 0.961887 | − | 0.273447i | \(-0.0881639\pi\) | ||||
0.961887 | + | 0.273447i | \(0.0881639\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.63224 | − | 20.2306i | −0.308645 | − | 1.10863i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.3430 | − | 34.8817i | −1.38464 | − | 1.90579i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.42433 | − | 1.89122i | −0.294609 | − | 0.102717i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.6490 | − | 10.8677i | 0.842516 | − | 0.585099i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 36.4829i | 1.94179i | 0.239511 | + | 0.970894i | \(0.423013\pi\) | ||||
−0.239511 | + | 0.970894i | \(0.576987\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.9959 | − | 52.3081i | 0.902051 | − | 2.77623i | ||||
\(356\) | 31.5430 | − | 10.2489i | 1.67177 | − | 0.543192i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3713 | − | 11.1679i | −0.809017 | − | 0.587785i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.4336 | − | 35.1891i | −0.596831 | − | 1.83686i | −0.545395 | − | 0.838179i | \(-0.683620\pi\) |
−0.0514358 | − | 0.998676i | \(-0.516380\pi\) | |||||||
\(368\) | 7.79785 | + | 10.7328i | 0.406491 | + | 0.559487i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.70223 | + | 16.3550i | −0.295647 | + | 0.847965i | ||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.50000 | + | 1.65831i | −0.284019 | + | 0.0856349i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.2254 | − | 14.6946i | 1.03891 | − | 0.754813i | 0.0688378 | − | 0.997628i | \(-0.478071\pi\) |
0.970073 | + | 0.242815i | \(0.0780709\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.94946 | + | 2.68321i | −0.0996129 | + | 0.137105i | −0.855914 | − | 0.517119i | \(-0.827005\pi\) |
0.756301 | + | 0.654224i | \(0.227005\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.5066 | + | 32.3359i | −0.533391 | + | 1.64161i | ||||
\(389\) | −34.6973 | + | 11.2738i | −1.75922 | + | 0.571606i | −0.997119 | − | 0.0758507i | \(-0.975833\pi\) |
−0.762102 | + | 0.647456i | \(0.775833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.41641 | − | 22.8254i | −0.370820 | − | 1.14127i | ||||
\(401\) | −15.5957 | − | 21.4656i | −0.778812 | − | 1.07194i | −0.995412 | − | 0.0956827i | \(-0.969497\pi\) |
0.216600 | − | 0.976261i | \(-0.430503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.4248 | + | 25.5553i | 0.766467 | + | 1.26985i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.9372 | + | 33.0285i | 1.13141 | + | 1.62918i | ||||
\(412\) | −6.47214 | + | 4.70228i | −0.318859 | + | 0.231665i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 33.1662i | − | 1.62028i | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||
0.586238 | − | 0.810139i | \(-0.300608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.09017 | + | 9.51057i | −0.150606 | + | 0.463517i | −0.997689 | − | 0.0679432i | \(-0.978356\pi\) |
0.847084 | + | 0.531460i | \(0.178356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.6465 | + | 6.95039i | 0.906624 | + | 0.337940i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(432\) | −17.5615 | + | 11.1173i | −0.844926 | + | 0.534883i | ||||
\(433\) | 8.96149 | + | 27.5806i | 0.430662 | + | 1.32544i | 0.897467 | + | 0.441081i | \(0.145405\pi\) |
−0.466805 | + | 0.884360i | \(0.654595\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.5000 | + | 11.6082i | −0.833333 | + | 0.552771i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.6973 | + | 11.2738i | 1.64852 | + | 0.535636i | 0.978418 | − | 0.206636i | \(-0.0662515\pi\) |
0.670099 | + | 0.742271i | \(0.266252\pi\) | |||||||
\(444\) | −19.9170 | + | 13.8316i | −0.945217 | + | 0.656421i | ||||
\(445\) | −44.4959 | + | 32.3282i | −2.10931 | + | 1.53250i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.74732 | − | 13.4160i | 0.460004 | − | 0.633142i | −0.514505 | − | 0.857487i | \(-0.672024\pi\) |
0.974510 | + | 0.224346i | \(0.0720244\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.63325i | 0.312002i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −17.7984 | − | 12.9313i | −0.829853 | − | 0.602924i | ||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.0000 | −1.44069 | −0.720346 | − | 0.693615i | \(-0.756017\pi\) | ||||
−0.720346 | + | 0.693615i | \(0.756017\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.612223 | − | 28.7163i | 0.0283912 | − | 1.33169i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.3430 | + | 34.8817i | 1.17274 | + | 1.61413i | 0.642523 | + | 0.766267i | \(0.277888\pi\) |
0.530212 | + | 0.847865i | \(0.322112\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.1151 | − | 37.6164i | 0.604313 | − | 1.73327i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.7446 | + | 31.1722i | −1.13298 | + | 1.42728i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 56.3826i | − | 2.56020i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.2877 | + | 40.8954i | −0.602125 | + | 1.85315i | −0.0866600 | + | 0.996238i | \(0.527619\pi\) |
−0.515465 | + | 0.856911i | \(0.672381\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.0678 | + | 16.7634i | 0.997942 | + | 0.758066i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0000 | 0.898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.3607 | − | 38.0423i | −0.553340 | − | 1.70301i | −0.700287 | − | 0.713861i | \(-0.746945\pi\) |
0.146947 | − | 0.989144i | \(-0.453055\pi\) | |||||||
\(500\) | 3.89893 | + | 5.36641i | 0.174365 | + | 0.239993i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.50000 | + | 21.5581i | 0.288675 | + | 0.957427i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.15430 | − | 1.02489i | −0.139812 | − | 0.0454276i | 0.238275 | − | 0.971198i | \(-0.423418\pi\) |
−0.378087 | + | 0.925770i | \(0.623418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.79785 | − | 10.7328i | 0.343614 | − | 0.472945i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.0059 | − | 13.3236i | 1.79650 | − | 0.583718i | 0.796713 | − | 0.604358i | \(-0.206570\pi\) |
0.999787 | + | 0.0206400i | \(0.00657038\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.0000 | 0.521739 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.58534 | − | 2.66858i | 0.415968 | − | 0.115806i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.1216 | + | 9.45608i | 1.17038 | + | 0.408060i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 22.0000 | − | 26.5330i | 0.946729 | − | 1.14180i | ||||
\(541\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35.5660 | − | 24.6994i | 1.52628 | − | 1.05995i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(548\) | 27.2925 | − | 37.5649i | 1.16588 | − | 1.60469i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.3240 | − | 32.0210i | 1.03250 | − | 1.35921i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(564\) | 0.489779 | − | 22.9730i | 0.0206234 | − | 0.967339i | ||||
\(565\) | −3.39919 | − | 10.4616i | −0.143005 | − | 0.440124i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38.5000 | − | 11.6082i | 1.60836 | − | 0.484939i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.9258 | + | 6.14936i | 0.789260 | + | 0.256446i | ||||
\(576\) | 18.7975 | + | 14.9216i | 0.783230 | + | 0.621732i | ||||
\(577\) | −38.0238 | + | 27.6259i | −1.58295 | + | 1.15008i | −0.669740 | + | 0.742596i | \(0.733594\pi\) |
−0.913212 | + | 0.407486i | \(0.866406\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.30860 | + | 2.04979i | −0.260384 | + | 0.0846038i | −0.436300 | − | 0.899801i | \(-0.643711\pi\) |
0.175916 | + | 0.984405i | \(0.443711\pi\) | |||||||
\(588\) | 19.3094 | + | 14.6679i | 0.796305 | + | 0.604896i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22.6525 | + | 16.4580i | 0.931011 | + | 0.676419i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34.6331 | + | 0.738369i | 1.41744 | + | 0.0302194i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.4946 | + | 26.8321i | 0.796529 | + | 1.09633i | 0.993264 | + | 0.115872i | \(0.0369661\pi\) |
−0.196735 | + | 0.980457i | \(0.563034\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −38.9646 | − | 1.66218i | −1.58676 | − | 0.0676893i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.5330i | 1.06818i | 0.845428 | + | 0.534089i | \(0.179345\pi\) | ||||
−0.845428 | + | 0.534089i | \(0.820655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.309017 | + | 0.951057i | −0.0124204 | + | 0.0382262i | −0.957075 | − | 0.289841i | \(-0.906397\pi\) |
0.944654 | + | 0.328068i | \(0.106397\pi\) | |||||||
\(620\) | −31.5430 | + | 10.2489i | −1.26680 | + | 0.411607i | ||||
\(621\) | 1.10133 | − | 17.1985i | 0.0441950 | − | 0.690150i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.3713 | + | 11.1679i | 0.614853 | + | 0.446717i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −46.0000 | −1.83560 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.16312 | − | 6.65740i | −0.0861124 | − | 0.265027i | 0.898723 | − | 0.438516i | \(-0.144496\pi\) |
−0.984836 | + | 0.173489i | \(0.944496\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 43.3946 | + | 15.1297i | 1.72071 | + | 0.599933i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.5000 | − | 41.4578i | −1.08788 | − | 1.64005i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.0801 | − | 7.17425i | −0.872111 | − | 0.283366i | −0.161433 | − | 0.986884i | \(-0.551612\pi\) |
−0.710678 | + | 0.703518i | \(0.751612\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.1697 | + | 24.0992i | −1.30809 | + | 0.950379i | −1.00000 | 0.000979141i | \(-0.999688\pi\) | |
−0.308086 | + | 0.951359i | \(0.599688\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.3430 | + | 34.8817i | −0.996337 | + | 1.37134i | −0.0687910 | + | 0.997631i | \(0.521914\pi\) |
−0.927546 | + | 0.373709i | \(0.878086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.88854 | − | 30.4338i | 0.387265 | − | 1.19188i | ||||
\(653\) | 3.15430 | − | 1.02489i | 0.123437 | − | 0.0401072i | −0.246647 | − | 0.969105i | \(-0.579329\pi\) |
0.370084 | + | 0.928998i | \(0.379329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.0000 | −0.505641 | −0.252821 | − | 0.967513i | \(-0.581358\pi\) | ||||
−0.252821 | + | 0.967513i | \(0.581358\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.570223 | + | 1.63550i | −0.0220461 | + | 0.0632319i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.5094 | + | 28.9747i | −0.442996 | + | 1.11524i | ||||
\(676\) | 21.0344 | − | 15.2824i | 0.809017 | − | 0.587785i | ||||
\(677\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46.4327i | 1.77670i | 0.459167 | + | 0.888350i | \(0.348148\pi\) | ||||
−0.459167 | + | 0.888350i | \(0.651852\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.7943 | + | 73.2314i | −0.909134 | + | 2.79803i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.89620 | − | 5.23855i | −0.263106 | − | 0.199863i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.7533 | − | 9.99235i | −0.523200 | − | 0.380127i | 0.294608 | − | 0.955618i | \(-0.404811\pi\) |
−0.817808 | + | 0.575491i | \(0.804811\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.0000 | + | 36.4829i | 0.414284 | + | 1.37402i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.55348 | − | 9.43673i | −0.246295 | − | 0.354654i | ||||
\(709\) | 15.3713 | − | 11.1679i | 0.577282 | − | 0.419420i | −0.260461 | − | 0.965484i | \(-0.583875\pi\) |
0.837743 | + | 0.546064i | \(0.183875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.74732 | + | 13.4160i | −0.365040 | + | 0.502434i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 33.1662i | − | 1.23948i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.7715 | + | 5.12447i | −0.588177 | + | 0.191110i | −0.587961 | − | 0.808890i | \(-0.700069\pi\) |
−0.000216702 | 1.00000i | \(0.500069\pi\) | ||||||||
\(720\) | −37.2930 | − | 13.9008i | −1.38983 | − | 0.518052i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −40.4508 | − | 29.3893i | −1.50334 | − | 1.09224i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 53.0000 | 1.96566 | 0.982831 | − | 0.184510i | \(-0.0590699\pi\) | ||||
0.982831 | + | 0.184510i | \(0.0590699\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.7795 | + | 3.44386i | 0.991832 | + | 0.127551i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −37.9703 | − | 13.2385i | −1.40055 | − | 0.488310i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(740\) | −44.1602 | − | 14.3485i | −1.62336 | − | 0.527462i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.10739 | − | 21.8743i | 0.259352 | − | 0.798205i | −0.733588 | − | 0.679594i | \(-0.762156\pi\) |
0.992941 | − | 0.118611i | \(-0.0378440\pi\) | |||||||
\(752\) | −25.2344 | + | 8.19915i | −0.920203 | + | 0.298992i | ||||
\(753\) | 17.3743 | − | 22.8721i | 0.633155 | − | 0.833506i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.7426 | − | 22.3358i | −1.11736 | − | 0.811810i | −0.133554 | − | 0.991042i | \(-0.542639\pi\) |
−0.983807 | + | 0.179232i | \(0.942639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −27.2925 | − | 37.5649i | −0.987407 | − | 1.35905i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 9.12357 | − | 26.1679i | 0.329218 | − | 0.944254i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.0000 | + | 13.2665i | −1.58462 | + | 0.477781i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.6172 | − | 4.09957i | −0.453809 | − | 0.147451i | 0.0731890 | − | 0.997318i | \(-0.476682\pi\) |
−0.526998 | + | 0.849867i | \(0.676682\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.2705 | − | 17.6336i | 0.871822 | − | 0.633416i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.65248 | − | 26.6296i | 0.309017 | − | 0.951057i | ||||
\(785\) | 72.5488 | − | 23.5725i | 2.58938 | − | 0.841340i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −76.1929 | − | 1.62441i | −2.70228 | − | 0.0576120i | ||||
\(796\) | −12.3607 | − | 38.0423i | −0.438113 | − | 1.34837i | ||||
\(797\) | −33.1409 | − | 45.6145i | −1.17391 | − | 1.61575i | −0.629940 | − | 0.776644i | \(-0.716921\pi\) |
−0.543970 | − | 0.839105i | \(-0.683079\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.12032 | + | 49.7042i | −0.0749179 | + | 1.75621i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 13.0000 | + | 43.1161i | 0.458475 | + | 1.52059i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.1070 | + | 18.8735i | 0.461387 | + | 0.664377i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 53.0660i | 1.85882i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.6418 | + | 28.8015i | 1.38183 | + | 1.00396i | 0.996707 | + | 0.0810902i | \(0.0258402\pi\) |
0.385121 | + | 0.922866i | \(0.374160\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(828\) | −19.1707 | + | 5.33715i | −0.666227 | + | 0.185479i | ||||
\(829\) | 8.96149 | + | 27.5806i | 0.311246 | + | 0.957915i | 0.977272 | + | 0.211987i | \(0.0679936\pi\) |
−0.666027 | + | 0.745928i | \(0.732006\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.0000 | − | 16.5831i | −0.691301 | − | 0.573197i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.6973 | + | 11.2738i | 1.19788 | + | 0.389216i | 0.838982 | − | 0.544160i | \(-0.183151\pi\) |
0.358901 | + | 0.933376i | \(0.383151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.4615 | − | 17.0458i | 0.809017 | − | 0.587785i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.3430 | + | 34.8817i | −0.871826 | + | 1.19997i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 53.0660i | − | 1.82229i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.0801 | + | 7.17425i | −0.756896 | + | 0.245930i | ||||
\(852\) | −34.7486 | + | 45.7442i | −1.19047 | + | 1.56717i | ||||
\(853\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.0000 | −1.05771 | −0.528853 | − | 0.848713i | \(-0.677378\pi\) | ||||
−0.528853 | + | 0.848713i | \(0.677378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.2925 | − | 37.5649i | −0.929047 | − | 1.27872i | −0.960230 | − | 0.279210i | \(-0.909928\pi\) |
0.0311832 | − | 0.999514i | \(-0.490072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.69379 | + | 27.8034i | −0.329218 | + | 0.944254i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.9448 | − | 31.7083i | −1.35193 | − | 1.07316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.5831i | 0.558700i | 0.960189 | + | 0.279350i | \(0.0901189\pi\) | ||||
−0.960189 | + | 0.279350i | \(0.909881\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.3050 | − | 53.2592i | 0.582358 | − | 1.79231i | −0.0272727 | − | 0.999628i | \(-0.508682\pi\) |
0.609631 | − | 0.792686i | \(-0.291318\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.1716 | + | 11.5248i | 0.509989 | + | 0.387402i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.00000 | 0.0669650 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.9959 | + | 52.3081i | 0.568111 | + | 1.74847i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 35.9673 | + | 1.53432i | 1.19891 | + | 0.0511441i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 78.8574 | + | 25.6223i | 2.62131 | + | 0.851715i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.47214 | + | 4.70228i | −0.214904 | + | 0.156137i | −0.690030 | − | 0.723781i | \(-0.742403\pi\) |
0.475126 | + | 0.879918i | \(0.342403\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.89893 | − | 5.36641i | 0.129177 | − | 0.177797i | −0.739529 | − | 0.673124i | \(-0.764952\pi\) |
0.868706 | + | 0.495327i | \(0.164952\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.09017 | + | 9.51057i | −0.102102 | + | 0.314238i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.0000 | 1.38095 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.21843 | − | 11.5604i | −0.105707 | − | 0.379692i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.1914 | + | 42.9313i | 1.02336 | + | 1.40853i | 0.909823 | + | 0.414996i | \(0.136217\pi\) |
0.113534 | + | 0.993534i | \(0.463783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −54.2433 | − | 18.9122i | −1.77584 | − | 0.619156i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.0302 | − | 18.7715i | 0.882096 | − | 0.612586i | ||||
\(940\) | 35.5967 | − | 25.8626i | 1.16104 | − | 0.843543i | ||||
\(941\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −7.79785 | + | 10.7328i | −0.253798 | + | 0.349324i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 23.2164i | − | 0.754431i | −0.926126 | − | 0.377215i | \(-0.876882\pi\) | ||
0.926126 | − | 0.377215i | \(-0.123118\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.3240 | + | 32.0210i | −0.788761 | + | 1.03835i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 62.2943 | + | 45.2595i | 2.01580 | + | 1.46456i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.979557 | + | 45.9461i | −0.0316151 | + | 1.48290i | ||||
\(961\) | −1.85410 | − | 5.70634i | −0.0598097 | − | 0.184075i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.0059 | − | 13.3236i | −1.31594 | − | 0.427575i | −0.434842 | − | 0.900507i | \(-0.643196\pi\) |
−0.881099 | + | 0.472932i | \(0.843196\pi\) | |||||||
\(972\) | −6.42523 | − | 30.5076i | −0.206089 | − | 0.978533i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.1409 | − | 45.6145i | 1.06027 | − | 1.45934i | 0.180718 | − | 0.983535i | \(-0.442158\pi\) |
0.879552 | − | 0.475802i | \(-0.157842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 46.4327i | 1.48324i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.6973 | + | 11.2738i | −1.10667 | + | 0.359579i | −0.804666 | − | 0.593727i | \(-0.797656\pi\) |
−0.302005 | + | 0.953306i | \(0.597656\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 60.6080 | + | 1.29215i | 1.92334 | + | 0.0410050i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 38.9893 | + | 53.6641i | 1.23604 | + | 1.70127i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.00623 | − | 35.2404i | −0.284945 | − | 1.11496i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))