Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(341,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.341");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.w (of order \(6\), 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.6 | ||
Root | \(-0.268067 + 1.71118i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.521 |
Dual form | 756.2.w.a.341.6 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.842869 | − | 1.45989i | 0.376942 | − | 0.652883i | −0.613673 | − | 0.789560i | \(-0.710309\pi\) |
0.990616 | + | 0.136677i | \(0.0436422\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.27938 | + | 1.34329i | −0.861524 | + | 0.507717i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.38216 | + | 1.95269i | −1.01976 | + | 0.588758i | −0.914034 | − | 0.405637i | \(-0.867050\pi\) |
−0.105725 | + | 0.994395i | \(0.533716\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.24391 | + | 3.02757i | −1.45440 | + | 0.839698i | −0.998727 | − | 0.0504496i | \(-0.983935\pi\) |
−0.455673 | + | 0.890147i | \(0.650601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.201244 | − | 0.348565i | 0.0488088 | − | 0.0845393i | −0.840589 | − | 0.541674i | \(-0.817791\pi\) |
0.889398 | + | 0.457134i | \(0.151124\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.145617 | + | 0.0840718i | −0.0334067 | + | 0.0192874i | −0.516610 | − | 0.856221i | \(-0.672806\pi\) |
0.483204 | + | 0.875508i | \(0.339473\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.69373 | − | 4.44198i | −1.60425 | − | 0.926216i | −0.990623 | − | 0.136623i | \(-0.956375\pi\) |
−0.613630 | − | 0.789593i | \(-0.710291\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.07914 | + | 1.86913i | 0.215829 | + | 0.373827i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.15380 | + | 3.55290i | 1.14273 | + | 0.659757i | 0.947106 | − | 0.320921i | \(-0.103993\pi\) |
0.195627 | + | 0.980678i | \(0.437326\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.28766i | 1.12930i | 0.825331 | + | 0.564649i | \(0.190988\pi\) | ||||
−0.825331 | + | 0.564649i | \(0.809012\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0398441 | + | 4.45986i | 0.00673488 | + | 0.753855i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.13257 | + | 5.42578i | 0.514992 | + | 0.891992i | 0.999849 | + | 0.0173987i | \(0.00553846\pi\) |
−0.484857 | + | 0.874594i | \(0.661128\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.64707 | − | 2.85281i | −0.257229 | − | 0.445534i | 0.708269 | − | 0.705942i | \(-0.249476\pi\) |
−0.965499 | + | 0.260408i | \(0.916143\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.80474 | − | 3.12590i | 0.275220 | − | 0.476695i | −0.694971 | − | 0.719038i | \(-0.744583\pi\) |
0.970191 | + | 0.242343i | \(0.0779161\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.76965 | −1.27918 | −0.639592 | − | 0.768714i | \(-0.720897\pi\) | ||||
−0.639592 | + | 0.768714i | \(0.720897\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.39113 | − | 6.12374i | 0.484447 | − | 0.874820i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.94628 | − | 2.85574i | −0.679424 | − | 0.392266i | 0.120214 | − | 0.992748i | \(-0.461642\pi\) |
−0.799638 | + | 0.600482i | \(0.794975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.58345i | 0.887712i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.50326 | −0.586275 | −0.293138 | − | 0.956070i | \(-0.594699\pi\) | ||||
−0.293138 | + | 0.956070i | \(0.594699\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.12315i | − | 0.655952i | −0.944686 | − | 0.327976i | \(-0.893634\pi\) | ||
0.944686 | − | 0.327976i | \(-0.106366\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.2074i | 1.26607i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.91041 | −0.722072 | −0.361036 | − | 0.932552i | \(-0.617577\pi\) | ||||
−0.361036 | + | 0.932552i | \(0.617577\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4308i | 1.35658i | 0.734792 | + | 0.678292i | \(0.237280\pi\) | ||||
−0.734792 | + | 0.678292i | \(0.762720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.05559 | − | 3.49620i | −0.708753 | − | 0.409199i | 0.101846 | − | 0.994800i | \(-0.467525\pi\) |
−0.810599 | + | 0.585601i | \(0.800858\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.08619 | − | 8.99415i | 0.579625 | − | 1.02498i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.20794 | 0.135903 | 0.0679517 | − | 0.997689i | \(-0.478354\pi\) | ||||
0.0679517 | + | 0.997689i | \(0.478354\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.181350 | + | 0.314108i | −0.0199058 | + | 0.0344779i | −0.875807 | − | 0.482662i | \(-0.839670\pi\) |
0.855901 | + | 0.517140i | \(0.173003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.339244 | − | 0.587588i | −0.0367962 | − | 0.0637329i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.38526 | + | 2.39934i | 0.146837 | + | 0.254329i | 0.930057 | − | 0.367416i | \(-0.119757\pi\) |
−0.783220 | + | 0.621745i | \(0.786424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.88594 | − | 13.9451i | 0.826671 | − | 1.46184i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.283446i | 0.0290809i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.508914 | − | 0.293821i | −0.0516723 | − | 0.0298330i | 0.473941 | − | 0.880556i | \(-0.342831\pi\) |
−0.525614 | + | 0.850723i | \(0.676164\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.92329 | − | 11.9915i | −0.688893 | − | 1.19320i | −0.972196 | − | 0.234167i | \(-0.924764\pi\) |
0.283303 | − | 0.959030i | \(-0.408570\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.4610 | + | 6.03967i | 1.03075 | + | 0.595106i | 0.917201 | − | 0.398425i | \(-0.130443\pi\) |
0.113554 | + | 0.993532i | \(0.463777\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.9299 | − | 9.19711i | 1.54000 | − | 0.889118i | 0.541159 | − | 0.840920i | \(-0.317986\pi\) |
0.998838 | − | 0.0481978i | \(-0.0153478\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.51036 | + | 9.54422i | −0.527796 | + | 0.914170i | 0.471679 | + | 0.881771i | \(0.343648\pi\) |
−0.999475 | + | 0.0323997i | \(0.989685\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.36811 | − | 4.25398i | 0.693133 | − | 0.400181i | −0.111652 | − | 0.993747i | \(-0.535614\pi\) |
0.804785 | + | 0.593567i | \(0.202281\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.9696 | + | 7.48801i | −1.20942 | + | 0.698260i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.00951320 | + | 1.06484i | 0.000872074 | + | 0.0976137i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.12600 | − | 3.68234i | 0.193273 | − | 0.334758i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0670 | 1.07930 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6312 | −0.943365 | −0.471682 | − | 0.881769i | \(-0.656353\pi\) | ||||
−0.471682 | + | 0.881769i | \(0.656353\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.16740 | + | 5.48610i | −0.276737 | + | 0.479322i | −0.970572 | − | 0.240812i | \(-0.922586\pi\) |
0.693835 | + | 0.720134i | \(0.255920\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.218982 | − | 0.387237i | 0.0189882 | − | 0.0335777i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.4158 | + | 8.32296i | −1.23162 | + | 0.711078i | −0.967368 | − | 0.253375i | \(-0.918459\pi\) |
−0.264255 | + | 0.964453i | \(0.585126\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.24007 | − | 2.44800i | 0.359638 | − | 0.207637i | −0.309284 | − | 0.950970i | \(-0.600089\pi\) |
0.668922 | + | 0.743333i | \(0.266756\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.8238 | − | 20.4795i | 0.988758 | − | 1.71258i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.3737 | − | 5.98926i | 0.861489 | − | 0.497381i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.57864 | + | 2.64348i | 0.375097 | + | 0.216562i | 0.675683 | − | 0.737192i | \(-0.263849\pi\) |
−0.300586 | + | 0.953755i | \(0.597182\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.29163 | + | 12.6295i | 0.593385 | + | 1.02777i | 0.993773 | + | 0.111427i | \(0.0355421\pi\) |
−0.400388 | + | 0.916346i | \(0.631125\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.17930 | + | 5.29967i | 0.737299 | + | 0.425680i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.8009i | − | 1.42066i | −0.703867 | − | 0.710332i | \(-0.748545\pi\) | ||
0.703867 | − | 0.710332i | \(-0.251455\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.5038 | − | 0.209981i | 1.85236 | − | 0.0165488i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0482228 | + | 0.0835243i | 0.00377710 | + | 0.00654213i | 0.867908 | − | 0.496725i | \(-0.165464\pi\) |
−0.864131 | + | 0.503267i | \(0.832131\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.47872 | − | 4.29327i | −0.191809 | − | 0.332224i | 0.754041 | − | 0.656828i | \(-0.228102\pi\) |
−0.945850 | + | 0.324604i | \(0.894769\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8324 | − | 20.4943i | 0.910185 | − | 1.57649i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.8007 | 1.12527 | 0.562637 | − | 0.826704i | \(-0.309787\pi\) | ||||
0.562637 | + | 0.826704i | \(0.309787\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.97057 | − | 2.81086i | −0.375740 | − | 0.212481i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.592751 | + | 0.342225i | 0.0443043 | + | 0.0255791i | 0.521989 | − | 0.852952i | \(-0.325190\pi\) |
−0.477684 | + | 0.878532i | \(0.658524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.84745i | − | 0.583297i | −0.956526 | − | 0.291648i | \(-0.905796\pi\) | ||
0.956526 | − | 0.291648i | \(-0.0942037\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.5614 | 0.776489 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.57187i | 0.114946i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.5946i | 1.41781i | 0.705302 | + | 0.708907i | \(0.250811\pi\) | ||||
−0.705302 | + | 0.708907i | \(0.749189\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.3623 | 1.32175 | 0.660875 | − | 0.750496i | \(-0.270186\pi\) | ||||
0.660875 | + | 0.750496i | \(0.270186\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.92313i | 0.422006i | 0.977485 | + | 0.211003i | \(0.0676730\pi\) | ||||
−0.977485 | + | 0.211003i | \(0.932327\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.6268 | − | 7.86741i | −0.965975 | − | 0.557706i | −0.0679681 | − | 0.997687i | \(-0.521652\pi\) |
−0.898007 | + | 0.439982i | \(0.854985\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.7994 | + | 0.167953i | −1.31946 | + | 0.0117880i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.55306 | −0.387842 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.328332 | − | 0.568688i | 0.0227112 | − | 0.0393370i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.06619 | + | 8.77489i | 0.348771 | + | 0.604088i | 0.986031 | − | 0.166560i | \(-0.0532659\pi\) |
−0.637261 | + | 0.770648i | \(0.719933\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.04231 | − | 5.26944i | −0.207484 | − | 0.359373i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.44616 | − | 14.3320i | −0.573363 | − | 0.972917i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.43712i | 0.163939i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.3944 | + | 7.73325i | 0.896955 | + | 0.517857i | 0.876211 | − | 0.481928i | \(-0.160063\pi\) |
0.0207437 | + | 0.999785i | \(0.493397\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.0360 | − | 24.3110i | −0.931600 | − | 1.61358i | −0.780588 | − | 0.625046i | \(-0.785080\pi\) |
−0.151011 | − | 0.988532i | \(-0.548253\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.7453 | − | 8.51319i | −0.974396 | − | 0.562568i | −0.0738222 | − | 0.997271i | \(-0.523520\pi\) |
−0.900573 | + | 0.434704i | \(0.856853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.0015 | + | 9.23847i | −1.04829 | + | 0.605233i | −0.922171 | − | 0.386782i | \(-0.873587\pi\) |
−0.126122 | + | 0.992015i | \(0.540253\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.39166 | + | 12.8027i | −0.482179 | + | 0.835158i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.06656 | − | 3.50253i | 0.392413 | − | 0.226560i | −0.290792 | − | 0.956786i | \(-0.593919\pi\) |
0.683205 | + | 0.730226i | \(0.260585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.38459 | − | 3.10879i | 0.346852 | − | 0.200255i | −0.316446 | − | 0.948611i | \(-0.602490\pi\) |
0.663298 | + | 0.748355i | \(0.269156\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.08172 | − | 10.1122i | −0.388547 | − | 0.646044i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.509067 | − | 0.881730i | 0.0323912 | − | 0.0561031i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.81844 | −0.619734 | −0.309867 | − | 0.950780i | \(-0.600285\pi\) | ||||
−0.309867 | + | 0.950780i | \(0.600285\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.6952 | 2.18127 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.667904 | − | 1.15684i | 0.0416627 | − | 0.0721619i | −0.844442 | − | 0.535647i | \(-0.820068\pi\) |
0.886105 | + | 0.463485i | \(0.153401\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.4287 | − | 8.15944i | −0.896558 | − | 0.507003i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.6238 | + | 10.1751i | −1.08673 | + | 0.627424i | −0.932704 | − | 0.360643i | \(-0.882557\pi\) |
−0.154026 | + | 0.988067i | \(0.549224\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.33814 | + | 4.81402i | −0.512208 | + | 0.295723i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.3614 | + | 23.1426i | −0.814659 | + | 1.41103i | 0.0949131 | + | 0.995486i | \(0.469743\pi\) |
−0.909572 | + | 0.415546i | \(0.863591\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.76517 | − | 2.17382i | 0.228718 | − | 0.132050i | −0.381263 | − | 0.924467i | \(-0.624511\pi\) |
0.609980 | + | 0.792417i | \(0.291177\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.29968 | − | 4.21447i | −0.440187 | − | 0.254142i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.19901 | + | 3.80880i | 0.132126 | + | 0.228849i | 0.924496 | − | 0.381192i | \(-0.124486\pi\) |
−0.792370 | + | 0.610041i | \(0.791153\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.62273 | − | 2.66893i | −0.275769 | − | 0.159215i | 0.355738 | − | 0.934586i | \(-0.384230\pi\) |
−0.631506 | + | 0.775371i | \(0.717563\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 17.9476i | − | 1.06687i | −0.845840 | − | 0.533437i | \(-0.820900\pi\) | ||
0.845840 | − | 0.533437i | \(-0.179100\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.58645 | + | 4.29014i | 0.447814 | + | 0.253239i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.41900 | + | 14.5821i | 0.495235 | + | 0.857773i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.1126 | + | 22.7117i | 0.766048 | + | 1.32683i | 0.939691 | + | 0.342026i | \(0.111113\pi\) |
−0.173642 | + | 0.984809i | \(0.555554\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.79566 | + | 6.57428i | −0.220992 | + | 0.382769i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 53.7936 | 3.11097 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0853135 | + | 9.54939i | 0.00491739 | + | 0.550417i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.47924 | − | 4.31814i | −0.428260 | − | 0.247256i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.19520i | − | 0.410652i | −0.978694 | − | 0.205326i | \(-0.934175\pi\) | ||
0.978694 | − | 0.205326i | \(-0.0658254\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.17443 | −0.123301 | −0.0616503 | − | 0.998098i | \(-0.519636\pi\) | ||||
−0.0616503 | + | 0.998098i | \(0.519636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.8784i | 0.671409i | 0.941967 | + | 0.335704i | \(0.108974\pi\) | ||||
−0.941967 | + | 0.335704i | \(0.891026\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 8.19801i | − | 0.460446i | −0.973138 | − | 0.230223i | \(-0.926054\pi\) | ||
0.973138 | − | 0.230223i | \(-0.0739456\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.7509 | −1.55375 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0676757i | 0.00376558i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.3179 | − | 6.53438i | −0.627803 | − | 0.362462i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.9893 | − | 11.7802i | 1.10205 | − | 0.649463i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1708 | 0.943793 | 0.471897 | − | 0.881654i | \(-0.343570\pi\) | ||||
0.471897 | + | 0.881654i | \(0.343570\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.98170 | + | 8.62856i | −0.272179 | + | 0.471428i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.95399 | + | 6.84850i | 0.215387 | + | 0.373062i | 0.953392 | − | 0.301733i | \(-0.0975653\pi\) |
−0.738005 | + | 0.674795i | \(0.764232\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.2779 | − | 21.2659i | −0.664883 | − | 1.15161i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.496303 | + | 18.5136i | 0.0267979 | + | 0.999641i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 0.512514i | − | 0.0275132i | −0.999905 | − | 0.0137566i | \(-0.995621\pi\) | ||
0.999905 | − | 0.0137566i | \(-0.00437900\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.74612 | + | 3.31752i | 0.307583 | + | 0.177583i | 0.645844 | − | 0.763469i | \(-0.276506\pi\) |
−0.338262 | + | 0.941052i | \(0.609839\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.03437 | − | 15.6480i | −0.480851 | − | 0.832858i | 0.518908 | − | 0.854830i | \(-0.326339\pi\) |
−0.999759 | + | 0.0219721i | \(0.993006\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.6877 | + | 9.63465i | 0.885691 | + | 0.511354i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.52677 | + | 0.881479i | −0.0805796 | + | 0.0465227i | −0.539748 | − | 0.841826i | \(-0.681481\pi\) |
0.459169 | + | 0.888349i | \(0.348147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.48586 | + | 16.4300i | −0.499256 | + | 0.864737i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.2081 | + | 5.89367i | −0.534318 | + | 0.308489i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.9614 | + | 16.7209i | −1.51177 | + | 0.872822i | −0.511867 | + | 0.859065i | \(0.671046\pi\) |
−0.999905 | + | 0.0137576i | \(0.995621\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.1105 | − | 0.134996i | 0.784500 | − | 0.00700867i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.7844 | + | 22.1433i | −0.661952 | + | 1.14653i | 0.318150 | + | 0.948040i | \(0.396938\pi\) |
−0.980102 | + | 0.198494i | \(0.936395\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −43.0267 | −2.21599 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.7920 | 1.32485 | 0.662423 | − | 0.749130i | \(-0.269528\pi\) | ||||
0.662423 | + | 0.749130i | \(0.269528\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.4158 | + | 28.4330i | −0.838808 | + | 1.45286i | 0.0520838 | + | 0.998643i | \(0.483414\pi\) |
−0.890892 | + | 0.454215i | \(0.849920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.84349 | − | 15.0062i | −0.450706 | − | 0.764785i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.4542 | − | 10.0772i | 0.884965 | − | 0.510935i | 0.0126730 | − | 0.999920i | \(-0.495966\pi\) |
0.872292 | + | 0.488985i | \(0.162633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.09663 | + | 1.78784i | −0.156603 | + | 0.0904150i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.01813 | − | 1.76346i | 0.0512278 | − | 0.0887291i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.2125 | + | 17.4432i | −1.51632 | + | 0.875449i | −0.516506 | + | 0.856284i | \(0.672768\pi\) |
−0.999816 | + | 0.0191652i | \(0.993899\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.36793 | − | 4.83122i | −0.417874 | − | 0.241260i | 0.276293 | − | 0.961073i | \(-0.410894\pi\) |
−0.694167 | + | 0.719814i | \(0.744227\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.0364 | − | 32.9719i | −0.948268 | − | 1.64245i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1897 | − | 12.2339i | −1.05034 | − | 0.606412i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.0893i | 1.83395i | 0.398949 | + | 0.916973i | \(0.369375\pi\) | ||||
−0.398949 | + | 0.916973i | \(0.630625\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.2646 | − | 6.04920i | 0.505090 | − | 0.297662i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.305709 | + | 0.529504i | 0.0150067 | + | 0.0259923i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.84193 | − | 3.19031i | −0.0899841 | − | 0.155857i | 0.817520 | − | 0.575900i | \(-0.195348\pi\) |
−0.907504 | + | 0.420043i | \(0.862015\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.55139 | + | 14.8114i | −0.416769 | + | 0.721866i | −0.995612 | − | 0.0935732i | \(-0.970171\pi\) |
0.578843 | + | 0.815439i | \(0.303504\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.868685 | 0.0421374 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.88188 | + | 11.6776i | 0.333038 | + | 0.565118i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.3242 | − | 15.7756i | −1.31616 | − | 0.759885i | −0.333051 | − | 0.942909i | \(-0.608078\pi\) |
−0.983108 | + | 0.183024i | \(0.941411\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.0692i | − | 0.483893i | −0.970290 | − | 0.241947i | \(-0.922214\pi\) | ||
0.970290 | − | 0.241947i | \(-0.0777859\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.49378 | 0.0714572 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 27.9398i | − | 1.33350i | −0.745283 | − | 0.666748i | \(-0.767686\pi\) | ||
0.745283 | − | 0.666748i | \(-0.232314\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.8638i | 1.65643i | 0.560411 | + | 0.828215i | \(0.310643\pi\) | ||||
−0.560411 | + | 0.828215i | \(0.689357\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.67037 | 0.221397 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.2411i | 1.09682i | 0.836211 | + | 0.548408i | \(0.184766\pi\) | ||||
−0.836211 | + | 0.548408i | \(0.815234\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.1413 | + | 6.43244i | 0.524624 | + | 0.302892i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.7115 | − | 23.2665i | −0.642805 | − | 1.09075i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.21876 | −0.290901 | −0.145451 | − | 0.989366i | \(-0.546463\pi\) | ||||
−0.145451 | + | 0.989366i | \(0.546463\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.17165 | − | 3.76140i | 0.101144 | − | 0.175186i | −0.811012 | − | 0.585029i | \(-0.801083\pi\) |
0.912156 | + | 0.409843i | \(0.134416\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.57451 | + | 6.19124i | 0.166122 | + | 0.287731i | 0.937053 | − | 0.349187i | \(-0.113542\pi\) |
−0.770931 | + | 0.636918i | \(0.780209\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.944451 | − | 1.63584i | −0.0437040 | − | 0.0756975i | 0.843346 | − | 0.537371i | \(-0.180583\pi\) |
−0.887050 | + | 0.461673i | \(0.847249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4721 | − | 7.93941i | 0.622082 | − | 0.366608i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.0964i | 0.648152i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.314283 | − | 0.181451i | −0.0144203 | − | 0.00832555i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.22491 | + | 9.04981i | 0.238732 | + | 0.413497i | 0.960351 | − | 0.278794i | \(-0.0899348\pi\) |
−0.721618 | + | 0.692291i | \(0.756601\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.8539 | − | 18.9682i | −1.49801 | − | 0.864875i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.857895 | + | 0.495306i | −0.0389550 | + | 0.0224907i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.8298 | + | 20.4898i | −0.536060 | + | 0.928483i | 0.463052 | + | 0.886331i | \(0.346754\pi\) |
−0.999111 | + | 0.0421513i | \(0.986579\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.6767 | − | 6.74152i | 0.526960 | − | 0.304241i | −0.212817 | − | 0.977092i | \(-0.568264\pi\) |
0.739778 | + | 0.672851i | \(0.234931\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.47683 | − | 1.43000i | 0.111551 | − | 0.0644039i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.3549 | − | 26.0551i | −0.688761 | − | 1.16873i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.04035 | − | 10.4622i | 0.270403 | − | 0.468352i | −0.698562 | − | 0.715550i | \(-0.746176\pi\) |
0.968965 | + | 0.247197i | \(0.0795096\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.5283 | −0.915310 | −0.457655 | − | 0.889130i | \(-0.651310\pi\) | ||||
−0.457655 | + | 0.889130i | \(0.651310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.3417 | −1.03869 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.09043 | + | 7.08483i | −0.181305 | + | 0.314029i | −0.942325 | − | 0.334699i | \(-0.891365\pi\) |
0.761020 | + | 0.648728i | \(0.224699\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.4994 | − | 0.165272i | 0.818365 | − | 0.00731121i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.6345 | − | 10.1813i | 0.777070 | − | 0.448642i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.6603 | − | 17.1244i | 1.30446 | − | 0.753131i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.8746 | + | 24.0314i | −0.607856 | + | 1.05284i | 0.383738 | + | 0.923442i | \(0.374637\pi\) |
−0.991593 | + | 0.129395i | \(0.958697\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.8843 | − | 11.4802i | 0.869478 | − | 0.501993i | 0.00230311 | − | 0.999997i | \(-0.499267\pi\) |
0.867175 | + | 0.498004i | \(0.165934\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.19166 | + | 1.26535i | 0.0954700 | + | 0.0551196i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.9623 | + | 48.4322i | 1.21575 | + | 2.10575i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.2742 | + | 9.97325i | 0.748228 | + | 0.431990i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 31.0078i | − | 1.34058i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.488426 | + | 27.3333i | 0.0210380 | + | 1.17733i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.60405 | − | 4.51035i | −0.111957 | − | 0.193915i | 0.804602 | − | 0.593814i | \(-0.202379\pi\) |
−0.916559 | + | 0.399899i | \(0.869045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.28902 | + | 16.0890i | 0.397898 | + | 0.689179i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6224 | − | 18.3985i | 0.454181 | − | 0.786664i | −0.544460 | − | 0.838787i | \(-0.683265\pi\) |
0.998641 | + | 0.0521229i | \(0.0165988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.19479 | −0.0509000 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.75334 | + | 1.62261i | −0.117084 | + | 0.0690005i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.0945 | − | 6.40543i | −0.470090 | − | 0.271407i | 0.246187 | − | 0.969222i | \(-0.420822\pi\) |
−0.716277 | + | 0.697816i | \(0.754156\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.8559i | 0.924406i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.4793 | 1.57956 | 0.789781 | − | 0.613388i | \(-0.210194\pi\) | ||||
0.789781 | + | 0.613388i | \(0.210194\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 14.3422i | − | 0.603380i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.86938i | − | 0.287979i | −0.989579 | − | 0.143990i | \(-0.954007\pi\) | ||
0.989579 | − | 0.143990i | \(-0.0459932\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.169582 | 0.00709678 | 0.00354839 | − | 0.999994i | \(-0.498871\pi\) | ||||
0.00354839 | + | 0.999994i | \(0.498871\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 19.1741i | − | 0.799617i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.41193 | − | 3.12458i | −0.225302 | − | 0.130078i | 0.383101 | − | 0.923706i | \(-0.374856\pi\) |
−0.608403 | + | 0.793628i | \(0.708189\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.00857280 | − | 0.959578i | −0.000355660 | − | 0.0398100i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.3055 | 0.923799 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.7881 | − | 18.6855i | 0.445273 | − | 0.771235i | −0.552799 | − | 0.833315i | \(-0.686440\pi\) |
0.998071 | + | 0.0620801i | \(0.0197734\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.528615 | − | 0.915588i | −0.0217812 | − | 0.0377261i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.13036 | + | 7.15399i | 0.169613 | + | 0.293779i | 0.938284 | − | 0.345866i | \(-0.112415\pi\) |
−0.768671 | + | 0.639645i | \(0.779081\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.56257 | + | 0.883632i | 0.0640591 | + | 0.0362254i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.5206i | 1.45133i | 0.688047 | + | 0.725667i | \(0.258468\pi\) | ||||
−0.688047 | + | 0.725667i | \(0.741532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.8981 | − | 20.7258i | −1.46432 | − | 0.845423i | −0.465109 | − | 0.885254i | \(-0.653985\pi\) |
−0.999206 | + | 0.0398308i | \(0.987318\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.58388 | − | 6.20746i | −0.145705 | − | 0.252369i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.09569 | − | 1.20995i | −0.0850616 | − | 0.0491103i | 0.456866 | − | 0.889536i | \(-0.348972\pi\) |
−0.541927 | + | 0.840425i | \(0.682305\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 45.9873 | − | 26.5508i | 1.86045 | − | 1.07413i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.3228 | − | 36.9321i | 0.861219 | − | 1.49168i | −0.00953416 | − | 0.999955i | \(-0.503035\pi\) |
0.870753 | − | 0.491720i | \(-0.163632\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.2535 | + | 7.65193i | −0.533567 | + | 0.308055i | −0.742468 | − | 0.669882i | \(-0.766345\pi\) |
0.208901 | + | 0.977937i | \(0.433011\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.9177 | − | 13.8089i | 0.961334 | − | 0.555026i | 0.0647505 | − | 0.997901i | \(-0.479375\pi\) |
0.896583 | + | 0.442875i | \(0.146042\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.38054 | − | 3.60819i | −0.255631 | − | 0.144559i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.77517 | − | 8.27084i | 0.191007 | − | 0.330834i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.52164 | 0.100545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.28775 | 0.329930 | 0.164965 | − | 0.986299i | \(-0.447249\pi\) | ||||
0.164965 | + | 0.986299i | \(0.447249\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.96069 | + | 15.5204i | −0.355594 | + | 0.615907i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.757287 | + | 42.3793i | 0.0300048 | + | 1.67913i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.58307 | − | 4.95544i | 0.339011 | − | 0.195728i | −0.320824 | − | 0.947139i | \(-0.603960\pi\) |
0.659835 | + | 0.751411i | \(0.270626\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.83668 | + | 3.94716i | −0.269612 | + | 0.155661i | −0.628711 | − | 0.777639i | \(-0.716417\pi\) |
0.359099 | + | 0.933299i | \(0.383084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.15966 | − | 3.74063i | 0.0849049 | − | 0.147060i | −0.820446 | − | 0.571724i | \(-0.806275\pi\) |
0.905351 | + | 0.424665i | \(0.139608\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.2308 | − | 8.79348i | 0.597859 | − | 0.345174i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.5853 | − | 21.6999i | −1.47082 | − | 0.849181i | −0.471361 | − | 0.881940i | \(-0.656237\pi\) |
−0.999463 | + | 0.0327591i | \(0.989571\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.33940 | + | 9.24812i | 0.208628 | + | 0.361354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.34894 | + | 5.39761i | 0.364183 | + | 0.210261i | 0.670914 | − | 0.741535i | \(-0.265902\pi\) |
−0.306731 | + | 0.951796i | \(0.599235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.92015i | 0.152476i | 0.997090 | + | 0.0762381i | \(0.0242909\pi\) | ||||
−0.997090 | + | 0.0762381i | \(0.975709\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.380751 | − | 0.646081i | −0.0147649 | − | 0.0250539i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.5638 | − | 54.6701i | −1.22216 | − | 2.11683i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0039 | + | 17.3273i | 0.386197 | + | 0.668913i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.3404 | + | 21.3742i | −0.475687 | + | 0.823915i | −0.999612 | − | 0.0278497i | \(-0.991134\pi\) |
0.523925 | + | 0.851765i | \(0.324467\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.7265 | −0.565987 | −0.282994 | − | 0.959122i | \(-0.591328\pi\) | ||||
−0.282994 | + | 0.959122i | \(0.591328\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.55469 | − | 0.0138895i | 0.0596637 | − | 0.000533031i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.60128 | − | 0.924499i | −0.0612712 | − | 0.0353750i | 0.469051 | − | 0.883171i | \(-0.344596\pi\) |
−0.530323 | + | 0.847796i | \(0.677929\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.0606i | 1.07214i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.5838 | 1.31754 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.9842i | 1.48303i | 0.670938 | + | 0.741514i | \(0.265892\pi\) | ||||
−0.670938 | + | 0.741514i | \(0.734108\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8.25339i | − | 0.313069i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.32585 | −0.0502202 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 25.4389i | − | 0.960813i | −0.877046 | − | 0.480406i | \(-0.840489\pi\) | ||
0.877046 | − | 0.480406i | \(-0.159511\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.912310 | − | 0.526722i | −0.0344084 | − | 0.0198657i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.8889 | + | 18.0331i | 1.19930 | + | 0.678206i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.2903 | −0.536685 | −0.268342 | − | 0.963324i | \(-0.586476\pi\) | ||||
−0.268342 | + | 0.963324i | \(0.586476\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.9296 | − | 48.3756i | 1.04597 | − | 1.81168i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.9319 | − | 34.5230i | −0.745410 | − | 1.29109i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.7344 | − | 28.9848i | −0.624088 | − | 1.08095i | −0.988716 | − | 0.149799i | \(-0.952137\pi\) |
0.364629 | − | 0.931153i | \(-0.381196\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.9577 | + | 0.285507i | −1.19017 | + | 0.0106329i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.3364i | 0.569579i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.1354 | − | 7.00636i | −0.450076 | − | 0.259851i | 0.257786 | − | 0.966202i | \(-0.417007\pi\) |
−0.707862 | + | 0.706350i | \(0.750340\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.726384 | − | 1.25813i | −0.0268663 | − | 0.0465338i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.6491 | + | 13.6538i | 0.873501 | + | 0.504316i | 0.868510 | − | 0.495672i | \(-0.165078\pi\) |
0.00499085 | + | 0.999988i | \(0.498411\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.9899 | − | 11.5412i | 0.736339 | − | 0.425126i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.3157 | − | 45.5801i | 0.968039 | − | 1.67669i | 0.266819 | − | 0.963747i | \(-0.414027\pi\) |
0.701220 | − | 0.712945i | \(-0.252639\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.9523 | − | 17.8703i | 1.13553 | − | 0.655599i | 0.190211 | − | 0.981743i | \(-0.439083\pi\) |
0.945320 | + | 0.326144i | \(0.105750\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.71839 | − | 4.45621i | 0.282780 | − | 0.163263i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.9558 | + | 42.3621i | −0.875325 | + | 1.54788i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.5641 | − | 28.6899i | 0.604433 | − | 1.04691i | −0.387708 | − | 0.921782i | \(-0.626733\pi\) |
0.992141 | − | 0.125126i | \(-0.0399336\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.5836 | 0.894687 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6903 | −0.497584 | −0.248792 | − | 0.968557i | \(-0.580034\pi\) | ||||
−0.248792 | + | 0.968557i | \(0.580034\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.51737 | − | 11.2884i | 0.236255 | − | 0.409205i | −0.723382 | − | 0.690448i | \(-0.757413\pi\) |
0.959637 | + | 0.281243i | \(0.0907467\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.260486 | − | 29.1569i | −0.00943021 | − | 1.05555i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.6147 | − | 13.6340i | 0.852678 | − | 0.492294i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.4866 | − | 10.6732i | 0.666642 | − | 0.384886i | −0.128161 | − | 0.991753i | \(-0.540907\pi\) |
0.794803 | + | 0.606867i | \(0.207574\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.73940 | + | 9.94093i | −0.206432 | + | 0.357550i | −0.950588 | − | 0.310455i | \(-0.899518\pi\) |
0.744156 | + | 0.668006i | \(0.232852\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.7525 | + | 6.78529i | −0.422161 | + | 0.243735i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.479682 | + | 0.276944i | 0.0171864 | + | 0.00992256i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.3208 | − | 38.6607i | −0.798701 | − | 1.38339i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.9873 | − | 15.0038i | −0.927528 | − | 0.535509i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.2006i | 1.46864i | 0.678802 | + | 0.734322i | \(0.262500\pi\) | ||||
−0.678802 | + | 0.734322i | \(0.737500\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.0804 | + | 19.5939i | −0.393972 | + | 0.696681i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.5107 | + | 26.8653i | 0.550801 | + | 0.954016i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.0066 | + | 43.3127i | 0.885779 | + | 1.53421i | 0.844819 | + | 0.535053i | \(0.179708\pi\) |
0.0409600 | + | 0.999161i | \(0.486958\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.76484 | + | 3.05679i | −0.0624355 | + | 0.108141i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.3079 | 0.963677 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.5041 | − | 34.4900i | 0.687428 | − | 1.21561i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.8995 | + | 25.3454i | 1.54343 | + | 0.891097i | 0.998619 | + | 0.0525356i | \(0.0167303\pi\) |
0.544807 | + | 0.838562i | \(0.316603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.96566i | − | 0.314827i | −0.987533 | − | 0.157413i | \(-0.949684\pi\) | ||
0.987533 | − | 0.157413i | \(-0.0503155\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.162582 | 0.00569500 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.606910i | 0.0212331i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.5845i | 1.13721i | 0.822612 | + | 0.568603i | \(0.192516\pi\) | ||||
−0.822612 | + | 0.568603i | \(0.807484\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.1754 | −0.703271 | −0.351636 | − | 0.936137i | \(-0.614374\pi\) | ||||
−0.351636 | + | 0.936137i | \(0.614374\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 0.253288i | − | 0.00880770i | −0.999990 | − | 0.00440385i | \(-0.998598\pi\) | ||
0.999990 | − | 0.00440385i | \(-0.00140179\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.10909 | − | 3.52708i | −0.212177 | − | 0.122501i | 0.390146 | − | 0.920753i | \(-0.372425\pi\) |
−0.602323 | + | 0.798253i | \(0.705758\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.45208 | − | 2.41439i | −0.0503114 | − | 0.0836538i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.35695 | −0.289204 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.0936 | + | 29.6069i | −0.590136 | + | 1.02215i | 0.404078 | + | 0.914725i | \(0.367592\pi\) |
−0.994214 | + | 0.107420i | \(0.965741\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7462 | + | 18.6130i | 0.370558 | + | 0.641826i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.9463 | − | 34.5480i | −0.686174 | − | 1.18849i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.100500 | + | 11.2493i | 0.00345323 | + | 0.386530i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 55.6593i | − | 1.90798i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.7586 | + | 12.5623i | 0.745000 | + | 0.430126i | 0.823884 | − | 0.566758i | \(-0.191802\pi\) |
−0.0788844 | + | 0.996884i | \(0.525136\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.0954 | − | 36.5383i | −0.720604 | − | 1.24812i | −0.960758 | − | 0.277388i | \(-0.910531\pi\) |
0.240154 | − | 0.970735i | \(-0.422802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.08139 | + | 2.35639i | 0.139255 | + | 0.0803990i | 0.568009 | − | 0.823022i | \(-0.307714\pi\) |
−0.428754 | + | 0.903421i | \(0.641047\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.8409 | − | 17.8060i | 1.04984 | − | 0.606123i | 0.127232 | − | 0.991873i | \(-0.459391\pi\) |
0.922603 | + | 0.385750i | \(0.126057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.4750 | − | 21.6074i | 0.424163 | − | 0.734672i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.08543 | + | 2.35873i | −0.138589 | + | 0.0800143i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.9937 | − | 17.8942i | 1.05018 | − | 0.606322i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.5053 | + | 16.2095i | −0.929847 | + | 0.547981i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.4532 | + | 35.4260i | −0.690655 | + | 1.19625i | 0.280969 | + | 0.959717i | \(0.409344\pi\) |
−0.971624 | + | 0.236532i | \(0.923989\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.4443 | 1.26153 | 0.630765 | − | 0.775974i | \(-0.282741\pi\) | ||||
0.630765 | + | 0.775974i | \(0.282741\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.8357 | −1.67711 | −0.838553 | − | 0.544821i | \(-0.816598\pi\) | ||||
−0.838553 | + | 0.544821i | \(0.816598\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.4482 | + | 25.0251i | −0.485124 | + | 0.840260i | −0.999854 | − | 0.0170929i | \(-0.994559\pi\) |
0.514730 | + | 0.857352i | \(0.327892\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.2325 | − | 14.2808i | 0.812731 | − | 0.478962i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.27701 | − | 0.737280i | 0.0427334 | − | 0.0246721i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.999223 | − | 0.576902i | 0.0334003 | − | 0.0192837i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22.3394 | + | 38.6930i | −0.745062 | + | 1.29048i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.99082 | + | 1.14940i | −0.0663238 | + | 0.0382920i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.4564 | − | 6.61437i | −0.380825 | − | 0.219869i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.43498 | + | 12.8778i | 0.246874 | + | 0.427599i | 0.962657 | − | 0.270724i | \(-0.0872632\pi\) |
−0.715783 | + | 0.698323i | \(0.753930\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.81616 | − | 4.51266i | −0.258961 | − | 0.149511i | 0.364899 | − | 0.931047i | \(-0.381103\pi\) |
−0.623861 | + | 0.781536i | \(0.714437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.41649i | − | 0.0468788i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.149729 | − | 16.7596i | −0.00494450 | − | 0.553452i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.2083 | + | 22.8774i | 0.435702 | + | 0.754657i | 0.997353 | − | 0.0727170i | \(-0.0231670\pi\) |
−0.561651 | + | 0.827374i | \(0.689834\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.6075 | − | 59.9420i | −1.13912 | − | 1.97302i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.76100 | + | 11.7104i | −0.222300 | + | 0.385036i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.2518 | −0.730058 | −0.365029 | − | 0.930996i | \(-0.618941\pi\) | ||||
−0.365029 | + | 0.930996i | \(0.618941\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0210289 | + | 1.17682i | 0.000689194 | + | 0.0385686i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.29476 | + | 1.32488i | 0.0750465 | + | 0.0433281i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.6822i | 0.479647i | 0.970817 | + | 0.239823i | \(0.0770896\pi\) | ||||
−0.970817 | + | 0.239823i | \(0.922910\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.0792 | −1.50214 | −0.751070 | − | 0.660223i | \(-0.770462\pi\) | ||||
−0.751070 | + | 0.660223i | \(0.770462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.2650i | 0.952999i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 8.03805i | − | 0.261202i | −0.991435 | − | 0.130601i | \(-0.958309\pi\) | ||
0.991435 | − | 0.130601i | \(-0.0416906\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.3400 | 1.37441 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.9348i | 1.77951i | 0.456437 | + | 0.889756i | \(0.349125\pi\) | ||||
−0.456437 | + | 0.889756i | \(0.650875\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.6060 | + | 16.5157i | 0.925667 | + | 0.534434i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.6789 | − | 38.3358i | 0.700047 | − | 1.23793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.53466 | −0.275312 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.4770 | − | 26.8070i | 0.498223 | − | 0.862948i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.5917 | − | 46.0582i | −0.855132 | − | 1.48113i | −0.876522 | − | 0.481361i | \(-0.840143\pi\) |
0.0213900 | − | 0.999771i | \(-0.493191\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.61403 | + | 13.1879i | 0.244346 | + | 0.423219i | 0.961947 | − | 0.273234i | \(-0.0880935\pi\) |
−0.717602 | + | 0.696454i | \(0.754760\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.37634 | + | 11.2756i | −0.204416 | + | 0.361479i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.72533i | 0.0551983i | 0.999619 | + | 0.0275992i | \(0.00878620\pi\) | ||||
−0.999619 | + | 0.0275992i | \(0.991214\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.37033 | − | 5.40997i | −0.299477 | − | 0.172903i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.1191 | + | 52.1679i | 0.960651 | + | 1.66390i | 0.720871 | + | 0.693070i | \(0.243742\pi\) |
0.239780 | + | 0.970827i | \(0.422925\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.64713 | + | 4.99242i | 0.275521 | + | 0.159072i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.7703 | + | 16.0332i | −0.883044 | + | 0.509826i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.87312 | + | 4.97639i | −0.0912676 | + | 0.158080i | −0.908045 | − | 0.418873i | \(-0.862425\pi\) |
0.816777 | + | 0.576953i | \(0.195759\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.9711 | + | 13.2624i | −0.728234 | + | 0.420446i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0224508 | − | 0.0129620i | 0.000711024 | − | 0.000410510i | −0.499644 | − | 0.866231i | \(-0.666536\pi\) |
0.500355 | + | 0.865820i | \(0.333203\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))