Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(361,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.h (of order \(3\), 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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.2 | ||
Root | \(1.68614 - 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.667 |
Dual form | 2646.2.h.k.361.2 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.37228 | 0.613703 | 0.306851 | − | 0.951757i | \(-0.400725\pi\) | ||||
0.306851 | + | 0.951757i | \(0.400725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.686141 | − | 1.18843i | −0.216977 | − | 0.375815i | ||||
\(11\) | −4.37228 | −1.31829 | −0.659146 | − | 0.752015i | \(-0.729082\pi\) | ||||
−0.659146 | + | 0.752015i | \(0.729082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | − | 1.73205i | −0.277350 | − | 0.480384i | 0.693375 | − | 0.720577i | \(-0.256123\pi\) |
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.18614 | − | 3.78651i | −0.530217 | − | 0.918363i | −0.999379 | − | 0.0352504i | \(-0.988777\pi\) |
0.469162 | − | 0.883112i | \(-0.344556\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50000 | + | 4.33013i | −0.573539 | + | 0.993399i | 0.422659 | + | 0.906289i | \(0.361097\pi\) |
−0.996199 | + | 0.0871106i | \(0.972237\pi\) | |||||||
\(20\) | −0.686141 | + | 1.18843i | −0.153426 | + | 0.265741i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.18614 | + | 3.78651i | 0.466087 | + | 0.807286i | ||||
\(23\) | 7.37228 | 1.53723 | 0.768613 | − | 0.639713i | \(-0.220947\pi\) | ||||
0.768613 | + | 0.639713i | \(0.220947\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.11684 | −0.623369 | ||||||||
\(26\) | −1.00000 | + | 1.73205i | −0.196116 | + | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.37228 | − | 2.37686i | 0.254826 | − | 0.441372i | −0.710022 | − | 0.704179i | \(-0.751315\pi\) |
0.964848 | + | 0.262807i | \(0.0846484\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | + | 1.73205i | −0.179605 | + | 0.311086i | −0.941745 | − | 0.336327i | \(-0.890815\pi\) |
0.762140 | + | 0.647412i | \(0.224149\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.18614 | + | 3.78651i | −0.374920 | + | 0.649381i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | + | 1.73205i | −0.164399 | + | 0.284747i | −0.936442 | − | 0.350823i | \(-0.885902\pi\) |
0.772043 | + | 0.635571i | \(0.219235\pi\) | |||||||
\(38\) | 5.00000 | 0.811107 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.37228 | 0.216977 | ||||||||
\(41\) | 5.18614 | + | 8.98266i | 0.809939 | + | 1.40286i | 0.912906 | + | 0.408171i | \(0.133833\pi\) |
−0.102966 | + | 0.994685i | \(0.532833\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.55842 | + | 7.89542i | −0.695153 | + | 1.20404i | 0.274976 | + | 0.961451i | \(0.411330\pi\) |
−0.970129 | + | 0.242589i | \(0.922003\pi\) | |||||||
\(44\) | 2.18614 | − | 3.78651i | 0.329573 | − | 0.570837i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.68614 | − | 6.38458i | −0.543492 | − | 0.941355i | ||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.55842 | + | 2.69927i | 0.220394 | + | 0.381734i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 1.37228 | + | 2.37686i | 0.188497 | + | 0.326487i | 0.944749 | − | 0.327793i | \(-0.106305\pi\) |
−0.756252 | + | 0.654280i | \(0.772972\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | −0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.74456 | −0.360379 | ||||||||
\(59\) | 3.55842 | − | 6.16337i | 0.463267 | − | 0.802402i | −0.535854 | − | 0.844310i | \(-0.680010\pi\) |
0.999121 | + | 0.0419083i | \(0.0133437\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.05842 | + | 12.2255i | 0.903738 | + | 1.56532i | 0.822602 | + | 0.568618i | \(0.192522\pi\) |
0.0811364 | + | 0.996703i | \(0.474145\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.37228 | − | 2.37686i | −0.170211 | − | 0.294813i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.55842 | + | 13.0916i | −0.923408 | + | 1.59939i | −0.129307 | + | 0.991605i | \(0.541275\pi\) |
−0.794101 | + | 0.607785i | \(0.792058\pi\) | |||||||
\(68\) | 4.37228 | 0.530217 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1168 | −1.20065 | −0.600324 | − | 0.799757i | \(-0.704962\pi\) | ||||
−0.600324 | + | 0.799757i | \(0.704962\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.55842 | + | 4.43132i | 0.299441 | + | 0.518646i | 0.976008 | − | 0.217734i | \(-0.0698666\pi\) |
−0.676567 | + | 0.736381i | \(0.736533\pi\) | |||||||
\(74\) | 2.00000 | 0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.50000 | − | 4.33013i | −0.286770 | − | 0.496700i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.05842 | − | 10.4935i | −0.681626 | − | 1.18061i | −0.974485 | − | 0.224455i | \(-0.927940\pi\) |
0.292859 | − | 0.956156i | \(-0.405393\pi\) | |||||||
\(80\) | −0.686141 | − | 1.18843i | −0.0767129 | − | 0.132871i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.18614 | − | 8.98266i | 0.572713 | − | 0.991969i | ||||
\(83\) | −2.74456 | + | 4.75372i | −0.301255 | + | 0.521789i | −0.976420 | − | 0.215877i | \(-0.930739\pi\) |
0.675166 | + | 0.737666i | \(0.264072\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | − | 5.19615i | −0.325396 | − | 0.563602i | ||||
\(86\) | 9.11684 | 0.983095 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.37228 | −0.466087 | ||||||||
\(89\) | 1.62772 | − | 2.81929i | 0.172538 | − | 0.298844i | −0.766769 | − | 0.641924i | \(-0.778137\pi\) |
0.939306 | + | 0.343079i | \(0.111470\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.68614 | + | 6.38458i | −0.384307 | + | 0.665639i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.43070 | + | 5.94215i | −0.351983 | + | 0.609652i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.55842 | + | 7.89542i | −0.462838 | + | 0.801658i | −0.999101 | − | 0.0423924i | \(-0.986502\pi\) |
0.536263 | + | 0.844051i | \(0.319835\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.55842 | − | 2.69927i | 0.155842 | − | 0.269927i | ||||
\(101\) | −7.37228 | −0.733569 | −0.366785 | − | 0.930306i | \(-0.619541\pi\) | ||||
−0.366785 | + | 0.930306i | \(0.619541\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0000 | −0.985329 | −0.492665 | − | 0.870219i | \(-0.663977\pi\) | ||||
−0.492665 | + | 0.870219i | \(0.663977\pi\) | |||||||
\(104\) | −1.00000 | − | 1.73205i | −0.0980581 | − | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.37228 | − | 2.37686i | 0.133288 | − | 0.230861i | ||||
\(107\) | −0.813859 | + | 1.40965i | −0.0786788 | + | 0.136276i | −0.902680 | − | 0.430312i | \(-0.858403\pi\) |
0.824001 | + | 0.566588i | \(0.191737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | − | 12.1244i | −0.670478 | − | 1.16130i | −0.977769 | − | 0.209687i | \(-0.932756\pi\) |
0.307290 | − | 0.951616i | \(-0.400578\pi\) | |||||||
\(110\) | 3.00000 | + | 5.19615i | 0.286039 | + | 0.495434i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.686141 | + | 1.18843i | 0.0645467 | + | 0.111798i | 0.896493 | − | 0.443058i | \(-0.146107\pi\) |
−0.831946 | + | 0.554856i | \(0.812773\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.1168 | 0.943401 | ||||||||
\(116\) | 1.37228 | + | 2.37686i | 0.127413 | + | 0.220686i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.11684 | −0.655159 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.11684 | 0.737895 | ||||||||
\(122\) | 7.05842 | − | 12.2255i | 0.639040 | − | 1.10685i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.00000 | − | 1.73205i | −0.0898027 | − | 0.155543i | ||||
\(125\) | −11.1386 | −0.996266 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1168 | −1.25267 | −0.626334 | − | 0.779555i | \(-0.715445\pi\) | ||||
−0.626334 | + | 0.779555i | \(0.715445\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.37228 | + | 2.37686i | −0.120357 | + | 0.208464i | ||||
\(131\) | 7.37228 | 0.644119 | 0.322060 | − | 0.946719i | \(-0.395625\pi\) | ||||
0.322060 | + | 0.946719i | \(0.395625\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.1168 | 1.30590 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.18614 | − | 3.78651i | −0.187460 | − | 0.324690i | ||||
\(137\) | −16.3723 | −1.39878 | −0.699389 | − | 0.714741i | \(-0.746545\pi\) | ||||
−0.699389 | + | 0.714741i | \(0.746545\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.6168 | + | 18.3889i | 0.900509 | + | 1.55973i | 0.826835 | + | 0.562445i | \(0.190139\pi\) |
0.0736742 | + | 0.997282i | \(0.476528\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.05842 | + | 8.76144i | 0.424493 | + | 0.735244i | ||||
\(143\) | 4.37228 | + | 7.57301i | 0.365629 | + | 0.633287i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.88316 | − | 3.26172i | 0.156388 | − | 0.270871i | ||||
\(146\) | 2.55842 | − | 4.43132i | 0.211737 | − | 0.366738i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | − | 1.73205i | −0.0821995 | − | 0.142374i | ||||
\(149\) | −14.7446 | −1.20792 | −0.603961 | − | 0.797014i | \(-0.706412\pi\) | ||||
−0.603961 | + | 0.797014i | \(0.706412\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.11684 | −0.660539 | −0.330270 | − | 0.943887i | \(-0.607140\pi\) | ||||
−0.330270 | + | 0.943887i | \(0.607140\pi\) | |||||||
\(152\) | −2.50000 | + | 4.33013i | −0.202777 | + | 0.351220i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.37228 | + | 2.37686i | −0.110224 | + | 0.190914i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.05842 | − | 7.02939i | 0.323897 | − | 0.561007i | −0.657391 | − | 0.753549i | \(-0.728340\pi\) |
0.981289 | + | 0.192543i | \(0.0616734\pi\) | |||||||
\(158\) | −6.05842 | + | 10.4935i | −0.481982 | + | 0.834818i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.686141 | + | 1.18843i | −0.0542442 | + | 0.0939537i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.11684 | + | 14.0588i | −0.635760 | + | 1.10117i | 0.350593 | + | 0.936528i | \(0.385980\pi\) |
−0.986354 | + | 0.164641i | \(0.947353\pi\) | |||||||
\(164\) | −10.3723 | −0.809939 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.48913 | 0.426039 | ||||||||
\(167\) | 8.74456 | + | 15.1460i | 0.676675 | + | 1.17203i | 0.975976 | + | 0.217876i | \(0.0699129\pi\) |
−0.299302 | + | 0.954158i | \(0.596754\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | −3.00000 | + | 5.19615i | −0.230089 | + | 0.398527i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.55842 | − | 7.89542i | −0.347576 | − | 0.602020i | ||||
\(173\) | −3.00000 | − | 5.19615i | −0.228086 | − | 0.395056i | 0.729155 | − | 0.684349i | \(-0.239913\pi\) |
−0.957241 | + | 0.289292i | \(0.906580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.18614 | + | 3.78651i | 0.164787 | + | 0.285419i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.25544 | −0.244005 | ||||||||
\(179\) | 7.37228 | + | 12.7692i | 0.551030 | + | 0.954412i | 0.998201 | + | 0.0599635i | \(0.0190984\pi\) |
−0.447170 | + | 0.894449i | \(0.647568\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.1168 | 1.34661 | 0.673307 | − | 0.739363i | \(-0.264873\pi\) | ||||
0.673307 | + | 0.739363i | \(0.264873\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.37228 | 0.543492 | ||||||||
\(185\) | −1.37228 | + | 2.37686i | −0.100892 | + | 0.174750i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.55842 | + | 16.5557i | 0.698981 | + | 1.21067i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.86141 | 0.497779 | ||||||||
\(191\) | −0.941578 | − | 1.63086i | −0.0681302 | − | 0.118005i | 0.829948 | − | 0.557841i | \(-0.188370\pi\) |
−0.898078 | + | 0.439836i | \(0.855037\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.50000 | − | 6.06218i | 0.251936 | − | 0.436365i | −0.712123 | − | 0.702055i | \(-0.752266\pi\) |
0.964059 | + | 0.265689i | \(0.0855996\pi\) | |||||||
\(194\) | 9.11684 | 0.654551 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.00000 | + | 8.66025i | 0.354441 | + | 0.613909i | 0.987022 | − | 0.160585i | \(-0.0513380\pi\) |
−0.632581 | + | 0.774494i | \(0.718005\pi\) | |||||||
\(200\) | −3.11684 | −0.220394 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.68614 | + | 6.38458i | 0.259356 | + | 0.449218i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.11684 | + | 12.3267i | 0.497062 | + | 0.860937i | ||||
\(206\) | 5.00000 | + | 8.66025i | 0.348367 | + | 0.603388i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | + | 1.73205i | −0.0693375 | + | 0.120096i | ||||
\(209\) | 10.9307 | − | 18.9325i | 0.756093 | − | 1.30959i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | + | 13.8564i | 0.550743 | + | 0.953914i | 0.998221 | + | 0.0596196i | \(0.0189888\pi\) |
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | −2.74456 | −0.188497 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.62772 | 0.111269 | ||||||||
\(215\) | −6.25544 | + | 10.8347i | −0.426617 | + | 0.738923i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.00000 | + | 12.1244i | −0.474100 | + | 0.821165i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.00000 | − | 5.19615i | 0.202260 | − | 0.350325i | ||||
\(221\) | −4.37228 | + | 7.57301i | −0.294111 | + | 0.509416i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00000 | − | 3.46410i | 0.133930 | − | 0.231973i | −0.791258 | − | 0.611482i | \(-0.790574\pi\) |
0.925188 | + | 0.379509i | \(0.123907\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.686141 | − | 1.18843i | 0.0456414 | − | 0.0790532i | ||||
\(227\) | 23.7446 | 1.57598 | 0.787991 | − | 0.615687i | \(-0.211121\pi\) | ||||
0.787991 | + | 0.615687i | \(0.211121\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.1168 | −1.32936 | −0.664679 | − | 0.747129i | \(-0.731432\pi\) | ||||
−0.664679 | + | 0.747129i | \(0.731432\pi\) | |||||||
\(230\) | −5.05842 | − | 8.76144i | −0.333542 | − | 0.577713i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.37228 | − | 2.37686i | 0.0900947 | − | 0.156049i | ||||
\(233\) | −5.87228 | + | 10.1711i | −0.384706 | + | 0.666330i | −0.991728 | − | 0.128354i | \(-0.959030\pi\) |
0.607022 | + | 0.794685i | \(0.292364\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.55842 | + | 6.16337i | 0.231634 | + | 0.401201i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.43070 | − | 16.3345i | −0.610021 | − | 1.05659i | −0.991236 | − | 0.132102i | \(-0.957827\pi\) |
0.381215 | − | 0.924487i | \(-0.375506\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.883156 | 0.0568891 | 0.0284445 | − | 0.999595i | \(-0.490945\pi\) | ||||
0.0284445 | + | 0.999595i | \(0.490945\pi\) | |||||||
\(242\) | −4.05842 | − | 7.02939i | −0.260885 | − | 0.451867i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.1168 | −0.903738 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0000 | 0.636285 | ||||||||
\(248\) | −1.00000 | + | 1.73205i | −0.0635001 | + | 0.109985i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.56930 | + | 9.64630i | 0.352233 | + | 0.610086i | ||||
\(251\) | 9.00000 | 0.568075 | 0.284037 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284037 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.2337 | −2.02651 | ||||||||
\(254\) | 7.05842 | + | 12.2255i | 0.442885 | + | 0.767099i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −21.8614 | −1.36368 | −0.681839 | − | 0.731503i | \(-0.738819\pi\) | ||||
−0.681839 | + | 0.731503i | \(0.738819\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.74456 | 0.170211 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.68614 | − | 6.38458i | −0.227731 | − | 0.394441i | ||||
\(263\) | −13.3723 | −0.824570 | −0.412285 | − | 0.911055i | \(-0.635269\pi\) | ||||
−0.412285 | + | 0.911055i | \(0.635269\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.88316 | + | 3.26172i | 0.115681 | + | 0.200366i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.55842 | − | 13.0916i | −0.461704 | − | 0.799695i | ||||
\(269\) | −3.68614 | − | 6.38458i | −0.224748 | − | 0.389275i | 0.731496 | − | 0.681846i | \(-0.238823\pi\) |
−0.956244 | + | 0.292571i | \(0.905489\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.11684 | − | 15.7908i | 0.553809 | − | 0.959225i | −0.444186 | − | 0.895934i | \(-0.646507\pi\) |
0.997995 | − | 0.0632906i | \(-0.0201595\pi\) | |||||||
\(272\) | −2.18614 | + | 3.78651i | −0.132554 | + | 0.229591i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.18614 | + | 14.1788i | 0.494543 | + | 0.856573i | ||||
\(275\) | 13.6277 | 0.821782 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.2337 | 1.33589 | 0.667946 | − | 0.744209i | \(-0.267174\pi\) | ||||
0.667946 | + | 0.744209i | \(0.267174\pi\) | |||||||
\(278\) | 10.6168 | − | 18.3889i | 0.636756 | − | 1.10289i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.31386 | − | 9.20387i | 0.316998 | − | 0.549057i | −0.662862 | − | 0.748742i | \(-0.730658\pi\) |
0.979860 | + | 0.199685i | \(0.0639917\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.94158 | + | 8.55906i | −0.293746 | + | 0.508784i | −0.974692 | − | 0.223550i | \(-0.928235\pi\) |
0.680946 | + | 0.732333i | \(0.261569\pi\) | |||||||
\(284\) | 5.05842 | − | 8.76144i | 0.300162 | − | 0.519896i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.37228 | − | 7.57301i | 0.258538 | − | 0.447802i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.05842 | + | 1.83324i | −0.0622601 | + | 0.107838i | ||||
\(290\) | −3.76631 | −0.221165 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.11684 | −0.299441 | ||||||||
\(293\) | −2.31386 | − | 4.00772i | −0.135177 | − | 0.234134i | 0.790488 | − | 0.612478i | \(-0.209827\pi\) |
−0.925665 | + | 0.378344i | \(0.876494\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.88316 | − | 8.45787i | 0.284308 | − | 0.492436i | ||||
\(296\) | −1.00000 | + | 1.73205i | −0.0581238 | + | 0.100673i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.37228 | + | 12.7692i | 0.427065 | + | 0.739698i | ||||
\(299\) | −7.37228 | − | 12.7692i | −0.426350 | − | 0.738460i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.05842 | + | 7.02939i | 0.233536 | + | 0.404496i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.00000 | 0.286770 | ||||||||
\(305\) | 9.68614 | + | 16.7769i | 0.554627 | + | 0.960642i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.0000 | −0.741949 | −0.370975 | − | 0.928643i | \(-0.620976\pi\) | ||||
−0.370975 | + | 0.928643i | \(0.620976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.74456 | 0.155881 | ||||||||
\(311\) | −13.1168 | + | 22.7190i | −0.743788 | + | 1.28828i | 0.206971 | + | 0.978347i | \(0.433639\pi\) |
−0.950759 | + | 0.309931i | \(0.899694\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.44158 | + | 2.49689i | 0.0814828 | + | 0.141132i | 0.903887 | − | 0.427771i | \(-0.140701\pi\) |
−0.822404 | + | 0.568904i | \(0.807368\pi\) | |||||||
\(314\) | −8.11684 | −0.458060 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.1168 | 0.681626 | ||||||||
\(317\) | −3.00000 | − | 5.19615i | −0.168497 | − | 0.291845i | 0.769395 | − | 0.638774i | \(-0.220558\pi\) |
−0.937892 | + | 0.346929i | \(0.887225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | + | 10.3923i | −0.335936 | + | 0.581857i | ||||
\(320\) | 1.37228 | 0.0767129 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.8614 | 1.21640 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.11684 | + | 5.39853i | 0.172891 | + | 0.299457i | ||||
\(326\) | 16.2337 | 0.899101 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.18614 | + | 8.98266i | 0.286357 | + | 0.495984i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.11684 | + | 10.5947i | 0.336212 | + | 0.582337i | 0.983717 | − | 0.179725i | \(-0.0575207\pi\) |
−0.647505 | + | 0.762061i | \(0.724187\pi\) | |||||||
\(332\) | −2.74456 | − | 4.75372i | −0.150627 | − | 0.260894i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.74456 | − | 15.1460i | 0.478481 | − | 0.828754i | ||||
\(335\) | −10.3723 | + | 17.9653i | −0.566698 | + | 0.981550i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.55842 | − | 7.89542i | −0.248313 | − | 0.430091i | 0.714745 | − | 0.699385i | \(-0.246543\pi\) |
−0.963058 | + | 0.269294i | \(0.913210\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.00000 | 0.325396 | ||||||||
\(341\) | 4.37228 | − | 7.57301i | 0.236772 | − | 0.410102i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.55842 | + | 7.89542i | −0.245774 | + | 0.425692i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.00000 | + | 5.19615i | −0.161281 | + | 0.279347i | ||||
\(347\) | 3.55842 | − | 6.16337i | 0.191026 | − | 0.330867i | −0.754564 | − | 0.656226i | \(-0.772152\pi\) |
0.945591 | + | 0.325359i | \(0.105485\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.0000 | − | 19.0526i | 0.588817 | − | 1.01986i | −0.405571 | − | 0.914063i | \(-0.632927\pi\) |
0.994388 | − | 0.105797i | \(-0.0337393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.18614 | − | 3.78651i | 0.116522 | − | 0.201821i | ||||
\(353\) | 7.62772 | 0.405983 | 0.202991 | − | 0.979181i | \(-0.434934\pi\) | ||||
0.202991 | + | 0.979181i | \(0.434934\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.8832 | −0.736841 | ||||||||
\(356\) | 1.62772 | + | 2.81929i | 0.0862689 | + | 0.149422i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.37228 | − | 12.7692i | 0.389637 | − | 0.674871i | ||||
\(359\) | −3.43070 | + | 5.94215i | −0.181066 | + | 0.313615i | −0.942244 | − | 0.334928i | \(-0.891288\pi\) |
0.761178 | + | 0.648543i | \(0.224621\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | −9.05842 | − | 15.6896i | −0.476100 | − | 0.824630i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.51087 | + | 6.08101i | 0.183768 | + | 0.318295i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.2337 | 1.16059 | 0.580295 | − | 0.814407i | \(-0.302937\pi\) | ||||
0.580295 | + | 0.814407i | \(0.302937\pi\) | |||||||
\(368\) | −3.68614 | − | 6.38458i | −0.192153 | − | 0.332819i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.74456 | 0.142683 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 9.55842 | − | 16.5557i | 0.494254 | − | 0.856073i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.48913 | −0.282704 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.11684 | 0.468301 | 0.234150 | − | 0.972200i | \(-0.424769\pi\) | ||||
0.234150 | + | 0.972200i | \(0.424769\pi\) | |||||||
\(380\) | −3.43070 | − | 5.94215i | −0.175991 | − | 0.304826i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.941578 | + | 1.63086i | −0.0481753 | + | 0.0834421i | ||||
\(383\) | 21.2554 | 1.08610 | 0.543051 | − | 0.839700i | \(-0.317269\pi\) | ||||
0.543051 | + | 0.839700i | \(0.317269\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.00000 | −0.356291 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.55842 | − | 7.89542i | −0.231419 | − | 0.400829i | ||||
\(389\) | 34.9783 | 1.77347 | 0.886734 | − | 0.462280i | \(-0.152969\pi\) | ||||
0.886734 | + | 0.462280i | \(0.152969\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.1168 | − | 27.9152i | −0.815064 | − | 1.41173i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.00000 | − | 5.19615i | −0.151138 | − | 0.261778i | ||||
\(395\) | −8.31386 | − | 14.4000i | −0.418316 | − | 0.724544i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.0000 | − | 19.0526i | 0.552074 | − | 0.956221i | −0.446051 | − | 0.895008i | \(-0.647170\pi\) |
0.998125 | − | 0.0612128i | \(-0.0194968\pi\) | |||||||
\(398\) | 5.00000 | − | 8.66025i | 0.250627 | − | 0.434099i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.55842 | + | 2.69927i | 0.0779211 | + | 0.134963i | ||||
\(401\) | 0.255437 | 0.0127559 | 0.00637797 | − | 0.999980i | \(-0.497970\pi\) | ||||
0.00637797 | + | 0.999980i | \(0.497970\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | 0.199254 | ||||||||
\(404\) | 3.68614 | − | 6.38458i | 0.183392 | − | 0.317645i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.37228 | − | 7.57301i | 0.216726 | − | 0.375380i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.6753 | + | 25.4183i | −0.725645 | + | 1.25685i | 0.233063 | + | 0.972462i | \(0.425125\pi\) |
−0.958708 | + | 0.284393i | \(0.908208\pi\) | |||||||
\(410\) | 7.11684 | − | 12.3267i | 0.351476 | − | 0.608774i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.00000 | − | 8.66025i | 0.246332 | − | 0.426660i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.76631 | + | 6.52344i | −0.184881 | + | 0.320223i | ||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −21.8614 | −1.06928 | ||||||||
\(419\) | 13.8030 | + | 23.9075i | 0.674320 | + | 1.16796i | 0.976667 | + | 0.214759i | \(0.0688964\pi\) |
−0.302347 | + | 0.953198i | \(0.597770\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.116844 | − | 0.202380i | 0.00569463 | − | 0.00986338i | −0.863164 | − | 0.504924i | \(-0.831521\pi\) |
0.868859 | + | 0.495060i | \(0.164854\pi\) | |||||||
\(422\) | 8.00000 | − | 13.8564i | 0.389434 | − | 0.674519i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.37228 | + | 2.37686i | 0.0666439 | + | 0.115431i | ||||
\(425\) | 6.81386 | + | 11.8020i | 0.330521 | + | 0.572479i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.813859 | − | 1.40965i | −0.0393394 | − | 0.0681378i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.5109 | 0.603328 | ||||||||
\(431\) | −14.7446 | − | 25.5383i | −0.710221 | − | 1.23014i | −0.964774 | − | 0.263079i | \(-0.915262\pi\) |
0.254554 | − | 0.967059i | \(-0.418071\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.88316 | −0.138556 | −0.0692778 | − | 0.997597i | \(-0.522069\pi\) | ||||
−0.0692778 | + | 0.997597i | \(0.522069\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.0000 | 0.670478 | ||||||||
\(437\) | −18.4307 | + | 31.9229i | −0.881660 | + | 1.52708i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | − | 6.92820i | −0.190910 | − | 0.330665i | 0.754642 | − | 0.656136i | \(-0.227810\pi\) |
−0.945552 | + | 0.325471i | \(0.894477\pi\) | |||||||
\(440\) | −6.00000 | −0.286039 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.74456 | 0.415936 | ||||||||
\(443\) | −11.4416 | − | 19.8174i | −0.543606 | − | 0.941553i | −0.998693 | − | 0.0511061i | \(-0.983725\pi\) |
0.455087 | − | 0.890447i | \(-0.349608\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.23369 | − | 3.86886i | 0.105887 | − | 0.183402i | ||||
\(446\) | −4.00000 | −0.189405 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.0000 | −1.55737 | −0.778683 | − | 0.627417i | \(-0.784112\pi\) | ||||
−0.778683 | + | 0.627417i | \(0.784112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.6753 | − | 39.2747i | −1.06774 | − | 1.84937i | ||||
\(452\) | −1.37228 | −0.0645467 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.8723 | − | 20.5634i | −0.557194 | − | 0.965088i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.7337 | − | 28.9836i | −0.782769 | − | 1.35580i | −0.930323 | − | 0.366742i | \(-0.880473\pi\) |
0.147554 | − | 0.989054i | \(-0.452860\pi\) | |||||||
\(458\) | 10.0584 | + | 17.4217i | 0.469999 | + | 0.814062i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.05842 | + | 8.76144i | −0.235850 | + | 0.408504i | ||||
\(461\) | 15.4307 | − | 26.7268i | 0.718680 | − | 1.24479i | −0.242844 | − | 0.970065i | \(-0.578080\pi\) |
0.961523 | − | 0.274724i | \(-0.0885865\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.94158 | + | 5.09496i | 0.136707 | + | 0.236783i | 0.926248 | − | 0.376914i | \(-0.123015\pi\) |
−0.789541 | + | 0.613697i | \(0.789682\pi\) | |||||||
\(464\) | −2.74456 | −0.127413 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.7446 | 0.544056 | ||||||||
\(467\) | −15.0475 | + | 26.0631i | −0.696317 | + | 1.20606i | 0.273417 | + | 0.961896i | \(0.411846\pi\) |
−0.969735 | + | 0.244162i | \(0.921487\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.55842 | − | 6.16337i | 0.163790 | − | 0.283692i | ||||
\(473\) | 19.9307 | − | 34.5210i | 0.916415 | − | 1.58728i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.79211 | − | 13.4963i | 0.357527 | − | 0.619254i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.43070 | + | 16.3345i | −0.431350 | + | 0.747121i | ||||
\(479\) | −21.2554 | −0.971186 | −0.485593 | − | 0.874185i | \(-0.661396\pi\) | ||||
−0.485593 | + | 0.874185i | \(0.661396\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | −0.441578 | − | 0.764836i | −0.0201133 | − | 0.0348373i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.05842 | + | 7.02939i | −0.184474 | + | 0.319518i | ||||
\(485\) | −6.25544 | + | 10.8347i | −0.284045 | + | 0.491980i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.17527 | + | 14.1600i | 0.370457 | + | 0.641650i | 0.989636 | − | 0.143600i | \(-0.0458679\pi\) |
−0.619179 | + | 0.785250i | \(0.712535\pi\) | |||||||
\(488\) | 7.05842 | + | 12.2255i | 0.319520 | + | 0.553424i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.81386 | − | 16.9981i | −0.442893 | − | 0.767114i | 0.555010 | − | 0.831844i | \(-0.312715\pi\) |
−0.997903 | + | 0.0647303i | \(0.979381\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0000 | −0.540453 | ||||||||
\(494\) | −5.00000 | − | 8.66025i | −0.224961 | − | 0.389643i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.883156 | 0.0395355 | 0.0197677 | − | 0.999805i | \(-0.493707\pi\) | ||||
0.0197677 | + | 0.999805i | \(0.493707\pi\) | |||||||
\(500\) | 5.56930 | − | 9.64630i | 0.249067 | − | 0.431396i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.50000 | − | 7.79423i | −0.200845 | − | 0.347873i | ||||
\(503\) | −2.23369 | −0.0995952 | −0.0497976 | − | 0.998759i | \(-0.515858\pi\) | ||||
−0.0497976 | + | 0.998759i | \(0.515858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.1168 | −0.450194 | ||||||||
\(506\) | 16.1168 | + | 27.9152i | 0.716481 | + | 1.24098i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.05842 | − | 12.2255i | 0.313167 | − | 0.542421i | ||||
\(509\) | −16.9783 | −0.752548 | −0.376274 | − | 0.926508i | \(-0.622795\pi\) | ||||
−0.376274 | + | 0.926508i | \(0.622795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.9307 | + | 18.9325i | 0.482133 | + | 0.835078i | ||||
\(515\) | −13.7228 | −0.604699 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.37228 | − | 2.37686i | −0.0601785 | − | 0.104232i | ||||
\(521\) | 1.93070 | + | 3.34408i | 0.0845856 | + | 0.146507i | 0.905215 | − | 0.424955i | \(-0.139710\pi\) |
−0.820629 | + | 0.571461i | \(0.806377\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.94158 | − | 15.4873i | 0.390988 | − | 0.677211i | −0.601592 | − | 0.798803i | \(-0.705467\pi\) |
0.992580 | + | 0.121592i | \(0.0388001\pi\) | |||||||
\(524\) | −3.68614 | + | 6.38458i | −0.161030 | + | 0.278912i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.68614 | + | 11.5807i | 0.291530 | + | 0.504944i | ||||
\(527\) | 8.74456 | 0.380919 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.3505 | 1.36307 | ||||||||
\(530\) | 1.88316 | − | 3.26172i | 0.0817991 | − | 0.141680i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3723 | − | 17.9653i | 0.449273 | − | 0.778164i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.11684 | + | 1.93443i | −0.0482854 | + | 0.0836327i | ||||
\(536\) | −7.55842 | + | 13.0916i | −0.326474 | + | 0.565470i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.68614 | + | 6.38458i | −0.158921 | + | 0.275259i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.1168 | + | 24.4511i | −0.606931 | + | 1.05123i | 0.384813 | + | 0.922995i | \(0.374266\pi\) |
−0.991743 | + | 0.128240i | \(0.959067\pi\) | |||||||
\(542\) | −18.2337 | −0.783204 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.37228 | 0.187460 | ||||||||
\(545\) | −9.60597 | − | 16.6380i | −0.411475 | − | 0.712695i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.441578 | + | 0.764836i | −0.0188805 | + | 0.0327020i | −0.875311 | − | 0.483560i | \(-0.839344\pi\) |
0.856431 | + | 0.516262i | \(0.172677\pi\) | |||||||
\(548\) | 8.18614 | − | 14.1788i | 0.349695 | − | 0.605689i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.81386 | − | 11.8020i | −0.290544 | − | 0.503237i | ||||
\(551\) | 6.86141 | + | 11.8843i | 0.292306 | + | 0.506288i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −11.1168 | − | 19.2549i | −0.472309 | − | 0.818064i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.2337 | −0.900509 | ||||||||
\(557\) | 3.25544 | + | 5.63858i | 0.137937 | + | 0.238914i | 0.926716 | − | 0.375763i | \(-0.122619\pi\) |
−0.788778 | + | 0.614678i | \(0.789286\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.2337 | 0.771203 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.6277 | −0.448303 | ||||||||
\(563\) | 1.50000 | − | 2.59808i | 0.0632175 | − | 0.109496i | −0.832684 | − | 0.553748i | \(-0.813197\pi\) |
0.895902 | + | 0.444252i | \(0.146530\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.941578 | + | 1.63086i | 0.0396125 | + | 0.0686108i | ||||
\(566\) | 9.88316 | 0.415420 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.1168 | −0.424493 | ||||||||
\(569\) | −0.558422 | − | 0.967215i | −0.0234103 | − | 0.0405478i | 0.854083 | − | 0.520137i | \(-0.174119\pi\) |
−0.877493 | + | 0.479589i | \(0.840786\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.6753 | + | 25.4183i | −0.614141 | + | 1.06372i | 0.376394 | + | 0.926460i | \(0.377164\pi\) |
−0.990535 | + | 0.137263i | \(0.956169\pi\) | |||||||
\(572\) | −8.74456 | −0.365629 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.9783 | −0.958259 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.5584 | − | 23.4839i | −0.564444 | − | 0.977647i | −0.997101 | − | 0.0760878i | \(-0.975757\pi\) |
0.432657 | − | 0.901559i | \(-0.357576\pi\) | |||||||
\(578\) | 2.11684 | 0.0880491 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.88316 | + | 3.26172i | 0.0781938 | + | 0.135436i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | − | 10.3923i | −0.248495 | − | 0.430405i | ||||
\(584\) | 2.55842 | + | 4.43132i | 0.105868 | + | 0.183369i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.31386 | + | 4.00772i | −0.0955846 | + | 0.165557i | ||||
\(587\) | −4.24456 | + | 7.35180i | −0.175192 | + | 0.303441i | −0.940228 | − | 0.340547i | \(-0.889388\pi\) |
0.765036 | + | 0.643988i | \(0.222721\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.00000 | − | 8.66025i | −0.206021 | − | 0.356840i | ||||
\(590\) | −9.76631 | −0.402073 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | 1.62772 | − | 2.81929i | 0.0668424 | − | 0.115774i | −0.830667 | − | 0.556769i | \(-0.812041\pi\) |
0.897510 | + | 0.440995i | \(0.145374\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.37228 | − | 12.7692i | 0.301980 | − | 0.523045i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.37228 | + | 12.7692i | −0.301475 | + | 0.522170i | ||||
\(599\) | 12.0000 | − | 20.7846i | 0.490307 | − | 0.849236i | −0.509631 | − | 0.860393i | \(-0.670218\pi\) |
0.999938 | + | 0.0111569i | \(0.00355143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.44158 | + | 5.96099i | −0.140385 | + | 0.243154i | −0.927642 | − | 0.373472i | \(-0.878167\pi\) |
0.787257 | + | 0.616625i | \(0.211501\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.05842 | − | 7.02939i | 0.165135 | − | 0.286022i | ||||
\(605\) | 11.1386 | 0.452848 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.2337 | −0.496550 | −0.248275 | − | 0.968690i | \(-0.579864\pi\) | ||||
−0.248275 | + | 0.968690i | \(0.579864\pi\) | |||||||
\(608\) | −2.50000 | − | 4.33013i | −0.101388 | − | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.68614 | − | 16.7769i | 0.392180 | − | 0.679276i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.883156 | + | 1.52967i | 0.0356703 | + | 0.0617828i | 0.883309 | − | 0.468790i | \(-0.155310\pi\) |
−0.847639 | + | 0.530573i | \(0.821977\pi\) | |||||||
\(614\) | 6.50000 | + | 11.2583i | 0.262319 | + | 0.454349i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.93070 | − | 8.54023i | −0.198503 | − | 0.343817i | 0.749540 | − | 0.661959i | \(-0.230275\pi\) |
−0.948043 | + | 0.318142i | \(0.896941\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.4674 | −0.943233 | −0.471617 | − | 0.881804i | \(-0.656329\pi\) | ||||
−0.471617 | + | 0.881804i | \(0.656329\pi\) | |||||||
\(620\) | −1.37228 | − | 2.37686i | −0.0551121 | − | 0.0954570i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.2337 | 1.05188 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.298936 | 0.0119574 | ||||||||
\(626\) | 1.44158 | − | 2.49689i | 0.0576170 | − | 0.0997956i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.05842 | + | 7.02939i | 0.161949 | + | 0.280503i | ||||
\(629\) | 8.74456 | 0.348669 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.3505 | 0.571286 | 0.285643 | − | 0.958336i | \(-0.407793\pi\) | ||||
0.285643 | + | 0.958336i | \(0.407793\pi\) | |||||||
\(632\) | −6.05842 | − | 10.4935i | −0.240991 | − | 0.417409i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.00000 | + | 5.19615i | −0.119145 | + | 0.206366i | ||||
\(635\) | −19.3723 | −0.768766 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.0000 | 0.475085 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.686141 | − | 1.18843i | −0.0271221 | − | 0.0469768i | ||||
\(641\) | 46.2119 | 1.82526 | 0.912631 | − | 0.408785i | \(-0.134047\pi\) | ||||
0.912631 | + | 0.408785i | \(0.134047\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.6753 | + | 21.9542i | 0.499864 | + | 0.865789i | 1.00000 | 0.000157386i | \(-5.00974e-5\pi\) | |
−0.500136 | + | 0.865947i | \(0.666717\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.9307 | − | 18.9325i | −0.430063 | − | 0.744891i | ||||
\(647\) | −8.74456 | − | 15.1460i | −0.343784 | − | 0.595452i | 0.641348 | − | 0.767250i | \(-0.278376\pi\) |
−0.985132 | + | 0.171798i | \(0.945042\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.5584 | + | 26.9480i | −0.610721 | + | 1.05780i | ||||
\(650\) | 3.11684 | − | 5.39853i | 0.122253 | − | 0.211748i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.11684 | − | 14.0588i | −0.317880 | − | 0.550585i | ||||
\(653\) | 15.2554 | 0.596991 | 0.298496 | − | 0.954411i | \(-0.403515\pi\) | ||||
0.298496 | + | 0.954411i | \(0.403515\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.1168 | 0.395298 | ||||||||
\(656\) | 5.18614 | − | 8.98266i | 0.202485 | − | 0.350714i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.62772 | + | 8.01544i | −0.180270 | + | 0.312237i | −0.941973 | − | 0.335690i | \(-0.891031\pi\) |
0.761702 | + | 0.647927i | \(0.224364\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.94158 | + | 8.55906i | −0.192205 | + | 0.332909i | −0.945981 | − | 0.324223i | \(-0.894897\pi\) |
0.753776 | + | 0.657132i | \(0.228231\pi\) | |||||||
\(662\) | 6.11684 | − | 10.5947i | 0.237738 | − | 0.411774i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.74456 | + | 4.75372i | −0.106510 | + | 0.184480i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.1168 | − | 17.5229i | 0.391726 | − | 0.678489i | ||||
\(668\) | −17.4891 | −0.676675 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.7446 | 0.801432 | ||||||||
\(671\) | −30.8614 | − | 53.4535i | −1.19139 | − | 2.06355i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0584 | − | 17.4217i | 0.387724 | − | 0.671557i | −0.604419 | − | 0.796666i | \(-0.706595\pi\) |
0.992143 | + | 0.125109i | \(0.0399281\pi\) | |||||||
\(674\) | −4.55842 | + | 7.89542i | −0.175584 | + | 0.304120i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | + | 7.79423i | 0.173077 | + | 0.299778i | ||||
\(677\) | −17.2337 | − | 29.8496i | −0.662344 | − | 1.14721i | −0.979998 | − | 0.199007i | \(-0.936228\pi\) |
0.317654 | − | 0.948207i | \(-0.397105\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.00000 | − | 5.19615i | −0.115045 | − | 0.199263i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.74456 | −0.334847 | ||||||||
\(683\) | −22.4198 | − | 38.8323i | −0.857871 | − | 1.48588i | −0.873956 | − | 0.486005i | \(-0.838454\pi\) |
0.0160849 | − | 0.999871i | \(-0.494880\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.4674 | −0.858434 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.11684 | 0.347576 | ||||||||
\(689\) | 2.74456 | − | 4.75372i | 0.104560 | − | 0.181102i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.94158 | + | 5.09496i | 0.111903 | + | 0.193822i | 0.916537 | − | 0.399949i | \(-0.130972\pi\) |
−0.804635 | + | 0.593770i | \(0.797639\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.11684 | −0.270152 | ||||||||
\(695\) | 14.5693 | + | 25.2348i | 0.552645 | + | 0.957209i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.6753 | − | 39.2747i | 0.858887 | − | 1.48764i | ||||
\(698\) | −22.0000 | −0.832712 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.76631 | 0.142252 | 0.0711258 | − | 0.997467i | \(-0.477341\pi\) | ||||
0.0711258 | + | 0.997467i | \(0.477341\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.00000 | − | 8.66025i | −0.188579 | − | 0.326628i | ||||
\(704\) | −4.37228 | −0.164787 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.81386 | − | 6.60580i | −0.143536 | − | 0.248612i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.0000 | − | 38.1051i | −0.826227 | − | 1.43107i | −0.900978 | − | 0.433865i | \(-0.857149\pi\) |
0.0747503 | − | 0.997202i | \(-0.476184\pi\) | |||||||
\(710\) | 6.94158 | + | 12.0232i | 0.260513 | + | 0.451221i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.62772 | − | 2.81929i | 0.0610013 | − | 0.105657i | ||||
\(713\) | −7.37228 | + | 12.7692i | −0.276094 | + | 0.478209i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | + | 10.3923i | 0.224387 | + | 0.388650i | ||||
\(716\) | −14.7446 | −0.551030 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.86141 | 0.256065 | ||||||||
\(719\) | −4.37228 | + | 7.57301i | −0.163059 | + | 0.282426i | −0.935964 | − | 0.352095i | \(-0.885469\pi\) |
0.772906 | + | 0.634521i | \(0.218803\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.00000 | + | 5.19615i | −0.111648 | + | 0.193381i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.05842 | + | 15.6896i | −0.336654 | + | 0.583101i | ||||
\(725\) | −4.27719 | + | 7.40830i | −0.158851 | + | 0.275138i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.883156 | − | 1.52967i | 0.0327544 | − | 0.0567324i | −0.849183 | − | 0.528098i | \(-0.822905\pi\) |
0.881938 | + | 0.471366i | \(0.156239\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.51087 | − | 6.08101i | 0.129943 | − | 0.225068i | ||||
\(731\) | 39.8614 | 1.47433 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.8832 | −0.882144 | −0.441072 | − | 0.897472i | \(-0.645402\pi\) | ||||
−0.441072 | + | 0.897472i | \(0.645402\pi\) | |||||||
\(734\) | −11.1168 | − | 19.2549i | −0.410330 | − | 0.710713i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.68614 | + | 6.38458i | −0.135873 | + | 0.235339i | ||||
\(737\) | 33.0475 | − | 57.2400i | 1.21732 | − | 2.10846i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.55842 | − | 7.89542i | −0.167684 | − | 0.290438i | 0.769921 | − | 0.638139i | \(-0.220296\pi\) |
−0.937605 | + | 0.347702i | \(0.886962\pi\) | |||||||
\(740\) | −1.37228 | − | 2.37686i | −0.0504461 | − | 0.0873751i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.8614 | + | 37.8651i | 0.802017 | + | 1.38913i | 0.918286 | + | 0.395917i | \(0.129573\pi\) |
−0.116269 | + | 0.993218i | \(0.537094\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.2337 | −0.741305 | ||||||||
\(746\) | 5.00000 | + | 8.66025i | 0.183063 | + | 0.317074i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −19.1168 | −0.698981 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.116844 | 0.00426370 | 0.00213185 | − | 0.999998i | \(-0.499321\pi\) | ||||
0.00213185 | + | 0.999998i | \(0.499321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.74456 | + | 4.75372i | 0.0999511 | + | 0.173120i | ||||
\(755\) | −11.1386 | −0.405375 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.7663 | 0.427654 | 0.213827 | − | 0.976872i | \(-0.431407\pi\) | ||||
0.213827 | + | 0.976872i | \(0.431407\pi\) | |||||||
\(758\) | −4.55842 | − | 7.89542i | −0.165569 | − | 0.286775i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.43070 | + | 5.94215i | −0.124445 | + | 0.215545i | ||||
\(761\) | −12.5109 | −0.453519 | −0.226759 | − | 0.973951i | \(-0.572813\pi\) | ||||
−0.226759 | + | 0.973951i | \(0.572813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.88316 | 0.0681302 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.6277 | − | 18.4077i | −0.383995 | − | 0.665099i | ||||
\(767\) | −14.2337 | −0.513949 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.00000 | + | 8.66025i | 0.180305 | + | 0.312297i | 0.941984 | − | 0.335657i | \(-0.108958\pi\) |
−0.761680 | + | 0.647954i | \(0.775625\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.50000 | + | 6.06218i | 0.125968 | + | 0.218183i | ||||
\(773\) | −5.56930 | − | 9.64630i | −0.200314 | − | 0.346953i | 0.748316 | − | 0.663343i | \(-0.230863\pi\) |
−0.948629 | + | 0.316389i | \(0.897529\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.11684 | − | 5.39853i | 0.111960 | − | 0.193921i | ||||
\(776\) | −4.55842 | + | 7.89542i | −0.163638 | + | 0.283429i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.4891 | − | 30.2921i | −0.627016 | − | 1.08602i | ||||
\(779\) | −51.8614 | −1.85813 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.2337 | 1.58281 | ||||||||
\(782\) | −16.1168 | + | 27.9152i | −0.576337 | + | 0.998245i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.56930 | − | 9.64630i | 0.198777 | − | 0.344291i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.00000 | − | 3.46410i | 0.0712923 | − | 0.123482i | −0.828176 | − | 0.560469i | \(-0.810621\pi\) |
0.899468 | + | 0.436987i | \(0.143954\pi\) | |||||||
\(788\) | −3.00000 | + | 5.19615i | −0.106871 | + | 0.185105i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.31386 | + | 14.4000i | −0.295794 | + | 0.512330i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.1168 | − | 24.4511i | 0.501304 | − | 0.868284i | ||||
\(794\) | −22.0000 | −0.780751 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.0000 | −0.354441 | ||||||||
\(797\) | −18.4307 | − | 31.9229i | −0.652849 | − | 1.13077i | −0.982428 | − | 0.186640i | \(-0.940240\pi\) |
0.329579 | − | 0.944128i | \(-0.393093\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.55842 | − | 2.69927i | 0.0550985 | − | 0.0954335i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.127719 | − | 0.221215i | −0.00450990 | − | 0.00781138i | ||||
\(803\) | −11.1861 | − | 19.3750i | −0.394750 | − | 0.683728i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.00000 | − | 3.46410i | −0.0704470 | − | 0.122018i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.37228 | −0.259356 | ||||||||
\(809\) | 10.9307 | + | 18.9325i | 0.384303 | + | 0.665632i | 0.991672 | − | 0.128787i | \(-0.0411084\pi\) |
−0.607369 | + | 0.794420i | \(0.707775\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.8832 | 0.873766 | 0.436883 | − | 0.899518i | \(-0.356082\pi\) | ||||
0.436883 | + | 0.899518i | \(0.356082\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.74456 | −0.306497 | ||||||||
\(815\) | −11.1386 | + | 19.2926i | −0.390168 | + | 0.675791i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.7921 | − | 39.4771i | −0.797395 | − | 1.38113i | ||||
\(818\) | 29.3505 | 1.02622 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.2337 | −0.497062 | ||||||||
\(821\) | −19.1168 | − | 33.1113i | −0.667182 | − | 1.15559i | −0.978689 | − | 0.205350i | \(-0.934167\pi\) |
0.311506 | − | 0.950244i | \(-0.399167\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.1168 | + | 19.2549i | −0.387509 | + | 0.671185i | −0.992114 | − | 0.125341i | \(-0.959998\pi\) |
0.604605 | + | 0.796525i | \(0.293331\pi\) | |||||||
\(824\) | −10.0000 | −0.348367 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.1168 | + | 41.7716i | 0.837613 | + | 1.45079i | 0.891885 | + | 0.452261i | \(0.149383\pi\) |
−0.0542728 | + | 0.998526i | \(0.517284\pi\) | |||||||
\(830\) | 7.53262 | 0.261461 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.00000 | − | 1.73205i | −0.0346688 | − | 0.0600481i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0000 | + | 20.7846i | 0.415277 | + | 0.719281i | ||||
\(836\) | 10.9307 | + | 18.9325i | 0.378046 | + | 0.654795i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.8030 | − | 23.9075i | 0.476816 | − | 0.825870i | ||||
\(839\) | −8.74456 | + | 15.1460i | −0.301896 | + | 0.522899i | −0.976565 | − | 0.215221i | \(-0.930953\pi\) |
0.674670 | + | 0.738120i | \(0.264286\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7337 | + | 18.5913i | 0.370127 | + | 0.641079i | ||||
\(842\) | −0.233688 | −0.00805342 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.0000 | −0.550743 | ||||||||
\(845\) | 6.17527 | − | 10.6959i | 0.212436 | − | 0.367949i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.37228 | − | 2.37686i | 0.0471243 | − | 0.0816217i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.81386 | − | 11.8020i | 0.233713 | − | 0.404804i | ||||
\(851\) | −7.37228 | + | 12.7692i | −0.252719 | + | 0.437721i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.94158 | − | 15.4873i | 0.306154 | − | 0.530274i | −0.671364 | − | 0.741128i | \(-0.734291\pi\) |
0.977518 | + | 0.210854i | \(0.0676245\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.813859 | + | 1.40965i | −0.0278171 | + | 0.0481807i | ||||
\(857\) | −51.9565 | −1.77480 | −0.887400 | − | 0.461000i | \(-0.847491\pi\) | ||||
−0.887400 | + | 0.461000i | \(0.847491\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.1168 | 1.74408 | 0.872042 | − | 0.489431i | \(-0.162795\pi\) | ||||
0.872042 | + | 0.489431i | \(0.162795\pi\) | |||||||
\(860\) | −6.25544 | − | 10.8347i | −0.213309 | − | 0.369461i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.7446 | + | 25.5383i | −0.502202 | + | 0.869839i | ||||
\(863\) | −9.43070 | + | 16.3345i | −0.321025 | + | 0.556031i | −0.980700 | − | 0.195520i | \(-0.937361\pi\) |
0.659675 | + | 0.751551i | \(0.270694\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.11684 | − | 7.13058i | −0.139977 | − | 0.242447i | ||||
\(866\) | 1.44158 | + | 2.49689i | 0.0489868 | + | 0.0848477i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.4891 | + | 45.8805i | 0.898582 | + | 1.55639i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.2337 | 1.02443 | ||||||||
\(872\) | −7.00000 | − | 12.1244i | −0.237050 | − | 0.410582i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 36.8614 | 1.24686 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.7011 | 1.50945 | 0.754724 | − | 0.656043i | \(-0.227771\pi\) | ||||
0.754724 | + | 0.656043i | \(0.227771\pi\) | |||||||
\(878\) | −4.00000 | + | 6.92820i | −0.134993 | + | 0.233816i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.00000 | + | 5.19615i | 0.101130 | + | 0.175162i | ||||
\(881\) | −14.2337 | −0.479545 | −0.239773 | − | 0.970829i | \(-0.577073\pi\) | ||||
−0.239773 | + | 0.970829i | \(0.577073\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.3505 | 0.381976 | 0.190988 | − | 0.981592i | \(-0.438831\pi\) | ||||
0.190988 | + | 0.981592i | \(0.438831\pi\) | |||||||
\(884\) | −4.37228 | − | 7.57301i | −0.147056 | − | 0.254708i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.4416 | + | 19.8174i | −0.384387 | + | 0.665778i | ||||
\(887\) | 31.7228 | 1.06515 | 0.532574 | − | 0.846383i | \(-0.321225\pi\) | ||||
0.532574 | + | 0.846383i | \(0.321225\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.46738 | −0.149747 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.00000 | + | 3.46410i | 0.0669650 | + | 0.115987i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.1168 | + | 17.5229i | 0.338169 | + | 0.585726i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.5000 | + | 28.5788i | 0.550612 | + | 0.953688i | ||||
\(899\) | 2.74456 | + | 4.75372i | 0.0915363 | + | 0.158546i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.00000 | − | 10.3923i | 0.199889 | − | 0.346218i | ||||
\(902\) | −22.6753 | + | 39.2747i | −0.755004 | + | 1.30770i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.686141 | + | 1.18843i | 0.0228207 | + | 0.0395266i | ||||
\(905\) | 24.8614 | 0.826421 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.88316 | −0.294960 | −0.147480 | − | 0.989065i | \(-0.547116\pi\) | ||||
−0.147480 | + | 0.989065i | \(0.547116\pi\) | |||||||
\(908\) | −11.8723 | + | 20.5634i | −0.393995 | + | 0.682420i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.6861 | + | 37.5615i | −0.718494 | + | 1.24447i | 0.243103 | + | 0.970001i | \(0.421835\pi\) |
−0.961596 | + | 0.274467i | \(0.911498\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000 | − | 20.7846i | 0.397142 | − | 0.687870i | ||||
\(914\) | −16.7337 | + | 28.9836i | −0.553501 | + | 0.958692i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.0584 | − | 17.4217i | 0.332340 | − | 0.575629i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.9416 | − | 25.8796i | 0.492877 | − | 0.853688i | −0.507089 | − | 0.861894i | \(-0.669279\pi\) |
0.999966 | + | 0.00820529i | \(0.00261185\pi\) | |||||||
\(920\) | 10.1168 | 0.333542 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −30.8614 | −1.01637 | ||||||||
\(923\) | 10.1168 | + | 17.5229i | 0.333000 | + | 0.576773i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.11684 | − | 5.39853i | 0.102481 | − | 0.177503i | ||||
\(926\) | 2.94158 | − | 5.09496i | 0.0966663 | − | 0.167431i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.37228 | + | 2.37686i | 0.0450473 | + | 0.0780243i | ||||
\(929\) | 4.88316 | + | 8.45787i | 0.160211 | + | 0.277494i | 0.934944 | − | 0.354794i | \(-0.115449\pi\) |
−0.774733 | + | 0.632288i | \(0.782116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.87228 | − | 10.1711i | −0.192353 | − | 0.333165i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.0951 | 0.984742 | ||||||||
\(935\) | 13.1168 | + | 22.7190i | 0.428967 | + | 0.742992i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.4674 | −1.25667 | −0.628337 | − | 0.777941i | \(-0.716264\pi\) | ||||
−0.628337 | + | 0.777941i | \(0.716264\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.941578 | − | 1.63086i | 0.0306946 | − | 0.0531645i | −0.850270 | − | 0.526347i | \(-0.823561\pi\) |
0.880965 | + | 0.473182i | \(0.156895\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.2337 | + | 66.2227i | 1.24506 | + | 2.15651i | ||||
\(944\) | −7.11684 | −0.231634 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39.8614 | −1.29601 | ||||||||
\(947\) | 8.44158 | + | 14.6212i | 0.274314 | + | 0.475127i | 0.969962 | − | 0.243257i | \(-0.0782158\pi\) |
−0.695648 | + | 0.718383i | \(0.744882\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.11684 | − | 8.86263i | 0.166100 | − | 0.287693i | ||||
\(950\) | −15.5842 | −0.505619 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.8832 | −0.352540 | −0.176270 | − | 0.984342i | \(-0.556403\pi\) | ||||
−0.176270 | + | 0.984342i | \(0.556403\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.29211 | − | 2.23800i | −0.0418117 | − | 0.0724200i | ||||
\(956\) | 18.8614 | 0.610021 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.6277 | + | 18.4077i | 0.343366 | + | 0.594727i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | −2.00000 | − | 3.46410i | −0.0644826 | − | 0.111687i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.441578 | + | 0.764836i | −0.0142223 | + | 0.0246337i | ||||
\(965\) | 4.80298 | − | 8.31901i | 0.154614 | − | 0.267799i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.0584 | − | 41.6704i | −0.773667 | − | 1.34003i | −0.935541 | − | 0.353219i | \(-0.885087\pi\) |
0.161874 | − | 0.986811i | \(-0.448246\pi\) | |||||||
\(968\) | 8.11684 | 0.260885 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.5109 | 0.401700 | ||||||||
\(971\) | 3.68614 | − | 6.38458i | 0.118294 | − | 0.204891i | −0.800798 | − | 0.598935i | \(-0.795591\pi\) |
0.919092 | + | 0.394044i | \(0.128924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.17527 | − | 14.1600i | 0.261952 | − | 0.453715i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.05842 | − | 12.2255i | 0.225935 | − | 0.391330i | ||||
\(977\) | 11.4416 | − | 19.8174i | 0.366049 | − | 0.634015i | −0.622895 | − | 0.782305i | \(-0.714044\pi\) |
0.988944 | + | 0.148291i | \(0.0473771\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.11684 | + | 12.3267i | −0.227455 | + | 0.393964i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.81386 | + | 16.9981i | −0.313173 | + | 0.542431i | ||||
\(983\) | 50.7446 | 1.61850 | 0.809250 | − | 0.587464i | \(-0.199874\pi\) | ||||
0.809250 | + | 0.587464i | \(0.199874\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.23369 | 0.262347 | ||||||||
\(986\) | 6.00000 | + | 10.3923i | 0.191079 | + | 0.330958i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.00000 | + | 8.66025i | −0.159071 | + | 0.275519i | ||||
\(989\) | −33.6060 | + | 58.2072i | −1.06861 | + | 1.85088i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.2337 | + | 17.7253i | 0.325084 | + | 0.563062i | 0.981529 | − | 0.191312i | \(-0.0612742\pi\) |
−0.656446 | + | 0.754373i | \(0.727941\pi\) | |||||||
\(992\) | −1.00000 | − | 1.73205i | −0.0317500 | − | 0.0549927i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.86141 | + | 11.8843i | 0.217521 | + | 0.376758i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.1168 | 0.383744 | 0.191872 | − | 0.981420i | \(-0.438544\pi\) | ||||
0.191872 | + | 0.981420i | \(0.438544\pi\) | |||||||
\(998\) | −0.441578 | − | 0.764836i | −0.0139779 | − | 0.0242104i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))