Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,2,Mod(16,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.838429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 46.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.46 |
Dual form | 105.2.i.d.16.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | + | 2.36603i | 0.965926 | + | 1.67303i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −2.73205 | + | 4.73205i | −1.36603 | + | 2.36603i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 2.73205 | 1.11536 | ||||||||
\(7\) | 0.866025 | − | 2.50000i | 0.327327 | − | 0.944911i | ||||
\(8\) | −9.46410 | −3.34607 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.36603 | − | 2.36603i | 0.431975 | − | 0.748203i | ||||
\(11\) | −0.366025 | + | 0.633975i | −0.110361 | + | 0.191151i | −0.915916 | − | 0.401371i | \(-0.868534\pi\) |
0.805555 | + | 0.592521i | \(0.201867\pi\) | |||||||
\(12\) | 2.73205 | + | 4.73205i | 0.788675 | + | 1.36603i | ||||
\(13\) | 2.26795 | 0.629016 | 0.314508 | − | 0.949255i | \(-0.398160\pi\) | ||||
0.314508 | + | 0.949255i | \(0.398160\pi\) | |||||||
\(14\) | 7.09808 | − | 1.36603i | 1.89704 | − | 0.365086i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −7.46410 | − | 12.9282i | −1.86603 | − | 3.23205i | ||||
\(17\) | −1.63397 | + | 2.83013i | −0.396297 | + | 0.686407i | −0.993266 | − | 0.115858i | \(-0.963038\pi\) |
0.596969 | + | 0.802264i | \(0.296372\pi\) | |||||||
\(18\) | 1.36603 | − | 2.36603i | 0.321975 | − | 0.557678i | ||||
\(19\) | −2.23205 | − | 3.86603i | −0.512068 | − | 0.886927i | −0.999902 | − | 0.0139909i | \(-0.995546\pi\) |
0.487835 | − | 0.872936i | \(-0.337787\pi\) | |||||||
\(20\) | 5.46410 | 1.22181 | ||||||||
\(21\) | −1.73205 | − | 2.00000i | −0.377964 | − | 0.436436i | ||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 2.36603 | + | 4.09808i | 0.493350 | + | 0.854508i | 0.999971 | − | 0.00766135i | \(-0.00243871\pi\) |
−0.506620 | + | 0.862169i | \(0.669105\pi\) | |||||||
\(24\) | −4.73205 | + | 8.19615i | −0.965926 | + | 1.67303i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 3.09808 | + | 5.36603i | 0.607583 | + | 1.05236i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 9.46410 | + | 10.9282i | 1.78855 | + | 2.06524i | ||||
\(29\) | −4.19615 | −0.779206 | −0.389603 | − | 0.920983i | \(-0.627388\pi\) | ||||
−0.389603 | + | 0.920983i | \(0.627388\pi\) | |||||||
\(30\) | −1.36603 | − | 2.36603i | −0.249401 | − | 0.431975i | ||||
\(31\) | 0.232051 | − | 0.401924i | 0.0416776 | − | 0.0721876i | −0.844434 | − | 0.535659i | \(-0.820063\pi\) |
0.886112 | + | 0.463472i | \(0.153396\pi\) | |||||||
\(32\) | 10.9282 | − | 18.9282i | 1.93185 | − | 3.34607i | ||||
\(33\) | 0.366025 | + | 0.633975i | 0.0637168 | + | 0.110361i | ||||
\(34\) | −8.92820 | −1.53117 | ||||||||
\(35\) | −2.59808 | + | 0.500000i | −0.439155 | + | 0.0845154i | ||||
\(36\) | 5.46410 | 0.910684 | ||||||||
\(37\) | 1.59808 | + | 2.76795i | 0.262722 | + | 0.455048i | 0.966964 | − | 0.254912i | \(-0.0820464\pi\) |
−0.704242 | + | 0.709960i | \(0.748713\pi\) | |||||||
\(38\) | 6.09808 | − | 10.5622i | 0.989239 | − | 1.71341i | ||||
\(39\) | 1.13397 | − | 1.96410i | 0.181581 | − | 0.314508i | ||||
\(40\) | 4.73205 | + | 8.19615i | 0.748203 | + | 1.29593i | ||||
\(41\) | −0.732051 | −0.114327 | −0.0571636 | − | 0.998365i | \(-0.518206\pi\) | ||||
−0.0571636 | + | 0.998365i | \(0.518206\pi\) | |||||||
\(42\) | 2.36603 | − | 6.83013i | 0.365086 | − | 1.05391i | ||||
\(43\) | 3.19615 | 0.487409 | 0.243704 | − | 0.969850i | \(-0.421637\pi\) | ||||
0.243704 | + | 0.969850i | \(0.421637\pi\) | |||||||
\(44\) | −2.00000 | − | 3.46410i | −0.301511 | − | 0.522233i | ||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | −6.46410 | + | 11.1962i | −0.953080 | + | 1.65078i | ||||
\(47\) | −1.00000 | − | 1.73205i | −0.145865 | − | 0.252646i | 0.783830 | − | 0.620975i | \(-0.213263\pi\) |
−0.929695 | + | 0.368329i | \(0.879930\pi\) | |||||||
\(48\) | −14.9282 | −2.15470 | ||||||||
\(49\) | −5.50000 | − | 4.33013i | −0.785714 | − | 0.618590i | ||||
\(50\) | −2.73205 | −0.386370 | ||||||||
\(51\) | 1.63397 | + | 2.83013i | 0.228802 | + | 0.396297i | ||||
\(52\) | −6.19615 | + | 10.7321i | −0.859252 | + | 1.48827i | ||||
\(53\) | −6.19615 | + | 10.7321i | −0.851107 | + | 1.47416i | 0.0291032 | + | 0.999576i | \(0.490735\pi\) |
−0.880210 | + | 0.474584i | \(0.842598\pi\) | |||||||
\(54\) | −1.36603 | − | 2.36603i | −0.185893 | − | 0.321975i | ||||
\(55\) | 0.732051 | 0.0987097 | ||||||||
\(56\) | −8.19615 | + | 23.6603i | −1.09526 | + | 3.16173i | ||||
\(57\) | −4.46410 | −0.591285 | ||||||||
\(58\) | −5.73205 | − | 9.92820i | −0.752655 | − | 1.30364i | ||||
\(59\) | 0.0980762 | − | 0.169873i | 0.0127684 | − | 0.0221156i | −0.859571 | − | 0.511017i | \(-0.829269\pi\) |
0.872339 | + | 0.488901i | \(0.162602\pi\) | |||||||
\(60\) | 2.73205 | − | 4.73205i | 0.352706 | − | 0.610905i | ||||
\(61\) | −2.00000 | − | 3.46410i | −0.256074 | − | 0.443533i | 0.709113 | − | 0.705095i | \(-0.249096\pi\) |
−0.965187 | + | 0.261562i | \(0.915762\pi\) | |||||||
\(62\) | 1.26795 | 0.161030 | ||||||||
\(63\) | −2.59808 | + | 0.500000i | −0.327327 | + | 0.0629941i | ||||
\(64\) | 29.8564 | 3.73205 | ||||||||
\(65\) | −1.13397 | − | 1.96410i | −0.140652 | − | 0.243617i | ||||
\(66\) | −1.00000 | + | 1.73205i | −0.123091 | + | 0.213201i | ||||
\(67\) | 7.33013 | − | 12.6962i | 0.895518 | − | 1.55108i | 0.0623548 | − | 0.998054i | \(-0.480139\pi\) |
0.833163 | − | 0.553028i | \(-0.186528\pi\) | |||||||
\(68\) | −8.92820 | − | 15.4641i | −1.08270 | − | 1.87530i | ||||
\(69\) | 4.73205 | 0.569672 | ||||||||
\(70\) | −4.73205 | − | 5.46410i | −0.565588 | − | 0.653085i | ||||
\(71\) | 6.19615 | 0.735348 | 0.367674 | − | 0.929955i | \(-0.380154\pi\) | ||||
0.367674 | + | 0.929955i | \(0.380154\pi\) | |||||||
\(72\) | 4.73205 | + | 8.19615i | 0.557678 | + | 0.965926i | ||||
\(73\) | −6.33013 | + | 10.9641i | −0.740885 | + | 1.28325i | 0.211207 | + | 0.977441i | \(0.432260\pi\) |
−0.952093 | + | 0.305810i | \(0.901073\pi\) | |||||||
\(74\) | −4.36603 | + | 7.56218i | −0.507540 | + | 0.879085i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | 24.3923 | 2.79799 | ||||||||
\(77\) | 1.26795 | + | 1.46410i | 0.144496 | + | 0.166850i | ||||
\(78\) | 6.19615 | 0.701576 | ||||||||
\(79\) | 3.69615 | + | 6.40192i | 0.415850 | + | 0.720273i | 0.995517 | − | 0.0945803i | \(-0.0301509\pi\) |
−0.579668 | + | 0.814853i | \(0.696818\pi\) | |||||||
\(80\) | −7.46410 | + | 12.9282i | −0.834512 | + | 1.44542i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.00000 | − | 1.73205i | −0.110432 | − | 0.191273i | ||||
\(83\) | 15.1244 | 1.66011 | 0.830057 | − | 0.557679i | \(-0.188308\pi\) | ||||
0.830057 | + | 0.557679i | \(0.188308\pi\) | |||||||
\(84\) | 14.1962 | − | 2.73205i | 1.54893 | − | 0.298091i | ||||
\(85\) | 3.26795 | 0.354459 | ||||||||
\(86\) | 4.36603 | + | 7.56218i | 0.470801 | + | 0.815451i | ||||
\(87\) | −2.09808 | + | 3.63397i | −0.224937 | + | 0.389603i | ||||
\(88\) | 3.46410 | − | 6.00000i | 0.369274 | − | 0.639602i | ||||
\(89\) | −7.56218 | − | 13.0981i | −0.801589 | − | 1.38839i | −0.918570 | − | 0.395259i | \(-0.870655\pi\) |
0.116980 | − | 0.993134i | \(-0.462679\pi\) | |||||||
\(90\) | −2.73205 | −0.287983 | ||||||||
\(91\) | 1.96410 | − | 5.66987i | 0.205894 | − | 0.594364i | ||||
\(92\) | −25.8564 | −2.69572 | ||||||||
\(93\) | −0.232051 | − | 0.401924i | −0.0240625 | − | 0.0416776i | ||||
\(94\) | 2.73205 | − | 4.73205i | 0.281790 | − | 0.488074i | ||||
\(95\) | −2.23205 | + | 3.86603i | −0.229004 | + | 0.396646i | ||||
\(96\) | −10.9282 | − | 18.9282i | −1.11536 | − | 1.93185i | ||||
\(97\) | 14.9282 | 1.51573 | 0.757865 | − | 0.652412i | \(-0.226243\pi\) | ||||
0.757865 | + | 0.652412i | \(0.226243\pi\) | |||||||
\(98\) | 2.73205 | − | 18.9282i | 0.275979 | − | 1.91204i | ||||
\(99\) | 0.732051 | 0.0735739 | ||||||||
\(100\) | −2.73205 | − | 4.73205i | −0.273205 | − | 0.473205i | ||||
\(101\) | 3.63397 | − | 6.29423i | 0.361594 | − | 0.626299i | −0.626629 | − | 0.779317i | \(-0.715566\pi\) |
0.988223 | + | 0.153018i | \(0.0488993\pi\) | |||||||
\(102\) | −4.46410 | + | 7.73205i | −0.442012 | + | 0.765587i | ||||
\(103\) | 4.59808 | + | 7.96410i | 0.453062 | + | 0.784726i | 0.998574 | − | 0.0533764i | \(-0.0169983\pi\) |
−0.545513 | + | 0.838103i | \(0.683665\pi\) | |||||||
\(104\) | −21.4641 | −2.10473 | ||||||||
\(105\) | −0.866025 | + | 2.50000i | −0.0845154 | + | 0.243975i | ||||
\(106\) | −33.8564 | −3.28842 | ||||||||
\(107\) | −1.09808 | − | 1.90192i | −0.106155 | − | 0.183866i | 0.808054 | − | 0.589108i | \(-0.200521\pi\) |
−0.914210 | + | 0.405242i | \(0.867187\pi\) | |||||||
\(108\) | 2.73205 | − | 4.73205i | 0.262892 | − | 0.455342i | ||||
\(109\) | −5.50000 | + | 9.52628i | −0.526804 | + | 0.912452i | 0.472708 | + | 0.881219i | \(0.343277\pi\) |
−0.999512 | + | 0.0312328i | \(0.990057\pi\) | |||||||
\(110\) | 1.00000 | + | 1.73205i | 0.0953463 | + | 0.165145i | ||||
\(111\) | 3.19615 | 0.303365 | ||||||||
\(112\) | −38.7846 | + | 7.46410i | −3.66480 | + | 0.705291i | ||||
\(113\) | 8.92820 | 0.839895 | 0.419947 | − | 0.907548i | \(-0.362049\pi\) | ||||
0.419947 | + | 0.907548i | \(0.362049\pi\) | |||||||
\(114\) | −6.09808 | − | 10.5622i | −0.571137 | − | 0.989239i | ||||
\(115\) | 2.36603 | − | 4.09808i | 0.220633 | − | 0.382148i | ||||
\(116\) | 11.4641 | − | 19.8564i | 1.06442 | − | 1.84362i | ||||
\(117\) | −1.13397 | − | 1.96410i | −0.104836 | − | 0.181581i | ||||
\(118\) | 0.535898 | 0.0493334 | ||||||||
\(119\) | 5.66025 | + | 6.53590i | 0.518875 | + | 0.599145i | ||||
\(120\) | 9.46410 | 0.863950 | ||||||||
\(121\) | 5.23205 | + | 9.06218i | 0.475641 | + | 0.823834i | ||||
\(122\) | 5.46410 | − | 9.46410i | 0.494697 | − | 0.856840i | ||||
\(123\) | −0.366025 | + | 0.633975i | −0.0330034 | + | 0.0571636i | ||||
\(124\) | 1.26795 | + | 2.19615i | 0.113865 | + | 0.197220i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.73205 | − | 5.46410i | −0.421565 | − | 0.486781i | ||||
\(127\) | 4.80385 | 0.426273 | 0.213136 | − | 0.977022i | \(-0.431632\pi\) | ||||
0.213136 | + | 0.977022i | \(0.431632\pi\) | |||||||
\(128\) | 18.9282 | + | 32.7846i | 1.67303 | + | 2.89778i | ||||
\(129\) | 1.59808 | − | 2.76795i | 0.140703 | − | 0.243704i | ||||
\(130\) | 3.09808 | − | 5.36603i | 0.271719 | − | 0.470632i | ||||
\(131\) | −7.73205 | − | 13.3923i | −0.675552 | − | 1.17009i | −0.976307 | − | 0.216390i | \(-0.930572\pi\) |
0.300755 | − | 0.953702i | \(-0.402761\pi\) | |||||||
\(132\) | −4.00000 | −0.348155 | ||||||||
\(133\) | −11.5981 | + | 2.23205i | −1.00568 | + | 0.193543i | ||||
\(134\) | 40.0526 | 3.46001 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 15.4641 | − | 26.7846i | 1.32604 | − | 2.29676i | ||||
\(137\) | −1.09808 | + | 1.90192i | −0.0938150 | + | 0.162492i | −0.909113 | − | 0.416549i | \(-0.863240\pi\) |
0.815298 | + | 0.579041i | \(0.196573\pi\) | |||||||
\(138\) | 6.46410 | + | 11.1962i | 0.550261 | + | 0.953080i | ||||
\(139\) | 5.92820 | 0.502824 | 0.251412 | − | 0.967880i | \(-0.419105\pi\) | ||||
0.251412 | + | 0.967880i | \(0.419105\pi\) | |||||||
\(140\) | 4.73205 | − | 13.6603i | 0.399931 | − | 1.15450i | ||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | 8.46410 | + | 14.6603i | 0.710292 | + | 1.23026i | ||||
\(143\) | −0.830127 | + | 1.43782i | −0.0694187 | + | 0.120237i | ||||
\(144\) | −7.46410 | + | 12.9282i | −0.622008 | + | 1.07735i | ||||
\(145\) | 2.09808 | + | 3.63397i | 0.174236 | + | 0.301785i | ||||
\(146\) | −34.5885 | −2.86256 | ||||||||
\(147\) | −6.50000 | + | 2.59808i | −0.536111 | + | 0.214286i | ||||
\(148\) | −17.4641 | −1.43554 | ||||||||
\(149\) | −2.92820 | − | 5.07180i | −0.239888 | − | 0.415498i | 0.720794 | − | 0.693149i | \(-0.243777\pi\) |
−0.960682 | + | 0.277651i | \(0.910444\pi\) | |||||||
\(150\) | −1.36603 | + | 2.36603i | −0.111536 | + | 0.193185i | ||||
\(151\) | 4.46410 | − | 7.73205i | 0.363283 | − | 0.629225i | −0.625216 | − | 0.780452i | \(-0.714989\pi\) |
0.988499 | + | 0.151227i | \(0.0483223\pi\) | |||||||
\(152\) | 21.1244 | + | 36.5885i | 1.71341 | + | 2.96772i | ||||
\(153\) | 3.26795 | 0.264198 | ||||||||
\(154\) | −1.73205 | + | 5.00000i | −0.139573 | + | 0.402911i | ||||
\(155\) | −0.464102 | −0.0372775 | ||||||||
\(156\) | 6.19615 | + | 10.7321i | 0.496089 | + | 0.859252i | ||||
\(157\) | −3.19615 | + | 5.53590i | −0.255081 | + | 0.441813i | −0.964917 | − | 0.262553i | \(-0.915435\pi\) |
0.709837 | + | 0.704366i | \(0.248769\pi\) | |||||||
\(158\) | −10.0981 | + | 17.4904i | −0.803360 | + | 1.39146i | ||||
\(159\) | 6.19615 | + | 10.7321i | 0.491387 | + | 0.851107i | ||||
\(160\) | −21.8564 | −1.72790 | ||||||||
\(161\) | 12.2942 | − | 2.36603i | 0.968921 | − | 0.186469i | ||||
\(162\) | −2.73205 | −0.214650 | ||||||||
\(163\) | −10.9282 | − | 18.9282i | −0.855963 | − | 1.48257i | −0.875749 | − | 0.482767i | \(-0.839632\pi\) |
0.0197859 | − | 0.999804i | \(-0.493702\pi\) | |||||||
\(164\) | 2.00000 | − | 3.46410i | 0.156174 | − | 0.270501i | ||||
\(165\) | 0.366025 | − | 0.633975i | 0.0284950 | − | 0.0493549i | ||||
\(166\) | 20.6603 | + | 35.7846i | 1.60355 | + | 2.77742i | ||||
\(167\) | −17.6603 | −1.36659 | −0.683296 | − | 0.730142i | \(-0.739454\pi\) | ||||
−0.683296 | + | 0.730142i | \(0.739454\pi\) | |||||||
\(168\) | 16.3923 | + | 18.9282i | 1.26469 | + | 1.46034i | ||||
\(169\) | −7.85641 | −0.604339 | ||||||||
\(170\) | 4.46410 | + | 7.73205i | 0.342381 | + | 0.593021i | ||||
\(171\) | −2.23205 | + | 3.86603i | −0.170689 | + | 0.295642i | ||||
\(172\) | −8.73205 | + | 15.1244i | −0.665813 | + | 1.15322i | ||||
\(173\) | −7.26795 | − | 12.5885i | −0.552572 | − | 0.957083i | −0.998088 | − | 0.0618087i | \(-0.980313\pi\) |
0.445516 | − | 0.895274i | \(-0.353020\pi\) | |||||||
\(174\) | −11.4641 | −0.869091 | ||||||||
\(175\) | 1.73205 | + | 2.00000i | 0.130931 | + | 0.151186i | ||||
\(176\) | 10.9282 | 0.823744 | ||||||||
\(177\) | −0.0980762 | − | 0.169873i | −0.00737186 | − | 0.0127684i | ||||
\(178\) | 20.6603 | − | 35.7846i | 1.54855 | − | 2.68217i | ||||
\(179\) | 5.00000 | − | 8.66025i | 0.373718 | − | 0.647298i | −0.616417 | − | 0.787420i | \(-0.711416\pi\) |
0.990134 | + | 0.140122i | \(0.0447496\pi\) | |||||||
\(180\) | −2.73205 | − | 4.73205i | −0.203635 | − | 0.352706i | ||||
\(181\) | −24.3205 | −1.80773 | −0.903865 | − | 0.427819i | \(-0.859282\pi\) | ||||
−0.903865 | + | 0.427819i | \(0.859282\pi\) | |||||||
\(182\) | 16.0981 | − | 3.09808i | 1.19327 | − | 0.229645i | ||||
\(183\) | −4.00000 | −0.295689 | ||||||||
\(184\) | −22.3923 | − | 38.7846i | −1.65078 | − | 2.85924i | ||||
\(185\) | 1.59808 | − | 2.76795i | 0.117493 | − | 0.203504i | ||||
\(186\) | 0.633975 | − | 1.09808i | 0.0464853 | − | 0.0805149i | ||||
\(187\) | −1.19615 | − | 2.07180i | −0.0874713 | − | 0.151505i | ||||
\(188\) | 10.9282 | 0.797021 | ||||||||
\(189\) | −0.866025 | + | 2.50000i | −0.0629941 | + | 0.181848i | ||||
\(190\) | −12.1962 | −0.884802 | ||||||||
\(191\) | 4.46410 | + | 7.73205i | 0.323011 | + | 0.559472i | 0.981108 | − | 0.193462i | \(-0.0619716\pi\) |
−0.658097 | + | 0.752933i | \(0.728638\pi\) | |||||||
\(192\) | 14.9282 | − | 25.8564i | 1.07735 | − | 1.86603i | ||||
\(193\) | −0.598076 | + | 1.03590i | −0.0430505 | + | 0.0745656i | −0.886748 | − | 0.462254i | \(-0.847041\pi\) |
0.843697 | + | 0.536819i | \(0.180374\pi\) | |||||||
\(194\) | 20.3923 | + | 35.3205i | 1.46408 | + | 2.53586i | ||||
\(195\) | −2.26795 | −0.162411 | ||||||||
\(196\) | 35.5167 | − | 14.1962i | 2.53690 | − | 1.01401i | ||||
\(197\) | −0.339746 | −0.0242059 | −0.0121029 | − | 0.999927i | \(-0.503853\pi\) | ||||
−0.0121029 | + | 0.999927i | \(0.503853\pi\) | |||||||
\(198\) | 1.00000 | + | 1.73205i | 0.0710669 | + | 0.123091i | ||||
\(199\) | −11.0000 | + | 19.0526i | −0.779769 | + | 1.35060i | 0.152305 | + | 0.988334i | \(0.451330\pi\) |
−0.932075 | + | 0.362267i | \(0.882003\pi\) | |||||||
\(200\) | 4.73205 | − | 8.19615i | 0.334607 | − | 0.579555i | ||||
\(201\) | −7.33013 | − | 12.6962i | −0.517027 | − | 0.895518i | ||||
\(202\) | 19.8564 | 1.39709 | ||||||||
\(203\) | −3.63397 | + | 10.4904i | −0.255055 | + | 0.736280i | ||||
\(204\) | −17.8564 | −1.25020 | ||||||||
\(205\) | 0.366025 | + | 0.633975i | 0.0255643 | + | 0.0442787i | ||||
\(206\) | −12.5622 | + | 21.7583i | −0.875248 | + | 1.51597i | ||||
\(207\) | 2.36603 | − | 4.09808i | 0.164450 | − | 0.284836i | ||||
\(208\) | −16.9282 | − | 29.3205i | −1.17376 | − | 2.03301i | ||||
\(209\) | 3.26795 | 0.226049 | ||||||||
\(210\) | −7.09808 | + | 1.36603i | −0.489814 | + | 0.0942647i | ||||
\(211\) | 7.07180 | 0.486843 | 0.243421 | − | 0.969921i | \(-0.421730\pi\) | ||||
0.243421 | + | 0.969921i | \(0.421730\pi\) | |||||||
\(212\) | −33.8564 | − | 58.6410i | −2.32527 | − | 4.02748i | ||||
\(213\) | 3.09808 | − | 5.36603i | 0.212277 | − | 0.367674i | ||||
\(214\) | 3.00000 | − | 5.19615i | 0.205076 | − | 0.355202i | ||||
\(215\) | −1.59808 | − | 2.76795i | −0.108988 | − | 0.188773i | ||||
\(216\) | 9.46410 | 0.643951 | ||||||||
\(217\) | −0.803848 | − | 0.928203i | −0.0545687 | − | 0.0630105i | ||||
\(218\) | −30.0526 | −2.03542 | ||||||||
\(219\) | 6.33013 | + | 10.9641i | 0.427750 | + | 0.740885i | ||||
\(220\) | −2.00000 | + | 3.46410i | −0.134840 | + | 0.233550i | ||||
\(221\) | −3.70577 | + | 6.41858i | −0.249277 | + | 0.431761i | ||||
\(222\) | 4.36603 | + | 7.56218i | 0.293028 | + | 0.507540i | ||||
\(223\) | −20.3923 | −1.36557 | −0.682785 | − | 0.730619i | \(-0.739231\pi\) | ||||
−0.682785 | + | 0.730619i | \(0.739231\pi\) | |||||||
\(224\) | −37.8564 | − | 43.7128i | −2.52939 | − | 2.92069i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 12.1962 | + | 21.1244i | 0.811276 | + | 1.40517i | ||||
\(227\) | 0.830127 | − | 1.43782i | 0.0550975 | − | 0.0954316i | −0.837161 | − | 0.546956i | \(-0.815786\pi\) |
0.892259 | + | 0.451525i | \(0.149120\pi\) | |||||||
\(228\) | 12.1962 | − | 21.1244i | 0.807710 | − | 1.39899i | ||||
\(229\) | 1.50000 | + | 2.59808i | 0.0991228 | + | 0.171686i | 0.911322 | − | 0.411695i | \(-0.135063\pi\) |
−0.812199 | + | 0.583380i | \(0.801730\pi\) | |||||||
\(230\) | 12.9282 | 0.852460 | ||||||||
\(231\) | 1.90192 | − | 0.366025i | 0.125137 | − | 0.0240827i | ||||
\(232\) | 39.7128 | 2.60727 | ||||||||
\(233\) | −8.66025 | − | 15.0000i | −0.567352 | − | 0.982683i | −0.996827 | − | 0.0796037i | \(-0.974635\pi\) |
0.429474 | − | 0.903079i | \(-0.358699\pi\) | |||||||
\(234\) | 3.09808 | − | 5.36603i | 0.202528 | − | 0.350788i | ||||
\(235\) | −1.00000 | + | 1.73205i | −0.0652328 | + | 0.112987i | ||||
\(236\) | 0.535898 | + | 0.928203i | 0.0348840 | + | 0.0604209i | ||||
\(237\) | 7.39230 | 0.480182 | ||||||||
\(238\) | −7.73205 | + | 22.3205i | −0.501194 | + | 1.44682i | ||||
\(239\) | 7.07180 | 0.457437 | 0.228718 | − | 0.973493i | \(-0.426547\pi\) | ||||
0.228718 | + | 0.973493i | \(0.426547\pi\) | |||||||
\(240\) | 7.46410 | + | 12.9282i | 0.481806 | + | 0.834512i | ||||
\(241\) | −6.73205 | + | 11.6603i | −0.433650 | + | 0.751103i | −0.997184 | − | 0.0749893i | \(-0.976108\pi\) |
0.563535 | + | 0.826092i | \(0.309441\pi\) | |||||||
\(242\) | −14.2942 | + | 24.7583i | −0.918868 | + | 1.59153i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 21.8564 | 1.39921 | ||||||||
\(245\) | −1.00000 | + | 6.92820i | −0.0638877 | + | 0.442627i | ||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | −5.06218 | − | 8.76795i | −0.322099 | − | 0.557891i | ||||
\(248\) | −2.19615 | + | 3.80385i | −0.139456 | + | 0.241545i | ||||
\(249\) | 7.56218 | − | 13.0981i | 0.479234 | − | 0.830057i | ||||
\(250\) | 1.36603 | + | 2.36603i | 0.0863950 | + | 0.149641i | ||||
\(251\) | −24.5885 | −1.55201 | −0.776005 | − | 0.630727i | \(-0.782757\pi\) | ||||
−0.776005 | + | 0.630727i | \(0.782757\pi\) | |||||||
\(252\) | 4.73205 | − | 13.6603i | 0.298091 | − | 0.860515i | ||||
\(253\) | −3.46410 | −0.217786 | ||||||||
\(254\) | 6.56218 | + | 11.3660i | 0.411748 | + | 0.713168i | ||||
\(255\) | 1.63397 | − | 2.83013i | 0.102323 | − | 0.177229i | ||||
\(256\) | −21.8564 | + | 37.8564i | −1.36603 | + | 2.36603i | ||||
\(257\) | 2.83013 | + | 4.90192i | 0.176538 | + | 0.305774i | 0.940693 | − | 0.339260i | \(-0.110177\pi\) |
−0.764154 | + | 0.645034i | \(0.776843\pi\) | |||||||
\(258\) | 8.73205 | 0.543634 | ||||||||
\(259\) | 8.30385 | − | 1.59808i | 0.515976 | − | 0.0992996i | ||||
\(260\) | 12.3923 | 0.768538 | ||||||||
\(261\) | 2.09808 | + | 3.63397i | 0.129868 | + | 0.224937i | ||||
\(262\) | 21.1244 | − | 36.5885i | 1.30507 | − | 2.26044i | ||||
\(263\) | −4.19615 | + | 7.26795i | −0.258746 | + | 0.448161i | −0.965906 | − | 0.258892i | \(-0.916643\pi\) |
0.707160 | + | 0.707053i | \(0.249976\pi\) | |||||||
\(264\) | −3.46410 | − | 6.00000i | −0.213201 | − | 0.369274i | ||||
\(265\) | 12.3923 | 0.761253 | ||||||||
\(266\) | −21.1244 | − | 24.3923i | −1.29522 | − | 1.49559i | ||||
\(267\) | −15.1244 | −0.925596 | ||||||||
\(268\) | 40.0526 | + | 69.3731i | 2.44660 | + | 4.23763i | ||||
\(269\) | 6.26795 | − | 10.8564i | 0.382164 | − | 0.661927i | −0.609208 | − | 0.793011i | \(-0.708512\pi\) |
0.991371 | + | 0.131084i | \(0.0418457\pi\) | |||||||
\(270\) | −1.36603 | + | 2.36603i | −0.0831337 | + | 0.143992i | ||||
\(271\) | −1.53590 | − | 2.66025i | −0.0932992 | − | 0.161599i | 0.815598 | − | 0.578619i | \(-0.196408\pi\) |
−0.908897 | + | 0.417020i | \(0.863075\pi\) | |||||||
\(272\) | 48.7846 | 2.95800 | ||||||||
\(273\) | −3.92820 | − | 4.53590i | −0.237746 | − | 0.274525i | ||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | −0.366025 | − | 0.633975i | −0.0220722 | − | 0.0382301i | ||||
\(276\) | −12.9282 | + | 22.3923i | −0.778186 | + | 1.34786i | ||||
\(277\) | 7.33013 | − | 12.6962i | 0.440425 | − | 0.762838i | −0.557296 | − | 0.830314i | \(-0.688161\pi\) |
0.997721 | + | 0.0674759i | \(0.0214946\pi\) | |||||||
\(278\) | 8.09808 | + | 14.0263i | 0.485690 | + | 0.841240i | ||||
\(279\) | −0.464102 | −0.0277850 | ||||||||
\(280\) | 24.5885 | − | 4.73205i | 1.46944 | − | 0.282794i | ||||
\(281\) | 13.8564 | 0.826604 | 0.413302 | − | 0.910594i | \(-0.364375\pi\) | ||||
0.413302 | + | 0.910594i | \(0.364375\pi\) | |||||||
\(282\) | −2.73205 | − | 4.73205i | −0.162691 | − | 0.281790i | ||||
\(283\) | 12.0622 | − | 20.8923i | 0.717022 | − | 1.24192i | −0.245152 | − | 0.969485i | \(-0.578838\pi\) |
0.962174 | − | 0.272434i | \(-0.0878287\pi\) | |||||||
\(284\) | −16.9282 | + | 29.3205i | −1.00450 | + | 1.73985i | ||||
\(285\) | 2.23205 | + | 3.86603i | 0.132215 | + | 0.229004i | ||||
\(286\) | −4.53590 | −0.268213 | ||||||||
\(287\) | −0.633975 | + | 1.83013i | −0.0374223 | + | 0.108029i | ||||
\(288\) | −21.8564 | −1.28790 | ||||||||
\(289\) | 3.16025 | + | 5.47372i | 0.185897 | + | 0.321984i | ||||
\(290\) | −5.73205 | + | 9.92820i | −0.336598 | + | 0.583004i | ||||
\(291\) | 7.46410 | − | 12.9282i | 0.437553 | − | 0.757865i | ||||
\(292\) | −34.5885 | − | 59.9090i | −2.02414 | − | 3.50591i | ||||
\(293\) | 18.9282 | 1.10580 | 0.552899 | − | 0.833248i | \(-0.313522\pi\) | ||||
0.552899 | + | 0.833248i | \(0.313522\pi\) | |||||||
\(294\) | −15.0263 | − | 11.8301i | −0.876350 | − | 0.689947i | ||||
\(295\) | −0.196152 | −0.0114204 | ||||||||
\(296\) | −15.1244 | − | 26.1962i | −0.879085 | − | 1.52262i | ||||
\(297\) | 0.366025 | − | 0.633975i | 0.0212389 | − | 0.0367869i | ||||
\(298\) | 8.00000 | − | 13.8564i | 0.463428 | − | 0.802680i | ||||
\(299\) | 5.36603 | + | 9.29423i | 0.310325 | + | 0.537499i | ||||
\(300\) | −5.46410 | −0.315470 | ||||||||
\(301\) | 2.76795 | − | 7.99038i | 0.159542 | − | 0.460558i | ||||
\(302\) | 24.3923 | 1.40362 | ||||||||
\(303\) | −3.63397 | − | 6.29423i | −0.208766 | − | 0.361594i | ||||
\(304\) | −33.3205 | + | 57.7128i | −1.91106 | + | 3.31006i | ||||
\(305\) | −2.00000 | + | 3.46410i | −0.114520 | + | 0.198354i | ||||
\(306\) | 4.46410 | + | 7.73205i | 0.255196 | + | 0.442012i | ||||
\(307\) | −32.1244 | −1.83343 | −0.916717 | − | 0.399537i | \(-0.869171\pi\) | ||||
−0.916717 | + | 0.399537i | \(0.869171\pi\) | |||||||
\(308\) | −10.3923 | + | 2.00000i | −0.592157 | + | 0.113961i | ||||
\(309\) | 9.19615 | 0.523151 | ||||||||
\(310\) | −0.633975 | − | 1.09808i | −0.0360073 | − | 0.0623665i | ||||
\(311\) | −4.56218 | + | 7.90192i | −0.258697 | + | 0.448077i | −0.965893 | − | 0.258941i | \(-0.916627\pi\) |
0.707196 | + | 0.707018i | \(0.249960\pi\) | |||||||
\(312\) | −10.7321 | + | 18.5885i | −0.607583 | + | 1.05236i | ||||
\(313\) | 6.33013 | + | 10.9641i | 0.357800 | + | 0.619728i | 0.987593 | − | 0.157035i | \(-0.0501936\pi\) |
−0.629793 | + | 0.776763i | \(0.716860\pi\) | |||||||
\(314\) | −17.4641 | −0.985556 | ||||||||
\(315\) | 1.73205 | + | 2.00000i | 0.0975900 | + | 0.112687i | ||||
\(316\) | −40.3923 | −2.27224 | ||||||||
\(317\) | 14.2224 | + | 24.6340i | 0.798811 | + | 1.38358i | 0.920391 | + | 0.391000i | \(0.127871\pi\) |
−0.121579 | + | 0.992582i | \(0.538796\pi\) | |||||||
\(318\) | −16.9282 | + | 29.3205i | −0.949286 | + | 1.64421i | ||||
\(319\) | 1.53590 | − | 2.66025i | 0.0859938 | − | 0.148946i | ||||
\(320\) | −14.9282 | − | 25.8564i | −0.834512 | − | 1.44542i | ||||
\(321\) | −2.19615 | −0.122577 | ||||||||
\(322\) | 22.3923 | + | 25.8564i | 1.24787 | + | 1.44092i | ||||
\(323\) | 14.5885 | 0.811723 | ||||||||
\(324\) | −2.73205 | − | 4.73205i | −0.151781 | − | 0.262892i | ||||
\(325\) | −1.13397 | + | 1.96410i | −0.0629016 | + | 0.108949i | ||||
\(326\) | 29.8564 | − | 51.7128i | 1.65359 | − | 2.86411i | ||||
\(327\) | 5.50000 | + | 9.52628i | 0.304151 | + | 0.526804i | ||||
\(328\) | 6.92820 | 0.382546 | ||||||||
\(329\) | −5.19615 | + | 1.00000i | −0.286473 | + | 0.0551318i | ||||
\(330\) | 2.00000 | 0.110096 | ||||||||
\(331\) | −4.03590 | − | 6.99038i | −0.221833 | − | 0.384226i | 0.733532 | − | 0.679655i | \(-0.237871\pi\) |
−0.955365 | + | 0.295429i | \(0.904537\pi\) | |||||||
\(332\) | −41.3205 | + | 71.5692i | −2.26776 | + | 3.92787i | ||||
\(333\) | 1.59808 | − | 2.76795i | 0.0875740 | − | 0.151683i | ||||
\(334\) | −24.1244 | − | 41.7846i | −1.32003 | − | 2.28635i | ||||
\(335\) | −14.6603 | −0.800975 | ||||||||
\(336\) | −12.9282 | + | 37.3205i | −0.705291 | + | 2.03600i | ||||
\(337\) | 17.9808 | 0.979475 | 0.489737 | − | 0.871870i | \(-0.337093\pi\) | ||||
0.489737 | + | 0.871870i | \(0.337093\pi\) | |||||||
\(338\) | −10.7321 | − | 18.5885i | −0.583747 | − | 1.01108i | ||||
\(339\) | 4.46410 | − | 7.73205i | 0.242457 | − | 0.419947i | ||||
\(340\) | −8.92820 | + | 15.4641i | −0.484200 | + | 0.838659i | ||||
\(341\) | 0.169873 | + | 0.294229i | 0.00919914 | + | 0.0159334i | ||||
\(342\) | −12.1962 | −0.659492 | ||||||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | −30.2487 | −1.63090 | ||||||||
\(345\) | −2.36603 | − | 4.09808i | −0.127383 | − | 0.220633i | ||||
\(346\) | 19.8564 | − | 34.3923i | 1.06749 | − | 1.84894i | ||||
\(347\) | 10.5359 | − | 18.2487i | 0.565597 | − | 0.979642i | −0.431397 | − | 0.902162i | \(-0.641979\pi\) |
0.996994 | − | 0.0774801i | \(-0.0246874\pi\) | |||||||
\(348\) | −11.4641 | − | 19.8564i | −0.614540 | − | 1.06442i | ||||
\(349\) | 22.0000 | 1.17763 | 0.588817 | − | 0.808267i | \(-0.299594\pi\) | ||||
0.588817 | + | 0.808267i | \(0.299594\pi\) | |||||||
\(350\) | −2.36603 | + | 6.83013i | −0.126469 | + | 0.365086i | ||||
\(351\) | −2.26795 | −0.121054 | ||||||||
\(352\) | 8.00000 | + | 13.8564i | 0.426401 | + | 0.738549i | ||||
\(353\) | 1.56218 | − | 2.70577i | 0.0831463 | − | 0.144014i | −0.821453 | − | 0.570276i | \(-0.806836\pi\) |
0.904600 | + | 0.426262i | \(0.140170\pi\) | |||||||
\(354\) | 0.267949 | − | 0.464102i | 0.0142413 | − | 0.0246667i | ||||
\(355\) | −3.09808 | − | 5.36603i | −0.164429 | − | 0.284799i | ||||
\(356\) | 82.6410 | 4.37997 | ||||||||
\(357\) | 8.49038 | − | 1.63397i | 0.449359 | − | 0.0864791i | ||||
\(358\) | 27.3205 | 1.44393 | ||||||||
\(359\) | 0.633975 | + | 1.09808i | 0.0334599 | + | 0.0579542i | 0.882270 | − | 0.470743i | \(-0.156014\pi\) |
−0.848811 | + | 0.528697i | \(0.822681\pi\) | |||||||
\(360\) | 4.73205 | − | 8.19615i | 0.249401 | − | 0.431975i | ||||
\(361\) | −0.464102 | + | 0.803848i | −0.0244264 | + | 0.0423078i | ||||
\(362\) | −33.2224 | − | 57.5429i | −1.74613 | − | 3.02439i | ||||
\(363\) | 10.4641 | 0.549223 | ||||||||
\(364\) | 21.4641 | + | 24.7846i | 1.12502 | + | 1.29907i | ||||
\(365\) | 12.6603 | 0.662668 | ||||||||
\(366\) | −5.46410 | − | 9.46410i | −0.285613 | − | 0.494697i | ||||
\(367\) | −5.59808 | + | 9.69615i | −0.292217 | + | 0.506135i | −0.974334 | − | 0.225108i | \(-0.927726\pi\) |
0.682117 | + | 0.731244i | \(0.261060\pi\) | |||||||
\(368\) | 35.3205 | − | 61.1769i | 1.84121 | − | 3.18907i | ||||
\(369\) | 0.366025 | + | 0.633975i | 0.0190545 | + | 0.0330034i | ||||
\(370\) | 8.73205 | 0.453958 | ||||||||
\(371\) | 21.4641 | + | 24.7846i | 1.11436 | + | 1.28675i | ||||
\(372\) | 2.53590 | 0.131480 | ||||||||
\(373\) | −13.2583 | − | 22.9641i | −0.686490 | − | 1.18904i | −0.972966 | − | 0.230949i | \(-0.925817\pi\) |
0.286476 | − | 0.958088i | \(-0.407516\pi\) | |||||||
\(374\) | 3.26795 | − | 5.66025i | 0.168982 | − | 0.292685i | ||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | 9.46410 | + | 16.3923i | 0.488074 | + | 0.845369i | ||||
\(377\) | −9.51666 | −0.490133 | ||||||||
\(378\) | −7.09808 | + | 1.36603i | −0.365086 | + | 0.0702608i | ||||
\(379\) | 6.32051 | 0.324663 | 0.162331 | − | 0.986736i | \(-0.448099\pi\) | ||||
0.162331 | + | 0.986736i | \(0.448099\pi\) | |||||||
\(380\) | −12.1962 | − | 21.1244i | −0.625649 | − | 1.08366i | ||||
\(381\) | 2.40192 | − | 4.16025i | 0.123054 | − | 0.213136i | ||||
\(382\) | −12.1962 | + | 21.1244i | −0.624009 | + | 1.08082i | ||||
\(383\) | 11.6603 | + | 20.1962i | 0.595811 | + | 1.03198i | 0.993432 | + | 0.114425i | \(0.0365027\pi\) |
−0.397621 | + | 0.917550i | \(0.630164\pi\) | |||||||
\(384\) | 37.8564 | 1.93185 | ||||||||
\(385\) | 0.633975 | − | 1.83013i | 0.0323103 | − | 0.0932719i | ||||
\(386\) | −3.26795 | −0.166334 | ||||||||
\(387\) | −1.59808 | − | 2.76795i | −0.0812348 | − | 0.140703i | ||||
\(388\) | −40.7846 | + | 70.6410i | −2.07052 | + | 3.58625i | ||||
\(389\) | −2.70577 | + | 4.68653i | −0.137188 | + | 0.237617i | −0.926431 | − | 0.376464i | \(-0.877140\pi\) |
0.789243 | + | 0.614081i | \(0.210473\pi\) | |||||||
\(390\) | −3.09808 | − | 5.36603i | −0.156877 | − | 0.271719i | ||||
\(391\) | −15.4641 | −0.782053 | ||||||||
\(392\) | 52.0526 | + | 40.9808i | 2.62905 | + | 2.06984i | ||||
\(393\) | −15.4641 | −0.780061 | ||||||||
\(394\) | −0.464102 | − | 0.803848i | −0.0233811 | − | 0.0404973i | ||||
\(395\) | 3.69615 | − | 6.40192i | 0.185974 | − | 0.322116i | ||||
\(396\) | −2.00000 | + | 3.46410i | −0.100504 | + | 0.174078i | ||||
\(397\) | 15.5981 | + | 27.0167i | 0.782845 | + | 1.35593i | 0.930278 | + | 0.366855i | \(0.119566\pi\) |
−0.147433 | + | 0.989072i | \(0.547101\pi\) | |||||||
\(398\) | −60.1051 | −3.01280 | ||||||||
\(399\) | −3.86603 | + | 11.1603i | −0.193543 | + | 0.558712i | ||||
\(400\) | 14.9282 | 0.746410 | ||||||||
\(401\) | 8.19615 | + | 14.1962i | 0.409296 | + | 0.708922i | 0.994811 | − | 0.101740i | \(-0.0324409\pi\) |
−0.585515 | + | 0.810662i | \(0.699108\pi\) | |||||||
\(402\) | 20.0263 | − | 34.6865i | 0.998820 | − | 1.73001i | ||||
\(403\) | 0.526279 | − | 0.911543i | 0.0262158 | − | 0.0454072i | ||||
\(404\) | 19.8564 | + | 34.3923i | 0.987893 | + | 1.71108i | ||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −29.7846 | + | 5.73205i | −1.47819 | + | 0.284477i | ||||
\(407\) | −2.33975 | −0.115977 | ||||||||
\(408\) | −15.4641 | − | 26.7846i | −0.765587 | − | 1.32604i | ||||
\(409\) | −1.57180 | + | 2.72243i | −0.0777203 | + | 0.134616i | −0.902266 | − | 0.431180i | \(-0.858097\pi\) |
0.824546 | + | 0.565795i | \(0.191431\pi\) | |||||||
\(410\) | −1.00000 | + | 1.73205i | −0.0493865 | + | 0.0855399i | ||||
\(411\) | 1.09808 | + | 1.90192i | 0.0541641 | + | 0.0938150i | ||||
\(412\) | −50.2487 | −2.47558 | ||||||||
\(413\) | −0.339746 | − | 0.392305i | −0.0167178 | − | 0.0193041i | ||||
\(414\) | 12.9282 | 0.635387 | ||||||||
\(415\) | −7.56218 | − | 13.0981i | −0.371213 | − | 0.642959i | ||||
\(416\) | 24.7846 | − | 42.9282i | 1.21517 | − | 2.10473i | ||||
\(417\) | 2.96410 | − | 5.13397i | 0.145153 | − | 0.251412i | ||||
\(418\) | 4.46410 | + | 7.73205i | 0.218346 | + | 0.378187i | ||||
\(419\) | −35.4641 | −1.73253 | −0.866267 | − | 0.499581i | \(-0.833487\pi\) | ||||
−0.866267 | + | 0.499581i | \(0.833487\pi\) | |||||||
\(420\) | −9.46410 | − | 10.9282i | −0.461801 | − | 0.533242i | ||||
\(421\) | 0.0717968 | 0.00349916 | 0.00174958 | − | 0.999998i | \(-0.499443\pi\) | ||||
0.00174958 | + | 0.999998i | \(0.499443\pi\) | |||||||
\(422\) | 9.66025 | + | 16.7321i | 0.470254 | + | 0.814503i | ||||
\(423\) | −1.00000 | + | 1.73205i | −0.0486217 | + | 0.0842152i | ||||
\(424\) | 58.6410 | − | 101.569i | 2.84786 | − | 4.93264i | ||||
\(425\) | −1.63397 | − | 2.83013i | −0.0792594 | − | 0.137281i | ||||
\(426\) | 16.9282 | 0.820174 | ||||||||
\(427\) | −10.3923 | + | 2.00000i | −0.502919 | + | 0.0967868i | ||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0.830127 | + | 1.43782i | 0.0400789 | + | 0.0694187i | ||||
\(430\) | 4.36603 | − | 7.56218i | 0.210548 | − | 0.364681i | ||||
\(431\) | −8.66025 | + | 15.0000i | −0.417150 | + | 0.722525i | −0.995651 | − | 0.0931566i | \(-0.970304\pi\) |
0.578502 | + | 0.815681i | \(0.303638\pi\) | |||||||
\(432\) | 7.46410 | + | 12.9282i | 0.359117 | + | 0.622008i | ||||
\(433\) | 15.1962 | 0.730280 | 0.365140 | − | 0.930953i | \(-0.381021\pi\) | ||||
0.365140 | + | 0.930953i | \(0.381021\pi\) | |||||||
\(434\) | 1.09808 | − | 3.16987i | 0.0527093 | − | 0.152159i | ||||
\(435\) | 4.19615 | 0.201190 | ||||||||
\(436\) | −30.0526 | − | 52.0526i | −1.43926 | − | 2.49287i | ||||
\(437\) | 10.5622 | − | 18.2942i | 0.505257 | − | 0.875132i | ||||
\(438\) | −17.2942 | + | 29.9545i | −0.826350 | + | 1.43128i | ||||
\(439\) | −0.267949 | − | 0.464102i | −0.0127885 | − | 0.0221504i | 0.859560 | − | 0.511034i | \(-0.170737\pi\) |
−0.872349 | + | 0.488884i | \(0.837404\pi\) | |||||||
\(440\) | −6.92820 | −0.330289 | ||||||||
\(441\) | −1.00000 | + | 6.92820i | −0.0476190 | + | 0.329914i | ||||
\(442\) | −20.2487 | −0.963133 | ||||||||
\(443\) | −4.73205 | − | 8.19615i | −0.224827 | − | 0.389411i | 0.731441 | − | 0.681905i | \(-0.238848\pi\) |
−0.956267 | + | 0.292494i | \(0.905515\pi\) | |||||||
\(444\) | −8.73205 | + | 15.1244i | −0.414405 | + | 0.717770i | ||||
\(445\) | −7.56218 | + | 13.0981i | −0.358482 | + | 0.620908i | ||||
\(446\) | −27.8564 | − | 48.2487i | −1.31904 | − | 2.28464i | ||||
\(447\) | −5.85641 | −0.276999 | ||||||||
\(448\) | 25.8564 | − | 74.6410i | 1.22160 | − | 3.52646i | ||||
\(449\) | −35.8564 | −1.69217 | −0.846084 | − | 0.533049i | \(-0.821046\pi\) | ||||
−0.846084 | + | 0.533049i | \(0.821046\pi\) | |||||||
\(450\) | 1.36603 | + | 2.36603i | 0.0643951 | + | 0.111536i | ||||
\(451\) | 0.267949 | − | 0.464102i | 0.0126172 | − | 0.0218537i | ||||
\(452\) | −24.3923 | + | 42.2487i | −1.14732 | + | 1.98721i | ||||
\(453\) | −4.46410 | − | 7.73205i | −0.209742 | − | 0.363283i | ||||
\(454\) | 4.53590 | 0.212880 | ||||||||
\(455\) | −5.89230 | + | 1.13397i | −0.276236 | + | 0.0531615i | ||||
\(456\) | 42.2487 | 1.97848 | ||||||||
\(457\) | 8.33013 | + | 14.4282i | 0.389667 | + | 0.674923i | 0.992405 | − | 0.123016i | \(-0.0392568\pi\) |
−0.602738 | + | 0.797939i | \(0.705923\pi\) | |||||||
\(458\) | −4.09808 | + | 7.09808i | −0.191491 | + | 0.331671i | ||||
\(459\) | 1.63397 | − | 2.83013i | 0.0762674 | − | 0.132099i | ||||
\(460\) | 12.9282 | + | 22.3923i | 0.602781 | + | 1.04405i | ||||
\(461\) | 16.9808 | 0.790873 | 0.395436 | − | 0.918493i | \(-0.370593\pi\) | ||||
0.395436 | + | 0.918493i | \(0.370593\pi\) | |||||||
\(462\) | 3.46410 | + | 4.00000i | 0.161165 | + | 0.186097i | ||||
\(463\) | 25.7321 | 1.19587 | 0.597935 | − | 0.801545i | \(-0.295988\pi\) | ||||
0.597935 | + | 0.801545i | \(0.295988\pi\) | |||||||
\(464\) | 31.3205 | + | 54.2487i | 1.45402 | + | 2.51843i | ||||
\(465\) | −0.232051 | + | 0.401924i | −0.0107611 | + | 0.0186388i | ||||
\(466\) | 23.6603 | − | 40.9808i | 1.09604 | − | 1.89840i | ||||
\(467\) | 0.0717968 | + | 0.124356i | 0.00332236 | + | 0.00575449i | 0.867682 | − | 0.497120i | \(-0.165609\pi\) |
−0.864359 | + | 0.502874i | \(0.832276\pi\) | |||||||
\(468\) | 12.3923 | 0.572834 | ||||||||
\(469\) | −25.3923 | − | 29.3205i | −1.17251 | − | 1.35390i | ||||
\(470\) | −5.46410 | −0.252040 | ||||||||
\(471\) | 3.19615 | + | 5.53590i | 0.147271 | + | 0.255081i | ||||
\(472\) | −0.928203 | + | 1.60770i | −0.0427240 | + | 0.0740002i | ||||
\(473\) | −1.16987 | + | 2.02628i | −0.0537908 | + | 0.0931684i | ||||
\(474\) | 10.0981 | + | 17.4904i | 0.463820 | + | 0.803360i | ||||
\(475\) | 4.46410 | 0.204827 | ||||||||
\(476\) | −46.3923 | + | 8.92820i | −2.12639 | + | 0.409224i | ||||
\(477\) | 12.3923 | 0.567405 | ||||||||
\(478\) | 9.66025 | + | 16.7321i | 0.441850 | + | 0.765306i | ||||
\(479\) | −4.39230 | + | 7.60770i | −0.200690 | + | 0.347604i | −0.948751 | − | 0.316025i | \(-0.897652\pi\) |
0.748061 | + | 0.663630i | \(0.230985\pi\) | |||||||
\(480\) | −10.9282 | + | 18.9282i | −0.498802 | + | 0.863950i | ||||
\(481\) | 3.62436 | + | 6.27757i | 0.165256 | + | 0.286232i | ||||
\(482\) | −36.7846 | −1.67549 | ||||||||
\(483\) | 4.09808 | − | 11.8301i | 0.186469 | − | 0.538289i | ||||
\(484\) | −57.1769 | −2.59895 | ||||||||
\(485\) | −7.46410 | − | 12.9282i | −0.338927 | − | 0.587039i | ||||
\(486\) | −1.36603 | + | 2.36603i | −0.0619642 | + | 0.107325i | ||||
\(487\) | 0.205771 | − | 0.356406i | 0.00932439 | − | 0.0161503i | −0.861326 | − | 0.508053i | \(-0.830365\pi\) |
0.870650 | + | 0.491903i | \(0.163699\pi\) | |||||||
\(488\) | 18.9282 | + | 32.7846i | 0.856840 | + | 1.48409i | ||||
\(489\) | −21.8564 | −0.988381 | ||||||||
\(490\) | −17.7583 | + | 7.09808i | −0.802240 | + | 0.320658i | ||||
\(491\) | −38.2487 | −1.72614 | −0.863070 | − | 0.505084i | \(-0.831461\pi\) | ||||
−0.863070 | + | 0.505084i | \(0.831461\pi\) | |||||||
\(492\) | −2.00000 | − | 3.46410i | −0.0901670 | − | 0.156174i | ||||
\(493\) | 6.85641 | − | 11.8756i | 0.308797 | − | 0.534852i | ||||
\(494\) | 13.8301 | − | 23.9545i | 0.622247 | − | 1.07776i | ||||
\(495\) | −0.366025 | − | 0.633975i | −0.0164516 | − | 0.0284950i | ||||
\(496\) | −6.92820 | −0.311086 | ||||||||
\(497\) | 5.36603 | − | 15.4904i | 0.240699 | − | 0.694839i | ||||
\(498\) | 41.3205 | 1.85162 | ||||||||
\(499\) | 6.76795 | + | 11.7224i | 0.302975 | + | 0.524768i | 0.976808 | − | 0.214115i | \(-0.0686868\pi\) |
−0.673833 | + | 0.738883i | \(0.735353\pi\) | |||||||
\(500\) | −2.73205 | + | 4.73205i | −0.122181 | + | 0.211624i | ||||
\(501\) | −8.83013 | + | 15.2942i | −0.394501 | + | 0.683296i | ||||
\(502\) | −33.5885 | − | 58.1769i | −1.49913 | − | 2.59656i | ||||
\(503\) | 14.3923 | 0.641721 | 0.320861 | − | 0.947126i | \(-0.396028\pi\) | ||||
0.320861 | + | 0.947126i | \(0.396028\pi\) | |||||||
\(504\) | 24.5885 | − | 4.73205i | 1.09526 | − | 0.210782i | ||||
\(505\) | −7.26795 | −0.323419 | ||||||||
\(506\) | −4.73205 | − | 8.19615i | −0.210365 | − | 0.364363i | ||||
\(507\) | −3.92820 | + | 6.80385i | −0.174458 | + | 0.302169i | ||||
\(508\) | −13.1244 | + | 22.7321i | −0.582299 | + | 1.00857i | ||||
\(509\) | −2.26795 | − | 3.92820i | −0.100525 | − | 0.174115i | 0.811376 | − | 0.584525i | \(-0.198719\pi\) |
−0.911901 | + | 0.410410i | \(0.865386\pi\) | |||||||
\(510\) | 8.92820 | 0.395347 | ||||||||
\(511\) | 21.9282 | + | 25.3205i | 0.970047 | + | 1.12011i | ||||
\(512\) | −43.7128 | −1.93185 | ||||||||
\(513\) | 2.23205 | + | 3.86603i | 0.0985475 | + | 0.170689i | ||||
\(514\) | −7.73205 | + | 13.3923i | −0.341046 | + | 0.590709i | ||||
\(515\) | 4.59808 | − | 7.96410i | 0.202615 | − | 0.350940i | ||||
\(516\) | 8.73205 | + | 15.1244i | 0.384407 | + | 0.665813i | ||||
\(517\) | 1.46410 | 0.0643911 | ||||||||
\(518\) | 15.1244 | + | 17.4641i | 0.664526 | + | 0.767329i | ||||
\(519\) | −14.5359 | −0.638055 | ||||||||
\(520\) | 10.7321 | + | 18.5885i | 0.470632 | + | 0.815158i | ||||
\(521\) | 2.73205 | − | 4.73205i | 0.119693 | − | 0.207315i | −0.799953 | − | 0.600063i | \(-0.795142\pi\) |
0.919646 | + | 0.392748i | \(0.128476\pi\) | |||||||
\(522\) | −5.73205 | + | 9.92820i | −0.250885 | + | 0.434546i | ||||
\(523\) | 13.8660 | + | 24.0167i | 0.606319 | + | 1.05018i | 0.991842 | + | 0.127477i | \(0.0406878\pi\) |
−0.385523 | + | 0.922698i | \(0.625979\pi\) | |||||||
\(524\) | 84.4974 | 3.69129 | ||||||||
\(525\) | 2.59808 | − | 0.500000i | 0.113389 | − | 0.0218218i | ||||
\(526\) | −22.9282 | −0.999717 | ||||||||
\(527\) | 0.758330 | + | 1.31347i | 0.0330334 | + | 0.0572155i | ||||
\(528\) | 5.46410 | − | 9.46410i | 0.237795 | − | 0.411872i | ||||
\(529\) | 0.303848 | − | 0.526279i | 0.0132108 | − | 0.0228817i | ||||
\(530\) | 16.9282 | + | 29.3205i | 0.735314 | + | 1.27360i | ||||
\(531\) | −0.196152 | −0.00851229 | ||||||||
\(532\) | 21.1244 | − | 60.9808i | 0.915857 | − | 2.64385i | ||||
\(533\) | −1.66025 | −0.0719136 | ||||||||
\(534\) | −20.6603 | − | 35.7846i | −0.894057 | − | 1.54855i | ||||
\(535\) | −1.09808 | + | 1.90192i | −0.0474740 | + | 0.0822273i | ||||
\(536\) | −69.3731 | + | 120.158i | −2.99646 | + | 5.19002i | ||||
\(537\) | −5.00000 | − | 8.66025i | −0.215766 | − | 0.373718i | ||||
\(538\) | 34.2487 | 1.47657 | ||||||||
\(539\) | 4.75833 | − | 1.90192i | 0.204956 | − | 0.0819217i | ||||
\(540\) | −5.46410 | −0.235137 | ||||||||
\(541\) | −2.89230 | − | 5.00962i | −0.124350 | − | 0.215380i | 0.797129 | − | 0.603809i | \(-0.206351\pi\) |
−0.921479 | + | 0.388429i | \(0.873018\pi\) | |||||||
\(542\) | 4.19615 | − | 7.26795i | 0.180240 | − | 0.312185i | ||||
\(543\) | −12.1603 | + | 21.0622i | −0.521846 | + | 0.903865i | ||||
\(544\) | 35.7128 | + | 61.8564i | 1.53117 | + | 2.65207i | ||||
\(545\) | 11.0000 | 0.471188 | ||||||||
\(546\) | 5.36603 | − | 15.4904i | 0.229645 | − | 0.662927i | ||||
\(547\) | −26.2487 | −1.12231 | −0.561157 | − | 0.827709i | \(-0.689644\pi\) | ||||
−0.561157 | + | 0.827709i | \(0.689644\pi\) | |||||||
\(548\) | −6.00000 | − | 10.3923i | −0.256307 | − | 0.443937i | ||||
\(549\) | −2.00000 | + | 3.46410i | −0.0853579 | + | 0.147844i | ||||
\(550\) | 1.00000 | − | 1.73205i | 0.0426401 | − | 0.0738549i | ||||
\(551\) | 9.36603 | + | 16.2224i | 0.399006 | + | 0.691099i | ||||
\(552\) | −44.7846 | −1.90616 | ||||||||
\(553\) | 19.2058 | − | 3.69615i | 0.816712 | − | 0.157176i | ||||
\(554\) | 40.0526 | 1.70167 | ||||||||
\(555\) | −1.59808 | − | 2.76795i | −0.0678346 | − | 0.117493i | ||||
\(556\) | −16.1962 | + | 28.0526i | −0.686870 | + | 1.18969i | ||||
\(557\) | −7.39230 | + | 12.8038i | −0.313222 | + | 0.542516i | −0.979058 | − | 0.203582i | \(-0.934742\pi\) |
0.665836 | + | 0.746098i | \(0.268075\pi\) | |||||||
\(558\) | −0.633975 | − | 1.09808i | −0.0268383 | − | 0.0464853i | ||||
\(559\) | 7.24871 | 0.306588 | ||||||||
\(560\) | 25.8564 | + | 29.8564i | 1.09263 | + | 1.26166i | ||||
\(561\) | −2.39230 | −0.101003 | ||||||||
\(562\) | 18.9282 | + | 32.7846i | 0.798438 | + | 1.38294i | ||||
\(563\) | 9.00000 | − | 15.5885i | 0.379305 | − | 0.656975i | −0.611656 | − | 0.791123i | \(-0.709497\pi\) |
0.990961 | + | 0.134148i | \(0.0428299\pi\) | |||||||
\(564\) | 5.46410 | − | 9.46410i | 0.230080 | − | 0.398511i | ||||
\(565\) | −4.46410 | − | 7.73205i | −0.187806 | − | 0.325290i | ||||
\(566\) | 65.9090 | 2.77036 | ||||||||
\(567\) | 1.73205 | + | 2.00000i | 0.0727393 | + | 0.0839921i | ||||
\(568\) | −58.6410 | −2.46052 | ||||||||
\(569\) | −16.2224 | − | 28.0981i | −0.680080 | − | 1.17793i | −0.974956 | − | 0.222397i | \(-0.928612\pi\) |
0.294876 | − | 0.955535i | \(-0.404722\pi\) | |||||||
\(570\) | −6.09808 | + | 10.5622i | −0.255420 | + | 0.442401i | ||||
\(571\) | −9.30385 | + | 16.1147i | −0.389354 | + | 0.674381i | −0.992363 | − | 0.123354i | \(-0.960635\pi\) |
0.603009 | + | 0.797734i | \(0.293968\pi\) | |||||||
\(572\) | −4.53590 | − | 7.85641i | −0.189655 | − | 0.328493i | ||||
\(573\) | 8.92820 | 0.372981 | ||||||||
\(574\) | −5.19615 | + | 1.00000i | −0.216883 | + | 0.0417392i | ||||
\(575\) | −4.73205 | −0.197340 | ||||||||
\(576\) | −14.9282 | − | 25.8564i | −0.622008 | − | 1.07735i | ||||
\(577\) | −14.3301 | + | 24.8205i | −0.596571 | + | 1.03329i | 0.396752 | + | 0.917926i | \(0.370137\pi\) |
−0.993323 | + | 0.115365i | \(0.963196\pi\) | |||||||
\(578\) | −8.63397 | + | 14.9545i | −0.359126 | + | 0.622024i | ||||
\(579\) | 0.598076 | + | 1.03590i | 0.0248552 | + | 0.0430505i | ||||
\(580\) | −22.9282 | −0.952042 | ||||||||
\(581\) | 13.0981 | − | 37.8109i | 0.543400 | − | 1.56866i | ||||
\(582\) | 40.7846 | 1.69058 | ||||||||
\(583\) | −4.53590 | − | 7.85641i | −0.187858 | − | 0.325379i | ||||
\(584\) | 59.9090 | − | 103.765i | 2.47905 | − | 4.29384i | ||||
\(585\) | −1.13397 | + | 1.96410i | −0.0468841 | + | 0.0812056i | ||||
\(586\) | 25.8564 | + | 44.7846i | 1.06812 | + | 1.85004i | ||||
\(587\) | 40.7321 | 1.68119 | 0.840596 | − | 0.541663i | \(-0.182205\pi\) | ||||
0.840596 | + | 0.541663i | \(0.182205\pi\) | |||||||
\(588\) | 5.46410 | − | 37.8564i | 0.225336 | − | 1.56117i | ||||
\(589\) | −2.07180 | −0.0853669 | ||||||||
\(590\) | −0.267949 | − | 0.464102i | −0.0110313 | − | 0.0191068i | ||||
\(591\) | −0.169873 | + | 0.294229i | −0.00698764 | + | 0.0121029i | ||||
\(592\) | 23.8564 | − | 41.3205i | 0.980492 | − | 1.69826i | ||||
\(593\) | −13.9545 | − | 24.1699i | −0.573042 | − | 0.992538i | −0.996251 | − | 0.0865058i | \(-0.972430\pi\) |
0.423209 | − | 0.906032i | \(-0.360903\pi\) | |||||||
\(594\) | 2.00000 | 0.0820610 | ||||||||
\(595\) | 2.83013 | − | 8.16987i | 0.116024 | − | 0.334932i | ||||
\(596\) | 32.0000 | 1.31077 | ||||||||
\(597\) | 11.0000 | + | 19.0526i | 0.450200 | + | 0.779769i | ||||
\(598\) | −14.6603 | + | 25.3923i | −0.599502 | + | 1.03837i | ||||
\(599\) | 19.1244 | − | 33.1244i | 0.781400 | − | 1.35342i | −0.149726 | − | 0.988727i | \(-0.547839\pi\) |
0.931126 | − | 0.364697i | \(-0.118827\pi\) | |||||||
\(600\) | −4.73205 | − | 8.19615i | −0.193185 | − | 0.334607i | ||||
\(601\) | −0.0717968 | −0.00292865 | −0.00146433 | − | 0.999999i | \(-0.500466\pi\) | ||||
−0.00146433 | + | 0.999999i | \(0.500466\pi\) | |||||||
\(602\) | 22.6865 | − | 4.36603i | 0.924634 | − | 0.177946i | ||||
\(603\) | −14.6603 | −0.597012 | ||||||||
\(604\) | 24.3923 | + | 42.2487i | 0.992509 | + | 1.71908i | ||||
\(605\) | 5.23205 | − | 9.06218i | 0.212713 | − | 0.368430i | ||||
\(606\) | 9.92820 | − | 17.1962i | 0.403306 | − | 0.698546i | ||||
\(607\) | −1.59808 | − | 2.76795i | −0.0648639 | − | 0.112348i | 0.831770 | − | 0.555121i | \(-0.187328\pi\) |
−0.896634 | + | 0.442773i | \(0.853995\pi\) | |||||||
\(608\) | −97.5692 | −3.95695 | ||||||||
\(609\) | 7.26795 | + | 8.39230i | 0.294512 | + | 0.340073i | ||||
\(610\) | −10.9282 | −0.442470 | ||||||||
\(611\) | −2.26795 | − | 3.92820i | −0.0917514 | − | 0.158918i | ||||
\(612\) | −8.92820 | + | 15.4641i | −0.360901 | + | 0.625099i | ||||
\(613\) | 13.4641 | − | 23.3205i | 0.543810 | − | 0.941906i | −0.454871 | − | 0.890557i | \(-0.650315\pi\) |
0.998681 | − | 0.0513490i | \(-0.0163521\pi\) | |||||||
\(614\) | −43.8827 | − | 76.0070i | −1.77096 | − | 3.06739i | ||||
\(615\) | 0.732051 | 0.0295191 | ||||||||
\(616\) | −12.0000 | − | 13.8564i | −0.483494 | − | 0.558291i | ||||
\(617\) | −36.2487 | −1.45932 | −0.729659 | − | 0.683811i | \(-0.760321\pi\) | ||||
−0.729659 | + | 0.683811i | \(0.760321\pi\) | |||||||
\(618\) | 12.5622 | + | 21.7583i | 0.505325 | + | 0.875248i | ||||
\(619\) | 15.0359 | − | 26.0429i | 0.604344 | − | 1.04675i | −0.387811 | − | 0.921739i | \(-0.626769\pi\) |
0.992155 | − | 0.125015i | \(-0.0398980\pi\) | |||||||
\(620\) | 1.26795 | − | 2.19615i | 0.0509221 | − | 0.0881996i | ||||
\(621\) | −2.36603 | − | 4.09808i | −0.0949453 | − | 0.164450i | ||||
\(622\) | −24.9282 | −0.999530 | ||||||||
\(623\) | −39.2942 | + | 7.56218i | −1.57429 | + | 0.302972i | ||||
\(624\) | −33.8564 | −1.35534 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −17.2942 | + | 29.9545i | −0.691216 | + | 1.19722i | ||||
\(627\) | 1.63397 | − | 2.83013i | 0.0652547 | − | 0.113024i | ||||
\(628\) | −17.4641 | − | 30.2487i | −0.696894 | − | 1.20705i | ||||
\(629\) | −10.4449 | −0.416464 | ||||||||
\(630\) | −2.36603 | + | 6.83013i | −0.0942647 | + | 0.272119i | ||||
\(631\) | 48.7846 | 1.94208 | 0.971042 | − | 0.238908i | \(-0.0767893\pi\) | ||||
0.971042 | + | 0.238908i | \(0.0767893\pi\) | |||||||
\(632\) | −34.9808 | − | 60.5885i | −1.39146 | − | 2.41008i | ||||
\(633\) | 3.53590 | − | 6.12436i | 0.140539 | − | 0.243421i | ||||
\(634\) | −38.8564 | + | 67.3013i | −1.54319 | + | 2.67287i | ||||
\(635\) | −2.40192 | − | 4.16025i | −0.0953174 | − | 0.165095i | ||||
\(636\) | −67.7128 | −2.68499 | ||||||||
\(637\) | −12.4737 | − | 9.82051i | −0.494227 | − | 0.389103i | ||||
\(638\) | 8.39230 | 0.332255 | ||||||||
\(639\) | −3.09808 | − | 5.36603i | −0.122558 | − | 0.212277i | ||||
\(640\) | 18.9282 | − | 32.7846i | 0.748203 | − | 1.29593i | ||||
\(641\) | −1.90192 | + | 3.29423i | −0.0751215 | + | 0.130114i | −0.901139 | − | 0.433530i | \(-0.857268\pi\) |
0.826018 | + | 0.563644i | \(0.190601\pi\) | |||||||
\(642\) | −3.00000 | − | 5.19615i | −0.118401 | − | 0.205076i | ||||
\(643\) | 4.51666 | 0.178120 | 0.0890599 | − | 0.996026i | \(-0.471614\pi\) | ||||
0.0890599 | + | 0.996026i | \(0.471614\pi\) | |||||||
\(644\) | −22.3923 | + | 64.6410i | −0.882380 | + | 2.54721i | ||||
\(645\) | −3.19615 | −0.125848 | ||||||||
\(646\) | 19.9282 | + | 34.5167i | 0.784065 | + | 1.35804i | ||||
\(647\) | 13.9545 | − | 24.1699i | 0.548607 | − | 0.950216i | −0.449763 | − | 0.893148i | \(-0.648492\pi\) |
0.998370 | − | 0.0570678i | \(-0.0181751\pi\) | |||||||
\(648\) | 4.73205 | − | 8.19615i | 0.185893 | − | 0.321975i | ||||
\(649\) | 0.0717968 | + | 0.124356i | 0.00281827 | + | 0.00488139i | ||||
\(650\) | −6.19615 | −0.243033 | ||||||||
\(651\) | −1.20577 | + | 0.232051i | −0.0472579 | + | 0.00909479i | ||||
\(652\) | 119.426 | 4.67707 | ||||||||
\(653\) | 22.2942 | + | 38.6147i | 0.872441 | + | 1.51111i | 0.859464 | + | 0.511196i | \(0.170797\pi\) |
0.0129762 | + | 0.999916i | \(0.495869\pi\) | |||||||
\(654\) | −15.0263 | + | 26.0263i | −0.587574 | + | 1.01771i | ||||
\(655\) | −7.73205 | + | 13.3923i | −0.302116 | + | 0.523281i | ||||
\(656\) | 5.46410 | + | 9.46410i | 0.213337 | + | 0.369511i | ||||
\(657\) | 12.6603 | 0.493924 | ||||||||
\(658\) | −9.46410 | − | 10.9282i | −0.368949 | − | 0.426026i | ||||
\(659\) | 2.92820 | 0.114067 | 0.0570333 | − | 0.998372i | \(-0.481836\pi\) | ||||
0.0570333 | + | 0.998372i | \(0.481836\pi\) | |||||||
\(660\) | 2.00000 | + | 3.46410i | 0.0778499 | + | 0.134840i | ||||
\(661\) | −5.23205 | + | 9.06218i | −0.203503 | + | 0.352478i | −0.949655 | − | 0.313298i | \(-0.898566\pi\) |
0.746152 | + | 0.665776i | \(0.231899\pi\) | |||||||
\(662\) | 11.0263 | − | 19.0981i | 0.428549 | − | 0.742268i | ||||
\(663\) | 3.70577 | + | 6.41858i | 0.143920 | + | 0.249277i | ||||
\(664\) | −143.138 | −5.55485 | ||||||||
\(665\) | 7.73205 | + | 8.92820i | 0.299836 | + | 0.346221i | ||||
\(666\) | 8.73205 | 0.338360 | ||||||||
\(667\) | −9.92820 | − | 17.1962i | −0.384422 | − | 0.665838i | ||||
\(668\) | 48.2487 | − | 83.5692i | 1.86680 | − | 3.23339i | ||||
\(669\) | −10.1962 | + | 17.6603i | −0.394206 | + | 0.682785i | ||||
\(670\) | −20.0263 | − | 34.6865i | −0.773683 | − | 1.34006i | ||||
\(671\) | 2.92820 | 0.113042 | ||||||||
\(672\) | −56.7846 | + | 10.9282i | −2.19051 | + | 0.421565i | ||||
\(673\) | −27.3397 | −1.05387 | −0.526935 | − | 0.849906i | \(-0.676659\pi\) | ||||
−0.526935 | + | 0.849906i | \(0.676659\pi\) | |||||||
\(674\) | 24.5622 | + | 42.5429i | 0.946100 | + | 1.63869i | ||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | 21.4641 | − | 37.1769i | 0.825542 | − | 1.42988i | ||||
\(677\) | 16.5622 | + | 28.6865i | 0.636536 | + | 1.10251i | 0.986187 | + | 0.165633i | \(0.0529668\pi\) |
−0.349651 | + | 0.936880i | \(0.613700\pi\) | |||||||
\(678\) | 24.3923 | 0.936781 | ||||||||
\(679\) | 12.9282 | − | 37.3205i | 0.496139 | − | 1.43223i | ||||
\(680\) | −30.9282 | −1.18604 | ||||||||
\(681\) | −0.830127 | − | 1.43782i | −0.0318105 | − | 0.0550975i | ||||
\(682\) | −0.464102 | + | 0.803848i | −0.0177714 | + | 0.0307809i | ||||
\(683\) | 14.0263 | − | 24.2942i | 0.536701 | − | 0.929593i | −0.462378 | − | 0.886683i | \(-0.653004\pi\) |
0.999079 | − | 0.0429101i | \(-0.0136629\pi\) | |||||||
\(684\) | −12.1962 | − | 21.1244i | −0.466332 | − | 0.807710i | ||||
\(685\) | 2.19615 | 0.0839107 | ||||||||
\(686\) | −44.9545 | − | 23.2224i | −1.71637 | − | 0.886637i | ||||
\(687\) | 3.00000 | 0.114457 | ||||||||
\(688\) | −23.8564 | − | 41.3205i | −0.909517 | − | 1.57533i | ||||
\(689\) | −14.0526 | + | 24.3397i | −0.535360 | + | 0.927270i | ||||
\(690\) | 6.46410 | − | 11.1962i | 0.246084 | − | 0.426230i | ||||
\(691\) | −4.42820 | − | 7.66987i | −0.168457 | − | 0.291776i | 0.769421 | − | 0.638742i | \(-0.220545\pi\) |
−0.937877 | + | 0.346967i | \(0.887212\pi\) | |||||||
\(692\) | 79.4256 | 3.01931 | ||||||||
\(693\) | 0.633975 | − | 1.83013i | 0.0240827 | − | 0.0695208i | ||||
\(694\) | 57.5692 | 2.18530 | ||||||||
\(695\) | −2.96410 | − | 5.13397i | −0.112435 | − | 0.194743i | ||||
\(696\) | 19.8564 | − | 34.3923i | 0.752655 | − | 1.30364i | ||||
\(697\) | 1.19615 | − | 2.07180i | 0.0453075 | − | 0.0784749i | ||||
\(698\) | 30.0526 | + | 52.0526i | 1.13751 | + | 1.97022i | ||||
\(699\) | −17.3205 | −0.655122 | ||||||||
\(700\) | −14.1962 | + | 2.73205i | −0.536564 | + | 0.103262i | ||||
\(701\) | −8.58846 | −0.324382 | −0.162191 | − | 0.986759i | \(-0.551856\pi\) | ||||
−0.162191 | + | 0.986759i | \(0.551856\pi\) | |||||||
\(702\) | −3.09808 | − | 5.36603i | −0.116929 | − | 0.202528i | ||||
\(703\) | 7.13397 | − | 12.3564i | 0.269063 | − | 0.466031i | ||||
\(704\) | −10.9282 | + | 18.9282i | −0.411872 | + | 0.713384i | ||||
\(705\) | 1.00000 | + | 1.73205i | 0.0376622 | + | 0.0652328i | ||||
\(706\) | 8.53590 | 0.321253 | ||||||||
\(707\) | −12.5885 | − | 14.5359i | −0.473438 | − | 0.546679i | ||||
\(708\) | 1.07180 | 0.0402806 | ||||||||
\(709\) | 0.535898 | + | 0.928203i | 0.0201261 | + | 0.0348594i | 0.875913 | − | 0.482469i | \(-0.160260\pi\) |
−0.855787 | + | 0.517328i | \(0.826927\pi\) | |||||||
\(710\) | 8.46410 | − | 14.6603i | 0.317652 | − | 0.550190i | ||||
\(711\) | 3.69615 | − | 6.40192i | 0.138617 | − | 0.240091i | ||||
\(712\) | 71.5692 | + | 123.962i | 2.68217 | + | 4.64565i | ||||
\(713\) | 2.19615 | 0.0822466 | ||||||||
\(714\) | 15.4641 | + | 17.8564i | 0.578729 | + | 0.668259i | ||||
\(715\) | 1.66025 | 0.0620900 | ||||||||
\(716\) | 27.3205 | + | 47.3205i | 1.02102 | + | 1.76845i | ||||
\(717\) | 3.53590 | − | 6.12436i | 0.132051 | − | 0.228718i | ||||
\(718\) | −1.73205 | + | 3.00000i | −0.0646396 | + | 0.111959i | ||||
\(719\) | 10.2679 | + | 17.7846i | 0.382930 | + | 0.663254i | 0.991480 | − | 0.130262i | \(-0.0415817\pi\) |
−0.608550 | + | 0.793516i | \(0.708248\pi\) | |||||||
\(720\) | 14.9282 | 0.556341 | ||||||||
\(721\) | 23.8923 | − | 4.59808i | 0.889796 | − | 0.171241i | ||||
\(722\) | −2.53590 | −0.0943764 | ||||||||
\(723\) | 6.73205 | + | 11.6603i | 0.250368 | + | 0.433650i | ||||
\(724\) | 66.4449 | − | 115.086i | 2.46940 | − | 4.27713i | ||||
\(725\) | 2.09808 | − | 3.63397i | 0.0779206 | − | 0.134962i | ||||
\(726\) | 14.2942 | + | 24.7583i | 0.530509 | + | 0.918868i | ||||
\(727\) | −13.3397 | −0.494744 | −0.247372 | − | 0.968921i | \(-0.579567\pi\) | ||||
−0.247372 | + | 0.968921i | \(0.579567\pi\) | |||||||
\(728\) | −18.5885 | + | 53.6603i | −0.688934 | + | 1.98878i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 17.2942 | + | 29.9545i | 0.640088 | + | 1.10867i | ||||
\(731\) | −5.22243 | + | 9.04552i | −0.193159 | + | 0.334561i | ||||
\(732\) | 10.9282 | − | 18.9282i | 0.403918 | − | 0.699607i | ||||
\(733\) | 0.669873 | + | 1.16025i | 0.0247423 | + | 0.0428550i | 0.878131 | − | 0.478419i | \(-0.158790\pi\) |
−0.853389 | + | 0.521274i | \(0.825457\pi\) | |||||||
\(734\) | −30.5885 | −1.12904 | ||||||||
\(735\) | 5.50000 | + | 4.33013i | 0.202871 | + | 0.159719i | ||||
\(736\) | 103.426 | 3.81232 | ||||||||
\(737\) | 5.36603 | + | 9.29423i | 0.197660 | + | 0.342357i | ||||
\(738\) | −1.00000 | + | 1.73205i | −0.0368105 | + | 0.0637577i | ||||
\(739\) | −13.8923 | + | 24.0622i | −0.511037 | + | 0.885142i | 0.488881 | + | 0.872350i | \(0.337405\pi\) |
−0.999918 | + | 0.0127913i | \(0.995928\pi\) | |||||||
\(740\) | 8.73205 | + | 15.1244i | 0.320997 | + | 0.555982i | ||||
\(741\) | −10.1244 | −0.371927 | ||||||||
\(742\) | −29.3205 | + | 84.6410i | −1.07639 | + | 3.10727i | ||||
\(743\) | −15.9090 | −0.583643 | −0.291822 | − | 0.956473i | \(-0.594261\pi\) | ||||
−0.291822 | + | 0.956473i | \(0.594261\pi\) | |||||||
\(744\) | 2.19615 | + | 3.80385i | 0.0805149 | + | 0.139456i | ||||
\(745\) | −2.92820 | + | 5.07180i | −0.107281 | + | 0.185816i | ||||
\(746\) | 36.2224 | − | 62.7391i | 1.32620 | − | 2.29704i | ||||
\(747\) | −7.56218 | − | 13.0981i | −0.276686 | − | 0.479234i | ||||
\(748\) | 13.0718 | 0.477952 | ||||||||
\(749\) | −5.70577 | + | 1.09808i | −0.208484 | + | 0.0401228i | ||||
\(750\) | 2.73205 | 0.0997604 | ||||||||
\(751\) | −9.03590 | − | 15.6506i | −0.329725 | − | 0.571100i | 0.652732 | − | 0.757588i | \(-0.273623\pi\) |
−0.982457 | + | 0.186489i | \(0.940289\pi\) | |||||||
\(752\) | −14.9282 | + | 25.8564i | −0.544376 | + | 0.942886i | ||||
\(753\) | −12.2942 | + | 21.2942i | −0.448027 | + | 0.776005i | ||||
\(754\) | −13.0000 | − | 22.5167i | −0.473432 | − | 0.820008i | ||||
\(755\) | −8.92820 | −0.324931 | ||||||||
\(756\) | −9.46410 | − | 10.9282i | −0.344206 | − | 0.397455i | ||||
\(757\) | −27.8564 | −1.01246 | −0.506229 | − | 0.862399i | \(-0.668961\pi\) | ||||
−0.506229 | + | 0.862399i | \(0.668961\pi\) | |||||||
\(758\) | 8.63397 | + | 14.9545i | 0.313600 | + | 0.543171i | ||||
\(759\) | −1.73205 | + | 3.00000i | −0.0628695 | + | 0.108893i | ||||
\(760\) | 21.1244 | − | 36.5885i | 0.766261 | − | 1.32720i | ||||
\(761\) | −23.3660 | − | 40.4711i | −0.847018 | − | 1.46708i | −0.883857 | − | 0.467757i | \(-0.845062\pi\) |
0.0368396 | − | 0.999321i | \(-0.488271\pi\) | |||||||
\(762\) | 13.1244 | 0.475445 | ||||||||
\(763\) | 19.0526 | + | 22.0000i | 0.689749 | + | 0.796453i | ||||
\(764\) | −48.7846 | −1.76497 | ||||||||
\(765\) | −1.63397 | − | 2.83013i | −0.0590765 | − | 0.102323i | ||||
\(766\) | −31.8564 | + | 55.1769i | −1.15102 | + | 1.99362i | ||||
\(767\) | 0.222432 | − | 0.385263i | 0.00803155 | − | 0.0139111i | ||||
\(768\) | 21.8564 | + | 37.8564i | 0.788675 | + | 1.36603i | ||||
\(769\) | 52.3205 | 1.88673 | 0.943363 | − | 0.331763i | \(-0.107643\pi\) | ||||
0.943363 | + | 0.331763i | \(0.107643\pi\) | |||||||
\(770\) | 5.19615 | − | 1.00000i | 0.187256 | − | 0.0360375i | ||||
\(771\) | 5.66025 | 0.203849 | ||||||||
\(772\) | −3.26795 | − | 5.66025i | −0.117616 | − | 0.203717i | ||||
\(773\) | −21.7583 | + | 37.6865i | −0.782593 | + | 1.35549i | 0.147834 | + | 0.989012i | \(0.452770\pi\) |
−0.930427 | + | 0.366478i | \(0.880563\pi\) | |||||||
\(774\) | 4.36603 | − | 7.56218i | 0.156934 | − | 0.271817i | ||||
\(775\) | 0.232051 | + | 0.401924i | 0.00833551 | + | 0.0144375i | ||||
\(776\) | −141.282 | −5.07173 | ||||||||
\(777\) | 2.76795 | − | 7.99038i | 0.0992996 | − | 0.286653i | ||||
\(778\) | −14.7846 | −0.530054 | ||||||||
\(779\) | 1.63397 | + | 2.83013i | 0.0585432 | + | 0.101400i | ||||
\(780\) | 6.19615 | − | 10.7321i | 0.221858 | − | 0.384269i | ||||
\(781\) | −2.26795 | + | 3.92820i | −0.0811536 | + | 0.140562i | ||||
\(782\) | −21.1244 | − | 36.5885i | −0.755405 | − | 1.30840i | ||||
\(783\) | 4.19615 | 0.149958 | ||||||||
\(784\) | −14.9282 | + | 103.426i | −0.533150 | + | 3.69377i | ||||
\(785\) | 6.39230 | 0.228151 | ||||||||
\(786\) | −21.1244 | − | 36.5885i | −0.753481 | − | 1.30507i | ||||
\(787\) | −6.73205 | + | 11.6603i | −0.239972 | + | 0.415643i | −0.960706 | − | 0.277568i | \(-0.910471\pi\) |
0.720734 | + | 0.693212i | \(0.243805\pi\) | |||||||
\(788\) | 0.928203 | − | 1.60770i | 0.0330659 | − | 0.0572718i | ||||
\(789\) | 4.19615 | + | 7.26795i | 0.149387 | + | 0.258746i | ||||
\(790\) | 20.1962 | 0.718547 | ||||||||
\(791\) | 7.73205 | − | 22.3205i | 0.274920 | − | 0.793626i | ||||
\(792\) | −6.92820 | −0.246183 | ||||||||
\(793\) | −4.53590 | − | 7.85641i | −0.161074 | − | 0.278989i | ||||
\(794\) | −42.6147 | + | 73.8109i | −1.51234 | + | 2.61945i | ||||
\(795\) | 6.19615 | − | 10.7321i | 0.219755 | − | 0.380627i | ||||
\(796\) | −60.1051 | − | 104.105i | −2.13037 | − | 3.68991i | ||||
\(797\) | −3.94744 | −0.139826 | −0.0699128 | − | 0.997553i | \(-0.522272\pi\) | ||||
−0.0699128 | + | 0.997553i | \(0.522272\pi\) | |||||||
\(798\) | −31.6865 | + | 6.09808i | −1.12169 | + | 0.215870i | ||||
\(799\) | 6.53590 | 0.231223 | ||||||||
\(800\) | 10.9282 | + | 18.9282i | 0.386370 | + | 0.669213i | ||||
\(801\) | −7.56218 | + | 13.0981i | −0.267196 | + | 0.462798i | ||||
\(802\) | −22.3923 | + | 38.7846i | −0.790700 | + | 1.36953i | ||||
\(803\) | −4.63397 | − | 8.02628i | −0.163529 | − | 0.283241i | ||||
\(804\) | 80.1051 | 2.82509 | ||||||||
\(805\) | −8.19615 | − | 9.46410i | −0.288876 | − | 0.333566i | ||||
\(806\) | 2.87564 | 0.101290 | ||||||||
\(807\) | −6.26795 | − | 10.8564i | −0.220642 | − | 0.382164i | ||||
\(808\) | −34.3923 | + | 59.5692i | −1.20992 | + | 2.09564i | ||||
\(809\) | −12.8564 | + | 22.2679i | −0.452007 | + | 0.782899i | −0.998511 | − | 0.0545574i | \(-0.982625\pi\) |
0.546503 | + | 0.837457i | \(0.315959\pi\) | |||||||
\(810\) | 1.36603 | + | 2.36603i | 0.0479972 | + | 0.0831337i | ||||
\(811\) | −3.46410 | −0.121641 | −0.0608205 | − | 0.998149i | \(-0.519372\pi\) | ||||
−0.0608205 | + | 0.998149i | \(0.519372\pi\) | |||||||
\(812\) | −39.7128 | − | 45.8564i | −1.39365 | − | 1.60924i | ||||
\(813\) | −3.07180 | −0.107733 | ||||||||
\(814\) | −3.19615 | − | 5.53590i | −0.112025 | − | 0.194033i | ||||
\(815\) | −10.9282 | + | 18.9282i | −0.382798 | + | 0.663026i | ||||
\(816\) | 24.3923 | − | 42.2487i | 0.853901 | − | 1.47900i | ||||
\(817\) | −7.13397 | − | 12.3564i | −0.249586 | − | 0.432296i | ||||
\(818\) | −8.58846 | −0.300288 | ||||||||
\(819\) | −5.89230 | + | 1.13397i | −0.205894 | + | 0.0396243i | ||||
\(820\) | −4.00000 | −0.139686 | ||||||||
\(821\) | 12.7583 | + | 22.0981i | 0.445269 | + | 0.771228i | 0.998071 | − | 0.0620844i | \(-0.0197748\pi\) |
−0.552802 | + | 0.833313i | \(0.686441\pi\) | |||||||
\(822\) | −3.00000 | + | 5.19615i | −0.104637 | + | 0.181237i | ||||
\(823\) | −19.5885 | + | 33.9282i | −0.682811 | + | 1.18266i | 0.291309 | + | 0.956629i | \(0.405909\pi\) |
−0.974119 | + | 0.226034i | \(0.927424\pi\) | |||||||
\(824\) | −43.5167 | − | 75.3731i | −1.51597 | − | 2.62575i | ||||
\(825\) | −0.732051 | −0.0254867 | ||||||||
\(826\) | 0.464102 | − | 1.33975i | 0.0161482 | − | 0.0466157i | ||||
\(827\) | −3.75129 | −0.130445 | −0.0652225 | − | 0.997871i | \(-0.520776\pi\) | ||||
−0.0652225 | + | 0.997871i | \(0.520776\pi\) | |||||||
\(828\) | 12.9282 | + | 22.3923i | 0.449286 | + | 0.778186i | ||||
\(829\) | 2.30385 | − | 3.99038i | 0.0800159 | − | 0.138592i | −0.823241 | − | 0.567693i | \(-0.807836\pi\) |
0.903257 | + | 0.429101i | \(0.141170\pi\) | |||||||
\(830\) | 20.6603 | − | 35.7846i | 0.717128 | − | 1.24210i | ||||
\(831\) | −7.33013 | − | 12.6962i | −0.254279 | − | 0.440425i | ||||
\(832\) | 67.7128 | 2.34752 | ||||||||
\(833\) | 21.2417 | − | 8.49038i | 0.735980 | − | 0.294174i | ||||
\(834\) | 16.1962 | 0.560827 | ||||||||
\(835\) | 8.83013 | + | 15.2942i | 0.305579 | + | 0.529279i | ||||
\(836\) | −8.92820 | + | 15.4641i | −0.308788 | + | 0.534837i | ||||
\(837\) | −0.232051 | + | 0.401924i | −0.00802085 | + | 0.0138925i | ||||
\(838\) | −48.4449 | − | 83.9090i | −1.67350 | − | 2.89859i | ||||
\(839\) | 18.4449 | 0.636787 | 0.318394 | − | 0.947959i | \(-0.396857\pi\) | ||||
0.318394 | + | 0.947959i | \(0.396857\pi\) | |||||||
\(840\) | 8.19615 | − | 23.6603i | 0.282794 | − | 0.816356i | ||||
\(841\) | −11.3923 | −0.392838 | ||||||||
\(842\) | 0.0980762 | + | 0.169873i | 0.00337993 | + | 0.00585421i | ||||
\(843\) | 6.92820 | − | 12.0000i | 0.238620 | − | 0.413302i | ||||
\(844\) | −19.3205 | + | 33.4641i | −0.665039 | + | 1.15188i | ||||
\(845\) | 3.92820 | + | 6.80385i | 0.135134 | + | 0.234059i | ||||
\(846\) | −5.46410 | −0.187860 | ||||||||
\(847\) | 27.1865 | − | 5.23205i | 0.934140 | − | 0.179775i | ||||
\(848\) | 184.995 | 6.35275 | ||||||||
\(849\) | −12.0622 | − | 20.8923i | −0.413973 | − | 0.717022i | ||||
\(850\) | 4.46410 | − | 7.73205i | 0.153117 | − | 0.265207i | ||||
\(851\) | −7.56218 | + | 13.0981i | −0.259228 | + | 0.448996i | ||||
\(852\) | 16.9282 | + | 29.3205i | 0.579951 | + | 1.00450i | ||||
\(853\) | −31.9808 | −1.09500 | −0.547500 | − | 0.836806i | \(-0.684420\pi\) | ||||
−0.547500 | + | 0.836806i | \(0.684420\pi\) | |||||||
\(854\) | −18.9282 | − | 21.8564i | −0.647710 | − | 0.747911i | ||||
\(855\) | 4.46410 | 0.152669 | ||||||||
\(856\) | 10.3923 | + | 18.0000i | 0.355202 | + | 0.615227i | ||||
\(857\) | −14.5622 | + | 25.2224i | −0.497435 | + | 0.861582i | −0.999996 | − | 0.00295983i | \(-0.999058\pi\) |
0.502561 | + | 0.864542i | \(0.332391\pi\) | |||||||
\(858\) | −2.26795 | + | 3.92820i | −0.0774265 | + | 0.134107i | ||||
\(859\) | −3.73205 | − | 6.46410i | −0.127336 | − | 0.220552i | 0.795308 | − | 0.606206i | \(-0.207309\pi\) |
−0.922644 | + | 0.385654i | \(0.873976\pi\) | |||||||
\(860\) | 17.4641 | 0.595521 | ||||||||
\(861\) | 1.26795 | + | 1.46410i | 0.0432116 | + | 0.0498964i | ||||
\(862\) | −47.3205 | −1.61174 | ||||||||
\(863\) | −7.19615 | − | 12.4641i | −0.244960 | − | 0.424283i | 0.717160 | − | 0.696908i | \(-0.245441\pi\) |
−0.962120 | + | 0.272625i | \(0.912108\pi\) | |||||||
\(864\) | −10.9282 | + | 18.9282i | −0.371785 | + | 0.643951i | ||||
\(865\) | −7.26795 | + | 12.5885i | −0.247118 | + | 0.428020i | ||||
\(866\) | 20.7583 | + | 35.9545i | 0.705397 | + | 1.22178i | ||||
\(867\) | 6.32051 | 0.214656 | ||||||||
\(868\) | 6.58846 | − | 1.26795i | 0.223627 | − | 0.0430370i | ||||
\(869\) | −5.41154 | −0.183574 | ||||||||
\(870\) | 5.73205 | + | 9.92820i | 0.194335 | + | 0.336598i | ||||
\(871\) | 16.6244 | − | 28.7942i | 0.563295 | − | 0.975655i | ||||
\(872\) | 52.0526 | − | 90.1577i | 1.76272 | − | 3.05312i | ||||
\(873\) | −7.46410 | − | 12.9282i | −0.252622 | − | 0.437553i | ||||
\(874\) | 57.7128 | 1.95217 | ||||||||
\(875\) | 0.866025 | − | 2.50000i | 0.0292770 | − | 0.0845154i | ||||
\(876\) | −69.1769 | −2.33727 | ||||||||
\(877\) | 2.07180 | + | 3.58846i | 0.0699596 | + | 0.121174i | 0.898883 | − | 0.438188i | \(-0.144380\pi\) |
−0.828924 | + | 0.559362i | \(0.811046\pi\) | |||||||
\(878\) | 0.732051 | − | 1.26795i | 0.0247055 | − | 0.0427912i | ||||
\(879\) | 9.46410 | − | 16.3923i | 0.319216 | − | 0.552899i | ||||
\(880\) | −5.46410 | − | 9.46410i | −0.184195 | − | 0.319035i | ||||
\(881\) | 9.85641 | 0.332071 | 0.166035 | − | 0.986120i | \(-0.446903\pi\) | ||||
0.166035 | + | 0.986120i | \(0.446903\pi\) | |||||||
\(882\) | −17.7583 | + | 7.09808i | −0.597954 | + | 0.239005i | ||||
\(883\) | 53.5885 | 1.80340 | 0.901698 | − | 0.432367i | \(-0.142322\pi\) | ||||
0.901698 | + | 0.432367i | \(0.142322\pi\) | |||||||
\(884\) | −20.2487 | − | 35.0718i | −0.681038 | − | 1.17959i | ||||
\(885\) | −0.0980762 | + | 0.169873i | −0.00329680 | + | 0.00571022i | ||||
\(886\) | 12.9282 | − | 22.3923i | 0.434331 | − | 0.752284i | ||||
\(887\) | 12.6340 | + | 21.8827i | 0.424207 | + | 0.734749i | 0.996346 | − | 0.0854082i | \(-0.0272194\pi\) |
−0.572139 | + | 0.820157i | \(0.693886\pi\) | |||||||
\(888\) | −30.2487 | −1.01508 | ||||||||
\(889\) | 4.16025 | − | 12.0096i | 0.139530 | − | 0.402790i | ||||
\(890\) | −41.3205 | −1.38507 | ||||||||
\(891\) | −0.366025 | − | 0.633975i | −0.0122623 | − | 0.0212389i | ||||
\(892\) | 55.7128 | − | 96.4974i | 1.86540 | − | 3.23097i | ||||
\(893\) | −4.46410 | + | 7.73205i | −0.149385 | + | 0.258743i | ||||
\(894\) | −8.00000 | − | 13.8564i | −0.267560 | − | 0.463428i | ||||
\(895\) | −10.0000 | −0.334263 | ||||||||
\(896\) | 98.3538 | − | 18.9282i | 3.28577 | − | 0.632347i | ||||
\(897\) | 10.7321 | 0.358333 | ||||||||
\(898\) | −48.9808 | − | 84.8372i | −1.63451 | − | 2.83105i | ||||
\(899\) | −0.973721 | + | 1.68653i | −0.0324754 | + | 0.0562490i | ||||
\(900\) | −2.73205 | + | 4.73205i | −0.0910684 | + | 0.157735i | ||||
\(901\) | −20.2487 | − | 35.0718i | −0.674582 | − | 1.16841i | ||||
\(902\) | 1.46410 | 0.0487493 | ||||||||
\(903\) | −5.53590 | − | 6.39230i | −0.184223 | − | 0.212723i | ||||
\(904\) | −84.4974 | −2.81034 | ||||||||
\(905\) | 12.1603 | + | 21.0622i | 0.404221 | + | 0.700130i | ||||
\(906\) | 12.1962 | − | 21.1244i | 0.405190 | − | 0.701810i | ||||
\(907\) | −16.7942 | + | 29.0885i | −0.557643 | + | 0.965866i | 0.440049 | + | 0.897974i | \(0.354961\pi\) |
−0.997693 | + | 0.0678928i | \(0.978372\pi\) | |||||||
\(908\) | 4.53590 | + | 7.85641i | 0.150529 | + | 0.260724i | ||||
\(909\) | −7.26795 | −0.241063 | ||||||||
\(910\) | −10.7321 | − | 12.3923i | −0.355764 | − | 0.410801i | ||||
\(911\) | −14.7321 | −0.488095 | −0.244047 | − | 0.969763i | \(-0.578475\pi\) | ||||
−0.244047 | + | 0.969763i | \(0.578475\pi\) | |||||||
\(912\) | 33.3205 | + | 57.7128i | 1.10335 | + | 1.91106i | ||||
\(913\) | −5.53590 | + | 9.58846i | −0.183211 | + | 0.317332i | ||||
\(914\) | −22.7583 | + | 39.4186i | −0.752779 | + | 1.30385i | ||||
\(915\) | 2.00000 | + | 3.46410i | 0.0661180 | + | 0.114520i | ||||
\(916\) | −16.3923 | −0.541617 | ||||||||
\(917\) | −40.1769 | + | 7.73205i | −1.32676 | + | 0.255335i | ||||
\(918\) | 8.92820 | 0.294675 | ||||||||
\(919\) | 15.4282 | + | 26.7224i | 0.508929 | + | 0.881492i | 0.999947 | + | 0.0103417i | \(0.00329193\pi\) |
−0.491017 | + | 0.871150i | \(0.663375\pi\) | |||||||
\(920\) | −22.3923 | + | 38.7846i | −0.738252 | + | 1.27869i | ||||
\(921\) | −16.0622 | + | 27.8205i | −0.529267 | + | 0.916717i | ||||
\(922\) | 23.1962 | + | 40.1769i | 0.763925 | + | 1.32316i | ||||
\(923\) | 14.0526 | 0.462546 | ||||||||
\(924\) | −3.46410 | + | 10.0000i | −0.113961 | + | 0.328976i | ||||
\(925\) | −3.19615 | −0.105089 | ||||||||
\(926\) | 35.1506 | + | 60.8827i | 1.15512 | + | 2.00073i | ||||
\(927\) | 4.59808 | − | 7.96410i | 0.151021 | − | 0.261575i | ||||
\(928\) | −45.8564 | + | 79.4256i | −1.50531 | + | 2.60727i | ||||
\(929\) | 26.2224 | + | 45.4186i | 0.860330 | + | 1.49014i | 0.871611 | + | 0.490199i | \(0.163076\pi\) |
−0.0112804 | + | 0.999936i | \(0.503591\pi\) | |||||||
\(930\) | −1.26795 | −0.0415777 | ||||||||
\(931\) | −4.46410 | + | 30.9282i | −0.146305 | + | 1.01363i | ||||
\(932\) | 94.6410 | 3.10007 | ||||||||
\(933\) | 4.56218 | + | 7.90192i | 0.149359 | + | 0.258697i | ||||
\(934\) | −0.196152 | + | 0.339746i | −0.00641830 | + | 0.0111168i | ||||
\(935\) | −1.19615 | + | 2.07180i | −0.0391184 | + | 0.0677550i | ||||
\(936\) | 10.7321 | + | 18.5885i | 0.350788 | + | 0.607583i | ||||
\(937\) | 31.7321 | 1.03664 | 0.518320 | − | 0.855186i | \(-0.326557\pi\) | ||||
0.518320 | + | 0.855186i | \(0.326557\pi\) | |||||||
\(938\) | 34.6865 | − | 100.131i | 1.13256 | − | 3.26941i | ||||
\(939\) | 12.6603 | 0.413152 | ||||||||
\(940\) | −5.46410 | − | 9.46410i | −0.178219 | − | 0.308685i | ||||
\(941\) | 15.0263 | − | 26.0263i | 0.489843 | − | 0.848432i | −0.510089 | − | 0.860122i | \(-0.670388\pi\) |
0.999932 | + | 0.0116892i | \(0.00372087\pi\) | |||||||
\(942\) | −8.73205 | + | 15.1244i | −0.284506 | + | 0.492778i | ||||
\(943\) | −1.73205 | − | 3.00000i | −0.0564033 | − | 0.0976934i | ||||
\(944\) | −2.92820 | −0.0953049 | ||||||||
\(945\) | 2.59808 | − | 0.500000i | 0.0845154 | − | 0.0162650i | ||||
\(946\) | −6.39230 | −0.207832 | ||||||||
\(947\) | 2.83013 | + | 4.90192i | 0.0919668 | + | 0.159291i | 0.908339 | − | 0.418235i | \(-0.137351\pi\) |
−0.816372 | + | 0.577527i | \(0.804018\pi\) | |||||||
\(948\) | −20.1962 | + | 34.9808i | −0.655941 | + | 1.13612i | ||||
\(949\) | −14.3564 | + | 24.8660i | −0.466029 | + | 0.807185i | ||||
\(950\) | 6.09808 | + | 10.5622i | 0.197848 | + | 0.342682i | ||||
\(951\) | 28.4449 | 0.922388 | ||||||||
\(952\) | −53.5692 | − | 61.8564i | −1.73619 | − | 2.00478i | ||||
\(953\) | −36.1051 | −1.16956 | −0.584780 | − | 0.811192i | \(-0.698819\pi\) | ||||
−0.584780 | + | 0.811192i | \(0.698819\pi\) | |||||||
\(954\) | 16.9282 | + | 29.3205i | 0.548071 | + | 0.949286i | ||||
\(955\) | 4.46410 | − | 7.73205i | 0.144455 | − | 0.250203i | ||||
\(956\) | −19.3205 | + | 33.4641i | −0.624870 | + | 1.08231i | ||||
\(957\) | −1.53590 | − | 2.66025i | −0.0496485 | − | 0.0859938i | ||||
\(958\) | −24.0000 | −0.775405 | ||||||||
\(959\) | 3.80385 | + | 4.39230i | 0.122833 | + | 0.141835i | ||||
\(960\) | −29.8564 | −0.963611 | ||||||||
\(961\) | 15.3923 | + | 26.6603i | 0.496526 | + | 0.860008i | ||||
\(962\) | −9.90192 | + | 17.1506i | −0.319251 | + | 0.552959i | ||||
\(963\) | −1.09808 | + | 1.90192i | −0.0353850 | + | 0.0612886i | ||||
\(964\) | −36.7846 | − | 63.7128i | −1.18475 | − | 2.05205i | ||||
\(965\) | 1.19615 | 0.0385055 | ||||||||
\(966\) | 33.5885 | − | 6.46410i | 1.08069 | − | 0.207979i | ||||
\(967\) | −10.1244 | −0.325577 | −0.162789 | − | 0.986661i | \(-0.552049\pi\) | ||||
−0.162789 | + | 0.986661i | \(0.552049\pi\) | |||||||
\(968\) | −49.5167 | − | 85.7654i | −1.59153 | − | 2.75660i | ||||
\(969\) | 7.29423 | − | 12.6340i | 0.234324 | − | 0.405862i | ||||
\(970\) | 20.3923 | − | 35.3205i | 0.654757 | − | 1.13407i | ||||
\(971\) | 12.0000 | + | 20.7846i | 0.385098 | + | 0.667010i | 0.991783 | − | 0.127933i | \(-0.0408342\pi\) |
−0.606685 | + | 0.794943i | \(0.707501\pi\) | |||||||
\(972\) | −5.46410 | −0.175261 | ||||||||
\(973\) | 5.13397 | − | 14.8205i | 0.164588 | − | 0.475124i | ||||
\(974\) | 1.12436 | 0.0360267 | ||||||||
\(975\) | 1.13397 | + | 1.96410i | 0.0363163 | + | 0.0629016i | ||||
\(976\) | −29.8564 | + | 51.7128i | −0.955680 | + | 1.65529i | ||||
\(977\) | 8.29423 | − | 14.3660i | 0.265356 | − | 0.459610i | −0.702301 | − | 0.711880i | \(-0.747844\pi\) |
0.967657 | + | 0.252270i | \(0.0811772\pi\) | |||||||
\(978\) | −29.8564 | − | 51.7128i | −0.954703 | − | 1.65359i | ||||
\(979\) | 11.0718 | 0.353856 | ||||||||
\(980\) | −30.0526 | − | 23.6603i | −0.959994 | − | 0.755799i | ||||
\(981\) | 11.0000 | 0.351203 | ||||||||
\(982\) | −52.2487 | − | 90.4974i | −1.66732 | − | 2.88789i | ||||
\(983\) | −4.90192 | + | 8.49038i | −0.156347 | + | 0.270801i | −0.933549 | − | 0.358451i | \(-0.883305\pi\) |
0.777202 | + | 0.629252i | \(0.216639\pi\) | |||||||
\(984\) | 3.46410 | − | 6.00000i | 0.110432 | − | 0.191273i | ||||
\(985\) | 0.169873 | + | 0.294229i | 0.00541260 | + | 0.00937490i | ||||
\(986\) | 37.4641 | 1.19310 | ||||||||
\(987\) | −1.73205 | + | 5.00000i | −0.0551318 | + | 0.159152i | ||||
\(988\) | 55.3205 | 1.75998 | ||||||||
\(989\) | 7.56218 | + | 13.0981i | 0.240463 | + | 0.416495i | ||||
\(990\) | 1.00000 | − | 1.73205i | 0.0317821 | − | 0.0550482i | ||||
\(991\) | 10.5526 | − | 18.2776i | 0.335213 | − | 0.580606i | −0.648313 | − | 0.761374i | \(-0.724525\pi\) |
0.983526 | + | 0.180768i | \(0.0578584\pi\) | |||||||
\(992\) | −5.07180 | − | 8.78461i | −0.161030 | − | 0.278912i | ||||
\(993\) | −8.07180 | −0.256151 | ||||||||
\(994\) | 43.9808 | − | 8.46410i | 1.39499 | − | 0.268465i | ||||
\(995\) | 22.0000 | 0.697447 | ||||||||
\(996\) | 41.3205 | + | 71.5692i | 1.30929 | + | 2.26776i | ||||
\(997\) | 27.9904 | − | 48.4808i | 0.886464 | − | 1.53540i | 0.0424381 | − | 0.999099i | \(-0.486487\pi\) |
0.844026 | − | 0.536302i | \(-0.180179\pi\) | |||||||
\(998\) | −18.4904 | + | 32.0263i | −0.585303 | + | 1.01377i | ||||
\(999\) | −1.59808 | − | 2.76795i | −0.0505609 | − | 0.0875740i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 105.2.i.d.46.2 | yes | 4 | |
3.2 | odd | 2 | 315.2.j.c.46.1 | 4 | |||
4.3 | odd | 2 | 1680.2.bg.o.1201.1 | 4 | |||
5.2 | odd | 4 | 525.2.r.a.424.1 | 4 | |||
5.3 | odd | 4 | 525.2.r.f.424.2 | 4 | |||
5.4 | even | 2 | 525.2.i.f.151.1 | 4 | |||
7.2 | even | 3 | inner | 105.2.i.d.16.2 | ✓ | 4 | |
7.3 | odd | 6 | 735.2.a.h.1.1 | 2 | |||
7.4 | even | 3 | 735.2.a.g.1.1 | 2 | |||
7.5 | odd | 6 | 735.2.i.l.226.2 | 4 | |||
7.6 | odd | 2 | 735.2.i.l.361.2 | 4 | |||
21.2 | odd | 6 | 315.2.j.c.226.1 | 4 | |||
21.11 | odd | 6 | 2205.2.a.z.1.2 | 2 | |||
21.17 | even | 6 | 2205.2.a.ba.1.2 | 2 | |||
28.23 | odd | 6 | 1680.2.bg.o.961.1 | 4 | |||
35.2 | odd | 12 | 525.2.r.f.499.2 | 4 | |||
35.4 | even | 6 | 3675.2.a.bg.1.2 | 2 | |||
35.9 | even | 6 | 525.2.i.f.226.1 | 4 | |||
35.23 | odd | 12 | 525.2.r.a.499.1 | 4 | |||
35.24 | odd | 6 | 3675.2.a.be.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.d.16.2 | ✓ | 4 | 7.2 | even | 3 | inner | |
105.2.i.d.46.2 | yes | 4 | 1.1 | even | 1 | trivial | |
315.2.j.c.46.1 | 4 | 3.2 | odd | 2 | |||
315.2.j.c.226.1 | 4 | 21.2 | odd | 6 | |||
525.2.i.f.151.1 | 4 | 5.4 | even | 2 | |||
525.2.i.f.226.1 | 4 | 35.9 | even | 6 | |||
525.2.r.a.424.1 | 4 | 5.2 | odd | 4 | |||
525.2.r.a.499.1 | 4 | 35.23 | odd | 12 | |||
525.2.r.f.424.2 | 4 | 5.3 | odd | 4 | |||
525.2.r.f.499.2 | 4 | 35.2 | odd | 12 | |||
735.2.a.g.1.1 | 2 | 7.4 | even | 3 | |||
735.2.a.h.1.1 | 2 | 7.3 | odd | 6 | |||
735.2.i.l.226.2 | 4 | 7.5 | odd | 6 | |||
735.2.i.l.361.2 | 4 | 7.6 | odd | 2 | |||
1680.2.bg.o.961.1 | 4 | 28.23 | odd | 6 | |||
1680.2.bg.o.1201.1 | 4 | 4.3 | odd | 2 | |||
2205.2.a.z.1.2 | 2 | 21.11 | odd | 6 | |||
2205.2.a.ba.1.2 | 2 | 21.17 | even | 6 | |||
3675.2.a.be.1.2 | 2 | 35.24 | odd | 6 | |||
3675.2.a.bg.1.2 | 2 | 35.4 | even | 6 |