Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [77,2,Mod(6,77)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(77, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("77.6");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 77 = 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 77.l (of order \(10\), degree \(4\), 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: | \(0.614848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.37515625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - x^{6} + 3x^{5} - x^{4} + 6x^{3} - 4x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 13.2 | ||
Root | \(-1.41264 + 0.0667372i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 77.13 |
Dual form | 77.2.l.a.6.2 |
$q$-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 \(\left(\mathbb{Z}/77\mathbb{Z}\right)^\times\).
\(n\) | \(45\) | \(57\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.47668 | + | 0.479802i | 1.04417 | + | 0.339271i | 0.780378 | − | 0.625308i | \(-0.215027\pi\) |
0.263792 | + | 0.964580i | \(0.415027\pi\) | |||||||
\(3\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(4\) | 0.332338 | + | 0.241457i | 0.166169 | + | 0.120729i | ||||
\(5\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.55513 | + | 2.14046i | −0.587785 | + | 0.809017i | ||||
\(8\) | −1.45037 | − | 1.99627i | −0.512784 | − | 0.705786i | ||||
\(9\) | 0.927051 | − | 2.85317i | 0.309017 | − | 0.951057i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.89823 | + | 2.71970i | −0.572336 | + | 0.820019i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(14\) | −3.32343 | + | 2.41461i | −0.888224 | + | 0.645333i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.43780 | − | 4.42511i | −0.359451 | − | 1.10628i | ||||
\(17\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(18\) | 2.73791 | − | 3.76842i | 0.645333 | − | 0.888224i | ||||
\(19\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.10799 | + | 3.10535i | −0.875825 | + | 0.662062i | ||||
\(23\) | 9.58240 | 1.99807 | 0.999035 | − | 0.0439305i | \(-0.0139880\pi\) | ||||
0.999035 | + | 0.0439305i | \(0.0139880\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04508 | + | 2.93893i | −0.809017 | + | 0.587785i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.03366 | + | 0.335856i | −0.195343 | + | 0.0634708i | ||||
\(29\) | 0.804217 | − | 1.10691i | 0.149339 | − | 0.205548i | −0.727793 | − | 0.685797i | \(-0.759454\pi\) |
0.877132 | + | 0.480249i | \(0.159454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(32\) | − | 2.28929i | − | 0.404693i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.997013 | − | 0.724372i | 0.166169 | − | 0.120729i | ||||
\(37\) | 1.10547 | + | 0.803169i | 0.181738 | + | 0.132040i | 0.674935 | − | 0.737878i | \(-0.264172\pi\) |
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.77751i | 1.49106i | 0.666474 | + | 0.745528i | \(0.267803\pi\) | ||||
−0.666474 | + | 0.745528i | \(0.732197\pi\) | |||||||
\(44\) | −1.28754 | + | 0.445517i | −0.194104 | + | 0.0671642i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.1501 | + | 4.59766i | 2.08632 | + | 0.677888i | ||||
\(47\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.16312 | − | 6.65740i | −0.309017 | − | 0.951057i | ||||
\(50\) | −7.38340 | + | 2.39901i | −1.04417 | + | 0.339271i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.06518 | − | 12.5113i | 0.558396 | − | 1.71857i | −0.128407 | − | 0.991722i | \(-0.540986\pi\) |
0.686803 | − | 0.726844i | \(-0.259014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.52844 | 0.872400 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.71867 | − | 1.24869i | 0.225672 | − | 0.163960i | ||||
\(59\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.66540 | + | 6.42137i | 0.587785 | + | 0.809017i | ||||
\(64\) | −1.77720 | + | 5.46967i | −0.222151 | + | 0.683709i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.3336 | −1.99547 | −0.997735 | − | 0.0672706i | \(-0.978571\pi\) | ||||
−0.997735 | + | 0.0672706i | \(0.978571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.08300 | − | 9.48849i | −0.365885 | − | 1.12608i | −0.949425 | − | 0.313993i | \(-0.898333\pi\) |
0.583541 | − | 0.812084i | \(-0.301667\pi\) | |||||||
\(72\) | −7.04025 | + | 2.28752i | −0.829702 | + | 0.269586i | ||||
\(73\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(74\) | 1.24706 | + | 1.71643i | 0.144968 | + | 0.199531i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.86940 | − | 8.29256i | −0.326998 | − | 0.945025i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9015 | − | 3.86702i | −1.33902 | − | 0.435074i | −0.450035 | − | 0.893011i | \(-0.648589\pi\) |
−0.888985 | + | 0.457937i | \(0.848589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.28115 | − | 5.29007i | −0.809017 | − | 0.587785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.69127 | + | 14.4383i | −0.505873 | + | 1.55692i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.18236 | − | 0.155208i | 0.872243 | − | 0.0165452i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.18459 | + | 2.31374i | 0.332017 | + | 0.241224i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(98\) | − | 10.8687i | − | 1.09791i | ||||||
\(99\) | 6.00000 | + | 7.93725i | 0.603023 | + | 0.797724i | ||||
\(100\) | −2.05396 | −0.205396 | ||||||||
\(101\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0059 | − | 16.5248i | 1.16612 | − | 1.60503i | ||||
\(107\) | 9.42609 | + | 12.9739i | 0.911254 | + | 1.25423i | 0.966736 | + | 0.255774i | \(0.0823304\pi\) |
−0.0554821 | + | 0.998460i | \(0.517670\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.1420i | 1.83347i | 0.399498 | + | 0.916734i | \(0.369184\pi\) | ||||
−0.399498 | + | 0.916734i | \(0.630816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.7077 | + | 3.80407i | 1.10628 | + | 0.359451i | ||||
\(113\) | 15.7856 | − | 11.4689i | 1.48498 | − | 1.07890i | 0.509073 | − | 0.860724i | \(-0.329988\pi\) |
0.975909 | − | 0.218179i | \(-0.0700116\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.534543 | − | 0.173684i | 0.0496311 | − | 0.0161261i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.79348 | − | 10.3252i | −0.344862 | − | 0.938653i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.80831 | + | 11.7208i | 0.339271 | + | 1.04417i | ||||
\(127\) | 21.1584 | − | 6.87480i | 1.87751 | − | 0.610040i | 0.889212 | − | 0.457495i | \(-0.151253\pi\) |
0.988297 | − | 0.152545i | \(-0.0487468\pi\) | |||||||
\(128\) | −7.93994 | + | 10.9284i | −0.701798 | + | 0.965942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −24.1195 | − | 7.83691i | −2.08361 | − | 0.677006i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.34450 | + | 19.5264i | 0.542047 | + | 1.66825i | 0.727909 | + | 0.685674i | \(0.240493\pi\) |
−0.185861 | + | 0.982576i | \(0.559507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 15.4907i | − | 1.29995i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −13.9585 | −1.16321 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.173457 | + | 0.533847i | 0.0142581 | + | 0.0438819i | ||||
\(149\) | −10.0650 | + | 3.27033i | −0.824560 | + | 0.267916i | −0.690752 | − | 0.723092i | \(-0.742720\pi\) |
−0.133808 | + | 0.991007i | \(0.542720\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.77554 | − | 7.94934i | −0.470007 | − | 0.646909i | 0.506540 | − | 0.862217i | \(-0.330924\pi\) |
−0.976546 | + | 0.215308i | \(0.930924\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.258394 | − | 13.6222i | −0.0208220 | − | 1.09771i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(158\) | −15.7192 | − | 11.4207i | −1.25056 | − | 0.908582i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.9019 | + | 20.5107i | −1.17444 | + | 1.61647i | ||||
\(162\) | −8.21374 | − | 11.3052i | −0.645333 | − | 0.888224i | ||||
\(163\) | −2.11662 | + | 6.51430i | −0.165787 | + | 0.510239i | −0.999093 | − | 0.0425718i | \(-0.986445\pi\) |
0.833307 | + | 0.552811i | \(0.186445\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5172 | + | 7.64121i | 0.809017 | + | 0.587785i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.36085 | + | 3.24944i | −0.180013 | + | 0.247767i | ||||
\(173\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 13.2288i | − | 1.00000i | ||||||
\(176\) | 14.7642 | + | 4.48946i | 1.11290 | + | 0.338406i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.96326 | + | 7.23873i | −0.744689 | + | 0.541048i | −0.894176 | − | 0.447715i | \(-0.852238\pi\) |
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.8980 | − | 19.1290i | −1.02458 | − | 1.41021i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.3570 | + | 13.3371i | 1.32826 | + | 0.965040i | 0.999789 | + | 0.0205267i | \(0.00653431\pi\) |
0.328474 | + | 0.944513i | \(0.393466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.5017 | − | 7.31124i | 1.61971 | − | 0.526275i | 0.647834 | − | 0.761781i | \(-0.275675\pi\) |
0.971873 | + | 0.235507i | \(0.0756750\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.888592 | − | 2.73480i | 0.0634708 | − | 0.195343i | ||||
\(197\) | − | 6.72059i | − | 0.478822i | −0.970918 | − | 0.239411i | \(-0.923046\pi\) | ||
0.970918 | − | 0.239411i | \(-0.0769543\pi\) | |||||||
\(198\) | 5.05176 | + | 14.5996i | 0.359013 | + | 1.03755i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 11.7338 | + | 3.81253i | 0.829702 | + | 0.269586i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.11863 | + | 3.44278i | 0.0785123 | + | 0.241636i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.88338 | − | 27.3402i | 0.617437 | − | 1.90028i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.0652 | − | 8.79401i | −1.86324 | − | 0.605404i | −0.993774 | − | 0.111417i | \(-0.964461\pi\) |
−0.869469 | − | 0.493987i | \(-0.835539\pi\) | |||||||
\(212\) | 4.37197 | − | 3.17642i | 0.300268 | − | 0.218158i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.69441 | + | 23.6809i | 0.525979 | + | 1.61880i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.18436 | + | 28.2665i | −0.622043 | + | 1.91445i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(224\) | 4.90012 | + | 3.56015i | 0.327403 | + | 0.237872i | ||||
\(225\) | 4.63525 | + | 14.2658i | 0.309017 | + | 0.951057i | ||||
\(226\) | 28.8130 | − | 9.36192i | 1.91661 | − | 0.622746i | ||||
\(227\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.37610 | −0.221652 | ||||||||
\(233\) | −20.1301 | − | 6.54066i | −1.31876 | − | 0.428493i | −0.436694 | − | 0.899610i | \(-0.643851\pi\) |
−0.882071 | + | 0.471117i | \(0.843851\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.13864 | − | 5.69636i | −0.267707 | − | 0.368467i | 0.653907 | − | 0.756575i | \(-0.273129\pi\) |
−0.921614 | + | 0.388108i | \(0.873129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | −0.647711 | − | 17.0671i | −0.0416365 | − | 1.09712i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(252\) | 3.26056i | 0.205396i | ||||||||
\(253\) | −18.1896 | + | 26.0612i | −1.14357 | + | 1.63845i | ||||
\(254\) | 34.5428 | 2.16741 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.66265 | + | 5.56724i | −0.478916 | + | 0.347953i | ||||
\(257\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.43830 | + | 1.11717i | −0.213645 | + | 0.0694176i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.41265 | − | 3.32073i | −0.149339 | − | 0.205548i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 32.0690i | − | 1.97746i | −0.149718 | − | 0.988729i | \(-0.547836\pi\) | ||
0.149718 | − | 0.988729i | \(-0.452164\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.42828 | − | 3.94387i | −0.331585 | − | 0.240910i | ||||
\(269\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 31.8783i | 1.92584i | ||||||||
\(275\) | −0.314502 | − | 16.5801i | −0.0189652 | − | 0.999820i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.0185 | + | 9.75361i | 1.80364 | + | 0.586038i | 0.999959 | − | 0.00902525i | \(-0.00287287\pi\) |
0.803679 | + | 0.595063i | \(0.202873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.2967 | + | 5.62003i | −1.03183 | + | 0.335263i | −0.775515 | − | 0.631329i | \(-0.782510\pi\) |
−0.256319 | + | 0.966592i | \(0.582510\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(284\) | 1.26647 | − | 3.89780i | 0.0751512 | − | 0.231292i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −6.53173 | − | 2.12229i | −0.384886 | − | 0.125057i | ||||
\(289\) | 13.7533 | − | 9.99235i | 0.809017 | − | 0.587785i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 3.37170i | − | 0.195976i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.4319 | −0.951877 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.9284 | − | 15.2053i | −1.20629 | − | 0.876421i | ||||
\(302\) | −4.71450 | − | 14.5097i | −0.271289 | − | 0.834942i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 1.04869 | − | 3.44877i | 0.0597547 | − | 0.196512i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.02159 | − | 4.15886i | −0.169977 | − | 0.233954i | ||||
\(317\) | −0.136444 | + | 0.419931i | −0.00766345 | + | 0.0235857i | −0.954815 | − | 0.297200i | \(-0.903947\pi\) |
0.947152 | + | 0.320786i | \(0.103947\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.48387 | + | 4.28839i | 0.0830809 | + | 0.240104i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −31.8464 | + | 23.1378i | −1.77473 | + | 1.28942i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.14248 | − | 3.51618i | −0.0634708 | − | 0.195343i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.25115 | + | 8.60397i | −0.346219 | + | 0.476530i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.0143 | −1.42988 | −0.714939 | − | 0.699187i | \(-0.753545\pi\) | ||||
−0.714939 | + | 0.699187i | \(0.753545\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.31640 | − | 2.40951i | 0.181738 | − | 0.132040i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.299709 | − | 0.412514i | 0.0163262 | − | 0.0224711i | −0.800776 | − | 0.598964i | \(-0.795579\pi\) |
0.817102 | + | 0.576493i | \(0.195579\pi\) | |||||||
\(338\) | 11.8643 | + | 16.3298i | 0.645333 | + | 0.888224i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6138 | + | 5.72307i | 0.951057 | + | 0.309017i | ||||
\(344\) | 19.5185 | − | 14.1810i | 1.05237 | − | 0.764590i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.5040 | + | 4.71263i | −0.778614 | + | 0.252987i | −0.671248 | − | 0.741233i | \(-0.734242\pi\) |
−0.107366 | + | 0.994220i | \(0.534242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(350\) | 6.34719 | − | 19.5346i | 0.339271 | − | 1.04417i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.22617 | + | 4.34558i | 0.331856 | + | 0.231620i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.1857 | + | 5.90889i | −0.961144 | + | 0.312295i | ||||
\(359\) | 20.3777 | − | 28.0476i | 1.07550 | − | 1.48029i | 0.211112 | − | 0.977462i | \(-0.432292\pi\) |
0.864384 | − | 0.502832i | \(-0.167708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.87132 | + | 18.0701i | −0.309017 | + | 0.951057i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(368\) | −13.7776 | − | 42.4032i | −0.718208 | − | 2.21042i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.4581 | + | 28.1582i | 1.06213 | + | 1.46190i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.7490i | 1.64390i | 0.569558 | + | 0.821951i | \(0.307114\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.72788 | − | 29.9393i | −0.499688 | − | 1.53788i | −0.809522 | − | 0.587090i | \(-0.800274\pi\) |
0.309834 | − | 0.950791i | \(-0.399726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.7082 | + | 28.5024i | 1.05952 | + | 1.45831i | ||||
\(383\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 36.7357 | 1.86980 | ||||||||
\(387\) | 27.8969 | + | 9.06425i | 1.41808 | + | 0.460762i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.9038 | + | 21.7264i | 1.51618 | + | 1.10157i | 0.963338 | + | 0.268290i | \(0.0864585\pi\) |
0.552847 | + | 0.833283i | \(0.313542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −10.1526 | + | 13.9739i | −0.512784 | + | 0.705786i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.22455 | − | 9.92415i | 0.162451 | − | 0.499971i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0775169 | + | 4.08659i | 0.00389537 | + | 0.205359i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.8211 | + | 13.6743i | 0.941055 | + | 0.683717i | ||||
\(401\) | −4.65550 | − | 14.3282i | −0.232484 | − | 0.715514i | −0.997445 | − | 0.0714367i | \(-0.977242\pi\) |
0.764961 | − | 0.644077i | \(-0.222758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.62061i | 0.278946i | ||||||||
\(407\) | −4.28280 | + | 1.48194i | −0.212290 | + | 0.0734570i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 26.2358 | − | 36.1105i | 1.28942 | − | 1.77473i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.1148 | − | 23.3327i | 1.56518 | − | 1.13717i | 0.633581 | − | 0.773676i | \(-0.281584\pi\) |
0.931597 | − | 0.363492i | \(-0.118416\pi\) | |||||||
\(422\) | −35.7472 | − | 25.9719i | −1.74015 | − | 1.26429i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −30.8720 | + | 10.0309i | −1.49928 | + | 0.487144i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.58771i | 0.318429i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.46842 | − | 0.802038i | −0.118900 | − | 0.0386328i | 0.248963 | − | 0.968513i | \(-0.419910\pi\) |
−0.367862 | + | 0.929880i | \(0.619910\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.62197 | + | 6.36160i | −0.221352 | + | 0.304665i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.0000 | −1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.4997 | + | 17.0736i | −1.11651 | + | 0.811190i | −0.983676 | − | 0.179949i | \(-0.942407\pi\) |
−0.132831 | + | 0.991139i | \(0.542407\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.94381 | − | 12.3101i | −0.422555 | − | 0.581598i | ||||
\(449\) | −7.18900 | + | 22.1255i | −0.339270 | + | 1.04417i | 0.625310 | + | 0.780376i | \(0.284972\pi\) |
−0.964580 | + | 0.263790i | \(0.915028\pi\) | |||||||
\(450\) | 23.2901i | 1.09791i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 8.01539 | 0.377012 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.9252 | + | 11.6728i | −1.68051 | + | 0.546031i | −0.985011 | − | 0.172493i | \(-0.944818\pi\) |
−0.695501 | + | 0.718525i | \(0.744818\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.73687 | −0.127193 | −0.0635967 | − | 0.997976i | \(-0.520257\pi\) | ||||
−0.0635967 | + | 0.997976i | \(0.520257\pi\) | |||||||
\(464\) | −6.05450 | − | 1.96723i | −0.281073 | − | 0.0913262i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.5874 | − | 19.3169i | −1.23164 | − | 0.894838i | ||||
\(467\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.4010 | − | 34.9614i | 1.17291 | − | 1.61437i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.5919 | − | 18.5599i | −1.22269 | − | 0.853386i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −31.9284 | − | 23.1973i | −1.46190 | − | 1.06213i | ||||
\(478\) | −3.37833 | − | 10.3974i | −0.154521 | − | 0.475567i | ||||
\(479\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.23238 | − | 4.34741i | 0.0560171 | − | 0.197610i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.4997 | + | 25.0655i | −1.56333 | + | 1.13583i | −0.630123 | + | 0.776495i | \(0.716996\pi\) |
−0.933210 | + | 0.359333i | \(0.883004\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.11027 | + | 4.28092i | −0.140364 | + | 0.193195i | −0.873412 | − | 0.486983i | \(-0.838097\pi\) |
0.733047 | + | 0.680178i | \(0.238097\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.1042 | + | 8.15685i | 1.12608 | + | 0.365885i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.3570 | + | 21.3291i | 1.31420 | + | 0.954821i | 0.999985 | + | 0.00546838i | \(0.00174065\pi\) |
0.314213 | + | 0.949352i | \(0.398259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(504\) | 6.05220 | − | 18.6268i | 0.269586 | − | 0.829702i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −39.3644 | + | 29.7567i | −1.74996 | + | 1.32285i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.69172 | + | 2.82411i | 0.385633 | + | 0.125300i | ||||
\(509\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.7077 | − | 3.80407i | 0.517414 | − | 0.168118i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −5.61328 | −0.246634 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(522\) | −1.96942 | − | 6.06125i | −0.0861991 | − | 0.265294i | ||||
\(523\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.3868 | − | 47.3556i | 0.670895 | − | 2.06480i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 68.8225 | 2.99228 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 23.6898 | + | 32.6062i | 1.02324 | + | 1.40838i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.2122 | + | 6.75421i | 0.956746 | + | 0.290924i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.42178 | + | 1.76164i | 0.233100 | + | 0.0757389i | 0.423238 | − | 0.906019i | \(-0.360893\pi\) |
−0.190138 | + | 0.981757i | \(0.560893\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.33080 | + | 12.8427i | 0.398956 | + | 0.549116i | 0.960482 | − | 0.278343i | \(-0.0897853\pi\) |
−0.561525 | + | 0.827460i | \(0.689785\pi\) | |||||||
\(548\) | −2.60627 | + | 8.02128i | −0.111334 | + | 0.342652i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.49077 | − | 24.6345i | 0.319407 | − | 1.05042i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.7856 | − | 19.4609i | 1.13904 | − | 0.827560i | ||||
\(554\) | 39.6479 | + | 28.8059i | 1.68448 | + | 1.22385i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.7925 | + | 32.7476i | −1.00812 | + | 1.38756i | −0.0879152 | + | 0.996128i | \(0.528020\pi\) |
−0.920207 | + | 0.391433i | \(0.871980\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.2382 | −1.19116 | ||||||||
\(563\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.6463 | − | 7.35824i | 0.951057 | − | 0.309017i | ||||
\(568\) | −14.4701 | + | 19.9163i | −0.607150 | + | 0.835670i | ||||
\(569\) | −24.8821 | − | 34.2473i | −1.04311 | − | 1.43572i | −0.894630 | − | 0.446808i | \(-0.852561\pi\) |
−0.148483 | − | 0.988915i | \(-0.547439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 40.8794i | − | 1.71075i | −0.518010 | − | 0.855374i | \(-0.673327\pi\) | ||
0.518010 | − | 0.855374i | \(-0.326673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.7616 | + | 28.1620i | −1.61647 | + | 1.17444i | ||||
\(576\) | 13.9583 | + | 10.1413i | 0.581598 | + | 0.422555i | ||||
\(577\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(578\) | 25.1035 | − | 8.15664i | 1.04417 | − | 0.339271i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.3104 | + | 34.8054i | 1.08967 | + | 1.44149i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.96466 | − | 6.04661i | 0.0807472 | − | 0.248514i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.13464 | − | 1.34342i | −0.169361 | − | 0.0550288i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.27212 | + | 3.91519i | 0.0519775 | + | 0.159970i | 0.973676 | − | 0.227937i | \(-0.0731980\pi\) |
−0.921698 | + | 0.387907i | \(0.873198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(602\) | −23.6089 | − | 32.4949i | −0.962228 | − | 1.32439i | ||||
\(603\) | −15.1421 | + | 46.6026i | −0.616634 | + | 1.89780i | ||||
\(604\) | − | 4.03641i | − | 0.164239i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.0094 | − | 37.1752i | −1.09090 | − | 1.50149i | −0.846925 | − | 0.531712i | \(-0.821549\pi\) |
−0.243974 | − | 0.969782i | \(-0.578451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.3925 | + | 17.7554i | −0.499306 | + | 0.715384i | ||||
\(617\) | 32.2257 | 1.29736 | 0.648679 | − | 0.761062i | \(-0.275322\pi\) | ||||
0.648679 | + | 0.761062i | \(0.275322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.72542 | − | 23.7764i | 0.309017 | − | 0.951057i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.1742 | − | 8.84507i | −0.484647 | − | 0.352117i | 0.318475 | − | 0.947931i | \(-0.396829\pi\) |
−0.803122 | + | 0.595815i | \(0.796829\pi\) | |||||||
\(632\) | 9.54195 | + | 29.3671i | 0.379558 | + | 1.16816i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.402968 | + | 0.554638i | −0.0160039 | + | 0.0220275i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.133625 | + | 7.04454i | 0.00529026 | + | 0.278896i | ||||
\(639\) | −29.9304 | −1.18403 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.78557 | − | 3.47692i | 0.189019 | − | 0.137330i | −0.489251 | − | 0.872143i | \(-0.662730\pi\) |
0.678270 | + | 0.734813i | \(0.262730\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(644\) | −9.90494 | + | 3.21831i | −0.390309 | + | 0.126819i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(648\) | 22.2077i | 0.872400i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.27636 | + | 1.65387i | −0.0891491 | + | 0.0647706i | ||||
\(653\) | −27.6929 | − | 20.1201i | −1.08371 | − | 0.787359i | −0.105382 | − | 0.994432i | \(-0.533606\pi\) |
−0.978326 | + | 0.207072i | \(0.933606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 26.4575i | − | 1.03064i | −0.856998 | − | 0.515319i | \(-0.827673\pi\) | ||
0.856998 | − | 0.515319i | \(-0.172327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | −38.4148 | − | 12.4817i | −1.49304 | − | 0.485117i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.05335 | − | 1.96685i | 0.234562 | − | 0.0762140i | ||||
\(667\) | 7.70633 | − | 10.6069i | 0.298390 | − | 0.410699i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.6942 | − | 4.77443i | −0.566419 | − | 0.184041i | 0.0117883 | − | 0.999931i | \(-0.496248\pi\) |
−0.578208 | + | 0.815890i | \(0.696248\pi\) | |||||||
\(674\) | 0.640499 | − | 0.465350i | 0.0246711 | − | 0.0179246i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.65024 | + | 5.07892i | 0.0634708 | + | 0.195343i | ||||
\(677\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 45.1792 | 1.72873 | 0.864366 | − | 0.502863i | \(-0.167720\pi\) | ||||
0.864366 | + | 0.502863i | \(0.167720\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 23.2640 | + | 16.9023i | 0.888224 | + | 0.645333i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 43.2666 | − | 14.0582i | 1.64952 | − | 0.535962i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −26.3202 | + | 0.499256i | −0.999820 | + | 0.0189652i | ||||
\(694\) | −23.6788 | −0.898836 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.19418 | − | 4.39641i | 0.120729 | − | 0.166169i | ||||
\(701\) | −25.8536 | − | 35.5844i | −0.976476 | − | 1.34400i | −0.938707 | − | 0.344717i | \(-0.887975\pi\) |
−0.0377695 | − | 0.999286i | \(-0.512025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −11.5023 | − | 15.2161i | −0.433509 | − | 0.573479i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.1243 | + | 49.6254i | 0.605560 | + | 1.86372i | 0.492893 | + | 0.870090i | \(0.335939\pi\) |
0.112667 | + | 0.993633i | \(0.464061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.0665 | + | 30.3720i | −0.827560 | + | 1.13904i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.05901 | −0.189064 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 43.5487 | − | 31.6400i | 1.62522 | − | 1.18079i | ||||
\(719\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.3401 | + | 23.8666i | −0.645333 | + | 0.888224i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.84108i | 0.254071i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.8435 | + | 15.8702i | −0.809017 | + | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 21.9369i | − | 0.808604i | ||||||
\(737\) | 31.0049 | − | 44.4225i | 1.14208 | − | 1.63632i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.6998 | − | 16.7983i | −1.90181 | − | 0.617935i | −0.956425 | − | 0.291977i | \(-0.905687\pi\) |
−0.945384 | − | 0.325959i | \(-0.894313\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16.6997 | + | 51.3964i | 0.613066 | + | 1.88682i | ||||
\(743\) | 25.2944 | − | 8.21865i | 0.927962 | − | 0.301513i | 0.194233 | − | 0.980955i | \(-0.437778\pi\) |
0.733729 | + | 0.679442i | \(0.237778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.2332 | + | 46.8831i | −0.557729 | + | 1.71651i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.4289 | −1.55032 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.8351 | − | 13.6845i | 0.687303 | − | 0.499355i | −0.188469 | − | 0.982079i | \(-0.560353\pi\) |
0.875772 | + | 0.482724i | \(0.160353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.26681 | − | 25.4426i | 0.300462 | − | 0.924728i | −0.680869 | − | 0.732405i | \(-0.738398\pi\) |
0.981332 | − | 0.192323i | \(-0.0616021\pi\) | |||||||
\(758\) | − | 48.8782i | − | 1.77534i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −40.9726 | − | 29.7683i | −1.48331 | − | 1.07769i | ||||
\(764\) | 2.88036 | + | 8.86485i | 0.104208 | + | 0.320719i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.24351 | + | 3.00340i | 0.332681 | + | 0.108095i | ||||
\(773\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(774\) | 36.8457 | + | 26.7700i | 1.32439 | + | 0.962228i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.7340 | + | 46.4309i | 1.20942 | + | 1.66463i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.6580 | + | 9.62648i | 1.13281 | + | 0.344462i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −26.3496 | + | 19.1441i | −0.941055 | + | 0.683717i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(788\) | 1.62274 | − | 2.23350i | 0.0578076 | − | 0.0795653i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 51.6240i | 1.83554i | ||||||||
\(792\) | 7.14263 | − | 23.4896i | 0.253802 | − | 0.834665i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 6.72805 | + | 9.26036i | 0.237872 | + | 0.327403i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 23.3918i | − | 0.825993i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.3285 | + | 3.68085i | −0.398289 | + | 0.129412i | −0.501311 | − | 0.865267i | \(-0.667149\pi\) |
0.103022 | + | 0.994679i | \(0.467149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(812\) | −0.459524 | + | 1.41427i | −0.0161261 | + | 0.0496311i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.03536 | + | 0.133451i | −0.246589 | + | 0.00467745i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.1027 | − | 42.8092i | 1.08549 | − | 1.49405i | 0.232162 | − | 0.972677i | \(-0.425420\pi\) |
0.853329 | − | 0.521373i | \(-0.174580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.9405 | + | 33.6713i | −0.381361 | + | 1.17371i | 0.557725 | + | 0.830026i | \(0.311674\pi\) |
−0.939086 | + | 0.343683i | \(0.888326\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.2276 | + | 11.4461i | 1.22498 | + | 0.398022i | 0.848895 | − | 0.528562i | \(-0.177268\pi\) |
0.376090 | + | 0.926583i | \(0.377268\pi\) | |||||||
\(828\) | 9.55378 | − | 6.94123i | 0.332017 | − | 0.241224i | ||||
\(829\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.38301 | + | 25.8002i | 0.289069 | + | 0.889664i | ||||
\(842\) | 58.6183 | − | 19.0462i | 2.02012 | − | 0.656377i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.87140 | − | 9.45767i | −0.236523 | − | 0.325546i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.0000 | + | 7.93725i | 0.962091 | + | 0.272727i | ||||
\(848\) | −61.2090 | −2.10193 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.5930 | + | 7.69629i | 0.363124 | + | 0.263825i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.2280 | − | 37.6339i | 0.417945 | − | 1.28630i | ||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.26024 | − | 2.36871i | −0.111044 | − | 0.0806784i | ||||
\(863\) | 2.47214 | + | 7.60845i | 0.0841525 | + | 0.258995i | 0.984275 | − | 0.176642i | \(-0.0565234\pi\) |
−0.900123 | + | 0.435636i | \(0.856523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.1088 | − | 25.0279i | 1.12314 | − | 0.849013i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 38.2124 | − | 27.7630i | 1.29404 | − | 0.940173i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.1841 | + | 30.5338i | 0.749104 | + | 1.03105i | 0.998043 | + | 0.0625337i | \(0.0199181\pi\) |
−0.248939 | + | 0.968519i | \(0.580082\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −31.0103 | − | 10.0758i | −1.04417 | − | 0.339271i | ||||
\(883\) | 9.70820 | − | 7.05342i | 0.326707 | − | 0.237367i | −0.412325 | − | 0.911037i | \(-0.635283\pi\) |
0.739032 | + | 0.673670i | \(0.235283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −42.8935 | + | 13.9370i | −1.44104 | + | 0.468221i | ||||
\(887\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.1890 | + | 55.9800i | −0.610040 | + | 1.87751i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.2086 | − | 9.76078i | 0.945025 | − | 0.326998i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −11.0441 | − | 33.9902i | −0.368957 | − | 1.13553i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21.2317 | + | 29.2229i | −0.708511 | + | 0.975182i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.90413 | + | 5.86030i | −0.0634708 | + | 0.195343i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −45.7899 | − | 14.8780i | −1.52295 | − | 0.494836i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.28462 | − | 22.4198i | −0.241882 | − | 0.744436i | −0.996134 | − | 0.0878507i | \(-0.972000\pi\) |
0.754252 | − | 0.656585i | \(-0.228000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.94427 | + | 15.2169i | −0.163811 | + | 0.504159i | −0.998947 | − | 0.0458855i | \(-0.985389\pi\) |
0.835136 | + | 0.550044i | \(0.185389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −58.6507 | −1.93999 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54.3023 | + | 17.6439i | −1.79127 | + | 0.582019i | −0.999582 | − | 0.0289084i | \(-0.990797\pi\) |
−0.791687 | + | 0.610927i | \(0.790797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.83216 | −0.224640 | ||||||||
\(926\) | −4.04149 | − | 1.31316i | −0.132811 | − | 0.0431531i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.53403 | − | 1.84108i | −0.0831838 | − | 0.0604365i | ||||
\(929\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.11069 | − | 7.03426i | −0.167406 | − | 0.230415i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(938\) | 54.2836 | − | 39.4394i | 1.77242 | − | 1.28774i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −30.3626 | − | 40.1659i | −0.987172 | − | 1.30591i | ||||
\(947\) | −20.0000 | −0.649913 | −0.324956 | − | 0.945729i | \(-0.605350\pi\) | ||||
−0.324956 | + | 0.945729i | \(0.605350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.1035 | + | 41.4340i | −0.975149 | + | 1.34218i | −0.0357473 | + | 0.999361i | \(0.511381\pi\) |
−0.939402 | + | 0.342817i | \(0.888619\pi\) | |||||||
\(954\) | −36.0178 | − | 49.5743i | −1.16612 | − | 1.60503i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 2.89242i | − | 0.0935476i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −51.6619 | − | 16.7860i | −1.66825 | − | 0.542047i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0795 | − | 18.2213i | −0.809017 | − | 0.587785i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 45.7552 | − | 14.8668i | 1.47444 | − | 0.479075i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 15.0168i | − | 0.482909i | −0.970412 | − | 0.241454i | \(-0.922376\pi\) | ||
0.970412 | − | 0.241454i | \(-0.0776244\pi\) | |||||||
\(968\) | −15.1099 | + | 22.5482i | −0.485649 | + | 0.724725i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −62.9716 | + | 20.4607i | −2.01774 | + | 0.655603i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.81100 | − | 11.7290i | 0.121925 | − | 0.375245i | −0.871404 | − | 0.490567i | \(-0.836790\pi\) |
0.993328 | + | 0.115321i | \(0.0367898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 54.6153 | + | 17.7456i | 1.74373 | + | 0.566573i | ||||
\(982\) | −6.64686 | + | 4.82923i | −0.212110 | + | 0.154107i | ||||
\(983\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 93.6921i | 2.97923i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.0000 | 0.762385 | 0.381193 | − | 0.924496i | \(-0.375513\pi\) | ||||
0.381193 | + | 0.924496i | \(0.375513\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 33.1572 | + | 24.0901i | 1.05168 | + | 0.764091i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(998\) | 33.1171 | + | 45.5817i | 1.04830 | + | 1.44287i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))