Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,2,Mod(28,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.b (of order \(2\), degree \(1\), 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: | \(0.231566165862\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-5}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 28.2 | ||
Root | \(2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.28 |
Dual form | 29.2.b.a.28.1 |
$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.23607i | 1.58114i | 0.612372 | + | 0.790569i | \(0.290215\pi\) | ||||
−0.612372 | + | 0.790569i | \(0.709785\pi\) | |||||||
\(3\) | − | 2.23607i | − | 1.29099i | −0.763763 | − | 0.645497i | \(-0.776650\pi\) | ||
0.763763 | − | 0.645497i | \(-0.223350\pi\) | |||||||
\(4\) | −3.00000 | −1.50000 | ||||||||
\(5\) | −3.00000 | −1.34164 | −0.670820 | − | 0.741620i | \(-0.734058\pi\) | ||||
−0.670820 | + | 0.741620i | \(0.734058\pi\) | |||||||
\(6\) | 5.00000 | 2.04124 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | − | 2.23607i | − | 0.790569i | ||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | − | 6.70820i | − | 2.12132i | ||||||
\(11\) | 2.23607i | 0.674200i | 0.941469 | + | 0.337100i | \(0.109446\pi\) | ||||
−0.941469 | + | 0.337100i | \(0.890554\pi\) | |||||||
\(12\) | 6.70820i | 1.93649i | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 4.47214i | 1.19523i | ||||||||
\(15\) | 6.70820i | 1.73205i | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | − | 4.47214i | − | 1.08465i | −0.840168 | − | 0.542326i | \(-0.817544\pi\) | ||
0.840168 | − | 0.542326i | \(-0.182456\pi\) | |||||||
\(18\) | − | 4.47214i | − | 1.05409i | ||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 9.00000 | 2.01246 | ||||||||
\(21\) | − | 4.47214i | − | 0.975900i | ||||||
\(22\) | −5.00000 | −1.06600 | ||||||||
\(23\) | 6.00000 | 1.25109 | 0.625543 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625543 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(24\) | −5.00000 | −1.02062 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | − | 2.23607i | − | 0.438529i | ||||||
\(27\) | − | 2.23607i | − | 0.430331i | ||||||
\(28\) | −6.00000 | −1.13389 | ||||||||
\(29\) | −3.00000 | + | 4.47214i | −0.557086 | + | 0.830455i | ||||
\(30\) | −15.0000 | −2.73861 | ||||||||
\(31\) | 6.70820i | 1.20483i | 0.798183 | + | 0.602414i | \(0.205795\pi\) | ||||
−0.798183 | + | 0.602414i | \(0.794205\pi\) | |||||||
\(32\) | − | 6.70820i | − | 1.18585i | ||||||
\(33\) | 5.00000 | 0.870388 | ||||||||
\(34\) | 10.0000 | 1.71499 | ||||||||
\(35\) | −6.00000 | −1.01419 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.23607i | 0.358057i | ||||||||
\(40\) | 6.70820i | 1.06066i | ||||||||
\(41\) | − | 4.47214i | − | 0.698430i | −0.937043 | − | 0.349215i | \(-0.886448\pi\) | ||
0.937043 | − | 0.349215i | \(-0.113552\pi\) | |||||||
\(42\) | 10.0000 | 1.54303 | ||||||||
\(43\) | − | 6.70820i | − | 1.02299i | −0.859286 | − | 0.511496i | \(-0.829092\pi\) | ||
0.859286 | − | 0.511496i | \(-0.170908\pi\) | |||||||
\(44\) | − | 6.70820i | − | 1.01130i | ||||||
\(45\) | 6.00000 | 0.894427 | ||||||||
\(46\) | 13.4164i | 1.97814i | ||||||||
\(47\) | 2.23607i | 0.326164i | 0.986613 | + | 0.163082i | \(0.0521435\pi\) | ||||
−0.986613 | + | 0.163082i | \(0.947856\pi\) | |||||||
\(48\) | 2.23607i | 0.322749i | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 8.94427i | 1.26491i | ||||||||
\(51\) | −10.0000 | −1.40028 | ||||||||
\(52\) | 3.00000 | 0.416025 | ||||||||
\(53\) | −9.00000 | −1.23625 | −0.618123 | − | 0.786082i | \(-0.712106\pi\) | ||||
−0.618123 | + | 0.786082i | \(0.712106\pi\) | |||||||
\(54\) | 5.00000 | 0.680414 | ||||||||
\(55\) | − | 6.70820i | − | 0.904534i | ||||||
\(56\) | − | 4.47214i | − | 0.597614i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.0000 | − | 6.70820i | −1.31306 | − | 0.880830i | ||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | − | 20.1246i | − | 2.59808i | ||||||
\(61\) | 13.4164i | 1.71780i | 0.512148 | + | 0.858898i | \(0.328850\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | −15.0000 | −1.90500 | ||||||||
\(63\) | −4.00000 | −0.503953 | ||||||||
\(64\) | 13.0000 | 1.62500 | ||||||||
\(65\) | 3.00000 | 0.372104 | ||||||||
\(66\) | 11.1803i | 1.37620i | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 13.4164i | 1.62698i | ||||||||
\(69\) | − | 13.4164i | − | 1.61515i | ||||||
\(70\) | − | 13.4164i | − | 1.60357i | ||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 4.47214i | 0.527046i | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 8.94427i | − | 1.03280i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.47214i | 0.509647i | ||||||||
\(78\) | −5.00000 | −0.566139 | ||||||||
\(79\) | − | 6.70820i | − | 0.754732i | −0.926064 | − | 0.377366i | \(-0.876830\pi\) | ||
0.926064 | − | 0.377366i | \(-0.123170\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 10.0000 | 1.10432 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 13.4164i | 1.46385i | ||||||||
\(85\) | 13.4164i | 1.45521i | ||||||||
\(86\) | 15.0000 | 1.61749 | ||||||||
\(87\) | 10.0000 | + | 6.70820i | 1.07211 | + | 0.719195i | ||||
\(88\) | 5.00000 | 0.533002 | ||||||||
\(89\) | − | 4.47214i | − | 0.474045i | −0.971504 | − | 0.237023i | \(-0.923828\pi\) | ||
0.971504 | − | 0.237023i | \(-0.0761716\pi\) | |||||||
\(90\) | 13.4164i | 1.41421i | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | −18.0000 | −1.87663 | ||||||||
\(93\) | 15.0000 | 1.55543 | ||||||||
\(94\) | −5.00000 | −0.515711 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −15.0000 | −1.53093 | ||||||||
\(97\) | 13.4164i | 1.36223i | 0.732177 | + | 0.681115i | \(0.238505\pi\) | ||||
−0.732177 | + | 0.681115i | \(0.761495\pi\) | |||||||
\(98\) | − | 6.70820i | − | 0.677631i | ||||||
\(99\) | − | 4.47214i | − | 0.449467i | ||||||
\(100\) | −12.0000 | −1.20000 | ||||||||
\(101\) | − | 17.8885i | − | 1.77998i | −0.455983 | − | 0.889988i | \(-0.650712\pi\) | ||
0.455983 | − | 0.889988i | \(-0.349288\pi\) | |||||||
\(102\) | − | 22.3607i | − | 2.21404i | ||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 2.23607i | 0.219265i | ||||||||
\(105\) | 13.4164i | 1.30931i | ||||||||
\(106\) | − | 20.1246i | − | 1.95468i | ||||||
\(107\) | 18.0000 | 1.74013 | 0.870063 | − | 0.492941i | \(-0.164078\pi\) | ||||
0.870063 | + | 0.492941i | \(0.164078\pi\) | |||||||
\(108\) | 6.70820i | 0.645497i | ||||||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | 15.0000 | 1.43019 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.00000 | −0.188982 | ||||||||
\(113\) | 8.94427i | 0.841406i | 0.907198 | + | 0.420703i | \(0.138217\pi\) | ||||
−0.907198 | + | 0.420703i | \(0.861783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.0000 | −1.67851 | ||||||||
\(116\) | 9.00000 | − | 13.4164i | 0.835629 | − | 1.24568i | ||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 13.4164i | 1.23508i | ||||||||
\(119\) | − | 8.94427i | − | 0.819920i | ||||||
\(120\) | 15.0000 | 1.36931 | ||||||||
\(121\) | 6.00000 | 0.545455 | ||||||||
\(122\) | −30.0000 | −2.71607 | ||||||||
\(123\) | −10.0000 | −0.901670 | ||||||||
\(124\) | − | 20.1246i | − | 1.80724i | ||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | − | 8.94427i | − | 0.796819i | ||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 15.6525i | 1.38350i | ||||||||
\(129\) | −15.0000 | −1.32068 | ||||||||
\(130\) | 6.70820i | 0.588348i | ||||||||
\(131\) | 8.94427i | 0.781465i | 0.920504 | + | 0.390732i | \(0.127778\pi\) | ||||
−0.920504 | + | 0.390732i | \(0.872222\pi\) | |||||||
\(132\) | −15.0000 | −1.30558 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 17.8885i | 1.54533i | ||||||||
\(135\) | 6.70820i | 0.577350i | ||||||||
\(136\) | −10.0000 | −0.857493 | ||||||||
\(137\) | 8.94427i | 0.764161i | 0.924129 | + | 0.382080i | \(0.124792\pi\) | ||||
−0.924129 | + | 0.382080i | \(0.875208\pi\) | |||||||
\(138\) | 30.0000 | 2.55377 | ||||||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | 18.0000 | 1.52128 | ||||||||
\(141\) | 5.00000 | 0.421076 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2.23607i | − | 0.186989i | ||||||
\(144\) | 2.00000 | 0.166667 | ||||||||
\(145\) | 9.00000 | − | 13.4164i | 0.747409 | − | 1.11417i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.70820i | 0.553283i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.0000 | 1.22885 | 0.614424 | − | 0.788976i | \(-0.289388\pi\) | ||||
0.614424 | + | 0.788976i | \(0.289388\pi\) | |||||||
\(150\) | 20.0000 | 1.63299 | ||||||||
\(151\) | −10.0000 | −0.813788 | −0.406894 | − | 0.913475i | \(-0.633388\pi\) | ||||
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.94427i | 0.723102i | ||||||||
\(154\) | −10.0000 | −0.805823 | ||||||||
\(155\) | − | 20.1246i | − | 1.61645i | ||||||
\(156\) | − | 6.70820i | − | 0.537086i | ||||||
\(157\) | − | 13.4164i | − | 1.07075i | −0.844616 | − | 0.535373i | \(-0.820171\pi\) | ||
0.844616 | − | 0.535373i | \(-0.179829\pi\) | |||||||
\(158\) | 15.0000 | 1.19334 | ||||||||
\(159\) | 20.1246i | 1.59599i | ||||||||
\(160\) | 20.1246i | 1.59099i | ||||||||
\(161\) | 12.0000 | 0.945732 | ||||||||
\(162\) | − | 24.5967i | − | 1.93250i | ||||||
\(163\) | − | 20.1246i | − | 1.57628i | −0.615495 | − | 0.788141i | \(-0.711044\pi\) | ||
0.615495 | − | 0.788141i | \(-0.288956\pi\) | |||||||
\(164\) | 13.4164i | 1.04765i | ||||||||
\(165\) | −15.0000 | −1.16775 | ||||||||
\(166\) | − | 13.4164i | − | 1.04132i | ||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | −10.0000 | −0.771517 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | −30.0000 | −2.30089 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 20.1246i | 1.53449i | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | −15.0000 | + | 22.3607i | −1.13715 | + | 1.69516i | ||||
\(175\) | 8.00000 | 0.604743 | ||||||||
\(176\) | − | 2.23607i | − | 0.168550i | ||||||
\(177\) | − | 13.4164i | − | 1.00844i | ||||||
\(178\) | 10.0000 | 0.749532 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | −18.0000 | −1.34164 | ||||||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | − | 4.47214i | − | 0.331497i | ||||||
\(183\) | 30.0000 | 2.21766 | ||||||||
\(184\) | − | 13.4164i | − | 0.989071i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 33.5410i | 2.45935i | ||||||||
\(187\) | 10.0000 | 0.731272 | ||||||||
\(188\) | − | 6.70820i | − | 0.489246i | ||||||
\(189\) | − | 4.47214i | − | 0.325300i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.94427i | 0.647185i | 0.946197 | + | 0.323592i | \(0.104891\pi\) | ||||
−0.946197 | + | 0.323592i | \(0.895109\pi\) | |||||||
\(192\) | − | 29.0689i | − | 2.09787i | ||||||
\(193\) | − | 13.4164i | − | 0.965734i | −0.875694 | − | 0.482867i | \(-0.839595\pi\) | ||
0.875694 | − | 0.482867i | \(-0.160405\pi\) | |||||||
\(194\) | −30.0000 | −2.15387 | ||||||||
\(195\) | − | 6.70820i | − | 0.480384i | ||||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 10.0000 | 0.710669 | ||||||||
\(199\) | 14.0000 | 0.992434 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(200\) | − | 8.94427i | − | 0.632456i | ||||||
\(201\) | − | 17.8885i | − | 1.26176i | ||||||
\(202\) | 40.0000 | 2.81439 | ||||||||
\(203\) | −6.00000 | + | 8.94427i | −0.421117 | + | 0.627765i | ||||
\(204\) | 30.0000 | 2.10042 | ||||||||
\(205\) | 13.4164i | 0.937043i | ||||||||
\(206\) | − | 8.94427i | − | 0.623177i | ||||||
\(207\) | −12.0000 | −0.834058 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −30.0000 | −2.07020 | ||||||||
\(211\) | 6.70820i | 0.461812i | 0.972976 | + | 0.230906i | \(0.0741690\pi\) | ||||
−0.972976 | + | 0.230906i | \(0.925831\pi\) | |||||||
\(212\) | 27.0000 | 1.85437 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 40.2492i | 2.75138i | ||||||||
\(215\) | 20.1246i | 1.37249i | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 13.4164i | 0.910765i | ||||||||
\(218\) | 11.1803i | 0.757228i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 20.1246i | 1.35680i | ||||||||
\(221\) | 4.47214i | 0.300828i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | − | 13.4164i | − | 0.896421i | ||||||
\(225\) | −8.00000 | −0.533333 | ||||||||
\(226\) | −20.0000 | −1.33038 | ||||||||
\(227\) | 12.0000 | 0.796468 | 0.398234 | − | 0.917284i | \(-0.369623\pi\) | ||||
0.398234 | + | 0.917284i | \(0.369623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.4164i | − | 0.886581i | −0.896378 | − | 0.443291i | \(-0.853811\pi\) | ||
0.896378 | − | 0.443291i | \(-0.146189\pi\) | |||||||
\(230\) | − | 40.2492i | − | 2.65396i | ||||||
\(231\) | 10.0000 | 0.657952 | ||||||||
\(232\) | 10.0000 | + | 6.70820i | 0.656532 | + | 0.440415i | ||||
\(233\) | −9.00000 | −0.589610 | −0.294805 | − | 0.955557i | \(-0.595255\pi\) | ||||
−0.294805 | + | 0.955557i | \(0.595255\pi\) | |||||||
\(234\) | 4.47214i | 0.292353i | ||||||||
\(235\) | − | 6.70820i | − | 0.437595i | ||||||
\(236\) | −18.0000 | −1.17170 | ||||||||
\(237\) | −15.0000 | −0.974355 | ||||||||
\(238\) | 20.0000 | 1.29641 | ||||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | − | 6.70820i | − | 0.433013i | ||||||
\(241\) | −25.0000 | −1.61039 | −0.805196 | − | 0.593009i | \(-0.797940\pi\) | ||||
−0.805196 | + | 0.593009i | \(0.797940\pi\) | |||||||
\(242\) | 13.4164i | 0.862439i | ||||||||
\(243\) | 17.8885i | 1.14755i | ||||||||
\(244\) | − | 40.2492i | − | 2.57669i | ||||||
\(245\) | 9.00000 | 0.574989 | ||||||||
\(246\) | − | 22.3607i | − | 1.42566i | ||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 15.0000 | 0.952501 | ||||||||
\(249\) | 13.4164i | 0.850230i | ||||||||
\(250\) | 6.70820i | 0.424264i | ||||||||
\(251\) | 15.6525i | 0.987976i | 0.869469 | + | 0.493988i | \(0.164461\pi\) | ||||
−0.869469 | + | 0.493988i | \(0.835539\pi\) | |||||||
\(252\) | 12.0000 | 0.755929 | ||||||||
\(253\) | 13.4164i | 0.843482i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 30.0000 | 1.87867 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | −3.00000 | −0.187135 | −0.0935674 | − | 0.995613i | \(-0.529827\pi\) | ||||
−0.0935674 | + | 0.995613i | \(0.529827\pi\) | |||||||
\(258\) | − | 33.5410i | − | 2.08817i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.00000 | −0.558156 | ||||||||
\(261\) | 6.00000 | − | 8.94427i | 0.371391 | − | 0.553637i | ||||
\(262\) | −20.0000 | −1.23560 | ||||||||
\(263\) | − | 11.1803i | − | 0.689409i | −0.938711 | − | 0.344705i | \(-0.887979\pi\) | ||
0.938711 | − | 0.344705i | \(-0.112021\pi\) | |||||||
\(264\) | − | 11.1803i | − | 0.688102i | ||||||
\(265\) | 27.0000 | 1.65860 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.0000 | −0.611990 | ||||||||
\(268\) | −24.0000 | −1.46603 | ||||||||
\(269\) | − | 4.47214i | − | 0.272671i | −0.990663 | − | 0.136335i | \(-0.956467\pi\) | ||
0.990663 | − | 0.136335i | \(-0.0435325\pi\) | |||||||
\(270\) | −15.0000 | −0.912871 | ||||||||
\(271\) | − | 20.1246i | − | 1.22248i | −0.791444 | − | 0.611242i | \(-0.790670\pi\) | ||
0.791444 | − | 0.611242i | \(-0.209330\pi\) | |||||||
\(272\) | 4.47214i | 0.271163i | ||||||||
\(273\) | 4.47214i | 0.270666i | ||||||||
\(274\) | −20.0000 | −1.20824 | ||||||||
\(275\) | 8.94427i | 0.539360i | ||||||||
\(276\) | 40.2492i | 2.42272i | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | − | 22.3607i | − | 1.34110i | ||||||
\(279\) | − | 13.4164i | − | 0.803219i | ||||||
\(280\) | 13.4164i | 0.801784i | ||||||||
\(281\) | 3.00000 | 0.178965 | 0.0894825 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894825 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(282\) | 11.1803i | 0.665780i | ||||||||
\(283\) | 14.0000 | 0.832214 | 0.416107 | − | 0.909316i | \(-0.363394\pi\) | ||||
0.416107 | + | 0.909316i | \(0.363394\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.00000 | 0.295656 | ||||||||
\(287\) | − | 8.94427i | − | 0.527964i | ||||||
\(288\) | 13.4164i | 0.790569i | ||||||||
\(289\) | −3.00000 | −0.176471 | ||||||||
\(290\) | 30.0000 | + | 20.1246i | 1.76166 | + | 1.18176i | ||||
\(291\) | 30.0000 | 1.75863 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.94427i | 0.522530i | 0.965267 | + | 0.261265i | \(0.0841396\pi\) | ||||
−0.965267 | + | 0.261265i | \(0.915860\pi\) | |||||||
\(294\) | −15.0000 | −0.874818 | ||||||||
\(295\) | −18.0000 | −1.04800 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.00000 | 0.290129 | ||||||||
\(298\) | 33.5410i | 1.94298i | ||||||||
\(299\) | −6.00000 | −0.346989 | ||||||||
\(300\) | 26.8328i | 1.54919i | ||||||||
\(301\) | − | 13.4164i | − | 0.773309i | ||||||
\(302\) | − | 22.3607i | − | 1.28671i | ||||||
\(303\) | −40.0000 | −2.29794 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 40.2492i | − | 2.30466i | ||||||
\(306\) | −20.0000 | −1.14332 | ||||||||
\(307\) | 20.1246i | 1.14857i | 0.818655 | + | 0.574286i | \(0.194720\pi\) | ||||
−0.818655 | + | 0.574286i | \(0.805280\pi\) | |||||||
\(308\) | − | 13.4164i | − | 0.764471i | ||||||
\(309\) | 8.94427i | 0.508822i | ||||||||
\(310\) | 45.0000 | 2.55583 | ||||||||
\(311\) | 8.94427i | 0.507183i | 0.967311 | + | 0.253592i | \(0.0816119\pi\) | ||||
−0.967311 | + | 0.253592i | \(0.918388\pi\) | |||||||
\(312\) | 5.00000 | 0.283069 | ||||||||
\(313\) | 29.0000 | 1.63918 | 0.819588 | − | 0.572953i | \(-0.194202\pi\) | ||||
0.819588 | + | 0.572953i | \(0.194202\pi\) | |||||||
\(314\) | 30.0000 | 1.69300 | ||||||||
\(315\) | 12.0000 | 0.676123 | ||||||||
\(316\) | 20.1246i | 1.13210i | ||||||||
\(317\) | 22.3607i | 1.25590i | 0.778253 | + | 0.627950i | \(0.216106\pi\) | ||||
−0.778253 | + | 0.627950i | \(0.783894\pi\) | |||||||
\(318\) | −45.0000 | −2.52347 | ||||||||
\(319\) | −10.0000 | − | 6.70820i | −0.559893 | − | 0.375587i | ||||
\(320\) | −39.0000 | −2.18017 | ||||||||
\(321\) | − | 40.2492i | − | 2.24649i | ||||||
\(322\) | 26.8328i | 1.49533i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 33.0000 | 1.83333 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 45.0000 | 2.49232 | ||||||||
\(327\) | − | 11.1803i | − | 0.618274i | ||||||
\(328\) | −10.0000 | −0.552158 | ||||||||
\(329\) | 4.47214i | 0.246557i | ||||||||
\(330\) | − | 33.5410i | − | 1.84637i | ||||||
\(331\) | 33.5410i | 1.84358i | 0.387688 | + | 0.921791i | \(0.373274\pi\) | ||||
−0.387688 | + | 0.921791i | \(0.626726\pi\) | |||||||
\(332\) | 18.0000 | 0.987878 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 26.8328i | − | 1.46823i | ||||||
\(335\) | −24.0000 | −1.31126 | ||||||||
\(336\) | 4.47214i | 0.243975i | ||||||||
\(337\) | − | 13.4164i | − | 0.730838i | −0.930843 | − | 0.365419i | \(-0.880926\pi\) | ||
0.930843 | − | 0.365419i | \(-0.119074\pi\) | |||||||
\(338\) | − | 26.8328i | − | 1.45951i | ||||||
\(339\) | 20.0000 | 1.08625 | ||||||||
\(340\) | − | 40.2492i | − | 2.18282i | ||||||
\(341\) | −15.0000 | −0.812296 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | −15.0000 | −0.808746 | ||||||||
\(345\) | 40.2492i | 2.16695i | ||||||||
\(346\) | − | 13.4164i | − | 0.721271i | ||||||
\(347\) | −12.0000 | −0.644194 | −0.322097 | − | 0.946707i | \(-0.604388\pi\) | ||||
−0.322097 | + | 0.946707i | \(0.604388\pi\) | |||||||
\(348\) | −30.0000 | − | 20.1246i | −1.60817 | − | 1.07879i | ||||
\(349\) | −1.00000 | −0.0535288 | −0.0267644 | − | 0.999642i | \(-0.508520\pi\) | ||||
−0.0267644 | + | 0.999642i | \(0.508520\pi\) | |||||||
\(350\) | 17.8885i | 0.956183i | ||||||||
\(351\) | 2.23607i | 0.119352i | ||||||||
\(352\) | 15.0000 | 0.799503 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 30.0000 | 1.59448 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.4164i | 0.711068i | ||||||||
\(357\) | −20.0000 | −1.05851 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.23607i | 0.118015i | 0.998258 | + | 0.0590076i | \(0.0187936\pi\) | ||||
−0.998258 | + | 0.0590076i | \(0.981206\pi\) | |||||||
\(360\) | − | 13.4164i | − | 0.707107i | ||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 11.1803i | 0.587626i | ||||||||
\(363\) | − | 13.4164i | − | 0.704179i | ||||||
\(364\) | 6.00000 | 0.314485 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 67.0820i | 3.50643i | ||||||||
\(367\) | − | 26.8328i | − | 1.40066i | −0.713818 | − | 0.700331i | \(-0.753036\pi\) | ||
0.713818 | − | 0.700331i | \(-0.246964\pi\) | |||||||
\(368\) | −6.00000 | −0.312772 | ||||||||
\(369\) | 8.94427i | 0.465620i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.0000 | −0.934513 | ||||||||
\(372\) | −45.0000 | −2.33314 | ||||||||
\(373\) | −31.0000 | −1.60512 | −0.802560 | − | 0.596572i | \(-0.796529\pi\) | ||||
−0.802560 | + | 0.596572i | \(0.796529\pi\) | |||||||
\(374\) | 22.3607i | 1.15624i | ||||||||
\(375\) | − | 6.70820i | − | 0.346410i | ||||||
\(376\) | 5.00000 | 0.257855 | ||||||||
\(377\) | 3.00000 | − | 4.47214i | 0.154508 | − | 0.230327i | ||||
\(378\) | 10.0000 | 0.514344 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.0000 | −1.02329 | ||||||||
\(383\) | 6.00000 | 0.306586 | 0.153293 | − | 0.988181i | \(-0.451012\pi\) | ||||
0.153293 | + | 0.988181i | \(0.451012\pi\) | |||||||
\(384\) | 35.0000 | 1.78609 | ||||||||
\(385\) | − | 13.4164i | − | 0.683763i | ||||||
\(386\) | 30.0000 | 1.52696 | ||||||||
\(387\) | 13.4164i | 0.681994i | ||||||||
\(388\) | − | 40.2492i | − | 2.04334i | ||||||
\(389\) | − | 17.8885i | − | 0.906985i | −0.891260 | − | 0.453493i | \(-0.850178\pi\) | ||
0.891260 | − | 0.453493i | \(-0.149822\pi\) | |||||||
\(390\) | 15.0000 | 0.759555 | ||||||||
\(391\) | − | 26.8328i | − | 1.35699i | ||||||
\(392\) | 6.70820i | 0.338815i | ||||||||
\(393\) | 20.0000 | 1.00887 | ||||||||
\(394\) | − | 40.2492i | − | 2.02773i | ||||||
\(395\) | 20.1246i | 1.01258i | ||||||||
\(396\) | 13.4164i | 0.674200i | ||||||||
\(397\) | −7.00000 | −0.351320 | −0.175660 | − | 0.984451i | \(-0.556206\pi\) | ||||
−0.175660 | + | 0.984451i | \(0.556206\pi\) | |||||||
\(398\) | 31.3050i | 1.56918i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | 15.0000 | 0.749064 | 0.374532 | − | 0.927214i | \(-0.377803\pi\) | ||||
0.374532 | + | 0.927214i | \(0.377803\pi\) | |||||||
\(402\) | 40.0000 | 1.99502 | ||||||||
\(403\) | − | 6.70820i | − | 0.334159i | ||||||
\(404\) | 53.6656i | 2.66996i | ||||||||
\(405\) | 33.0000 | 1.63978 | ||||||||
\(406\) | −20.0000 | − | 13.4164i | −0.992583 | − | 0.665845i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 22.3607i | 1.10702i | ||||||||
\(409\) | 26.8328i | 1.32680i | 0.748266 | + | 0.663399i | \(0.230887\pi\) | ||||
−0.748266 | + | 0.663399i | \(0.769113\pi\) | |||||||
\(410\) | −30.0000 | −1.48159 | ||||||||
\(411\) | 20.0000 | 0.986527 | ||||||||
\(412\) | 12.0000 | 0.591198 | ||||||||
\(413\) | 12.0000 | 0.590481 | ||||||||
\(414\) | − | 26.8328i | − | 1.31876i | ||||||
\(415\) | 18.0000 | 0.883585 | ||||||||
\(416\) | 6.70820i | 0.328897i | ||||||||
\(417\) | 22.3607i | 1.09501i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000 | 1.17248 | 0.586238 | − | 0.810139i | \(-0.300608\pi\) | ||||
0.586238 | + | 0.810139i | \(0.300608\pi\) | |||||||
\(420\) | − | 40.2492i | − | 1.96396i | ||||||
\(421\) | 13.4164i | 0.653876i | 0.945046 | + | 0.326938i | \(0.106017\pi\) | ||||
−0.945046 | + | 0.326938i | \(0.893983\pi\) | |||||||
\(422\) | −15.0000 | −0.730189 | ||||||||
\(423\) | − | 4.47214i | − | 0.217443i | ||||||
\(424\) | 20.1246i | 0.977338i | ||||||||
\(425\) | − | 17.8885i | − | 0.867722i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.8328i | 1.29853i | ||||||||
\(428\) | −54.0000 | −2.61019 | ||||||||
\(429\) | −5.00000 | −0.241402 | ||||||||
\(430\) | −45.0000 | −2.17009 | ||||||||
\(431\) | 18.0000 | 0.867029 | 0.433515 | − | 0.901146i | \(-0.357273\pi\) | ||||
0.433515 | + | 0.901146i | \(0.357273\pi\) | |||||||
\(432\) | 2.23607i | 0.107583i | ||||||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | −30.0000 | −1.44005 | ||||||||
\(435\) | −30.0000 | − | 20.1246i | −1.43839 | − | 0.964901i | ||||
\(436\) | −15.0000 | −0.718370 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.0000 | −1.62273 | −0.811366 | − | 0.584539i | \(-0.801275\pi\) | ||||
−0.811366 | + | 0.584539i | \(0.801275\pi\) | |||||||
\(440\) | −15.0000 | −0.715097 | ||||||||
\(441\) | 6.00000 | 0.285714 | ||||||||
\(442\) | −10.0000 | −0.475651 | ||||||||
\(443\) | − | 17.8885i | − | 0.849910i | −0.905214 | − | 0.424955i | \(-0.860290\pi\) | ||
0.905214 | − | 0.424955i | \(-0.139710\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.4164i | 0.635999i | ||||||||
\(446\) | − | 35.7771i | − | 1.69409i | ||||||
\(447\) | − | 33.5410i | − | 1.58644i | ||||||
\(448\) | 26.0000 | 1.22838 | ||||||||
\(449\) | 35.7771i | 1.68843i | 0.536009 | + | 0.844213i | \(0.319931\pi\) | ||||
−0.536009 | + | 0.844213i | \(0.680069\pi\) | |||||||
\(450\) | − | 17.8885i | − | 0.843274i | ||||||
\(451\) | 10.0000 | 0.470882 | ||||||||
\(452\) | − | 26.8328i | − | 1.26211i | ||||||
\(453\) | 22.3607i | 1.05060i | ||||||||
\(454\) | 26.8328i | 1.25933i | ||||||||
\(455\) | 6.00000 | 0.281284 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.00000 | 0.0935561 | 0.0467780 | − | 0.998905i | \(-0.485105\pi\) | ||||
0.0467780 | + | 0.998905i | \(0.485105\pi\) | |||||||
\(458\) | 30.0000 | 1.40181 | ||||||||
\(459\) | −10.0000 | −0.466760 | ||||||||
\(460\) | 54.0000 | 2.51776 | ||||||||
\(461\) | 8.94427i | 0.416576i | 0.978068 | + | 0.208288i | \(0.0667892\pi\) | ||||
−0.978068 | + | 0.208288i | \(0.933211\pi\) | |||||||
\(462\) | 22.3607i | 1.04031i | ||||||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | 3.00000 | − | 4.47214i | 0.139272 | − | 0.207614i | ||||
\(465\) | −45.0000 | −2.08683 | ||||||||
\(466\) | − | 20.1246i | − | 0.932255i | ||||||
\(467\) | 2.23607i | 0.103473i | 0.998661 | + | 0.0517364i | \(0.0164756\pi\) | ||||
−0.998661 | + | 0.0517364i | \(0.983524\pi\) | |||||||
\(468\) | −6.00000 | −0.277350 | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 15.0000 | 0.691898 | ||||||||
\(471\) | −30.0000 | −1.38233 | ||||||||
\(472\) | − | 13.4164i | − | 0.617540i | ||||||
\(473\) | 15.0000 | 0.689701 | ||||||||
\(474\) | − | 33.5410i | − | 1.54059i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 26.8328i | 1.22988i | ||||||||
\(477\) | 18.0000 | 0.824163 | ||||||||
\(478\) | 13.4164i | 0.613652i | ||||||||
\(479\) | − | 11.1803i | − | 0.510843i | −0.966830 | − | 0.255421i | \(-0.917786\pi\) | ||
0.966830 | − | 0.255421i | \(-0.0822142\pi\) | |||||||
\(480\) | 45.0000 | 2.05396 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 55.9017i | − | 2.54625i | ||||||
\(483\) | − | 26.8328i | − | 1.22094i | ||||||
\(484\) | −18.0000 | −0.818182 | ||||||||
\(485\) | − | 40.2492i | − | 1.82762i | ||||||
\(486\) | −40.0000 | −1.81444 | ||||||||
\(487\) | 2.00000 | 0.0906287 | 0.0453143 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453143 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(488\) | 30.0000 | 1.35804 | ||||||||
\(489\) | −45.0000 | −2.03497 | ||||||||
\(490\) | 20.1246i | 0.909137i | ||||||||
\(491\) | − | 24.5967i | − | 1.11004i | −0.831838 | − | 0.555018i | \(-0.812711\pi\) | ||
0.831838 | − | 0.555018i | \(-0.187289\pi\) | |||||||
\(492\) | 30.0000 | 1.35250 | ||||||||
\(493\) | 20.0000 | + | 13.4164i | 0.900755 | + | 0.604245i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.4164i | 0.603023i | ||||||||
\(496\) | − | 6.70820i | − | 0.301207i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −30.0000 | −1.34433 | ||||||||
\(499\) | −10.0000 | −0.447661 | −0.223831 | − | 0.974628i | \(-0.571856\pi\) | ||||
−0.223831 | + | 0.974628i | \(0.571856\pi\) | |||||||
\(500\) | −9.00000 | −0.402492 | ||||||||
\(501\) | 26.8328i | 1.19880i | ||||||||
\(502\) | −35.0000 | −1.56213 | ||||||||
\(503\) | 15.6525i | 0.697909i | 0.937140 | + | 0.348955i | \(0.113463\pi\) | ||||
−0.937140 | + | 0.348955i | \(0.886537\pi\) | |||||||
\(504\) | 8.94427i | 0.398410i | ||||||||
\(505\) | 53.6656i | 2.38809i | ||||||||
\(506\) | −30.0000 | −1.33366 | ||||||||
\(507\) | 26.8328i | 1.19169i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.0000 | 0.664863 | 0.332432 | − | 0.943127i | \(-0.392131\pi\) | ||||
0.332432 | + | 0.943127i | \(0.392131\pi\) | |||||||
\(510\) | 67.0820i | 2.97044i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.1803i | 0.494106i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 6.70820i | − | 0.295886i | ||||||
\(515\) | 12.0000 | 0.528783 | ||||||||
\(516\) | 45.0000 | 1.98101 | ||||||||
\(517\) | −5.00000 | −0.219900 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.4164i | 0.588915i | ||||||||
\(520\) | − | 6.70820i | − | 0.294174i | ||||||
\(521\) | −27.0000 | −1.18289 | −0.591446 | − | 0.806345i | \(-0.701443\pi\) | ||||
−0.591446 | + | 0.806345i | \(0.701443\pi\) | |||||||
\(522\) | 20.0000 | + | 13.4164i | 0.875376 | + | 0.587220i | ||||
\(523\) | −4.00000 | −0.174908 | −0.0874539 | − | 0.996169i | \(-0.527873\pi\) | ||||
−0.0874539 | + | 0.996169i | \(0.527873\pi\) | |||||||
\(524\) | − | 26.8328i | − | 1.17220i | ||||||
\(525\) | − | 17.8885i | − | 0.780720i | ||||||
\(526\) | 25.0000 | 1.09005 | ||||||||
\(527\) | 30.0000 | 1.30682 | ||||||||
\(528\) | −5.00000 | −0.217597 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 60.3738i | 2.62247i | ||||||||
\(531\) | −12.0000 | −0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.47214i | 0.193710i | ||||||||
\(534\) | − | 22.3607i | − | 0.967641i | ||||||
\(535\) | −54.0000 | −2.33462 | ||||||||
\(536\) | − | 17.8885i | − | 0.772667i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.0000 | 0.431131 | ||||||||
\(539\) | − | 6.70820i | − | 0.288943i | ||||||
\(540\) | − | 20.1246i | − | 0.866025i | ||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 45.0000 | 1.93292 | ||||||||
\(543\) | − | 11.1803i | − | 0.479794i | ||||||
\(544\) | −30.0000 | −1.28624 | ||||||||
\(545\) | −15.0000 | −0.642529 | ||||||||
\(546\) | −10.0000 | −0.427960 | ||||||||
\(547\) | 38.0000 | 1.62476 | 0.812381 | − | 0.583127i | \(-0.198171\pi\) | ||||
0.812381 | + | 0.583127i | \(0.198171\pi\) | |||||||
\(548\) | − | 26.8328i | − | 1.14624i | ||||||
\(549\) | − | 26.8328i | − | 1.14520i | ||||||
\(550\) | −20.0000 | −0.852803 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −30.0000 | −1.27688 | ||||||||
\(553\) | − | 13.4164i | − | 0.570524i | ||||||
\(554\) | 4.47214i | 0.190003i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 30.0000 | 1.27228 | ||||||||
\(557\) | 18.0000 | 0.762684 | 0.381342 | − | 0.924434i | \(-0.375462\pi\) | ||||
0.381342 | + | 0.924434i | \(0.375462\pi\) | |||||||
\(558\) | 30.0000 | 1.27000 | ||||||||
\(559\) | 6.70820i | 0.283727i | ||||||||
\(560\) | 6.00000 | 0.253546 | ||||||||
\(561\) | − | 22.3607i | − | 0.944069i | ||||||
\(562\) | 6.70820i | 0.282969i | ||||||||
\(563\) | − | 11.1803i | − | 0.471195i | −0.971851 | − | 0.235598i | \(-0.924295\pi\) | ||
0.971851 | − | 0.235598i | \(-0.0757047\pi\) | |||||||
\(564\) | −15.0000 | −0.631614 | ||||||||
\(565\) | − | 26.8328i | − | 1.12887i | ||||||
\(566\) | 31.3050i | 1.31585i | ||||||||
\(567\) | −22.0000 | −0.923913 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 17.8885i | − | 0.749927i | −0.927040 | − | 0.374963i | \(-0.877655\pi\) | ||
0.927040 | − | 0.374963i | \(-0.122345\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | 6.70820i | 0.280484i | ||||||||
\(573\) | 20.0000 | 0.835512 | ||||||||
\(574\) | 20.0000 | 0.834784 | ||||||||
\(575\) | 24.0000 | 1.00087 | ||||||||
\(576\) | −26.0000 | −1.08333 | ||||||||
\(577\) | − | 40.2492i | − | 1.67560i | −0.545979 | − | 0.837799i | \(-0.683842\pi\) | ||
0.545979 | − | 0.837799i | \(-0.316158\pi\) | |||||||
\(578\) | − | 6.70820i | − | 0.279024i | ||||||
\(579\) | −30.0000 | −1.24676 | ||||||||
\(580\) | −27.0000 | + | 40.2492i | −1.12111 | + | 1.67126i | ||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 67.0820i | 2.78064i | ||||||||
\(583\) | − | 20.1246i | − | 0.833476i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.00000 | −0.248069 | ||||||||
\(586\) | −20.0000 | −0.826192 | ||||||||
\(587\) | −42.0000 | −1.73353 | −0.866763 | − | 0.498721i | \(-0.833803\pi\) | ||||
−0.866763 | + | 0.498721i | \(0.833803\pi\) | |||||||
\(588\) | − | 20.1246i | − | 0.829925i | ||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | − | 40.2492i | − | 1.65703i | ||||||
\(591\) | 40.2492i | 1.65563i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.00000 | 0.369586 | 0.184793 | − | 0.982777i | \(-0.440839\pi\) | ||||
0.184793 | + | 0.982777i | \(0.440839\pi\) | |||||||
\(594\) | 11.1803i | 0.458735i | ||||||||
\(595\) | 26.8328i | 1.10004i | ||||||||
\(596\) | −45.0000 | −1.84327 | ||||||||
\(597\) | − | 31.3050i | − | 1.28123i | ||||||
\(598\) | − | 13.4164i | − | 0.548638i | ||||||
\(599\) | 29.0689i | 1.18772i | 0.804568 | + | 0.593861i | \(0.202397\pi\) | ||||
−0.804568 | + | 0.593861i | \(0.797603\pi\) | |||||||
\(600\) | −20.0000 | −0.816497 | ||||||||
\(601\) | 13.4164i | 0.547267i | 0.961834 | + | 0.273633i | \(0.0882255\pi\) | ||||
−0.961834 | + | 0.273633i | \(0.911775\pi\) | |||||||
\(602\) | 30.0000 | 1.22271 | ||||||||
\(603\) | −16.0000 | −0.651570 | ||||||||
\(604\) | 30.0000 | 1.22068 | ||||||||
\(605\) | −18.0000 | −0.731804 | ||||||||
\(606\) | − | 89.4427i | − | 3.63336i | ||||||
\(607\) | 6.70820i | 0.272278i | 0.990690 | + | 0.136139i | \(0.0434693\pi\) | ||||
−0.990690 | + | 0.136139i | \(0.956531\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.0000 | + | 13.4164i | 0.810441 | + | 0.543660i | ||||
\(610\) | 90.0000 | 3.64399 | ||||||||
\(611\) | − | 2.23607i | − | 0.0904616i | ||||||
\(612\) | − | 26.8328i | − | 1.08465i | ||||||
\(613\) | −31.0000 | −1.25208 | −0.626039 | − | 0.779792i | \(-0.715325\pi\) | ||||
−0.626039 | + | 0.779792i | \(0.715325\pi\) | |||||||
\(614\) | −45.0000 | −1.81605 | ||||||||
\(615\) | 30.0000 | 1.20972 | ||||||||
\(616\) | 10.0000 | 0.402911 | ||||||||
\(617\) | − | 44.7214i | − | 1.80041i | −0.435462 | − | 0.900207i | \(-0.643415\pi\) | ||
0.435462 | − | 0.900207i | \(-0.356585\pi\) | |||||||
\(618\) | −20.0000 | −0.804518 | ||||||||
\(619\) | 33.5410i | 1.34813i | 0.738673 | + | 0.674064i | \(0.235453\pi\) | ||||
−0.738673 | + | 0.674064i | \(0.764547\pi\) | |||||||
\(620\) | 60.3738i | 2.42467i | ||||||||
\(621\) | − | 13.4164i | − | 0.538382i | ||||||
\(622\) | −20.0000 | −0.801927 | ||||||||
\(623\) | − | 8.94427i | − | 0.358345i | ||||||
\(624\) | − | 2.23607i | − | 0.0895144i | ||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 64.8460i | 2.59177i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 40.2492i | 1.60612i | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 26.8328i | 1.06904i | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | −15.0000 | −0.596668 | ||||||||
\(633\) | 15.0000 | 0.596196 | ||||||||
\(634\) | −50.0000 | −1.98575 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 60.3738i | − | 2.39398i | ||||||
\(637\) | 3.00000 | 0.118864 | ||||||||
\(638\) | 15.0000 | − | 22.3607i | 0.593856 | − | 0.885268i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 46.9574i | − | 1.85616i | ||||||
\(641\) | 22.3607i | 0.883194i | 0.897214 | + | 0.441597i | \(0.145588\pi\) | ||||
−0.897214 | + | 0.441597i | \(0.854412\pi\) | |||||||
\(642\) | 90.0000 | 3.55202 | ||||||||
\(643\) | 26.0000 | 1.02534 | 0.512670 | − | 0.858586i | \(-0.328656\pi\) | ||||
0.512670 | + | 0.858586i | \(0.328656\pi\) | |||||||
\(644\) | −36.0000 | −1.41860 | ||||||||
\(645\) | 45.0000 | 1.77187 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.0000 | −0.707653 | −0.353827 | − | 0.935311i | \(-0.615120\pi\) | ||||
−0.353827 | + | 0.935311i | \(0.615120\pi\) | |||||||
\(648\) | 24.5967i | 0.966252i | ||||||||
\(649\) | 13.4164i | 0.526640i | ||||||||
\(650\) | − | 8.94427i | − | 0.350823i | ||||||
\(651\) | 30.0000 | 1.17579 | ||||||||
\(652\) | 60.3738i | 2.36442i | ||||||||
\(653\) | 49.1935i | 1.92509i | 0.271122 | + | 0.962545i | \(0.412605\pi\) | ||||
−0.271122 | + | 0.962545i | \(0.587395\pi\) | |||||||
\(654\) | 25.0000 | 0.977577 | ||||||||
\(655\) | − | 26.8328i | − | 1.04844i | ||||||
\(656\) | 4.47214i | 0.174608i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.0000 | −0.389841 | ||||||||
\(659\) | − | 38.0132i | − | 1.48078i | −0.672176 | − | 0.740391i | \(-0.734640\pi\) | ||
0.672176 | − | 0.740391i | \(-0.265360\pi\) | |||||||
\(660\) | 45.0000 | 1.75162 | ||||||||
\(661\) | −10.0000 | −0.388955 | −0.194477 | − | 0.980907i | \(-0.562301\pi\) | ||||
−0.194477 | + | 0.980907i | \(0.562301\pi\) | |||||||
\(662\) | −75.0000 | −2.91496 | ||||||||
\(663\) | 10.0000 | 0.388368 | ||||||||
\(664\) | 13.4164i | 0.520658i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.0000 | + | 26.8328i | −0.696963 | + | 1.03897i | ||||
\(668\) | 36.0000 | 1.39288 | ||||||||
\(669\) | 35.7771i | 1.38322i | ||||||||
\(670\) | − | 53.6656i | − | 2.07328i | ||||||
\(671\) | −30.0000 | −1.15814 | ||||||||
\(672\) | −30.0000 | −1.15728 | ||||||||
\(673\) | 11.0000 | 0.424019 | 0.212009 | − | 0.977268i | \(-0.431999\pi\) | ||||
0.212009 | + | 0.977268i | \(0.431999\pi\) | |||||||
\(674\) | 30.0000 | 1.15556 | ||||||||
\(675\) | − | 8.94427i | − | 0.344265i | ||||||
\(676\) | 36.0000 | 1.38462 | ||||||||
\(677\) | − | 17.8885i | − | 0.687513i | −0.939059 | − | 0.343756i | \(-0.888301\pi\) | ||
0.939059 | − | 0.343756i | \(-0.111699\pi\) | |||||||
\(678\) | 44.7214i | 1.71751i | ||||||||
\(679\) | 26.8328i | 1.02975i | ||||||||
\(680\) | 30.0000 | 1.15045 | ||||||||
\(681\) | − | 26.8328i | − | 1.02824i | ||||||
\(682\) | − | 33.5410i | − | 1.28435i | ||||||
\(683\) | −36.0000 | −1.37750 | −0.688751 | − | 0.724998i | \(-0.741841\pi\) | ||||
−0.688751 | + | 0.724998i | \(0.741841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 26.8328i | − | 1.02523i | ||||||
\(686\) | − | 44.7214i | − | 1.70747i | ||||||
\(687\) | −30.0000 | −1.14457 | ||||||||
\(688\) | 6.70820i | 0.255748i | ||||||||
\(689\) | 9.00000 | 0.342873 | ||||||||
\(690\) | −90.0000 | −3.42624 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | 18.0000 | 0.684257 | ||||||||
\(693\) | − | 8.94427i | − | 0.339765i | ||||||
\(694\) | − | 26.8328i | − | 1.01856i | ||||||
\(695\) | 30.0000 | 1.13796 | ||||||||
\(696\) | 15.0000 | − | 22.3607i | 0.568574 | − | 0.847579i | ||||
\(697\) | −20.0000 | −0.757554 | ||||||||
\(698\) | − | 2.23607i | − | 0.0846364i | ||||||
\(699\) | 20.1246i | 0.761183i | ||||||||
\(700\) | −24.0000 | −0.907115 | ||||||||
\(701\) | −45.0000 | −1.69963 | −0.849813 | − | 0.527084i | \(-0.823285\pi\) | ||||
−0.849813 | + | 0.527084i | \(0.823285\pi\) | |||||||
\(702\) | −5.00000 | −0.188713 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 29.0689i | 1.09557i | ||||||||
\(705\) | −15.0000 | −0.564933 | ||||||||
\(706\) | − | 13.4164i | − | 0.504933i | ||||||
\(707\) | − | 35.7771i | − | 1.34554i | ||||||
\(708\) | 40.2492i | 1.51266i | ||||||||
\(709\) | 35.0000 | 1.31445 | 0.657226 | − | 0.753693i | \(-0.271730\pi\) | ||||
0.657226 | + | 0.753693i | \(0.271730\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.4164i | 0.503155i | ||||||||
\(712\) | −10.0000 | −0.374766 | ||||||||
\(713\) | 40.2492i | 1.50735i | ||||||||
\(714\) | − | 44.7214i | − | 1.67365i | ||||||
\(715\) | 6.70820i | 0.250873i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 13.4164i | − | 0.501045i | ||||||
\(718\) | −5.00000 | −0.186598 | ||||||||
\(719\) | 36.0000 | 1.34257 | 0.671287 | − | 0.741198i | \(-0.265742\pi\) | ||||
0.671287 | + | 0.741198i | \(0.265742\pi\) | |||||||
\(720\) | −6.00000 | −0.223607 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 42.4853i | 1.58114i | ||||||||
\(723\) | 55.9017i | 2.07901i | ||||||||
\(724\) | −15.0000 | −0.557471 | ||||||||
\(725\) | −12.0000 | + | 17.8885i | −0.445669 | + | 0.664364i | ||||
\(726\) | 30.0000 | 1.11340 | ||||||||
\(727\) | − | 26.8328i | − | 0.995174i | −0.867414 | − | 0.497587i | \(-0.834220\pi\) | ||
0.867414 | − | 0.497587i | \(-0.165780\pi\) | |||||||
\(728\) | 4.47214i | 0.165748i | ||||||||
\(729\) | 7.00000 | 0.259259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.0000 | −1.10959 | ||||||||
\(732\) | −90.0000 | −3.32650 | ||||||||
\(733\) | 26.8328i | 0.991093i | 0.868582 | + | 0.495546i | \(0.165032\pi\) | ||||
−0.868582 | + | 0.495546i | \(0.834968\pi\) | |||||||
\(734\) | 60.0000 | 2.21464 | ||||||||
\(735\) | − | 20.1246i | − | 0.742307i | ||||||
\(736\) | − | 40.2492i | − | 1.48361i | ||||||
\(737\) | 17.8885i | 0.658933i | ||||||||
\(738\) | −20.0000 | −0.736210 | ||||||||
\(739\) | − | 20.1246i | − | 0.740296i | −0.928973 | − | 0.370148i | \(-0.879307\pi\) | ||
0.928973 | − | 0.370148i | \(-0.120693\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 40.2492i | − | 1.47760i | ||||||
\(743\) | 8.94427i | 0.328134i | 0.986449 | + | 0.164067i | \(0.0524612\pi\) | ||||
−0.986449 | + | 0.164067i | \(0.947539\pi\) | |||||||
\(744\) | − | 33.5410i | − | 1.22967i | ||||||
\(745\) | −45.0000 | −1.64867 | ||||||||
\(746\) | − | 69.3181i | − | 2.53792i | ||||||
\(747\) | 12.0000 | 0.439057 | ||||||||
\(748\) | −30.0000 | −1.09691 | ||||||||
\(749\) | 36.0000 | 1.31541 | ||||||||
\(750\) | 15.0000 | 0.547723 | ||||||||
\(751\) | 26.8328i | 0.979143i | 0.871963 | + | 0.489572i | \(0.162847\pi\) | ||||
−0.871963 | + | 0.489572i | \(0.837153\pi\) | |||||||
\(752\) | − | 2.23607i | − | 0.0815410i | ||||||
\(753\) | 35.0000 | 1.27547 | ||||||||
\(754\) | 10.0000 | + | 6.70820i | 0.364179 | + | 0.244298i | ||||
\(755\) | 30.0000 | 1.09181 | ||||||||
\(756\) | 13.4164i | 0.487950i | ||||||||
\(757\) | − | 40.2492i | − | 1.46288i | −0.681904 | − | 0.731441i | \(-0.738848\pi\) | ||
0.681904 | − | 0.731441i | \(-0.261152\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 30.0000 | 1.08893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.0000 | 0.362024 | ||||||||
\(764\) | − | 26.8328i | − | 0.970777i | ||||||
\(765\) | − | 26.8328i | − | 0.970143i | ||||||
\(766\) | 13.4164i | 0.484755i | ||||||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | 20.1246i | 0.726184i | ||||||||
\(769\) | − | 13.4164i | − | 0.483808i | −0.970300 | − | 0.241904i | \(-0.922228\pi\) | ||
0.970300 | − | 0.241904i | \(-0.0777719\pi\) | |||||||
\(770\) | 30.0000 | 1.08112 | ||||||||
\(771\) | 6.70820i | 0.241590i | ||||||||
\(772\) | 40.2492i | 1.44860i | ||||||||
\(773\) | 22.3607i | 0.804258i | 0.915583 | + | 0.402129i | \(0.131730\pi\) | ||||
−0.915583 | + | 0.402129i | \(0.868270\pi\) | |||||||
\(774\) | −30.0000 | −1.07833 | ||||||||
\(775\) | 26.8328i | 0.963863i | ||||||||
\(776\) | 30.0000 | 1.07694 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 40.0000 | 1.43407 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 20.1246i | 0.720577i | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 60.0000 | 2.14560 | ||||||||
\(783\) | 10.0000 | + | 6.70820i | 0.357371 | + | 0.239732i | ||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 40.2492i | 1.43656i | ||||||||
\(786\) | 44.7214i | 1.59516i | ||||||||
\(787\) | 32.0000 | 1.14068 | 0.570338 | − | 0.821410i | \(-0.306812\pi\) | ||||
0.570338 | + | 0.821410i | \(0.306812\pi\) | |||||||
\(788\) | 54.0000 | 1.92367 | ||||||||
\(789\) | −25.0000 | −0.890024 | ||||||||
\(790\) | −45.0000 | −1.60103 | ||||||||
\(791\) | 17.8885i | 0.636043i | ||||||||
\(792\) | −10.0000 | −0.355335 | ||||||||
\(793\) | − | 13.4164i | − | 0.476431i | ||||||
\(794\) | − | 15.6525i | − | 0.555486i | ||||||
\(795\) | − | 60.3738i | − | 2.14124i | ||||||
\(796\) | −42.0000 | −1.48865 | ||||||||
\(797\) | − | 4.47214i | − | 0.158411i | −0.996858 | − | 0.0792056i | \(-0.974762\pi\) | ||
0.996858 | − | 0.0792056i | \(-0.0252384\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.0000 | 0.353775 | ||||||||
\(800\) | − | 26.8328i | − | 0.948683i | ||||||
\(801\) | 8.94427i | 0.316030i | ||||||||
\(802\) | 33.5410i | 1.18437i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 53.6656i | 1.89264i | ||||||||
\(805\) | −36.0000 | −1.26883 | ||||||||
\(806\) | 15.0000 | 0.528352 | ||||||||
\(807\) | −10.0000 | −0.352017 | ||||||||
\(808\) | −40.0000 | −1.40720 | ||||||||
\(809\) | − | 44.7214i | − | 1.57232i | −0.618023 | − | 0.786160i | \(-0.712066\pi\) | ||
0.618023 | − | 0.786160i | \(-0.287934\pi\) | |||||||
\(810\) | 73.7902i | 2.59272i | ||||||||
\(811\) | −22.0000 | −0.772524 | −0.386262 | − | 0.922389i | \(-0.626234\pi\) | ||||
−0.386262 | + | 0.922389i | \(0.626234\pi\) | |||||||
\(812\) | 18.0000 | − | 26.8328i | 0.631676 | − | 0.941647i | ||||
\(813\) | −45.0000 | −1.57822 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 60.3738i | 2.11480i | ||||||||
\(816\) | 10.0000 | 0.350070 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −60.0000 | −2.09785 | ||||||||
\(819\) | 4.00000 | 0.139771 | ||||||||
\(820\) | − | 40.2492i | − | 1.40556i | ||||||
\(821\) | −33.0000 | −1.15171 | −0.575854 | − | 0.817553i | \(-0.695330\pi\) | ||||
−0.575854 | + | 0.817553i | \(0.695330\pi\) | |||||||
\(822\) | 44.7214i | 1.55984i | ||||||||
\(823\) | − | 53.6656i | − | 1.87067i | −0.353768 | − | 0.935333i | \(-0.615100\pi\) | ||
0.353768 | − | 0.935333i | \(-0.384900\pi\) | |||||||
\(824\) | 8.94427i | 0.311588i | ||||||||
\(825\) | 20.0000 | 0.696311 | ||||||||
\(826\) | 26.8328i | 0.933633i | ||||||||
\(827\) | − | 38.0132i | − | 1.32185i | −0.750453 | − | 0.660923i | \(-0.770165\pi\) | ||
0.750453 | − | 0.660923i | \(-0.229835\pi\) | |||||||
\(828\) | 36.0000 | 1.25109 | ||||||||
\(829\) | − | 40.2492i | − | 1.39791i | −0.715164 | − | 0.698957i | \(-0.753648\pi\) | ||
0.715164 | − | 0.698957i | \(-0.246352\pi\) | |||||||
\(830\) | 40.2492i | 1.39707i | ||||||||
\(831\) | − | 4.47214i | − | 0.155137i | ||||||
\(832\) | −13.0000 | −0.450694 | ||||||||
\(833\) | 13.4164i | 0.464851i | ||||||||
\(834\) | −50.0000 | −1.73136 | ||||||||
\(835\) | 36.0000 | 1.24583 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.0000 | 0.518476 | ||||||||
\(838\) | 53.6656i | 1.85385i | ||||||||
\(839\) | 2.23607i | 0.0771976i | 0.999255 | + | 0.0385988i | \(0.0122894\pi\) | ||||
−0.999255 | + | 0.0385988i | \(0.987711\pi\) | |||||||
\(840\) | 30.0000 | 1.03510 | ||||||||
\(841\) | −11.0000 | − | 26.8328i | −0.379310 | − | 0.925270i | ||||
\(842\) | −30.0000 | −1.03387 | ||||||||
\(843\) | − | 6.70820i | − | 0.231043i | ||||||
\(844\) | − | 20.1246i | − | 0.692718i | ||||||
\(845\) | 36.0000 | 1.23844 | ||||||||
\(846\) | 10.0000 | 0.343807 | ||||||||
\(847\) | 12.0000 | 0.412325 | ||||||||
\(848\) | 9.00000 | 0.309061 | ||||||||
\(849\) | − | 31.3050i | − | 1.07438i | ||||||
\(850\) | 40.0000 | 1.37199 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 26.8328i | − | 0.918738i | −0.888246 | − | 0.459369i | \(-0.848076\pi\) | ||
0.888246 | − | 0.459369i | \(-0.151924\pi\) | |||||||
\(854\) | −60.0000 | −2.05316 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 40.2492i | − | 1.37569i | ||||||
\(857\) | 57.0000 | 1.94708 | 0.973541 | − | 0.228510i | \(-0.0733855\pi\) | ||||
0.973541 | + | 0.228510i | \(0.0733855\pi\) | |||||||
\(858\) | − | 11.1803i | − | 0.381691i | ||||||
\(859\) | 46.9574i | 1.60217i | 0.598553 | + | 0.801083i | \(0.295743\pi\) | ||||
−0.598553 | + | 0.801083i | \(0.704257\pi\) | |||||||
\(860\) | − | 60.3738i | − | 2.05873i | ||||||
\(861\) | −20.0000 | −0.681598 | ||||||||
\(862\) | 40.2492i | 1.37089i | ||||||||
\(863\) | −36.0000 | −1.22545 | −0.612727 | − | 0.790295i | \(-0.709928\pi\) | ||||
−0.612727 | + | 0.790295i | \(0.709928\pi\) | |||||||
\(864\) | −15.0000 | −0.510310 | ||||||||
\(865\) | 18.0000 | 0.612018 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.70820i | 0.227823i | ||||||||
\(868\) | − | 40.2492i | − | 1.36615i | ||||||
\(869\) | 15.0000 | 0.508840 | ||||||||
\(870\) | 45.0000 | − | 67.0820i | 1.52564 | − | 2.27429i | ||||
\(871\) | −8.00000 | −0.271070 | ||||||||
\(872\) | − | 11.1803i | − | 0.378614i | ||||||
\(873\) | − | 26.8328i | − | 0.908153i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.00000 | 0.202837 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.0000 | −0.438979 | −0.219489 | − | 0.975615i | \(-0.570439\pi\) | ||||
−0.219489 | + | 0.975615i | \(0.570439\pi\) | |||||||
\(878\) | − | 76.0263i | − | 2.56576i | ||||||
\(879\) | 20.0000 | 0.674583 | ||||||||
\(880\) | 6.70820i | 0.226134i | ||||||||
\(881\) | 35.7771i | 1.20536i | 0.797983 | + | 0.602680i | \(0.205901\pi\) | ||||
−0.797983 | + | 0.602680i | \(0.794099\pi\) | |||||||
\(882\) | 13.4164i | 0.451754i | ||||||||
\(883\) | −34.0000 | −1.14419 | −0.572096 | − | 0.820187i | \(-0.693869\pi\) | ||||
−0.572096 | + | 0.820187i | \(0.693869\pi\) | |||||||
\(884\) | − | 13.4164i | − | 0.451243i | ||||||
\(885\) | 40.2492i | 1.35296i | ||||||||
\(886\) | 40.0000 | 1.34383 | ||||||||
\(887\) | − | 11.1803i | − | 0.375399i | −0.982226 | − | 0.187700i | \(-0.939897\pi\) | ||
0.982226 | − | 0.187700i | \(-0.0601031\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −30.0000 | −1.00560 | ||||||||
\(891\) | − | 24.5967i | − | 0.824022i | ||||||
\(892\) | 48.0000 | 1.60716 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 75.0000 | 2.50838 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 31.3050i | 1.04583i | ||||||||
\(897\) | 13.4164i | 0.447961i | ||||||||
\(898\) | −80.0000 | −2.66963 | ||||||||
\(899\) | −30.0000 | − | 20.1246i | −1.00056 | − | 0.671193i | ||||
\(900\) | 24.0000 | 0.800000 | ||||||||
\(901\) | 40.2492i | 1.34090i | ||||||||
\(902\) | 22.3607i | 0.744529i | ||||||||
\(903\) | −30.0000 | −0.998337 | ||||||||
\(904\) | 20.0000 | 0.665190 | ||||||||
\(905\) | −15.0000 | −0.498617 | ||||||||
\(906\) | −50.0000 | −1.66114 | ||||||||
\(907\) | 53.6656i | 1.78194i | 0.454064 | + | 0.890969i | \(0.349974\pi\) | ||||
−0.454064 | + | 0.890969i | \(0.650026\pi\) | |||||||
\(908\) | −36.0000 | −1.19470 | ||||||||
\(909\) | 35.7771i | 1.18665i | ||||||||
\(910\) | 13.4164i | 0.444750i | ||||||||
\(911\) | − | 38.0132i | − | 1.25943i | −0.776825 | − | 0.629716i | \(-0.783171\pi\) | ||
0.776825 | − | 0.629716i | \(-0.216829\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 13.4164i | − | 0.444018i | ||||||
\(914\) | 4.47214i | 0.147925i | ||||||||
\(915\) | −90.0000 | −2.97531 | ||||||||
\(916\) | 40.2492i | 1.32987i | ||||||||
\(917\) | 17.8885i | 0.590732i | ||||||||
\(918\) | − | 22.3607i | − | 0.738012i | ||||||
\(919\) | −4.00000 | −0.131948 | −0.0659739 | − | 0.997821i | \(-0.521015\pi\) | ||||
−0.0659739 | + | 0.997821i | \(0.521015\pi\) | |||||||
\(920\) | 40.2492i | 1.32698i | ||||||||
\(921\) | 45.0000 | 1.48280 | ||||||||
\(922\) | −20.0000 | −0.658665 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −30.0000 | −0.986928 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 58.1378i | 1.91053i | ||||||||
\(927\) | 8.00000 | 0.262754 | ||||||||
\(928\) | 30.0000 | + | 20.1246i | 0.984798 | + | 0.660623i | ||||
\(929\) | 30.0000 | 0.984268 | 0.492134 | − | 0.870519i | \(-0.336217\pi\) | ||||
0.492134 | + | 0.870519i | \(0.336217\pi\) | |||||||
\(930\) | − | 100.623i | − | 3.29956i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 27.0000 | 0.884414 | ||||||||
\(933\) | 20.0000 | 0.654771 | ||||||||
\(934\) | −5.00000 | −0.163605 | ||||||||
\(935\) | −30.0000 | −0.981105 | ||||||||
\(936\) | − | 4.47214i | − | 0.146176i | ||||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | 35.7771i | 1.16816i | ||||||||
\(939\) | − | 64.8460i | − | 2.11617i | ||||||
\(940\) | 20.1246i | 0.656392i | ||||||||
\(941\) | −3.00000 | −0.0977972 | −0.0488986 | − | 0.998804i | \(-0.515571\pi\) | ||||
−0.0488986 | + | 0.998804i | \(0.515571\pi\) | |||||||
\(942\) | − | 67.0820i | − | 2.18565i | ||||||
\(943\) | − | 26.8328i | − | 0.873797i | ||||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 13.4164i | 0.436436i | ||||||||
\(946\) | 33.5410i | 1.09051i | ||||||||
\(947\) | 2.23607i | 0.0726624i | 0.999340 | + | 0.0363312i | \(0.0115671\pi\) | ||||
−0.999340 | + | 0.0363312i | \(0.988433\pi\) | |||||||
\(948\) | 45.0000 | 1.46153 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 50.0000 | 1.62136 | ||||||||
\(952\) | −20.0000 | −0.648204 | ||||||||
\(953\) | −9.00000 | −0.291539 | −0.145769 | − | 0.989319i | \(-0.546566\pi\) | ||||
−0.145769 | + | 0.989319i | \(0.546566\pi\) | |||||||
\(954\) | 40.2492i | 1.30312i | ||||||||
\(955\) | − | 26.8328i | − | 0.868290i | ||||||
\(956\) | −18.0000 | −0.582162 | ||||||||
\(957\) | −15.0000 | + | 22.3607i | −0.484881 | + | 0.722818i | ||||
\(958\) | 25.0000 | 0.807713 | ||||||||
\(959\) | 17.8885i | 0.577651i | ||||||||
\(960\) | 87.2067i | 2.81458i | ||||||||
\(961\) | −14.0000 | −0.451613 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36.0000 | −1.16008 | ||||||||
\(964\) | 75.0000 | 2.41559 | ||||||||
\(965\) | 40.2492i | 1.29567i | ||||||||
\(966\) | 60.0000 | 1.93047 | ||||||||
\(967\) | 46.9574i | 1.51005i | 0.655697 | + | 0.755025i | \(0.272375\pi\) | ||||
−0.655697 | + | 0.755025i | \(0.727625\pi\) | |||||||
\(968\) | − | 13.4164i | − | 0.431220i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 90.0000 | 2.88973 | ||||||||
\(971\) | − | 17.8885i | − | 0.574071i | −0.957920 | − | 0.287035i | \(-0.907330\pi\) | ||
0.957920 | − | 0.287035i | \(-0.0926697\pi\) | |||||||
\(972\) | − | 53.6656i | − | 1.72133i | ||||||
\(973\) | −20.0000 | −0.641171 | ||||||||
\(974\) | 4.47214i | 0.143296i | ||||||||
\(975\) | 8.94427i | 0.286446i | ||||||||
\(976\) | − | 13.4164i | − | 0.429449i | ||||||
\(977\) | 33.0000 | 1.05576 | 0.527882 | − | 0.849318i | \(-0.322986\pi\) | ||||
0.527882 | + | 0.849318i | \(0.322986\pi\) | |||||||
\(978\) | − | 100.623i | − | 3.21757i | ||||||
\(979\) | 10.0000 | 0.319601 | ||||||||
\(980\) | −27.0000 | −0.862483 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | 55.0000 | 1.75512 | ||||||||
\(983\) | 29.0689i | 0.927153i | 0.886057 | + | 0.463577i | \(0.153434\pi\) | ||||
−0.886057 | + | 0.463577i | \(0.846566\pi\) | |||||||
\(984\) | 22.3607i | 0.712832i | ||||||||
\(985\) | 54.0000 | 1.72058 | ||||||||
\(986\) | −30.0000 | + | 44.7214i | −0.955395 | + | 1.42422i | ||||
\(987\) | 10.0000 | 0.318304 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 40.2492i | − | 1.27985i | ||||||
\(990\) | −30.0000 | −0.953463 | ||||||||
\(991\) | −40.0000 | −1.27064 | −0.635321 | − | 0.772248i | \(-0.719132\pi\) | ||||
−0.635321 | + | 0.772248i | \(0.719132\pi\) | |||||||
\(992\) | 45.0000 | 1.42875 | ||||||||
\(993\) | 75.0000 | 2.38005 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −42.0000 | −1.33149 | ||||||||
\(996\) | − | 40.2492i | − | 1.27535i | ||||||
\(997\) | − | 26.8328i | − | 0.849804i | −0.905239 | − | 0.424902i | \(-0.860309\pi\) | ||
0.905239 | − | 0.424902i | \(-0.139691\pi\) | |||||||
\(998\) | − | 22.3607i | − | 0.707815i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))