Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [891,2,Mod(298,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.298");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.11467082010\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 11) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 595.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 891.595 |
Dual form | 891.2.e.k.298.1 |
$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.707107 | + | 1.22474i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | −0.955901 | − | 0.293691i | \(-0.905116\pi\) |
0.732294 | + | 0.680989i | \(0.238450\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | + | 1.73205i | 0.377964 | + | 0.654654i | 0.990766 | − | 0.135583i | \(-0.0432908\pi\) |
−0.612801 | + | 0.790237i | \(0.709957\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.00000 | −0.632456 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | + | 3.46410i | −0.554700 | + | 0.960769i | 0.443227 | + | 0.896410i | \(0.353834\pi\) |
−0.997927 | + | 0.0643593i | \(0.979500\pi\) | |||||||
\(14\) | −2.00000 | + | 3.46410i | −0.534522 | + | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | −1.00000 | − | 1.73205i | −0.223607 | − | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | − | 1.73205i | 0.213201 | − | 0.369274i | ||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | −0.809177 | − | 0.587565i | \(-0.800087\pi\) |
0.913434 | + | 0.406986i | \(0.133420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | −8.00000 | −1.56893 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.00000 | −0.755929 | ||||||||
\(29\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.50000 | + | 6.06218i | −0.628619 | + | 1.08880i | 0.359211 | + | 0.933257i | \(0.383046\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | −4.00000 | + | 6.92820i | −0.707107 | + | 1.22474i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | − | 3.46410i | −0.342997 | − | 0.594089i | ||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | − | 6.92820i | 0.624695 | − | 1.08200i | −0.363905 | − | 0.931436i | \(-0.618557\pi\) |
0.988600 | − | 0.150567i | \(-0.0481100\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.00000 | + | 5.19615i | 0.457496 | + | 0.792406i | 0.998828 | − | 0.0484030i | \(-0.0154132\pi\) |
−0.541332 | + | 0.840809i | \(0.682080\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | −4.00000 | − | 6.92820i | −0.583460 | − | 1.01058i | −0.995066 | − | 0.0992202i | \(-0.968365\pi\) |
0.411606 | − | 0.911362i | \(-0.364968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | −4.00000 | + | 6.92820i | −0.565685 | + | 0.979796i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | − | 6.92820i | −0.554700 | − | 0.960769i | ||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.50000 | + | 4.33013i | −0.325472 | + | 0.563735i | −0.981608 | − | 0.190909i | \(-0.938857\pi\) |
0.656136 | + | 0.754643i | \(0.272190\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | − | 10.3923i | −0.768221 | − | 1.33060i | −0.938527 | − | 0.345207i | \(-0.887809\pi\) |
0.170305 | − | 0.985391i | \(-0.445525\pi\) | |||||||
\(62\) | −14.0000 | −1.77800 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −2.00000 | − | 3.46410i | −0.248069 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | − | 6.06218i | 0.427593 | − | 0.740613i | −0.569066 | − | 0.822292i | \(-0.692695\pi\) |
0.996659 | + | 0.0816792i | \(0.0260283\pi\) | |||||||
\(68\) | 2.00000 | − | 3.46410i | 0.242536 | − | 0.420084i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | − | 3.46410i | −0.239046 | − | 0.414039i | ||||
\(71\) | −3.00000 | −0.356034 | −0.178017 | − | 0.984027i | \(-0.556968\pi\) | ||||
−0.178017 | + | 0.984027i | \(0.556968\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 3.00000 | + | 5.19615i | 0.348743 | + | 0.604040i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | − | 1.73205i | 0.113961 | − | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.00000 | + | 8.66025i | 0.562544 | + | 0.974355i | 0.997274 | + | 0.0737937i | \(0.0235106\pi\) |
−0.434730 | + | 0.900561i | \(0.643156\pi\) | |||||||
\(80\) | −4.00000 | −0.447214 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 16.0000 | 1.76690 | ||||||||
\(83\) | 3.00000 | + | 5.19615i | 0.329293 | + | 0.570352i | 0.982372 | − | 0.186938i | \(-0.0598564\pi\) |
−0.653079 | + | 0.757290i | \(0.726523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | − | 1.73205i | 0.108465 | − | 0.187867i | ||||
\(86\) | −6.00000 | + | 10.3923i | −0.646997 | + | 1.12063i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.0000 | 1.59000 | 0.794998 | − | 0.606612i | \(-0.207472\pi\) | ||||
0.794998 | + | 0.606612i | \(0.207472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | −0.838628 | ||||||||
\(92\) | 1.00000 | + | 1.73205i | 0.104257 | + | 0.180579i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.00000 | − | 13.8564i | 0.825137 | − | 1.42918i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.50000 | + | 6.06218i | 0.355371 | + | 0.615521i | 0.987181 | − | 0.159602i | \(-0.0510211\pi\) |
−0.631810 | + | 0.775123i | \(0.717688\pi\) | |||||||
\(98\) | 6.00000 | 0.606092 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.00000 | −0.800000 | ||||||||
\(101\) | −1.00000 | − | 1.73205i | −0.0995037 | − | 0.172345i | 0.811976 | − | 0.583691i | \(-0.198392\pi\) |
−0.911479 | + | 0.411346i | \(0.865059\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | − | 13.8564i | 0.788263 | − | 1.36531i | −0.138767 | − | 0.990325i | \(-0.544314\pi\) |
0.927030 | − | 0.374987i | \(-0.122353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | − | 10.3923i | −0.582772 | − | 1.00939i | ||||
\(107\) | 18.0000 | 1.74013 | 0.870063 | − | 0.492941i | \(-0.164078\pi\) | ||||
0.870063 | + | 0.492941i | \(0.164078\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 1.00000 | + | 1.73205i | 0.0953463 | + | 0.165145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.00000 | + | 6.92820i | −0.377964 | + | 0.654654i | ||||
\(113\) | −4.50000 | + | 7.79423i | −0.423324 | + | 0.733219i | −0.996262 | − | 0.0863794i | \(-0.972470\pi\) |
0.572938 | + | 0.819599i | \(0.305804\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.500000 | + | 0.866025i | 0.0466252 | + | 0.0807573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.0000 | −0.920575 | ||||||||
\(119\) | −2.00000 | − | 3.46410i | −0.183340 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 12.0000 | − | 20.7846i | 1.08643 | − | 1.88175i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.00000 | − | 12.1244i | −0.628619 | − | 1.08880i | ||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.00000 | − | 6.92820i | 0.350823 | − | 0.607644i | ||||
\(131\) | 9.00000 | − | 15.5885i | 0.786334 | − | 1.36197i | −0.141865 | − | 0.989886i | \(-0.545310\pi\) |
0.928199 | − | 0.372084i | \(-0.121357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 14.0000 | 1.20942 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.50000 | + | 6.06218i | 0.299025 | + | 0.517927i | 0.975913 | − | 0.218159i | \(-0.0700052\pi\) |
−0.676888 | + | 0.736086i | \(0.736672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.00000 | + | 8.66025i | −0.424094 | + | 0.734553i | −0.996335 | − | 0.0855324i | \(-0.972741\pi\) |
0.572241 | + | 0.820086i | \(0.306074\pi\) | |||||||
\(140\) | 2.00000 | − | 3.46410i | 0.169031 | − | 0.292770i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.00000 | − | 5.19615i | −0.251754 | − | 0.436051i | ||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.00000 | + | 6.92820i | 0.331042 | + | 0.573382i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.00000 | + | 5.19615i | −0.246598 | + | 0.427121i | ||||
\(149\) | 5.00000 | − | 8.66025i | 0.409616 | − | 0.709476i | −0.585231 | − | 0.810867i | \(-0.698996\pi\) |
0.994847 | + | 0.101391i | \(0.0323294\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00000 | − | 1.73205i | −0.0813788 | − | 0.140952i | 0.822464 | − | 0.568818i | \(-0.192599\pi\) |
−0.903842 | + | 0.427865i | \(0.859266\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.00000 | 0.322329 | ||||||||
\(155\) | −3.50000 | − | 6.06218i | −0.281127 | − | 0.486926i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.50000 | − | 6.06218i | 0.279330 | − | 0.483814i | −0.691888 | − | 0.722005i | \(-0.743221\pi\) |
0.971219 | + | 0.238190i | \(0.0765542\pi\) | |||||||
\(158\) | −10.0000 | + | 17.3205i | −0.795557 | + | 1.37795i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.00000 | − | 6.92820i | −0.316228 | − | 0.547723i | ||||
\(161\) | 2.00000 | 0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 8.00000 | + | 13.8564i | 0.624695 | + | 1.08200i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | + | 10.3923i | −0.465690 | + | 0.806599i | ||||
\(167\) | 6.00000 | − | 10.3923i | 0.464294 | − | 0.804181i | −0.534875 | − | 0.844931i | \(-0.679641\pi\) |
0.999169 | + | 0.0407502i | \(0.0129748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | − | 2.59808i | −0.115385 | − | 0.199852i | ||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.0000 | −0.914991 | ||||||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.00000 | + | 6.92820i | −0.302372 | + | 0.523723i | ||||
\(176\) | 2.00000 | − | 3.46410i | 0.150756 | − | 0.261116i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.0000 | + | 25.9808i | 1.12430 | + | 1.94734i | ||||
\(179\) | −15.0000 | −1.12115 | −0.560576 | − | 0.828103i | \(-0.689420\pi\) | ||||
−0.560576 | + | 0.828103i | \(0.689420\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | −8.00000 | − | 13.8564i | −0.592999 | − | 1.02711i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.50000 | + | 2.59808i | −0.110282 | + | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.00000 | + | 1.73205i | 0.0731272 | + | 0.126660i | ||||
\(188\) | 16.0000 | 1.16692 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.50000 | − | 14.7224i | −0.615038 | − | 1.06528i | −0.990378 | − | 0.138390i | \(-0.955807\pi\) |
0.375339 | − | 0.926887i | \(-0.377526\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | + | 3.46410i | −0.143963 | + | 0.249351i | −0.928986 | − | 0.370116i | \(-0.879318\pi\) |
0.785022 | + | 0.619467i | \(0.212651\pi\) | |||||||
\(194\) | −7.00000 | + | 12.1244i | −0.502571 | + | 0.870478i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | + | 5.19615i | 0.214286 | + | 0.371154i | ||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.00000 | − | 3.46410i | 0.140720 | − | 0.243733i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | + | 6.92820i | 0.279372 | + | 0.483887i | ||||
\(206\) | 32.0000 | 2.22955 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −16.0000 | −1.10940 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.00000 | + | 10.3923i | −0.413057 | + | 0.715436i | −0.995222 | − | 0.0976347i | \(-0.968872\pi\) |
0.582165 | + | 0.813070i | \(0.302206\pi\) | |||||||
\(212\) | 6.00000 | − | 10.3923i | 0.412082 | − | 0.713746i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.0000 | + | 31.1769i | 1.23045 | + | 2.13121i | ||||
\(215\) | −6.00000 | −0.409197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.0000 | −0.950382 | ||||||||
\(218\) | 10.0000 | + | 17.3205i | 0.677285 | + | 1.17309i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.00000 | + | 1.73205i | −0.0674200 | + | 0.116775i | ||||
\(221\) | 4.00000 | − | 6.92820i | 0.269069 | − | 0.466041i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.50000 | − | 16.4545i | −0.636167 | − | 1.10187i | −0.986267 | − | 0.165161i | \(-0.947186\pi\) |
0.350100 | − | 0.936713i | \(-0.386148\pi\) | |||||||
\(224\) | −16.0000 | −1.06904 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.0000 | −1.19734 | ||||||||
\(227\) | −9.00000 | − | 15.5885i | −0.597351 | − | 1.03464i | −0.993210 | − | 0.116331i | \(-0.962887\pi\) |
0.395860 | − | 0.918311i | \(-0.370447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.50000 | + | 12.9904i | −0.495614 | + | 0.858429i | −0.999987 | − | 0.00505719i | \(-0.998390\pi\) |
0.504373 | + | 0.863486i | \(0.331724\pi\) | |||||||
\(230\) | −1.00000 | + | 1.73205i | −0.0659380 | + | 0.114208i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.0000 | 1.57229 | 0.786146 | − | 0.618041i | \(-0.212073\pi\) | ||||
0.786146 | + | 0.618041i | \(0.212073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | 0.521862 | ||||||||
\(236\) | −5.00000 | − | 8.66025i | −0.325472 | − | 0.563735i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.00000 | − | 6.92820i | 0.259281 | − | 0.449089i | ||||
\(239\) | 15.0000 | − | 25.9808i | 0.970269 | − | 1.68056i | 0.275533 | − | 0.961292i | \(-0.411146\pi\) |
0.694737 | − | 0.719264i | \(-0.255521\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | + | 6.92820i | 0.257663 | + | 0.446285i | 0.965615 | − | 0.259975i | \(-0.0837143\pi\) |
−0.707953 | + | 0.706260i | \(0.750381\pi\) | |||||||
\(242\) | −2.00000 | −0.128565 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 24.0000 | 1.53644 | ||||||||
\(245\) | 1.50000 | + | 2.59808i | 0.0958315 | + | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.00000 | − | 15.5885i | −0.569210 | − | 0.985901i | ||||
\(251\) | −23.0000 | −1.45175 | −0.725874 | − | 0.687828i | \(-0.758564\pi\) | ||||
−0.725874 | + | 0.687828i | \(0.758564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.00000 | −0.0628695 | ||||||||
\(254\) | 8.00000 | + | 13.8564i | 0.501965 | + | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 1.00000 | − | 1.73205i | 0.0623783 | − | 0.108042i | −0.833150 | − | 0.553047i | \(-0.813465\pi\) |
0.895528 | + | 0.445005i | \(0.146798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.00000 | + | 5.19615i | 0.186411 | + | 0.322873i | ||||
\(260\) | 8.00000 | 0.496139 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 36.0000 | 2.22409 | ||||||||
\(263\) | −7.00000 | − | 12.1244i | −0.431638 | − | 0.747620i | 0.565376 | − | 0.824833i | \(-0.308731\pi\) |
−0.997015 | + | 0.0772134i | \(0.975398\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.00000 | − | 5.19615i | 0.184289 | − | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.00000 | + | 12.1244i | 0.427593 | + | 0.740613i | ||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.0000 | −1.70088 | −0.850439 | − | 0.526073i | \(-0.823664\pi\) | ||||
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | −4.00000 | − | 6.92820i | −0.242536 | − | 0.420084i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.00000 | + | 12.1244i | −0.422885 | + | 0.732459i | ||||
\(275\) | 2.00000 | − | 3.46410i | 0.120605 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00000 | + | 1.73205i | 0.0600842 | + | 0.104069i | 0.894503 | − | 0.447062i | \(-0.147530\pi\) |
−0.834419 | + | 0.551131i | \(0.814196\pi\) | |||||||
\(278\) | −20.0000 | −1.19952 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.00000 | + | 15.5885i | 0.536895 | + | 0.929929i | 0.999069 | + | 0.0431402i | \(0.0137362\pi\) |
−0.462174 | + | 0.886789i | \(0.652930\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | + | 3.46410i | −0.118888 | + | 0.205919i | −0.919327 | − | 0.393494i | \(-0.871266\pi\) |
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(284\) | 3.00000 | − | 5.19615i | 0.178017 | − | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | + | 6.92820i | 0.236525 | + | 0.409673i | ||||
\(287\) | 16.0000 | 0.944450 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.00000 | + | 6.92820i | −0.234082 | + | 0.405442i | ||||
\(293\) | −12.0000 | + | 20.7846i | −0.701047 | + | 1.21425i | 0.267052 | + | 0.963682i | \(0.413951\pi\) |
−0.968099 | + | 0.250568i | \(0.919383\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.50000 | − | 4.33013i | −0.145556 | − | 0.252110i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 20.0000 | 1.15857 | ||||||||
\(299\) | 2.00000 | + | 3.46410i | 0.115663 | + | 0.200334i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | + | 10.3923i | −0.345834 | + | 0.599002i | ||||
\(302\) | 2.00000 | − | 3.46410i | 0.115087 | − | 0.199337i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.0000 | 0.687118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | 2.00000 | + | 3.46410i | 0.113961 | + | 0.197386i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.00000 | − | 12.1244i | 0.397573 | − | 0.688617i | ||||
\(311\) | −6.00000 | + | 10.3923i | −0.340229 | + | 0.589294i | −0.984475 | − | 0.175525i | \(-0.943838\pi\) |
0.644246 | + | 0.764818i | \(0.277171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.500000 | + | 0.866025i | 0.0282617 | + | 0.0489506i | 0.879810 | − | 0.475325i | \(-0.157669\pi\) |
−0.851549 | + | 0.524276i | \(0.824336\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.0000 | −1.12509 | ||||||||
\(317\) | −6.50000 | − | 11.2583i | −0.365076 | − | 0.632331i | 0.623712 | − | 0.781654i | \(-0.285624\pi\) |
−0.988788 | + | 0.149323i | \(0.952290\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4.00000 | − | 6.92820i | 0.223607 | − | 0.387298i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.00000 | + | 3.46410i | 0.111456 | + | 0.193047i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.0000 | −0.887520 | ||||||||
\(326\) | 4.00000 | + | 6.92820i | 0.221540 | + | 0.383718i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | − | 13.8564i | 0.441054 | − | 0.763928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.50000 | − | 6.06218i | −0.192377 | − | 0.333207i | 0.753660 | − | 0.657264i | \(-0.228286\pi\) |
−0.946038 | + | 0.324057i | \(0.894953\pi\) | |||||||
\(332\) | −12.0000 | −0.658586 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.0000 | 1.31322 | ||||||||
\(335\) | 3.50000 | + | 6.06218i | 0.191225 | + | 0.331212i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0000 | − | 19.0526i | 0.599208 | − | 1.03786i | −0.393730 | − | 0.919226i | \(-0.628816\pi\) |
0.992938 | − | 0.118633i | \(-0.0378512\pi\) | |||||||
\(338\) | 3.00000 | − | 5.19615i | 0.163178 | − | 0.282633i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.00000 | + | 3.46410i | 0.108465 | + | 0.187867i | ||||
\(341\) | 7.00000 | 0.379071 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.00000 | + | 10.3923i | −0.322562 | + | 0.558694i | ||||
\(347\) | −14.0000 | + | 24.2487i | −0.751559 | + | 1.30174i | 0.195507 | + | 0.980702i | \(0.437365\pi\) |
−0.947067 | + | 0.321037i | \(0.895969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.0000 | − | 25.9808i | −0.802932 | − | 1.39072i | −0.917679 | − | 0.397324i | \(-0.869939\pi\) |
0.114747 | − | 0.993395i | \(-0.463394\pi\) | |||||||
\(350\) | −16.0000 | −0.855236 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.00000 | 0.426401 | ||||||||
\(353\) | 10.5000 | + | 18.1865i | 0.558859 | + | 0.967972i | 0.997592 | + | 0.0693543i | \(0.0220939\pi\) |
−0.438733 | + | 0.898617i | \(0.644573\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.50000 | − | 2.59808i | 0.0796117 | − | 0.137892i | ||||
\(356\) | −15.0000 | + | 25.9808i | −0.794998 | + | 1.37698i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.0000 | − | 25.9808i | −0.792775 | − | 1.37313i | ||||
\(359\) | −20.0000 | −1.05556 | −0.527780 | − | 0.849381i | \(-0.676975\pi\) | ||||
−0.527780 | + | 0.849381i | \(0.676975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 7.00000 | + | 12.1244i | 0.367912 | + | 0.637242i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.00000 | − | 13.8564i | 0.419314 | − | 0.726273i | ||||
\(365\) | −2.00000 | + | 3.46410i | −0.104685 | + | 0.181319i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.50000 | + | 14.7224i | 0.443696 | + | 0.768505i | 0.997960 | − | 0.0638362i | \(-0.0203335\pi\) |
−0.554264 | + | 0.832341i | \(0.687000\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.00000 | −0.311925 | ||||||||
\(371\) | −6.00000 | − | 10.3923i | −0.311504 | − | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.0000 | − | 22.5167i | 0.673114 | − | 1.16587i | −0.303902 | − | 0.952703i | \(-0.598289\pi\) |
0.977016 | − | 0.213165i | \(-0.0683772\pi\) | |||||||
\(374\) | −2.00000 | + | 3.46410i | −0.103418 | + | 0.179124i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.00000 | −0.256833 | −0.128416 | − | 0.991720i | \(-0.540989\pi\) | ||||
−0.128416 | + | 0.991720i | \(0.540989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17.0000 | − | 29.4449i | 0.869796 | − | 1.50653i | ||||
\(383\) | 0.500000 | − | 0.866025i | 0.0255488 | − | 0.0442518i | −0.852968 | − | 0.521963i | \(-0.825200\pi\) |
0.878517 | + | 0.477711i | \(0.158533\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.00000 | + | 1.73205i | 0.0509647 | + | 0.0882735i | ||||
\(386\) | −8.00000 | −0.407189 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.0000 | −0.710742 | ||||||||
\(389\) | 7.50000 | + | 12.9904i | 0.380265 | + | 0.658638i | 0.991100 | − | 0.133120i | \(-0.0424994\pi\) |
−0.610835 | + | 0.791758i | \(0.709166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00000 | + | 1.73205i | −0.0505722 | + | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.00000 | − | 3.46410i | −0.100759 | − | 0.174519i | ||||
\(395\) | −10.0000 | −0.503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.00000 | −0.100377 | −0.0501886 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.00000 | + | 13.8564i | −0.400000 | + | 0.692820i | ||||
\(401\) | −1.00000 | + | 1.73205i | −0.0499376 | + | 0.0864945i | −0.889914 | − | 0.456129i | \(-0.849236\pi\) |
0.839976 | + | 0.542623i | \(0.182569\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.0000 | − | 24.2487i | −0.697390 | − | 1.20791i | ||||
\(404\) | 4.00000 | 0.199007 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.50000 | − | 2.59808i | −0.0743522 | − | 0.128782i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.0000 | − | 25.9808i | 0.741702 | − | 1.28467i | −0.210017 | − | 0.977698i | \(-0.567352\pi\) |
0.951720 | − | 0.306968i | \(-0.0993146\pi\) | |||||||
\(410\) | −8.00000 | + | 13.8564i | −0.395092 | + | 0.684319i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.0000 | + | 27.7128i | 0.788263 | + | 1.36531i | ||||
\(413\) | −10.0000 | −0.492068 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | −0.294528 | ||||||||
\(416\) | −16.0000 | − | 27.7128i | −0.784465 | − | 1.35873i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.0000 | + | 17.3205i | −0.488532 | + | 0.846162i | −0.999913 | − | 0.0131919i | \(-0.995801\pi\) |
0.511381 | + | 0.859354i | \(0.329134\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0000 | − | 19.0526i | −0.536107 | − | 0.928565i | −0.999109 | − | 0.0422075i | \(-0.986561\pi\) |
0.463002 | − | 0.886357i | \(-0.346772\pi\) | |||||||
\(422\) | −24.0000 | −1.16830 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.00000 | − | 6.92820i | −0.194029 | − | 0.336067i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0000 | − | 20.7846i | 0.580721 | − | 1.00584i | ||||
\(428\) | −18.0000 | + | 31.1769i | −0.870063 | + | 1.50699i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.00000 | − | 10.3923i | −0.289346 | − | 0.501161i | ||||
\(431\) | −18.0000 | −0.867029 | −0.433515 | − | 0.901146i | \(-0.642727\pi\) | ||||
−0.433515 | + | 0.901146i | \(0.642727\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.0000 | −0.528626 | −0.264313 | − | 0.964437i | \(-0.585145\pi\) | ||||
−0.264313 | + | 0.964437i | \(0.585145\pi\) | |||||||
\(434\) | −14.0000 | − | 24.2487i | −0.672022 | − | 1.16398i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | + | 17.3205i | −0.478913 | + | 0.829502i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.0000 | − | 34.6410i | −0.954548 | − | 1.65333i | −0.735399 | − | 0.677634i | \(-0.763005\pi\) |
−0.219149 | − | 0.975691i | \(-0.570328\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.0000 | 0.761042 | ||||||||
\(443\) | 5.50000 | + | 9.52628i | 0.261313 | + | 0.452607i | 0.966591 | − | 0.256323i | \(-0.0825112\pi\) |
−0.705278 | + | 0.708931i | \(0.749178\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.50000 | + | 12.9904i | −0.355534 | + | 0.615803i | ||||
\(446\) | 19.0000 | − | 32.9090i | 0.899676 | − | 1.55828i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.00000 | − | 13.8564i | −0.377964 | − | 0.654654i | ||||
\(449\) | 35.0000 | 1.65175 | 0.825876 | − | 0.563852i | \(-0.190681\pi\) | ||||
0.825876 | + | 0.563852i | \(0.190681\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.00000 | −0.376705 | ||||||||
\(452\) | −9.00000 | − | 15.5885i | −0.423324 | − | 0.733219i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.0000 | − | 31.1769i | 0.844782 | − | 1.46321i | ||||
\(455\) | 4.00000 | − | 6.92820i | 0.187523 | − | 0.324799i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.00000 | + | 10.3923i | 0.280668 | + | 0.486132i | 0.971549 | − | 0.236837i | \(-0.0761106\pi\) |
−0.690881 | + | 0.722968i | \(0.742777\pi\) | |||||||
\(458\) | −30.0000 | −1.40181 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.00000 | −0.0932505 | ||||||||
\(461\) | −6.00000 | − | 10.3923i | −0.279448 | − | 0.484018i | 0.691800 | − | 0.722089i | \(-0.256818\pi\) |
−0.971248 | + | 0.238071i | \(0.923485\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.50000 | − | 9.52628i | 0.255607 | − | 0.442724i | −0.709453 | − | 0.704752i | \(-0.751058\pi\) |
0.965060 | + | 0.262029i | \(0.0843915\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.0000 | + | 41.5692i | 1.11178 | + | 1.92566i | ||||
\(467\) | −27.0000 | −1.24941 | −0.624705 | − | 0.780860i | \(-0.714781\pi\) | ||||
−0.624705 | + | 0.780860i | \(0.714781\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.0000 | 0.646460 | ||||||||
\(470\) | 8.00000 | + | 13.8564i | 0.369012 | + | 0.639148i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | − | 5.19615i | 0.137940 | − | 0.238919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.00000 | 0.366679 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 60.0000 | 2.74434 | ||||||||
\(479\) | −10.0000 | − | 17.3205i | −0.456912 | − | 0.791394i | 0.541884 | − | 0.840453i | \(-0.317711\pi\) |
−0.998796 | + | 0.0490589i | \(0.984378\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | + | 10.3923i | −0.273576 | + | 0.473848i | ||||
\(482\) | −8.00000 | + | 13.8564i | −0.364390 | + | 0.631142i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.00000 | − | 1.73205i | −0.0454545 | − | 0.0787296i | ||||
\(485\) | −7.00000 | −0.317854 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.0000 | 1.04223 | 0.521115 | − | 0.853487i | \(-0.325516\pi\) | ||||
0.521115 | + | 0.853487i | \(0.325516\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.00000 | + | 5.19615i | −0.135526 | + | 0.234738i | ||||
\(491\) | 4.00000 | − | 6.92820i | 0.180517 | − | 0.312665i | −0.761539 | − | 0.648119i | \(-0.775556\pi\) |
0.942057 | + | 0.335453i | \(0.108889\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.0000 | −1.25724 | ||||||||
\(497\) | −3.00000 | − | 5.19615i | −0.134568 | − | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.0000 | + | 17.3205i | −0.447661 | + | 0.775372i | −0.998233 | − | 0.0594153i | \(-0.981076\pi\) |
0.550572 | + | 0.834788i | \(0.314410\pi\) | |||||||
\(500\) | 9.00000 | − | 15.5885i | 0.402492 | − | 0.697137i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −23.0000 | − | 39.8372i | −1.02654 | − | 1.77802i | ||||
\(503\) | −26.0000 | −1.15928 | −0.579641 | − | 0.814872i | \(-0.696807\pi\) | ||||
−0.579641 | + | 0.814872i | \(0.696807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | −1.00000 | − | 1.73205i | −0.0444554 | − | 0.0769991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.00000 | + | 13.8564i | −0.354943 | + | 0.614779i | ||||
\(509\) | −7.50000 | + | 12.9904i | −0.332432 | + | 0.575789i | −0.982988 | − | 0.183669i | \(-0.941202\pi\) |
0.650556 | + | 0.759458i | \(0.274536\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00000 | + | 6.92820i | 0.176950 | + | 0.306486i | ||||
\(512\) | −32.0000 | −1.41421 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.00000 | 0.176432 | ||||||||
\(515\) | 8.00000 | + | 13.8564i | 0.352522 | + | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.00000 | + | 6.92820i | −0.175920 | + | 0.304702i | ||||
\(518\) | −6.00000 | + | 10.3923i | −0.263625 | + | 0.456612i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | −0.131432 | −0.0657162 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657162 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.0000 | −0.699631 | −0.349816 | − | 0.936819i | \(-0.613756\pi\) | ||||
−0.349816 | + | 0.936819i | \(0.613756\pi\) | |||||||
\(524\) | 18.0000 | + | 31.1769i | 0.786334 | + | 1.36197i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.0000 | − | 24.2487i | 0.610429 | − | 1.05729i | ||||
\(527\) | 7.00000 | − | 12.1244i | 0.304925 | − | 0.528145i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | 12.0000 | 0.521247 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.0000 | + | 27.7128i | 0.693037 | + | 1.20038i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00000 | + | 15.5885i | −0.389104 | + | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.0000 | + | 17.3205i | 0.431131 | + | 0.746740i | ||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.00000 | −0.343947 | −0.171973 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171973 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(542\) | −28.0000 | − | 48.4974i | −1.20270 | − | 2.08314i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.00000 | − | 13.8564i | 0.342997 | − | 0.594089i | ||||
\(545\) | −5.00000 | + | 8.66025i | −0.214176 | + | 0.370965i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.00000 | − | 6.92820i | −0.171028 | − | 0.296229i | 0.767752 | − | 0.640747i | \(-0.221375\pi\) |
−0.938779 | + | 0.344519i | \(0.888042\pi\) | |||||||
\(548\) | −14.0000 | −0.598050 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.00000 | 0.341121 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0000 | + | 17.3205i | −0.425243 | + | 0.736543i | ||||
\(554\) | −2.00000 | + | 3.46410i | −0.0849719 | + | 0.147176i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.0000 | − | 17.3205i | −0.424094 | − | 0.734553i | ||||
\(557\) | −2.00000 | −0.0847427 | −0.0423714 | − | 0.999102i | \(-0.513491\pi\) | ||||
−0.0423714 | + | 0.999102i | \(0.513491\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.0000 | −1.01509 | ||||||||
\(560\) | −4.00000 | − | 6.92820i | −0.169031 | − | 0.292770i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.0000 | + | 31.1769i | −0.759284 | + | 1.31512i | ||||
\(563\) | −2.00000 | + | 3.46410i | −0.0842900 | + | 0.145994i | −0.905088 | − | 0.425223i | \(-0.860196\pi\) |
0.820798 | + | 0.571218i | \(0.193529\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.50000 | − | 7.79423i | −0.189316 | − | 0.327906i | ||||
\(566\) | −8.00000 | −0.336265 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0000 | − | 24.2487i | 0.585882 | − | 1.01478i | −0.408883 | − | 0.912587i | \(-0.634082\pi\) |
0.994765 | − | 0.102190i | \(-0.0325850\pi\) | |||||||
\(572\) | −4.00000 | + | 6.92820i | −0.167248 | + | 0.289683i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16.0000 | + | 27.7128i | 0.667827 | + | 1.15671i | ||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.0000 | 1.37381 | 0.686904 | − | 0.726748i | \(-0.258969\pi\) | ||||
0.686904 | + | 0.726748i | \(0.258969\pi\) | |||||||
\(578\) | −13.0000 | − | 22.5167i | −0.540729 | − | 0.936570i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | + | 10.3923i | −0.248922 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.00000 | + | 5.19615i | 0.124247 | + | 0.215203i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −48.0000 | −1.98286 | ||||||||
\(587\) | −14.0000 | − | 24.2487i | −0.577842 | − | 1.00085i | −0.995726 | − | 0.0923513i | \(-0.970562\pi\) |
0.417885 | − | 0.908500i | \(-0.362772\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 5.00000 | − | 8.66025i | 0.205847 | − | 0.356537i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.00000 | + | 10.3923i | 0.246598 | + | 0.427121i | ||||
\(593\) | 44.0000 | 1.80686 | 0.903432 | − | 0.428732i | \(-0.141040\pi\) | ||||
0.903432 | + | 0.428732i | \(0.141040\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | 0.163984 | ||||||||
\(596\) | 10.0000 | + | 17.3205i | 0.409616 | + | 0.709476i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.00000 | + | 6.92820i | −0.163572 | + | 0.283315i | ||||
\(599\) | −20.0000 | + | 34.6410i | −0.817178 | + | 1.41539i | 0.0905757 | + | 0.995890i | \(0.471129\pi\) |
−0.907754 | + | 0.419504i | \(0.862204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00000 | − | 1.73205i | −0.0407909 | − | 0.0706518i | 0.844909 | − | 0.534910i | \(-0.179654\pi\) |
−0.885700 | + | 0.464258i | \(0.846321\pi\) | |||||||
\(602\) | −24.0000 | −0.978167 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.00000 | 0.162758 | ||||||||
\(605\) | −0.500000 | − | 0.866025i | −0.0203279 | − | 0.0352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.0000 | − | 19.0526i | 0.446476 | − | 0.773320i | −0.551678 | − | 0.834058i | \(-0.686012\pi\) |
0.998154 | + | 0.0607380i | \(0.0193454\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.0000 | + | 20.7846i | 0.485866 | + | 0.841544i | ||||
\(611\) | 32.0000 | 1.29458 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.0000 | −0.646234 | −0.323117 | − | 0.946359i | \(-0.604731\pi\) | ||||
−0.323117 | + | 0.946359i | \(0.604731\pi\) | |||||||
\(614\) | 8.00000 | + | 13.8564i | 0.322854 | + | 0.559199i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.00000 | + | 15.5885i | −0.362326 | + | 0.627568i | −0.988343 | − | 0.152242i | \(-0.951351\pi\) |
0.626017 | + | 0.779809i | \(0.284684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.5000 | + | 21.6506i | 0.502417 | + | 0.870212i | 0.999996 | + | 0.00279365i | \(0.000889247\pi\) |
−0.497579 | + | 0.867419i | \(0.665777\pi\) | |||||||
\(620\) | 14.0000 | 0.562254 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.0000 | −0.962312 | ||||||||
\(623\) | 15.0000 | + | 25.9808i | 0.600962 | + | 1.04090i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | −1.00000 | + | 1.73205i | −0.0399680 | + | 0.0692267i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.00000 | + | 12.1244i | 0.279330 | + | 0.483814i | ||||
\(629\) | −6.00000 | −0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.00000 | 0.278666 | 0.139333 | − | 0.990246i | \(-0.455504\pi\) | ||||
0.139333 | + | 0.990246i | \(0.455504\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.0000 | − | 22.5167i | 0.516296 | − | 0.894251i | ||||
\(635\) | −4.00000 | + | 6.92820i | −0.158735 | + | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.00000 | + | 10.3923i | 0.237729 | + | 0.411758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5000 | + | 28.5788i | 0.651711 | + | 1.12880i | 0.982708 | + | 0.185164i | \(0.0592817\pi\) |
−0.330997 | + | 0.943632i | \(0.607385\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5000 | + | 25.1147i | −0.571824 | + | 0.990429i | 0.424555 | + | 0.905402i | \(0.360431\pi\) |
−0.996379 | + | 0.0850262i | \(0.972903\pi\) | |||||||
\(644\) | −2.00000 | + | 3.46410i | −0.0788110 | + | 0.136505i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.00000 | −0.275198 | −0.137599 | − | 0.990488i | \(-0.543939\pi\) | ||||
−0.137599 | + | 0.990488i | \(0.543939\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.00000 | 0.196267 | ||||||||
\(650\) | −16.0000 | − | 27.7128i | −0.627572 | − | 1.08699i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | + | 6.92820i | −0.156652 | + | 0.271329i | ||||
\(653\) | 20.5000 | − | 35.5070i | 0.802227 | − | 1.38950i | −0.115920 | − | 0.993259i | \(-0.536982\pi\) |
0.918147 | − | 0.396239i | \(-0.129685\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.00000 | + | 15.5885i | 0.351659 | + | 0.609091i | ||||
\(656\) | 32.0000 | 1.24939 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 32.0000 | 1.24749 | ||||||||
\(659\) | −5.00000 | − | 8.66025i | −0.194772 | − | 0.337356i | 0.752054 | − | 0.659102i | \(-0.229063\pi\) |
−0.946826 | + | 0.321746i | \(0.895730\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.5000 | + | 32.0429i | −0.719567 | + | 1.24633i | 0.241605 | + | 0.970375i | \(0.422326\pi\) |
−0.961172 | + | 0.275951i | \(0.911007\pi\) | |||||||
\(662\) | 7.00000 | − | 12.1244i | 0.272063 | − | 0.471226i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 12.0000 | + | 20.7846i | 0.464294 | + | 0.804181i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.00000 | + | 12.1244i | −0.270434 | + | 0.468405i | ||||
\(671\) | −6.00000 | + | 10.3923i | −0.231627 | + | 0.401190i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.00000 | − | 12.1244i | −0.269830 | − | 0.467360i | 0.698988 | − | 0.715134i | \(-0.253634\pi\) |
−0.968818 | + | 0.247774i | \(0.920301\pi\) | |||||||
\(674\) | 44.0000 | 1.69482 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.00000 | 0.230769 | ||||||||
\(677\) | 21.0000 | + | 36.3731i | 0.807096 | + | 1.39793i | 0.914867 | + | 0.403755i | \(0.132295\pi\) |
−0.107772 | + | 0.994176i | \(0.534372\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.00000 | + | 12.1244i | −0.268635 | + | 0.465290i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.00000 | + | 12.1244i | 0.268044 | + | 0.464266i | ||||
\(683\) | −16.0000 | −0.612223 | −0.306111 | − | 0.951996i | \(-0.599028\pi\) | ||||
−0.306111 | + | 0.951996i | \(0.599028\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.00000 | −0.267456 | ||||||||
\(686\) | 20.0000 | + | 34.6410i | 0.763604 | + | 1.32260i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12.0000 | + | 20.7846i | −0.457496 | + | 0.792406i | ||||
\(689\) | 12.0000 | − | 20.7846i | 0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.50000 | − | 14.7224i | −0.323355 | − | 0.560068i | 0.657823 | − | 0.753173i | \(-0.271478\pi\) |
−0.981178 | + | 0.193105i | \(0.938144\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −56.0000 | −2.12573 | ||||||||
\(695\) | −5.00000 | − | 8.66025i | −0.189661 | − | 0.328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.00000 | + | 13.8564i | −0.303022 | + | 0.524849i | ||||
\(698\) | 30.0000 | − | 51.9615i | 1.13552 | − | 1.96677i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.00000 | − | 13.8564i | −0.302372 | − | 0.523723i | ||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.00000 | + | 6.92820i | 0.150756 | + | 0.261116i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.0000 | + | 36.3731i | −0.790345 | + | 1.36892i | ||||
\(707\) | 2.00000 | − | 3.46410i | 0.0752177 | − | 0.130281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.5000 | + | 21.6506i | 0.469447 | + | 0.813107i | 0.999390 | − | 0.0349269i | \(-0.0111198\pi\) |
−0.529943 | + | 0.848034i | \(0.677787\pi\) | |||||||
\(710\) | 6.00000 | 0.225176 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.50000 | + | 6.06218i | 0.131076 | + | 0.227030i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.00000 | + | 3.46410i | −0.0747958 | + | 0.129550i | ||||
\(716\) | 15.0000 | − | 25.9808i | 0.560576 | − | 0.970947i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.0000 | − | 34.6410i | −0.746393 | − | 1.29279i | ||||
\(719\) | 15.0000 | 0.559406 | 0.279703 | − | 0.960087i | \(-0.409764\pi\) | ||||
0.279703 | + | 0.960087i | \(0.409764\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.0000 | 1.19174 | ||||||||
\(722\) | −19.0000 | − | 32.9090i | −0.707107 | − | 1.22474i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.00000 | + | 12.1244i | −0.260153 | + | 0.450598i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.50000 | − | 2.59808i | −0.0556319 | − | 0.0963573i | 0.836868 | − | 0.547404i | \(-0.184384\pi\) |
−0.892500 | + | 0.451047i | \(0.851051\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.00000 | −0.296093 | ||||||||
\(731\) | −6.00000 | − | 10.3923i | −0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.0000 | − | 31.1769i | 0.664845 | − | 1.15155i | −0.314482 | − | 0.949263i | \(-0.601831\pi\) |
0.979327 | − | 0.202282i | \(-0.0648358\pi\) | |||||||
\(734\) | −17.0000 | + | 29.4449i | −0.627481 | + | 1.08683i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | + | 6.92820i | 0.147442 | + | 0.255377i | ||||
\(737\) | −7.00000 | −0.257848 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.0000 | 1.83928 | 0.919640 | − | 0.392763i | \(-0.128481\pi\) | ||||
0.919640 | + | 0.392763i | \(0.128481\pi\) | |||||||
\(740\) | −3.00000 | − | 5.19615i | −0.110282 | − | 0.191014i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.0000 | − | 20.7846i | 0.440534 | − | 0.763027i | ||||
\(743\) | −2.00000 | + | 3.46410i | −0.0733729 | + | 0.127086i | −0.900378 | − | 0.435110i | \(-0.856710\pi\) |
0.827005 | + | 0.562195i | \(0.190043\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.00000 | + | 8.66025i | 0.183186 | + | 0.317287i | ||||
\(746\) | 52.0000 | 1.90386 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.00000 | −0.146254 | ||||||||
\(749\) | 18.0000 | + | 31.1769i | 0.657706 | + | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.5000 | − | 19.9186i | 0.419641 | − | 0.726839i | −0.576262 | − | 0.817265i | \(-0.695489\pi\) |
0.995903 | + | 0.0904254i | \(0.0288227\pi\) | |||||||
\(752\) | 16.0000 | − | 27.7128i | 0.583460 | − | 1.01058i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.00000 | 0.0727875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | −5.00000 | − | 8.66025i | −0.181608 | − | 0.314555i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | + | 10.3923i | −0.217500 | + | 0.376721i | −0.954043 | − | 0.299670i | \(-0.903123\pi\) |
0.736543 | + | 0.676391i | \(0.236457\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.0000 | + | 17.3205i | 0.362024 | + | 0.627044i | ||||
\(764\) | 34.0000 | 1.23008 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.00000 | 0.0722629 | ||||||||
\(767\) | −10.0000 | − | 17.3205i | −0.361079 | − | 0.625407i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0000 | + | 17.3205i | −0.360609 | + | 0.624593i | −0.988061 | − | 0.154062i | \(-0.950765\pi\) |
0.627452 | + | 0.778655i | \(0.284098\pi\) | |||||||
\(770\) | −2.00000 | + | 3.46410i | −0.0720750 | + | 0.124838i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.00000 | − | 6.92820i | −0.143963 | − | 0.249351i | ||||
\(773\) | −6.00000 | −0.215805 | −0.107903 | − | 0.994161i | \(-0.534413\pi\) | ||||
−0.107903 | + | 0.994161i | \(0.534413\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.0000 | −1.00579 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.0000 | + | 25.9808i | −0.537776 | + | 0.931455i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.50000 | + | 2.59808i | 0.0536742 | + | 0.0929665i | ||||
\(782\) | −4.00000 | −0.143040 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.0000 | 0.428571 | ||||||||
\(785\) | 3.50000 | + | 6.06218i | 0.124920 | + | 0.216368i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.0000 | − | 27.7128i | 0.570338 | − | 0.987855i | −0.426193 | − | 0.904632i | \(-0.640145\pi\) |
0.996531 | − | 0.0832226i | \(-0.0265213\pi\) | |||||||
\(788\) | 2.00000 | − | 3.46410i | 0.0712470 | − | 0.123404i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10.0000 | − | 17.3205i | −0.355784 | − | 0.616236i | ||||
\(791\) | −18.0000 | −0.640006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.0000 | 1.70453 | ||||||||
\(794\) | −2.00000 | − | 3.46410i | −0.0709773 | − | 0.122936i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.5000 | + | 45.8993i | −0.938678 | + | 1.62584i | −0.170738 | + | 0.985316i | \(0.554615\pi\) |
−0.767940 | + | 0.640522i | \(0.778718\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | + | 13.8564i | 0.283020 | + | 0.490204i | ||||
\(800\) | −32.0000 | −1.13137 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.00000 | −0.141245 | ||||||||
\(803\) | −2.00000 | − | 3.46410i | −0.0705785 | − | 0.122245i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.00000 | + | 1.73205i | −0.0352454 | + | 0.0610468i | ||||
\(806\) | 28.0000 | − | 48.4974i | 0.986258 | − | 1.70825i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.0000 | −1.33436 | −0.667180 | − | 0.744896i | \(-0.732499\pi\) | ||||
−0.667180 | + | 0.744896i | \(0.732499\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.00000 | − | 5.19615i | 0.105150 | − | 0.182125i | ||||
\(815\) | −2.00000 | + | 3.46410i | −0.0700569 | + | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 60.0000 | 2.09785 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16.0000 | −0.558744 | ||||||||
\(821\) | −11.0000 | − | 19.0526i | −0.383903 | − | 0.664939i | 0.607714 | − | 0.794156i | \(-0.292087\pi\) |
−0.991616 | + | 0.129217i | \(0.958754\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.5000 | + | 33.7750i | −0.679727 | + | 1.17732i | 0.295336 | + | 0.955394i | \(0.404569\pi\) |
−0.975063 | + | 0.221929i | \(0.928765\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.0000 | − | 17.3205i | −0.347945 | − | 0.602658i | ||||
\(827\) | −52.0000 | −1.80822 | −0.904109 | − | 0.427303i | \(-0.859464\pi\) | ||||
−0.904109 | + | 0.427303i | \(0.859464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.0000 | 0.868286 | 0.434143 | − | 0.900844i | \(-0.357051\pi\) | ||||
0.434143 | + | 0.900844i | \(0.357051\pi\) | |||||||
\(830\) | −6.00000 | − | 10.3923i | −0.208263 | − | 0.360722i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16.0000 | − | 27.7128i | 0.554700 | − | 0.960769i | ||||
\(833\) | −3.00000 | + | 5.19615i | −0.103944 | + | 0.180036i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.00000 | + | 10.3923i | 0.207639 | + | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −40.0000 | −1.38178 | ||||||||
\(839\) | 2.50000 | + | 4.33013i | 0.0863096 | + | 0.149493i | 0.905949 | − | 0.423388i | \(-0.139159\pi\) |
−0.819639 | + | 0.572880i | \(0.805826\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.5000 | − | 25.1147i | 0.500000 | − | 0.866025i | ||||
\(842\) | 22.0000 | − | 38.1051i | 0.758170 | − | 1.31319i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.0000 | − | 20.7846i | −0.413057 | − | 0.715436i | ||||
\(845\) | 3.00000 | 0.103203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | −12.0000 | − | 20.7846i | −0.412082 | − | 0.713746i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.00000 | − | 13.8564i | 0.274398 | − | 0.475271i | ||||
\(851\) | 1.50000 | − | 2.59808i | 0.0514193 | − | 0.0890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.00000 | − | 12.1244i | −0.239675 | − | 0.415130i | 0.720946 | − | 0.692992i | \(-0.243708\pi\) |
−0.960621 | + | 0.277862i | \(0.910374\pi\) | |||||||
\(854\) | 48.0000 | 1.64253 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.00000 | − | 6.92820i | −0.136637 | − | 0.236663i | 0.789584 | − | 0.613642i | \(-0.210296\pi\) |
−0.926222 | + | 0.376979i | \(0.876963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.50000 | − | 12.9904i | 0.255897 | − | 0.443226i | −0.709242 | − | 0.704965i | \(-0.750963\pi\) |
0.965139 | + | 0.261739i | \(0.0842960\pi\) | |||||||
\(860\) | 6.00000 | − | 10.3923i | 0.204598 | − | 0.354375i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.0000 | − | 31.1769i | −0.613082 | − | 1.06189i | ||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | −11.0000 | − | 19.0526i | −0.373795 | − | 0.647432i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.0000 | − | 24.2487i | 0.475191 | − | 0.823055i | ||||
\(869\) | 5.00000 | − | 8.66025i | 0.169613 | − | 0.293779i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.0000 | + | 24.2487i | 0.474372 | + | 0.821636i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.00000 | − | 15.5885i | −0.304256 | − | 0.526986i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.00000 | − | 10.3923i | 0.202606 | − | 0.350923i | −0.746762 | − | 0.665092i | \(-0.768392\pi\) |
0.949367 | + | 0.314169i | \(0.101726\pi\) | |||||||
\(878\) | 40.0000 | − | 69.2820i | 1.34993 | − | 2.33816i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.00000 | + | 3.46410i | 0.0674200 | + | 0.116775i | ||||
\(881\) | −43.0000 | −1.44871 | −0.724353 | − | 0.689429i | \(-0.757862\pi\) | ||||
−0.724353 | + | 0.689429i | \(0.757862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.00000 | 0.134611 | 0.0673054 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673054 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(884\) | 8.00000 | + | 13.8564i | 0.269069 | + | 0.466041i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.0000 | + | 19.0526i | −0.369552 | + | 0.640083i | ||||
\(887\) | 11.0000 | − | 19.0526i | 0.369344 | − | 0.639722i | −0.620119 | − | 0.784508i | \(-0.712916\pi\) |
0.989463 | + | 0.144785i | \(0.0462491\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | + | 13.8564i | 0.268311 | + | 0.464729i | ||||
\(890\) | −30.0000 | −1.00560 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 38.0000 | 1.27233 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.50000 | − | 12.9904i | 0.250697 | − | 0.434221i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 35.0000 | + | 60.6218i | 1.16797 | + | 2.02297i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | −8.00000 | − | 13.8564i | −0.266371 | − | 0.461368i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.50000 | + | 6.06218i | −0.116344 | + | 0.201514i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.00000 | + | 10.3923i | 0.199227 | + | 0.345071i | 0.948278 | − | 0.317441i | \(-0.102824\pi\) |
−0.749051 | + | 0.662512i | \(0.769490\pi\) | |||||||
\(908\) | 36.0000 | 1.19470 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 16.0000 | 0.530395 | ||||||||
\(911\) | −6.00000 | − | 10.3923i | −0.198789 | − | 0.344312i | 0.749347 | − | 0.662177i | \(-0.230367\pi\) |
−0.948136 | + | 0.317865i | \(0.897034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.00000 | − | 5.19615i | 0.0992855 | − | 0.171968i | ||||
\(914\) | −12.0000 | + | 20.7846i | −0.396925 | + | 0.687494i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.0000 | − | 25.9808i | −0.495614 | − | 0.858429i | ||||
\(917\) | 36.0000 | 1.18882 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.0000 | 0.329870 | 0.164935 | − | 0.986304i | \(-0.447259\pi\) | ||||
0.164935 | + | 0.986304i | \(0.447259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.0000 | − | 20.7846i | 0.395199 | − | 0.684505i | ||||
\(923\) | 6.00000 | − | 10.3923i | 0.197492 | − | 0.342067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | + | 10.3923i | 0.197279 | + | 0.341697i | ||||
\(926\) | 22.0000 | 0.722965 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.0000 | + | 25.9808i | 0.492134 | + | 0.852401i | 0.999959 | − | 0.00905914i | \(-0.00288365\pi\) |
−0.507825 | + | 0.861460i | \(0.669550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −24.0000 | + | 41.5692i | −0.786146 | + | 1.36165i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −27.0000 | − | 46.7654i | −0.883467 | − | 1.53021i | ||||
\(935\) | −2.00000 | −0.0654070 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.00000 | 0.261349 | 0.130674 | − | 0.991425i | \(-0.458286\pi\) | ||||
0.130674 | + | 0.991425i | \(0.458286\pi\) | |||||||
\(938\) | 14.0000 | + | 24.2487i | 0.457116 | + | 0.791748i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.00000 | + | 13.8564i | −0.260931 | + | 0.451946i | ||||
\(941\) | −21.0000 | + | 36.3731i | −0.684580 | + | 1.18573i | 0.288988 | + | 0.957333i | \(0.406681\pi\) |
−0.973568 | + | 0.228395i | \(0.926652\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.00000 | − | 6.92820i | −0.130258 | − | 0.225613i | ||||
\(944\) | −20.0000 | −0.650945 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | 13.5000 | + | 23.3827i | 0.438691 | + | 0.759835i | 0.997589 | − | 0.0694014i | \(-0.0221089\pi\) |
−0.558898 | + | 0.829237i | \(0.688776\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.00000 | + | 13.8564i | −0.259691 | + | 0.449798i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.0000 | 1.10137 | 0.550684 | − | 0.834714i | \(-0.314367\pi\) | ||||
0.550684 | + | 0.834714i | \(0.314367\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.0000 | 0.550107 | ||||||||
\(956\) | 30.0000 | + | 51.9615i | 0.970269 | + | 1.68056i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.0000 | − | 34.6410i | 0.646171 | − | 1.11920i | ||||
\(959\) | −7.00000 | + | 12.1244i | −0.226042 | + | 0.391516i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | − | 15.5885i | −0.290323 | − | 0.502853i | ||||
\(962\) | −24.0000 | −0.773791 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.0000 | −0.515325 | ||||||||
\(965\) | −2.00000 | − | 3.46410i | −0.0643823 | − | 0.111513i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0000 | − | 27.7128i | 0.514525 | − | 0.891184i | −0.485333 | − | 0.874330i | \(-0.661301\pi\) |
0.999858 | − | 0.0168544i | \(-0.00536518\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.00000 | − | 12.1244i | −0.224756 | − | 0.389290i | ||||
\(971\) | 47.0000 | 1.50830 | 0.754151 | − | 0.656701i | \(-0.228049\pi\) | ||||
0.754151 | + | 0.656701i | \(0.228049\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.0000 | −0.641171 | ||||||||
\(974\) | 23.0000 | + | 39.8372i | 0.736968 | + | 1.27647i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.0000 | − | 41.5692i | 0.768221 | − | 1.33060i | ||||
\(977\) | 13.5000 | − | 23.3827i | 0.431903 | − | 0.748078i | −0.565134 | − | 0.824999i | \(-0.691176\pi\) |
0.997037 | + | 0.0769208i | \(0.0245089\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.50000 | − | 12.9904i | −0.239701 | − | 0.415174i | ||||
\(980\) | −6.00000 | −0.191663 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.0000 | 0.510581 | ||||||||
\(983\) | −19.5000 | − | 33.7750i | −0.621953 | − | 1.07725i | −0.989122 | − | 0.147100i | \(-0.953006\pi\) |
0.367168 | − | 0.930155i | \(-0.380327\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.00000 | − | 1.73205i | 0.0318626 | − | 0.0551877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | −28.0000 | − | 48.4974i | −0.889001 | − | 1.53979i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.00000 | − | 10.3923i | 0.190308 | − | 0.329624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.0000 | − | 32.9090i | −0.601736 | − | 1.04224i | −0.992558 | − | 0.121771i | \(-0.961143\pi\) |
0.390822 | − | 0.920466i | \(-0.372191\pi\) | |||||||
\(998\) | −40.0000 | −1.26618 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))