Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,3,Mod(19,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.l (of order \(4\), 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: | \(1.30790526893\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.1 | ||
Root | \(1.84258 - 0.777752i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.43 |
Dual form | 48.3.l.a.19.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.84258 | − | 0.777752i | −0.921290 | − | 0.388876i | ||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | 2.79020 | + | 2.86614i | 0.697551 | + | 0.716535i | ||||
\(5\) | −4.78830 | − | 4.78830i | −0.957661 | − | 0.957661i | 0.0414785 | − | 0.999139i | \(-0.486793\pi\) |
−0.999139 | + | 0.0414785i | \(0.986793\pi\) | |||||||
\(6\) | 1.30414 | + | 3.20924i | 0.217357 | + | 0.534873i | ||||
\(7\) | −10.3302 | −1.47575 | −0.737875 | − | 0.674937i | \(-0.764171\pi\) | ||||
−0.737875 | + | 0.674937i | \(0.764171\pi\) | |||||||
\(8\) | −2.91202 | − | 7.45118i | −0.364003 | − | 0.931398i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 5.09872 | + | 12.5469i | 0.509872 | + | 1.25469i | ||||
\(11\) | −0.526169 | + | 0.526169i | −0.0478335 | + | 0.0478335i | −0.730619 | − | 0.682785i | \(-0.760768\pi\) |
0.682785 | + | 0.730619i | \(0.260768\pi\) | |||||||
\(12\) | 0.0930056 | − | 6.92758i | 0.00775047 | − | 0.577298i | ||||
\(13\) | 17.2840 | − | 17.2840i | 1.32953 | − | 1.32953i | 0.423761 | − | 0.905774i | \(-0.360710\pi\) |
0.905774 | − | 0.423761i | \(-0.139290\pi\) | |||||||
\(14\) | 19.0343 | + | 8.03437i | 1.35959 | + | 0.573884i | ||||
\(15\) | 11.7289i | 0.781927i | ||||||||
\(16\) | −0.429536 | + | 15.9942i | −0.0268460 | + | 0.999640i | ||||
\(17\) | 4.71650 | 0.277441 | 0.138721 | − | 0.990332i | \(-0.455701\pi\) | ||||
0.138721 | + | 0.990332i | \(0.455701\pi\) | |||||||
\(18\) | 2.33326 | − | 5.52774i | 0.129625 | − | 0.307097i | ||||
\(19\) | −2.53604 | − | 2.53604i | −0.133476 | − | 0.133476i | 0.637213 | − | 0.770688i | \(-0.280087\pi\) |
−0.770688 | + | 0.637213i | \(0.780087\pi\) | |||||||
\(20\) | 0.363618 | − | 27.0843i | 0.0181809 | − | 1.35422i | ||||
\(21\) | 12.6519 | + | 12.6519i | 0.602472 | + | 0.602472i | ||||
\(22\) | 1.37874 | − | 0.560279i | 0.0626698 | − | 0.0254672i | ||||
\(23\) | −12.5864 | −0.547236 | −0.273618 | − | 0.961838i | \(-0.588220\pi\) | ||||
−0.273618 | + | 0.961838i | \(0.588220\pi\) | |||||||
\(24\) | −5.55931 | + | 12.6923i | −0.231638 | + | 0.528845i | ||||
\(25\) | 20.8557i | 0.834229i | ||||||||
\(26\) | −45.2897 | + | 18.4044i | −1.74191 | + | 0.707863i | ||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | −28.8235 | − | 29.6080i | −1.02941 | − | 1.05743i | ||||
\(29\) | −2.19683 | + | 2.19683i | −0.0757526 | + | 0.0757526i | −0.743968 | − | 0.668215i | \(-0.767058\pi\) |
0.668215 | + | 0.743968i | \(0.267058\pi\) | |||||||
\(30\) | 9.12218 | − | 21.6114i | 0.304073 | − | 0.720381i | ||||
\(31\) | − | 28.0521i | − | 0.904908i | −0.891788 | − | 0.452454i | \(-0.850549\pi\) | ||
0.891788 | − | 0.452454i | \(-0.149451\pi\) | |||||||
\(32\) | 13.2310 | − | 29.1366i | 0.413469 | − | 0.910518i | ||||
\(33\) | 1.28884 | 0.0390559 | ||||||||
\(34\) | −8.69052 | − | 3.66827i | −0.255604 | − | 0.107890i | ||||
\(35\) | 49.4644 | + | 49.4644i | 1.41327 | + | 1.41327i | ||||
\(36\) | −8.59842 | + | 8.37061i | −0.238845 | + | 0.232517i | ||||
\(37\) | −32.1128 | − | 32.1128i | −0.867914 | − | 0.867914i | 0.124327 | − | 0.992241i | \(-0.460323\pi\) |
−0.992241 | + | 0.124327i | \(0.960323\pi\) | |||||||
\(38\) | 2.70044 | + | 6.64526i | 0.0710643 | + | 0.174875i | ||||
\(39\) | −42.3369 | −1.08556 | ||||||||
\(40\) | −21.7349 | + | 49.6222i | −0.543372 | + | 1.24055i | ||||
\(41\) | 23.1145i | 0.563768i | 0.959449 | + | 0.281884i | \(0.0909593\pi\) | ||||
−0.959449 | + | 0.281884i | \(0.909041\pi\) | |||||||
\(42\) | −13.4721 | − | 33.1522i | −0.320765 | − | 0.789339i | ||||
\(43\) | 4.79441 | − | 4.79441i | 0.111498 | − | 0.111498i | −0.649157 | − | 0.760655i | \(-0.724878\pi\) |
0.760655 | + | 0.649157i | \(0.224878\pi\) | |||||||
\(44\) | −2.97619 | − | 0.0399566i | −0.0676407 | − | 0.000908104i | ||||
\(45\) | 14.3649 | − | 14.3649i | 0.319220 | − | 0.319220i | ||||
\(46\) | 23.1915 | + | 9.78913i | 0.504163 | + | 0.212807i | ||||
\(47\) | 39.0095i | 0.829989i | 0.909824 | + | 0.414994i | \(0.136216\pi\) | ||||
−0.909824 | + | 0.414994i | \(0.863784\pi\) | |||||||
\(48\) | 20.1149 | − | 19.0628i | 0.419061 | − | 0.397141i | ||||
\(49\) | 57.7141 | 1.17784 | ||||||||
\(50\) | 16.2206 | − | 38.4283i | 0.324412 | − | 0.768567i | ||||
\(51\) | −5.77651 | − | 5.77651i | −0.113265 | − | 0.113265i | ||||
\(52\) | 97.7640 | + | 1.31252i | 1.88008 | + | 0.0252408i | ||||
\(53\) | −27.9768 | − | 27.9768i | −0.527864 | − | 0.527864i | 0.392071 | − | 0.919935i | \(-0.371759\pi\) |
−0.919935 | + | 0.392071i | \(0.871759\pi\) | |||||||
\(54\) | −9.62772 | + | 3.91243i | −0.178291 | + | 0.0724524i | ||||
\(55\) | 5.03891 | 0.0916166 | ||||||||
\(56\) | 30.0819 | + | 76.9726i | 0.537177 | + | 1.37451i | ||||
\(57\) | 6.21200i | 0.108982i | ||||||||
\(58\) | 5.75642 | − | 2.33924i | 0.0992485 | − | 0.0403318i | ||||
\(59\) | 79.8538 | − | 79.8538i | 1.35345 | − | 1.35345i | 0.471691 | − | 0.881764i | \(-0.343644\pi\) |
0.881764 | − | 0.471691i | \(-0.156356\pi\) | |||||||
\(60\) | −33.6167 | + | 32.7260i | −0.560278 | + | 0.545434i | ||||
\(61\) | −36.7762 | + | 36.7762i | −0.602888 | + | 0.602888i | −0.941078 | − | 0.338190i | \(-0.890185\pi\) |
0.338190 | + | 0.941078i | \(0.390185\pi\) | |||||||
\(62\) | −21.8176 | + | 51.6883i | −0.351897 | + | 0.833682i | ||||
\(63\) | − | 30.9907i | − | 0.491917i | ||||||
\(64\) | −47.0402 | + | 43.3960i | −0.735004 | + | 0.678063i | ||||
\(65\) | −165.522 | −2.54649 | ||||||||
\(66\) | −2.37480 | − | 1.00240i | −0.0359818 | − | 0.0151879i | ||||
\(67\) | −10.9869 | − | 10.9869i | −0.163984 | − | 0.163984i | 0.620345 | − | 0.784329i | \(-0.286992\pi\) |
−0.784329 | + | 0.620345i | \(0.786992\pi\) | |||||||
\(68\) | 13.1600 | + | 13.5181i | 0.193529 | + | 0.198796i | ||||
\(69\) | 15.4152 | + | 15.4152i | 0.223408 | + | 0.223408i | ||||
\(70\) | −52.6711 | − | 129.613i | −0.752444 | − | 1.85162i | ||||
\(71\) | 52.6605 | 0.741697 | 0.370849 | − | 0.928693i | \(-0.379067\pi\) | ||||
0.370849 | + | 0.928693i | \(0.379067\pi\) | |||||||
\(72\) | 22.3535 | − | 8.73607i | 0.310466 | − | 0.121334i | ||||
\(73\) | 67.8061i | 0.928850i | 0.885612 | + | 0.464425i | \(0.153739\pi\) | ||||
−0.885612 | + | 0.464425i | \(0.846261\pi\) | |||||||
\(74\) | 34.1946 | + | 84.1462i | 0.462089 | + | 1.13711i | ||||
\(75\) | 25.5429 | − | 25.5429i | 0.340573 | − | 0.340573i | ||||
\(76\) | 0.192584 | − | 14.3447i | 0.00253399 | − | 0.188746i | ||||
\(77\) | 5.43545 | − | 5.43545i | 0.0705903 | − | 0.0705903i | ||||
\(78\) | 78.0091 | + | 32.9276i | 1.00012 | + | 0.422149i | ||||
\(79\) | − | 56.4602i | − | 0.714686i | −0.933973 | − | 0.357343i | \(-0.883683\pi\) | ||
0.933973 | − | 0.357343i | \(-0.116317\pi\) | |||||||
\(80\) | 78.6420 | − | 74.5285i | 0.983025 | − | 0.931606i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 17.9773 | − | 42.5903i | 0.219236 | − | 0.519394i | ||||
\(83\) | −58.3697 | − | 58.3697i | −0.703249 | − | 0.703249i | 0.261857 | − | 0.965107i | \(-0.415665\pi\) |
−0.965107 | + | 0.261857i | \(0.915665\pi\) | |||||||
\(84\) | −0.960771 | + | 71.5636i | −0.0114378 | + | 0.851948i | ||||
\(85\) | −22.5840 | − | 22.5840i | −0.265694 | − | 0.265694i | ||||
\(86\) | −12.5629 | + | 5.10522i | −0.146081 | + | 0.0593630i | ||||
\(87\) | 5.38110 | 0.0618518 | ||||||||
\(88\) | 5.45279 | + | 2.38836i | 0.0619636 | + | 0.0271405i | ||||
\(89\) | − | 131.566i | − | 1.47827i | −0.673558 | − | 0.739135i | \(-0.735235\pi\) | ||
0.673558 | − | 0.739135i | \(-0.264765\pi\) | |||||||
\(90\) | −37.6408 | + | 15.2962i | −0.418232 | + | 0.169957i | ||||
\(91\) | −178.548 | + | 178.548i | −1.96206 | + | 1.96206i | ||||
\(92\) | −35.1187 | − | 36.0745i | −0.381725 | − | 0.392114i | ||||
\(93\) | −34.3567 | + | 34.3567i | −0.369427 | + | 0.369427i | ||||
\(94\) | 30.3397 | − | 71.8781i | 0.322763 | − | 0.764661i | ||||
\(95\) | 24.2866i | 0.255649i | ||||||||
\(96\) | −51.8895 | + | 19.4803i | −0.540515 | + | 0.202920i | ||||
\(97\) | 60.9413 | 0.628261 | 0.314131 | − | 0.949380i | \(-0.398287\pi\) | ||||
0.314131 | + | 0.949380i | \(0.398287\pi\) | |||||||
\(98\) | −106.343 | − | 44.8872i | −1.08513 | − | 0.458033i | ||||
\(99\) | −1.57851 | − | 1.57851i | −0.0159445 | − | 0.0159445i | ||||
\(100\) | −59.7755 | + | 58.1917i | −0.597755 | + | 0.581917i | ||||
\(101\) | 109.986 | + | 109.986i | 1.08897 | + | 1.08897i | 0.995635 | + | 0.0933326i | \(0.0297520\pi\) |
0.0933326 | + | 0.995635i | \(0.470248\pi\) | |||||||
\(102\) | 6.15098 | + | 15.1364i | 0.0603038 | + | 0.148396i | ||||
\(103\) | 173.295 | 1.68248 | 0.841239 | − | 0.540663i | \(-0.181826\pi\) | ||||
0.841239 | + | 0.540663i | \(0.181826\pi\) | |||||||
\(104\) | −179.117 | − | 78.4546i | −1.72228 | − | 0.754371i | ||||
\(105\) | − | 121.162i | − | 1.15393i | ||||||
\(106\) | 29.7905 | + | 73.3085i | 0.281042 | + | 0.691589i | ||||
\(107\) | −25.4747 | + | 25.4747i | −0.238081 | + | 0.238081i | −0.816055 | − | 0.577974i | \(-0.803844\pi\) |
0.577974 | + | 0.816055i | \(0.303844\pi\) | |||||||
\(108\) | 20.7827 | + | 0.279017i | 0.192433 | + | 0.00258349i | ||||
\(109\) | 33.0605 | − | 33.0605i | 0.303307 | − | 0.303307i | −0.538999 | − | 0.842306i | \(-0.681197\pi\) |
0.842306 | + | 0.538999i | \(0.181197\pi\) | |||||||
\(110\) | −9.28460 | − | 3.91902i | −0.0844054 | − | 0.0356275i | ||||
\(111\) | 78.6600i | 0.708649i | ||||||||
\(112\) | 4.43721 | − | 165.224i | 0.0396180 | − | 1.47522i | ||||
\(113\) | 140.159 | 1.24034 | 0.620171 | − | 0.784466i | \(-0.287063\pi\) | ||||
0.620171 | + | 0.784466i | \(0.287063\pi\) | |||||||
\(114\) | 4.83139 | − | 11.4461i | 0.0423806 | − | 0.100404i | ||||
\(115\) | 60.2677 | + | 60.2677i | 0.524067 | + | 0.524067i | ||||
\(116\) | −12.4260 | − | 0.166824i | −0.107121 | − | 0.00143814i | ||||
\(117\) | 51.8519 | + | 51.8519i | 0.443178 | + | 0.443178i | ||||
\(118\) | −209.244 | + | 85.0306i | −1.77325 | + | 0.720598i | ||||
\(119\) | −48.7226 | −0.409434 | ||||||||
\(120\) | 87.3942 | − | 34.1548i | 0.728285 | − | 0.284624i | ||||
\(121\) | 120.446i | 0.995424i | ||||||||
\(122\) | 96.3658 | − | 39.1603i | 0.789883 | − | 0.320986i | ||||
\(123\) | 28.3093 | − | 28.3093i | 0.230157 | − | 0.230157i | ||||
\(124\) | 80.4014 | − | 78.2712i | 0.648398 | − | 0.631219i | ||||
\(125\) | −19.8441 | + | 19.8441i | −0.158752 | + | 0.158752i | ||||
\(126\) | −24.1031 | + | 57.1029i | −0.191295 | + | 0.453198i | ||||
\(127\) | 40.8458i | 0.321620i | 0.986985 | + | 0.160810i | \(0.0514107\pi\) | ||||
−0.986985 | + | 0.160810i | \(0.948589\pi\) | |||||||
\(128\) | 120.427 | − | 43.3750i | 0.940834 | − | 0.338868i | ||||
\(129\) | −11.7439 | −0.0910377 | ||||||||
\(130\) | 304.987 | + | 128.735i | 2.34605 | + | 0.990268i | ||||
\(131\) | −75.0168 | − | 75.0168i | −0.572647 | − | 0.572647i | 0.360220 | − | 0.932867i | \(-0.382702\pi\) |
−0.932867 | + | 0.360220i | \(0.882702\pi\) | |||||||
\(132\) | 3.59614 | + | 3.69401i | 0.0272435 | + | 0.0279849i | ||||
\(133\) | 26.1979 | + | 26.1979i | 0.196977 | + | 0.196977i | ||||
\(134\) | 11.6992 | + | 28.7893i | 0.0873071 | + | 0.214846i | ||||
\(135\) | −35.1867 | −0.260642 | ||||||||
\(136\) | −13.7346 | − | 35.1435i | −0.100989 | − | 0.258408i | ||||
\(137\) | − | 134.028i | − | 0.978308i | −0.872197 | − | 0.489154i | \(-0.837306\pi\) | ||
0.872197 | − | 0.489154i | \(-0.162694\pi\) | |||||||
\(138\) | −16.4145 | − | 40.3929i | −0.118946 | − | 0.292702i | ||||
\(139\) | 22.8798 | − | 22.8798i | 0.164603 | − | 0.164603i | −0.619999 | − | 0.784602i | \(-0.712867\pi\) |
0.784602 | + | 0.619999i | \(0.212867\pi\) | |||||||
\(140\) | −3.75626 | + | 279.788i | −0.0268305 | + | 1.99848i | ||||
\(141\) | 47.7767 | − | 47.7767i | 0.338842 | − | 0.338842i | ||||
\(142\) | −97.0312 | − | 40.9568i | −0.683318 | − | 0.288428i | ||||
\(143\) | 18.1885i | 0.127193i | ||||||||
\(144\) | −47.9827 | − | 1.28861i | −0.333213 | − | 0.00894866i | ||||
\(145\) | 21.0381 | 0.145091 | ||||||||
\(146\) | 52.7363 | − | 124.938i | 0.361208 | − | 0.855740i | ||||
\(147\) | −70.6850 | − | 70.6850i | −0.480850 | − | 0.480850i | ||||
\(148\) | 2.43861 | − | 181.641i | 0.0164771 | − | 1.22730i | ||||
\(149\) | −9.32124 | − | 9.32124i | −0.0625587 | − | 0.0625587i | 0.675135 | − | 0.737694i | \(-0.264085\pi\) |
−0.737694 | + | 0.675135i | \(0.764085\pi\) | |||||||
\(150\) | −66.9310 | + | 27.1988i | −0.446207 | + | 0.181326i | ||||
\(151\) | −50.5403 | −0.334704 | −0.167352 | − | 0.985897i | \(-0.553522\pi\) | ||||
−0.167352 | + | 0.985897i | \(0.553522\pi\) | |||||||
\(152\) | −11.5115 | + | 26.2815i | −0.0757334 | + | 0.172904i | ||||
\(153\) | 14.1495i | 0.0924803i | ||||||||
\(154\) | −14.2427 | + | 5.78782i | −0.0924850 | + | 0.0375833i | ||||
\(155\) | −134.322 | + | 134.322i | −0.866595 | + | 0.866595i | ||||
\(156\) | −118.128 | − | 121.343i | −0.757234 | − | 0.777843i | ||||
\(157\) | −95.8844 | + | 95.8844i | −0.610729 | + | 0.610729i | −0.943136 | − | 0.332407i | \(-0.892139\pi\) |
0.332407 | + | 0.943136i | \(0.392139\pi\) | |||||||
\(158\) | −43.9120 | + | 104.032i | −0.277924 | + | 0.658433i | ||||
\(159\) | 68.5288i | 0.430999i | ||||||||
\(160\) | −202.869 | + | 76.1608i | −1.26793 | + | 0.476005i | ||||
\(161\) | 130.021 | 0.807584 | ||||||||
\(162\) | 16.5832 | + | 6.99977i | 0.102366 | + | 0.0432085i | ||||
\(163\) | −140.885 | − | 140.885i | −0.864324 | − | 0.864324i | 0.127513 | − | 0.991837i | \(-0.459301\pi\) |
−0.991837 | + | 0.127513i | \(0.959301\pi\) | |||||||
\(164\) | −66.2494 | + | 64.4941i | −0.403959 | + | 0.393257i | ||||
\(165\) | −6.17138 | − | 6.17138i | −0.0374023 | − | 0.0374023i | ||||
\(166\) | 62.1537 | + | 152.948i | 0.374420 | + | 0.921374i | ||||
\(167\) | −107.849 | −0.645800 | −0.322900 | − | 0.946433i | \(-0.604658\pi\) | ||||
−0.322900 | + | 0.946433i | \(0.604658\pi\) | |||||||
\(168\) | 57.4291 | − | 131.114i | 0.341840 | − | 0.780443i | ||||
\(169\) | − | 428.470i | − | 2.53533i | ||||||
\(170\) | 24.0481 | + | 59.1777i | 0.141459 | + | 0.348104i | ||||
\(171\) | 7.60811 | − | 7.60811i | 0.0444919 | − | 0.0444919i | ||||
\(172\) | 27.1188 | + | 0.364082i | 0.157668 | + | 0.00211675i | ||||
\(173\) | −53.8845 | + | 53.8845i | −0.311471 | + | 0.311471i | −0.845479 | − | 0.534008i | \(-0.820685\pi\) |
0.534008 | + | 0.845479i | \(0.320685\pi\) | |||||||
\(174\) | −9.91511 | − | 4.18517i | −0.0569834 | − | 0.0240527i | ||||
\(175\) | − | 215.445i | − | 1.23111i | ||||||
\(176\) | −8.18965 | − | 8.64167i | −0.0465321 | − | 0.0491004i | ||||
\(177\) | −195.601 | −1.10509 | ||||||||
\(178\) | −102.326 | + | 242.421i | −0.574864 | + | 1.36191i | ||||
\(179\) | 104.178 | + | 104.178i | 0.582002 | + | 0.582002i | 0.935453 | − | 0.353451i | \(-0.114992\pi\) |
−0.353451 | + | 0.935453i | \(0.614992\pi\) | |||||||
\(180\) | 81.2529 | + | 1.09085i | 0.451405 | + | 0.00606030i | ||||
\(181\) | −205.498 | − | 205.498i | −1.13535 | − | 1.13535i | −0.989274 | − | 0.146073i | \(-0.953336\pi\) |
−0.146073 | − | 0.989274i | \(-0.546664\pi\) | |||||||
\(182\) | 467.854 | − | 190.122i | 2.57063 | − | 1.04463i | ||||
\(183\) | 90.0828 | 0.492256 | ||||||||
\(184\) | 36.6520 | + | 93.7838i | 0.199196 | + | 0.509695i | ||||
\(185\) | 307.532i | 1.66233i | ||||||||
\(186\) | 90.0260 | − | 36.5840i | 0.484011 | − | 0.196688i | ||||
\(187\) | −2.48167 | + | 2.48167i | −0.0132710 | + | 0.0132710i | ||||
\(188\) | −111.807 | + | 108.844i | −0.594716 | + | 0.578959i | ||||
\(189\) | −37.9558 | + | 37.9558i | −0.200824 | + | 0.200824i | ||||
\(190\) | 18.8890 | − | 44.7501i | 0.0994157 | − | 0.235527i | ||||
\(191\) | − | 248.255i | − | 1.29977i | −0.760034 | − | 0.649883i | \(-0.774818\pi\) | ||
0.760034 | − | 0.649883i | \(-0.225182\pi\) | |||||||
\(192\) | 110.761 | + | 4.46320i | 0.576882 | + | 0.0232458i | ||||
\(193\) | −129.921 | −0.673166 | −0.336583 | − | 0.941654i | \(-0.609271\pi\) | ||||
−0.336583 | + | 0.941654i | \(0.609271\pi\) | |||||||
\(194\) | −112.289 | − | 47.3973i | −0.578811 | − | 0.244316i | ||||
\(195\) | 202.722 | + | 202.722i | 1.03960 | + | 1.03960i | ||||
\(196\) | 161.034 | + | 165.417i | 0.821602 | + | 0.843963i | ||||
\(197\) | 237.001 | + | 237.001i | 1.20305 | + | 1.20305i | 0.973234 | + | 0.229816i | \(0.0738123\pi\) |
0.229816 | + | 0.973234i | \(0.426188\pi\) | |||||||
\(198\) | 1.68084 | + | 4.13621i | 0.00848907 | + | 0.0208899i | ||||
\(199\) | 246.508 | 1.23873 | 0.619366 | − | 0.785102i | \(-0.287390\pi\) | ||||
0.619366 | + | 0.785102i | \(0.287390\pi\) | |||||||
\(200\) | 155.400 | − | 60.7324i | 0.776999 | − | 0.303662i | ||||
\(201\) | 26.9123i | 0.133892i | ||||||||
\(202\) | −117.116 | − | 288.199i | −0.579781 | − | 1.42673i | ||||
\(203\) | 22.6938 | − | 22.6938i | 0.111792 | − | 0.111792i | ||||
\(204\) | 0.438661 | − | 32.6739i | 0.00215030 | − | 0.160166i | ||||
\(205\) | 110.679 | − | 110.679i | 0.539898 | − | 0.539898i | ||||
\(206\) | −319.311 | − | 134.781i | −1.55005 | − | 0.654276i | ||||
\(207\) | − | 37.7593i | − | 0.182412i | ||||||
\(208\) | 269.020 | + | 283.868i | 1.29336 | + | 1.36475i | ||||
\(209\) | 2.66877 | 0.0127692 | ||||||||
\(210\) | −94.2344 | + | 223.252i | −0.448735 | + | 1.06310i | ||||
\(211\) | −13.4139 | − | 13.4139i | −0.0635728 | − | 0.0635728i | 0.674606 | − | 0.738178i | \(-0.264314\pi\) |
−0.738178 | + | 0.674606i | \(0.764314\pi\) | |||||||
\(212\) | 2.12452 | − | 158.246i | 0.0100213 | − | 0.746445i | ||||
\(213\) | −64.4957 | − | 64.4957i | −0.302797 | − | 0.302797i | ||||
\(214\) | 66.7522 | − | 27.1262i | 0.311926 | − | 0.126758i | ||||
\(215\) | −45.9142 | −0.213554 | ||||||||
\(216\) | −38.0769 | − | 16.6779i | −0.176282 | − | 0.0772126i | ||||
\(217\) | 289.786i | 1.33542i | ||||||||
\(218\) | −86.6295 | + | 35.2037i | −0.397383 | + | 0.161485i | ||||
\(219\) | 83.0451 | − | 83.0451i | 0.379201 | − | 0.379201i | ||||
\(220\) | 14.0596 | + | 14.4422i | 0.0639072 | + | 0.0656465i | ||||
\(221\) | 81.5197 | − | 81.5197i | 0.368867 | − | 0.368867i | ||||
\(222\) | 61.1780 | − | 144.937i | 0.275577 | − | 0.652871i | ||||
\(223\) | 295.580i | 1.32547i | 0.748854 | + | 0.662735i | \(0.230604\pi\) | ||||
−0.748854 | + | 0.662735i | \(0.769396\pi\) | |||||||
\(224\) | −136.680 | + | 300.988i | −0.610177 | + | 1.34370i | ||||
\(225\) | −62.5672 | −0.278076 | ||||||||
\(226\) | −258.254 | − | 109.009i | −1.14272 | − | 0.482340i | ||||
\(227\) | −97.0742 | − | 97.0742i | −0.427640 | − | 0.427640i | 0.460184 | − | 0.887824i | \(-0.347783\pi\) |
−0.887824 | + | 0.460184i | \(0.847783\pi\) | |||||||
\(228\) | −17.8045 | + | 17.3327i | −0.0780897 | + | 0.0760207i | ||||
\(229\) | 34.2565 | + | 34.2565i | 0.149592 | + | 0.149592i | 0.777936 | − | 0.628344i | \(-0.216267\pi\) |
−0.628344 | + | 0.777936i | \(0.716267\pi\) | |||||||
\(230\) | −64.1747 | − | 157.921i | −0.279021 | − | 0.686615i | ||||
\(231\) | −13.3141 | −0.0576367 | ||||||||
\(232\) | 22.7662 | + | 9.97174i | 0.0981300 | + | 0.0429816i | ||||
\(233\) | 62.8176i | 0.269604i | 0.990873 | + | 0.134802i | \(0.0430398\pi\) | ||||
−0.990873 | + | 0.134802i | \(0.956960\pi\) | |||||||
\(234\) | −55.2133 | − | 135.869i | −0.235954 | − | 0.580637i | ||||
\(235\) | 186.789 | − | 186.789i | 0.794848 | − | 0.794848i | ||||
\(236\) | 451.681 | + | 6.06400i | 1.91390 | + | 0.0256949i | ||||
\(237\) | −69.1493 | + | 69.1493i | −0.291769 | + | 0.291769i | ||||
\(238\) | 89.7753 | + | 37.8941i | 0.377207 | + | 0.159219i | ||||
\(239\) | 355.910i | 1.48916i | 0.667532 | + | 0.744581i | \(0.267351\pi\) | ||||
−0.667532 | + | 0.744581i | \(0.732649\pi\) | |||||||
\(240\) | −187.595 | − | 5.03798i | −0.781645 | − | 0.0209916i | ||||
\(241\) | 66.2545 | 0.274915 | 0.137458 | − | 0.990508i | \(-0.456107\pi\) | ||||
0.137458 | + | 0.990508i | \(0.456107\pi\) | |||||||
\(242\) | 93.6774 | − | 221.932i | 0.387097 | − | 0.917074i | ||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | −208.019 | − | 2.79274i | −0.852535 | − | 0.0114456i | ||||
\(245\) | −276.352 | − | 276.352i | −1.12797 | − | 1.12797i | ||||
\(246\) | −74.1799 | + | 30.1446i | −0.301544 | + | 0.122539i | ||||
\(247\) | −87.6655 | −0.354921 | ||||||||
\(248\) | −209.022 | + | 81.6885i | −0.842829 | + | 0.329389i | ||||
\(249\) | 142.976i | 0.574201i | ||||||||
\(250\) | 51.9980 | − | 21.1305i | 0.207992 | − | 0.0845220i | ||||
\(251\) | 325.395 | − | 325.395i | 1.29640 | − | 1.29640i | 0.365638 | − | 0.930757i | \(-0.380851\pi\) |
0.930757 | − | 0.365638i | \(-0.119149\pi\) | |||||||
\(252\) | 88.8239 | − | 86.4705i | 0.352476 | − | 0.343137i | ||||
\(253\) | 6.62259 | − | 6.62259i | 0.0261762 | − | 0.0261762i | ||||
\(254\) | 31.7679 | − | 75.2616i | 0.125070 | − | 0.296306i | ||||
\(255\) | 55.3193i | 0.216939i | ||||||||
\(256\) | −255.631 | − | 13.7402i | −0.998559 | − | 0.0536726i | ||||
\(257\) | −312.011 | −1.21405 | −0.607026 | − | 0.794682i | \(-0.707638\pi\) | ||||
−0.607026 | + | 0.794682i | \(0.707638\pi\) | |||||||
\(258\) | 21.6390 | + | 9.13381i | 0.0838721 | + | 0.0354024i | ||||
\(259\) | 331.733 | + | 331.733i | 1.28082 | + | 1.28082i | ||||
\(260\) | −461.839 | − | 474.409i | −1.77630 | − | 1.82465i | ||||
\(261\) | −6.59048 | − | 6.59048i | −0.0252509 | − | 0.0252509i | ||||
\(262\) | 79.8800 | + | 196.569i | 0.304885 | + | 0.750263i | ||||
\(263\) | −168.163 | −0.639403 | −0.319702 | − | 0.947518i | \(-0.603583\pi\) | ||||
−0.319702 | + | 0.947518i | \(0.603583\pi\) | |||||||
\(264\) | −3.75315 | − | 9.60342i | −0.0142165 | − | 0.0363766i | ||||
\(265\) | 267.923i | 1.01103i | ||||||||
\(266\) | −27.8962 | − | 68.6472i | −0.104873 | − | 0.258072i | ||||
\(267\) | −161.135 | + | 161.135i | −0.603501 | + | 0.603501i | ||||
\(268\) | 0.834331 | − | 62.1457i | 0.00311318 | − | 0.231887i | ||||
\(269\) | 212.116 | − | 212.116i | 0.788535 | − | 0.788535i | −0.192719 | − | 0.981254i | \(-0.561731\pi\) |
0.981254 | + | 0.192719i | \(0.0617306\pi\) | |||||||
\(270\) | 64.8343 | + | 27.3665i | 0.240127 | + | 0.101358i | ||||
\(271\) | − | 173.450i | − | 0.640037i | −0.947411 | − | 0.320019i | \(-0.896311\pi\) | ||
0.947411 | − | 0.320019i | \(-0.103689\pi\) | |||||||
\(272\) | −2.02590 | + | 75.4368i | −0.00744818 | + | 0.277341i | ||||
\(273\) | 437.350 | 1.60202 | ||||||||
\(274\) | −104.241 | + | 246.958i | −0.380441 | + | 0.901305i | ||||
\(275\) | −10.9736 | − | 10.9736i | −0.0399041 | − | 0.0399041i | ||||
\(276\) | −1.17061 | + | 87.1935i | −0.00424134 | + | 0.315919i | ||||
\(277\) | −38.4049 | − | 38.4049i | −0.138646 | − | 0.138646i | 0.634377 | − | 0.773023i | \(-0.281257\pi\) |
−0.773023 | + | 0.634377i | \(0.781257\pi\) | |||||||
\(278\) | −59.9526 | + | 24.3630i | −0.215657 | + | 0.0876368i | ||||
\(279\) | 84.1564 | 0.301636 | ||||||||
\(280\) | 224.527 | − | 512.610i | 0.801881 | − | 1.83075i | ||||
\(281\) | 223.573i | 0.795632i | 0.917465 | + | 0.397816i | \(0.130232\pi\) | ||||
−0.917465 | + | 0.397816i | \(0.869768\pi\) | |||||||
\(282\) | −125.191 | + | 50.8739i | −0.443939 | + | 0.180404i | ||||
\(283\) | 247.755 | − | 247.755i | 0.875459 | − | 0.875459i | −0.117602 | − | 0.993061i | \(-0.537521\pi\) |
0.993061 | + | 0.117602i | \(0.0375206\pi\) | |||||||
\(284\) | 146.933 | + | 150.932i | 0.517371 | + | 0.531452i | ||||
\(285\) | 29.7449 | − | 29.7449i | 0.104368 | − | 0.104368i | ||||
\(286\) | 14.1462 | − | 33.5139i | 0.0494622 | − | 0.117181i | ||||
\(287\) | − | 238.778i | − | 0.831980i | ||||||
\(288\) | 87.4098 | + | 39.6930i | 0.303506 | + | 0.137823i | ||||
\(289\) | −266.755 | −0.923026 | ||||||||
\(290\) | −38.7645 | − | 16.3625i | −0.133671 | − | 0.0564223i | ||||
\(291\) | −74.6376 | − | 74.6376i | −0.256487 | − | 0.256487i | ||||
\(292\) | −194.342 | + | 189.193i | −0.665554 | + | 0.647920i | ||||
\(293\) | −102.262 | − | 102.262i | −0.349016 | − | 0.349016i | 0.510727 | − | 0.859743i | \(-0.329376\pi\) |
−0.859743 | + | 0.510727i | \(0.829376\pi\) | |||||||
\(294\) | 75.2674 | + | 185.218i | 0.256011 | + | 0.629994i | ||||
\(295\) | −764.729 | −2.59230 | ||||||||
\(296\) | −145.765 | + | 332.792i | −0.492450 | + | 1.12430i | ||||
\(297\) | 3.86653i | 0.0130186i | ||||||||
\(298\) | 9.92552 | + | 24.4247i | 0.0333071 | + | 0.0819622i | ||||
\(299\) | −217.543 | + | 217.543i | −0.727570 | + | 0.727570i | ||||
\(300\) | 144.480 | + | 1.93970i | 0.481599 | + | 0.00646566i | ||||
\(301\) | −49.5275 | + | 49.5275i | −0.164543 | + | 0.164543i | ||||
\(302\) | 93.1246 | + | 39.3079i | 0.308360 | + | 0.130158i | ||||
\(303\) | − | 269.409i | − | 0.889138i | ||||||
\(304\) | 41.6513 | − | 39.4726i | 0.137011 | − | 0.129844i | ||||
\(305\) | 352.191 | 1.15472 | ||||||||
\(306\) | 11.0048 | − | 26.0716i | 0.0359634 | − | 0.0852012i | ||||
\(307\) | 138.292 | + | 138.292i | 0.450463 | + | 0.450463i | 0.895508 | − | 0.445045i | \(-0.146812\pi\) |
−0.445045 | + | 0.895508i | \(0.646812\pi\) | |||||||
\(308\) | 30.7448 | + | 0.412762i | 0.0998208 | + | 0.00134014i | ||||
\(309\) | −212.243 | − | 212.243i | −0.686869 | − | 0.686869i | ||||
\(310\) | 351.969 | − | 143.030i | 1.13538 | − | 0.461387i | ||||
\(311\) | 205.789 | 0.661702 | 0.330851 | − | 0.943683i | \(-0.392664\pi\) | ||||
0.330851 | + | 0.943683i | \(0.392664\pi\) | |||||||
\(312\) | 123.286 | + | 315.460i | 0.395147 | + | 1.01109i | ||||
\(313\) | − | 223.861i | − | 0.715209i | −0.933873 | − | 0.357605i | \(-0.883594\pi\) | ||
0.933873 | − | 0.357605i | \(-0.116406\pi\) | |||||||
\(314\) | 251.249 | − | 102.100i | 0.800156 | − | 0.325161i | ||||
\(315\) | −148.393 | + | 148.393i | −0.471089 | + | 0.471089i | ||||
\(316\) | 161.823 | − | 157.535i | 0.512098 | − | 0.498530i | ||||
\(317\) | −176.488 | + | 176.488i | −0.556744 | + | 0.556744i | −0.928379 | − | 0.371635i | \(-0.878797\pi\) |
0.371635 | + | 0.928379i | \(0.378797\pi\) | |||||||
\(318\) | 53.2985 | − | 126.270i | 0.167605 | − | 0.397075i | ||||
\(319\) | − | 2.31180i | − | 0.00724703i | ||||||
\(320\) | 433.036 | + | 17.4495i | 1.35324 | + | 0.0545296i | ||||
\(321\) | 62.4000 | 0.194393 | ||||||||
\(322\) | −239.574 | − | 101.124i | −0.744019 | − | 0.314050i | ||||
\(323\) | −11.9612 | − | 11.9612i | −0.0370316 | − | 0.0370316i | ||||
\(324\) | −25.1118 | − | 25.7953i | −0.0775056 | − | 0.0796150i | ||||
\(325\) | 360.469 | + | 360.469i | 1.10914 | + | 1.10914i | ||||
\(326\) | 150.018 | + | 369.165i | 0.460178 | + | 1.13241i | ||||
\(327\) | −80.9813 | −0.247649 | ||||||||
\(328\) | 172.230 | − | 67.3099i | 0.525092 | − | 0.205213i | ||||
\(329\) | − | 402.978i | − | 1.22486i | ||||||
\(330\) | 6.57146 | + | 16.1711i | 0.0199135 | + | 0.0490032i | ||||
\(331\) | −183.939 | + | 183.939i | −0.555706 | + | 0.555706i | −0.928082 | − | 0.372376i | \(-0.878543\pi\) |
0.372376 | + | 0.928082i | \(0.378543\pi\) | |||||||
\(332\) | 4.43252 | − | 330.159i | 0.0133510 | − | 0.994455i | ||||
\(333\) | 96.3384 | − | 96.3384i | 0.289305 | − | 0.289305i | ||||
\(334\) | 198.720 | + | 83.8795i | 0.594969 | + | 0.251136i | ||||
\(335\) | 105.217i | 0.314081i | ||||||||
\(336\) | −207.792 | + | 196.923i | −0.618429 | + | 0.586081i | ||||
\(337\) | 12.7162 | 0.0377336 | 0.0188668 | − | 0.999822i | \(-0.493994\pi\) | ||||
0.0188668 | + | 0.999822i | \(0.493994\pi\) | |||||||
\(338\) | −333.244 | + | 789.490i | −0.985928 | + | 2.33577i | ||||
\(339\) | −171.659 | − | 171.659i | −0.506368 | − | 0.506368i | ||||
\(340\) | 1.71500 | − | 127.743i | 0.00504413 | − | 0.375715i | ||||
\(341\) | 14.7602 | + | 14.7602i | 0.0432849 | + | 0.0432849i | ||||
\(342\) | −19.9358 | + | 8.10133i | −0.0582917 | + | 0.0236881i | ||||
\(343\) | −90.0184 | −0.262444 | ||||||||
\(344\) | −49.6855 | − | 21.7626i | −0.144435 | − | 0.0632633i | ||||
\(345\) | − | 147.625i | − | 0.427899i | ||||||
\(346\) | 141.195 | − | 57.3777i | 0.408079 | − | 0.165831i | ||||
\(347\) | −113.546 | + | 113.546i | −0.327221 | + | 0.327221i | −0.851529 | − | 0.524308i | \(-0.824324\pi\) |
0.524308 | + | 0.851529i | \(0.324324\pi\) | |||||||
\(348\) | 15.0144 | + | 15.4230i | 0.0431447 | + | 0.0443190i | ||||
\(349\) | 90.9653 | − | 90.9653i | 0.260645 | − | 0.260645i | −0.564671 | − | 0.825316i | \(-0.690997\pi\) |
0.825316 | + | 0.564671i | \(0.190997\pi\) | |||||||
\(350\) | −167.563 | + | 396.974i | −0.478751 | + | 1.13421i | ||||
\(351\) | − | 127.011i | − | 0.361854i | ||||||
\(352\) | 8.36902 | + | 22.2925i | 0.0237756 | + | 0.0633309i | ||||
\(353\) | 36.2208 | 0.102609 | 0.0513043 | − | 0.998683i | \(-0.483662\pi\) | ||||
0.0513043 | + | 0.998683i | \(0.483662\pi\) | |||||||
\(354\) | 360.411 | + | 152.129i | 1.01811 | + | 0.429744i | ||||
\(355\) | −252.155 | − | 252.155i | −0.710294 | − | 0.710294i | ||||
\(356\) | 377.087 | − | 367.096i | 1.05923 | − | 1.03117i | ||||
\(357\) | 59.6727 | + | 59.6727i | 0.167151 | + | 0.167151i | ||||
\(358\) | −110.932 | − | 272.982i | −0.309866 | − | 0.762520i | ||||
\(359\) | 142.121 | 0.395880 | 0.197940 | − | 0.980214i | \(-0.436575\pi\) | ||||
0.197940 | + | 0.980214i | \(0.436575\pi\) | |||||||
\(360\) | −148.867 | − | 65.2046i | −0.413518 | − | 0.181124i | ||||
\(361\) | − | 348.137i | − | 0.964369i | ||||||
\(362\) | 218.820 | + | 538.473i | 0.604475 | + | 1.48749i | ||||
\(363\) | 147.516 | − | 147.516i | 0.406380 | − | 0.406380i | ||||
\(364\) | −1009.93 | − | 13.5587i | −2.77452 | − | 0.0372491i | ||||
\(365\) | 324.676 | − | 324.676i | 0.889523 | − | 0.889523i | ||||
\(366\) | −165.985 | − | 70.0621i | −0.453510 | − | 0.191427i | ||||
\(367\) | 654.218i | 1.78261i | 0.453404 | + | 0.891305i | \(0.350209\pi\) | ||||
−0.453404 | + | 0.891305i | \(0.649791\pi\) | |||||||
\(368\) | 5.40633 | − | 201.310i | 0.0146911 | − | 0.547039i | ||||
\(369\) | −69.3434 | −0.187923 | ||||||||
\(370\) | 239.184 | − | 566.652i | 0.646442 | − | 1.53149i | ||||
\(371\) | 289.007 | + | 289.007i | 0.778995 | + | 0.778995i | ||||
\(372\) | −194.333 | − | 2.60901i | −0.522402 | − | 0.00701346i | ||||
\(373\) | 335.277 | + | 335.277i | 0.898867 | + | 0.898867i | 0.995336 | − | 0.0964690i | \(-0.0307549\pi\) |
−0.0964690 | + | 0.995336i | \(0.530755\pi\) | |||||||
\(374\) | 6.50281 | − | 2.64255i | 0.0173872 | − | 0.00706565i | ||||
\(375\) | 48.6078 | 0.129621 | ||||||||
\(376\) | 290.667 | − | 113.597i | 0.773050 | − | 0.302118i | ||||
\(377\) | 75.9397i | 0.201432i | ||||||||
\(378\) | 99.4567 | − | 40.4164i | 0.263113 | − | 0.106922i | ||||
\(379\) | −98.7497 | + | 98.7497i | −0.260553 | + | 0.260553i | −0.825279 | − | 0.564725i | \(-0.808982\pi\) |
0.564725 | + | 0.825279i | \(0.308982\pi\) | |||||||
\(380\) | −69.6089 | + | 67.7646i | −0.183181 | + | 0.178328i | ||||
\(381\) | 50.0257 | − | 50.0257i | 0.131301 | − | 0.131301i | ||||
\(382\) | −193.081 | + | 457.430i | −0.505448 | + | 1.19746i | ||||
\(383\) | − | 156.144i | − | 0.407687i | −0.979003 | − | 0.203844i | \(-0.934657\pi\) | ||
0.979003 | − | 0.203844i | \(-0.0653434\pi\) | |||||||
\(384\) | −200.615 | − | 94.3687i | −0.522436 | − | 0.245752i | ||||
\(385\) | −52.0532 | −0.135203 | ||||||||
\(386\) | 239.390 | + | 101.046i | 0.620181 | + | 0.261778i | ||||
\(387\) | 14.3832 | + | 14.3832i | 0.0371660 | + | 0.0371660i | ||||
\(388\) | 170.039 | + | 174.667i | 0.438244 | + | 0.450171i | ||||
\(389\) | −391.047 | − | 391.047i | −1.00526 | − | 1.00526i | −0.999986 | − | 0.00527486i | \(-0.998321\pi\) |
−0.00527486 | − | 0.999986i | \(-0.501679\pi\) | |||||||
\(390\) | −215.864 | − | 531.199i | −0.553497 | − | 1.36205i | ||||
\(391\) | −59.3639 | −0.151826 | ||||||||
\(392\) | −168.065 | − | 430.038i | −0.428737 | − | 1.09704i | ||||
\(393\) | 183.753i | 0.467565i | ||||||||
\(394\) | −252.365 | − | 621.021i | −0.640520 | − | 1.57620i | ||||
\(395\) | −270.349 | + | 270.349i | −0.684427 | + | 0.684427i | ||||
\(396\) | 0.119870 | − | 8.92857i | 0.000302701 | − | 0.0225469i | ||||
\(397\) | 243.862 | − | 243.862i | 0.614262 | − | 0.614262i | −0.329791 | − | 0.944054i | \(-0.606978\pi\) |
0.944054 | + | 0.329791i | \(0.106978\pi\) | |||||||
\(398\) | −454.210 | − | 191.722i | −1.14123 | − | 0.481713i | ||||
\(399\) | − | 64.1715i | − | 0.160831i | ||||||
\(400\) | −333.571 | − | 8.95828i | −0.833928 | − | 0.0223957i | ||||
\(401\) | −175.261 | −0.437059 | −0.218529 | − | 0.975830i | \(-0.570126\pi\) | ||||
−0.218529 | + | 0.975830i | \(0.570126\pi\) | |||||||
\(402\) | 20.9311 | − | 49.5881i | 0.0520674 | − | 0.123353i | ||||
\(403\) | −484.852 | − | 484.852i | −1.20311 | − | 1.20311i | ||||
\(404\) | −8.35218 | + | 622.117i | −0.0206737 | + | 1.53989i | ||||
\(405\) | 43.0947 | + | 43.0947i | 0.106407 | + | 0.106407i | ||||
\(406\) | −59.4652 | + | 24.1650i | −0.146466 | + | 0.0595196i | ||||
\(407\) | 33.7935 | 0.0830307 | ||||||||
\(408\) | −26.2205 | + | 59.8631i | −0.0642659 | + | 0.146723i | ||||
\(409\) | 44.4504i | 0.108681i | 0.998522 | + | 0.0543404i | \(0.0173056\pi\) | ||||
−0.998522 | + | 0.0543404i | \(0.982694\pi\) | |||||||
\(410\) | −290.016 | + | 117.854i | −0.707356 | + | 0.287449i | ||||
\(411\) | −164.150 | + | 164.150i | −0.399393 | + | 0.399393i | ||||
\(412\) | 483.529 | + | 496.689i | 1.17361 | + | 1.20556i | ||||
\(413\) | −824.910 | + | 824.910i | −1.99736 | + | 1.99736i | ||||
\(414\) | −29.3674 | + | 69.5746i | −0.0709357 | + | 0.168054i | ||||
\(415\) | 558.984i | 1.34695i | ||||||||
\(416\) | −274.911 | − | 732.279i | −0.660844 | − | 1.76029i | ||||
\(417\) | −56.0438 | −0.134398 | ||||||||
\(418\) | −4.91741 | − | 2.07564i | −0.0117641 | − | 0.00496564i | ||||
\(419\) | 14.9985 | + | 14.9985i | 0.0357959 | + | 0.0357959i | 0.724778 | − | 0.688982i | \(-0.241942\pi\) |
−0.688982 | + | 0.724778i | \(0.741942\pi\) | |||||||
\(420\) | 347.269 | − | 338.068i | 0.826831 | − | 0.804924i | ||||
\(421\) | 312.907 | + | 312.907i | 0.743247 | + | 0.743247i | 0.973201 | − | 0.229954i | \(-0.0738576\pi\) |
−0.229954 | + | 0.973201i | \(0.573858\pi\) | |||||||
\(422\) | 14.2834 | + | 35.1488i | 0.0338470 | + | 0.0832909i | ||||
\(423\) | −117.028 | −0.276663 | ||||||||
\(424\) | −126.991 | + | 289.929i | −0.299507 | + | 0.683795i | ||||
\(425\) | 98.3660i | 0.231449i | ||||||||
\(426\) | 68.6768 | + | 169.000i | 0.161213 | + | 0.396714i | ||||
\(427\) | 379.907 | − | 379.907i | 0.889712 | − | 0.889712i | ||||
\(428\) | −144.094 | − | 1.93452i | −0.336667 | − | 0.00451990i | ||||
\(429\) | 22.2763 | − | 22.2763i | 0.0519262 | − | 0.0519262i | ||||
\(430\) | 84.6006 | + | 35.7099i | 0.196746 | + | 0.0830462i | ||||
\(431\) | − | 532.400i | − | 1.23527i | −0.786466 | − | 0.617633i | \(-0.788092\pi\) | ||
0.786466 | − | 0.617633i | \(-0.211908\pi\) | |||||||
\(432\) | 57.1884 | + | 60.3448i | 0.132380 | + | 0.139687i | ||||
\(433\) | 553.451 | 1.27818 | 0.639089 | − | 0.769133i | \(-0.279312\pi\) | ||||
0.639089 | + | 0.769133i | \(0.279312\pi\) | |||||||
\(434\) | 225.381 | − | 533.953i | 0.519312 | − | 1.23031i | ||||
\(435\) | −25.7664 | − | 25.7664i | −0.0592330 | − | 0.0592330i | ||||
\(436\) | 187.001 | + | 2.51057i | 0.428903 | + | 0.00575819i | ||||
\(437\) | 31.9197 | + | 31.9197i | 0.0730427 | + | 0.0730427i | ||||
\(438\) | −217.606 | + | 88.4288i | −0.496817 | + | 0.201892i | ||||
\(439\) | 645.291 | 1.46991 | 0.734956 | − | 0.678115i | \(-0.237203\pi\) | ||||
0.734956 | + | 0.678115i | \(0.237203\pi\) | |||||||
\(440\) | −14.6734 | − | 37.5458i | −0.0333487 | − | 0.0853315i | ||||
\(441\) | 173.142i | 0.392613i | ||||||||
\(442\) | −213.609 | + | 86.8045i | −0.483278 | + | 0.196390i | ||||
\(443\) | 315.833 | − | 315.833i | 0.712941 | − | 0.712941i | −0.254208 | − | 0.967149i | \(-0.581815\pi\) |
0.967149 | + | 0.254208i | \(0.0818149\pi\) | |||||||
\(444\) | −225.451 | + | 219.477i | −0.507772 | + | 0.494318i | ||||
\(445\) | −629.978 | + | 629.978i | −1.41568 | + | 1.41568i | ||||
\(446\) | 229.888 | − | 544.630i | 0.515444 | − | 1.22114i | ||||
\(447\) | 22.8323i | 0.0510789i | ||||||||
\(448\) | 485.937 | − | 448.292i | 1.08468 | − | 1.00065i | ||||
\(449\) | 218.589 | 0.486835 | 0.243417 | − | 0.969922i | \(-0.421732\pi\) | ||||
0.243417 | + | 0.969922i | \(0.421732\pi\) | |||||||
\(450\) | 115.285 | + | 48.6618i | 0.256189 | + | 0.108137i | ||||
\(451\) | −12.1621 | − | 12.1621i | −0.0269670 | − | 0.0269670i | ||||
\(452\) | 391.071 | + | 401.715i | 0.865202 | + | 0.888749i | ||||
\(453\) | 61.8990 | + | 61.8990i | 0.136642 | + | 0.136642i | ||||
\(454\) | 103.367 | + | 254.367i | 0.227681 | + | 0.560279i | ||||
\(455\) | 1709.88 | 3.75798 | ||||||||
\(456\) | 46.2867 | − | 18.0895i | 0.101506 | − | 0.0396699i | ||||
\(457\) | − | 296.561i | − | 0.648930i | −0.945898 | − | 0.324465i | \(-0.894816\pi\) | ||
0.945898 | − | 0.324465i | \(-0.105184\pi\) | |||||||
\(458\) | −36.4773 | − | 89.7634i | −0.0796447 | − | 0.195990i | ||||
\(459\) | 17.3295 | − | 17.3295i | 0.0377549 | − | 0.0377549i | ||||
\(460\) | −4.57665 | + | 340.895i | −0.00994925 | + | 0.741076i | ||||
\(461\) | 118.061 | − | 118.061i | 0.256097 | − | 0.256097i | −0.567368 | − | 0.823465i | \(-0.692038\pi\) |
0.823465 | + | 0.567368i | \(0.192038\pi\) | |||||||
\(462\) | 24.5323 | + | 10.3551i | 0.0531001 | + | 0.0224135i | ||||
\(463\) | − | 409.453i | − | 0.884348i | −0.896929 | − | 0.442174i | \(-0.854207\pi\) | ||
0.896929 | − | 0.442174i | \(-0.145793\pi\) | |||||||
\(464\) | −34.1929 | − | 36.0802i | −0.0736917 | − | 0.0777590i | ||||
\(465\) | 329.021 | 0.707572 | ||||||||
\(466\) | 48.8565 | − | 115.747i | 0.104842 | − | 0.248383i | ||||
\(467\) | 494.764 | + | 494.764i | 1.05945 | + | 1.05945i | 0.998117 | + | 0.0613343i | \(0.0195356\pi\) |
0.0613343 | + | 0.998117i | \(0.480464\pi\) | |||||||
\(468\) | −3.93757 | + | 293.292i | −0.00841360 | + | 0.626692i | ||||
\(469\) | 113.497 | + | 113.497i | 0.241999 | + | 0.241999i | ||||
\(470\) | −489.450 | + | 198.898i | −1.04138 | + | 0.423188i | ||||
\(471\) | 234.868 | 0.498658 | ||||||||
\(472\) | −827.542 | − | 362.469i | −1.75327 | − | 0.767943i | ||||
\(473\) | 5.04534i | 0.0106667i | ||||||||
\(474\) | 181.194 | − | 73.6321i | 0.382266 | − | 0.155342i | ||||
\(475\) | 52.8909 | − | 52.8909i | 0.111349 | − | 0.111349i | ||||
\(476\) | −135.946 | − | 139.646i | −0.285601 | − | 0.293374i | ||||
\(477\) | 83.9303 | − | 83.9303i | 0.175955 | − | 0.175955i | ||||
\(478\) | 276.810 | − | 655.792i | 0.579100 | − | 1.37195i | ||||
\(479\) | 558.806i | 1.16661i | 0.812254 | + | 0.583305i | \(0.198241\pi\) | ||||
−0.812254 | + | 0.583305i | \(0.801759\pi\) | |||||||
\(480\) | 341.740 | + | 155.185i | 0.711959 | + | 0.323302i | ||||
\(481\) | −1110.07 | −2.30784 | ||||||||
\(482\) | −122.079 | − | 51.5296i | −0.253277 | − | 0.106908i | ||||
\(483\) | −159.243 | − | 159.243i | −0.329695 | − | 0.329695i | ||||
\(484\) | −345.216 | + | 336.070i | −0.713256 | + | 0.694359i | ||||
\(485\) | −291.806 | − | 291.806i | −0.601661 | − | 0.601661i | ||||
\(486\) | −11.7373 | − | 28.8831i | −0.0241508 | − | 0.0594303i | ||||
\(487\) | −361.328 | −0.741946 | −0.370973 | − | 0.928644i | \(-0.620976\pi\) | ||||
−0.370973 | + | 0.928644i | \(0.620976\pi\) | |||||||
\(488\) | 381.119 | + | 166.933i | 0.780981 | + | 0.342075i | ||||
\(489\) | 345.096i | 0.705718i | ||||||||
\(490\) | 294.268 | + | 724.135i | 0.600547 | + | 1.47783i | ||||
\(491\) | −488.975 | + | 488.975i | −0.995876 | + | 0.995876i | −0.999992 | − | 0.00411514i | \(-0.998690\pi\) |
0.00411514 | + | 0.999992i | \(0.498690\pi\) | |||||||
\(492\) | 160.127 | + | 2.14978i | 0.325462 | + | 0.00436946i | ||||
\(493\) | −10.3613 | + | 10.3613i | −0.0210169 | + | 0.0210169i | ||||
\(494\) | 161.531 | + | 68.1820i | 0.326985 | + | 0.138020i | ||||
\(495\) | 15.1167i | 0.0305389i | ||||||||
\(496\) | 448.672 | + | 12.0494i | 0.904582 | + | 0.0242931i | ||||
\(497\) | −543.996 | −1.09456 | ||||||||
\(498\) | 111.200 | − | 263.445i | 0.223293 | − | 0.529005i | ||||
\(499\) | −102.895 | − | 102.895i | −0.206203 | − | 0.206203i | 0.596448 | − | 0.802652i | \(-0.296578\pi\) |
−0.802652 | + | 0.596448i | \(0.796578\pi\) | |||||||
\(500\) | −112.245 | − | 1.50693i | −0.224490 | − | 0.00301387i | ||||
\(501\) | 132.087 | + | 132.087i | 0.263647 | + | 0.263647i | ||||
\(502\) | −852.643 | + | 346.490i | −1.69849 | + | 0.690219i | ||||
\(503\) | −881.975 | −1.75343 | −0.876715 | − | 0.481011i | \(-0.840270\pi\) | ||||
−0.876715 | + | 0.481011i | \(0.840270\pi\) | |||||||
\(504\) | −230.918 | + | 90.2458i | −0.458170 | + | 0.179059i | ||||
\(505\) | − | 1053.29i | − | 2.08572i | ||||||
\(506\) | −17.3534 | + | 7.05192i | −0.0342952 | + | 0.0139366i | ||||
\(507\) | −524.767 | + | 524.767i | −1.03504 | + | 1.03504i | ||||
\(508\) | −117.070 | + | 113.968i | −0.230452 | + | 0.224346i | ||||
\(509\) | 161.639 | − | 161.639i | 0.317563 | − | 0.317563i | −0.530268 | − | 0.847830i | \(-0.677909\pi\) |
0.847830 | + | 0.530268i | \(0.177909\pi\) | |||||||
\(510\) | 43.0247 | − | 101.930i | 0.0843622 | − | 0.199863i | ||||
\(511\) | − | 700.454i | − | 1.37075i | ||||||
\(512\) | 460.334 | + | 224.135i | 0.899090 | + | 0.437764i | ||||
\(513\) | −18.6360 | −0.0363275 | ||||||||
\(514\) | 574.906 | + | 242.668i | 1.11849 | + | 0.472116i | ||||
\(515\) | −829.791 | − | 829.791i | −1.61124 | − | 1.61124i | ||||
\(516\) | −32.7678 | − | 33.6596i | −0.0635034 | − | 0.0652317i | ||||
\(517\) | −20.5256 | − | 20.5256i | −0.0397013 | − | 0.0397013i | ||||
\(518\) | −353.239 | − | 869.252i | −0.681928 | − | 1.67809i | ||||
\(519\) | 131.989 | 0.254315 | ||||||||
\(520\) | 482.003 | + | 1233.33i | 0.926929 | + | 2.37179i | ||||
\(521\) | − | 763.931i | − | 1.46628i | −0.680078 | − | 0.733140i | \(-0.738054\pi\) | ||
0.680078 | − | 0.733140i | \(-0.261946\pi\) | |||||||
\(522\) | 7.01773 | + | 17.2692i | 0.0134439 | + | 0.0330828i | ||||
\(523\) | 295.573 | − | 295.573i | 0.565150 | − | 0.565150i | −0.365616 | − | 0.930766i | \(-0.619142\pi\) |
0.930766 | + | 0.365616i | \(0.119142\pi\) | |||||||
\(524\) | 5.69668 | − | 424.321i | 0.0108715 | − | 0.809773i | ||||
\(525\) | −263.865 | + | 263.865i | −0.502600 | + | 0.502600i | ||||
\(526\) | 309.854 | + | 130.789i | 0.589076 | + | 0.248649i | ||||
\(527\) | − | 132.308i | − | 0.251059i | ||||||
\(528\) | −0.553605 | + | 20.6141i | −0.00104849 | + | 0.0390418i | ||||
\(529\) | −370.582 | −0.700532 | ||||||||
\(530\) | 208.377 | − | 493.669i | 0.393165 | − | 0.931451i | ||||
\(531\) | 239.561 | + | 239.561i | 0.451152 | + | 0.451152i | ||||
\(532\) | −1.98944 | + | 148.184i | −0.00373954 | + | 0.278542i | ||||
\(533\) | 399.509 | + | 399.509i | 0.749549 | + | 0.749549i | ||||
\(534\) | 422.227 | − | 171.581i | 0.790686 | − | 0.321312i | ||||
\(535\) | 243.961 | 0.456002 | ||||||||
\(536\) | −49.8713 | + | 113.859i | −0.0930434 | + | 0.212424i | ||||
\(537\) | − | 255.184i | − | 0.475203i | ||||||
\(538\) | −555.814 | + | 225.867i | −1.03311 | + | 0.419827i | ||||
\(539\) | −30.3673 | + | 30.3673i | −0.0563401 | + | 0.0563401i | ||||
\(540\) | −98.1781 | − | 100.850i | −0.181811 | − | 0.186759i | ||||
\(541\) | 243.037 | − | 243.037i | 0.449236 | − | 0.449236i | −0.445865 | − | 0.895100i | \(-0.647104\pi\) |
0.895100 | + | 0.445865i | \(0.147104\pi\) | |||||||
\(542\) | −134.901 | + | 319.596i | −0.248895 | + | 0.589660i | ||||
\(543\) | 503.365i | 0.927007i | ||||||||
\(544\) | 62.4040 | − | 137.423i | 0.114713 | − | 0.252615i | ||||
\(545\) | −316.607 | −0.580931 | ||||||||
\(546\) | −805.853 | − | 340.150i | −1.47592 | − | 0.622986i | ||||
\(547\) | 424.574 | + | 424.574i | 0.776187 | + | 0.776187i | 0.979180 | − | 0.202993i | \(-0.0650669\pi\) |
−0.202993 | + | 0.979180i | \(0.565067\pi\) | |||||||
\(548\) | 384.144 | − | 373.966i | 0.700992 | − | 0.682419i | ||||
\(549\) | −110.328 | − | 110.328i | −0.200963 | − | 0.200963i | ||||
\(550\) | 11.6850 | + | 28.7545i | 0.0212455 | + | 0.0522810i | ||||
\(551\) | 11.1425 | 0.0202223 | ||||||||
\(552\) | 69.9719 | − | 159.751i | 0.126761 | − | 0.289403i | ||||
\(553\) | 583.248i | 1.05470i | ||||||||
\(554\) | 40.8946 | + | 100.634i | 0.0738171 | + | 0.181649i | ||||
\(555\) | 376.648 | − | 376.648i | 0.678645 | − | 0.678645i | ||||
\(556\) | 129.416 | + | 1.73746i | 0.232763 | + | 0.00312493i | ||||
\(557\) | −445.773 | + | 445.773i | −0.800311 | + | 0.800311i | −0.983144 | − | 0.182833i | \(-0.941473\pi\) |
0.182833 | + | 0.983144i | \(0.441473\pi\) | |||||||
\(558\) | −155.065 | − | 65.4528i | −0.277894 | − | 0.117299i | ||||
\(559\) | − | 165.733i | − | 0.296481i | ||||||
\(560\) | −812.392 | + | 769.898i | −1.45070 | + | 1.37482i | ||||
\(561\) | 6.07883 | 0.0108357 | ||||||||
\(562\) | 173.884 | − | 411.951i | 0.309402 | − | 0.733008i | ||||
\(563\) | −529.295 | − | 529.295i | −0.940133 | − | 0.940133i | 0.0581732 | − | 0.998307i | \(-0.481472\pi\) |
−0.998307 | + | 0.0581732i | \(0.981472\pi\) | |||||||
\(564\) | 270.241 | + | 3.62810i | 0.479151 | + | 0.00643280i | ||||
\(565\) | −671.123 | − | 671.123i | −1.18783 | − | 1.18783i | ||||
\(566\) | −649.200 | + | 263.816i | −1.14700 | + | 0.466107i | ||||
\(567\) | 92.9722 | 0.163972 | ||||||||
\(568\) | −153.349 | − | 392.383i | −0.269980 | − | 0.690815i | ||||
\(569\) | 346.814i | 0.609516i | 0.952430 | + | 0.304758i | \(0.0985755\pi\) | ||||
−0.952430 | + | 0.304758i | \(0.901424\pi\) | |||||||
\(570\) | −77.9416 | + | 31.6732i | −0.136740 | + | 0.0555671i | ||||
\(571\) | −155.711 | + | 155.711i | −0.272699 | + | 0.272699i | −0.830186 | − | 0.557487i | \(-0.811766\pi\) |
0.557487 | + | 0.830186i | \(0.311766\pi\) | |||||||
\(572\) | −52.1309 | + | 50.7497i | −0.0911380 | + | 0.0887233i | ||||
\(573\) | −304.049 | + | 304.049i | −0.530627 | + | 0.530627i | ||||
\(574\) | −185.710 | + | 439.968i | −0.323537 | + | 0.766495i | ||||
\(575\) | − | 262.499i | − | 0.456520i | ||||||
\(576\) | −130.188 | − | 141.121i | −0.226021 | − | 0.245001i | ||||
\(577\) | 620.510 | 1.07541 | 0.537704 | − | 0.843134i | \(-0.319292\pi\) | ||||
0.537704 | + | 0.843134i | \(0.319292\pi\) | |||||||
\(578\) | 491.517 | + | 207.469i | 0.850375 | + | 0.358943i | ||||
\(579\) | 159.120 | + | 159.120i | 0.274819 | + | 0.274819i | ||||
\(580\) | 58.7007 | + | 60.2983i | 0.101208 | + | 0.103963i | ||||
\(581\) | 602.974 | + | 602.974i | 1.03782 | + | 1.03782i | ||||
\(582\) | 79.4762 | + | 195.575i | 0.136557 | + | 0.336040i | ||||
\(583\) | 29.4410 | 0.0504992 | ||||||||
\(584\) | 505.235 | − | 197.453i | 0.865129 | − | 0.338104i | ||||
\(585\) | − | 496.565i | − | 0.848829i | ||||||
\(586\) | 108.891 | + | 267.960i | 0.185821 | + | 0.457269i | ||||
\(587\) | 561.656 | − | 561.656i | 0.956825 | − | 0.956825i | −0.0422810 | − | 0.999106i | \(-0.513462\pi\) |
0.999106 | + | 0.0422810i | \(0.0134625\pi\) | |||||||
\(588\) | 5.36773 | − | 399.819i | 0.00912880 | − | 0.679964i | ||||
\(589\) | −71.1413 | + | 71.1413i | −0.120783 | + | 0.120783i | ||||
\(590\) | 1409.07 | + | 594.770i | 2.38826 | + | 1.00808i | ||||
\(591\) | − | 580.531i | − | 0.982286i | ||||||
\(592\) | 527.413 | − | 499.826i | 0.890901 | − | 0.844301i | ||||
\(593\) | 851.739 | 1.43632 | 0.718161 | − | 0.695877i | \(-0.244984\pi\) | ||||
0.718161 | + | 0.695877i | \(0.244984\pi\) | |||||||
\(594\) | 3.00721 | − | 7.12440i | 0.00506263 | − | 0.0119939i | ||||
\(595\) | 233.299 | + | 233.299i | 0.392099 | + | 0.392099i | ||||
\(596\) | 0.707843 | − | 52.7241i | 0.00118766 | − | 0.0884633i | ||||
\(597\) | −301.909 | − | 301.909i | −0.505710 | − | 0.505710i | ||||
\(598\) | 570.036 | − | 231.646i | 0.953237 | − | 0.387368i | ||||
\(599\) | −1001.69 | −1.67228 | −0.836138 | − | 0.548519i | \(-0.815192\pi\) | ||||
−0.836138 | + | 0.548519i | \(0.815192\pi\) | |||||||
\(600\) | −264.707 | − | 115.943i | −0.441178 | − | 0.193239i | ||||
\(601\) | 955.182i | 1.58932i | 0.607054 | + | 0.794661i | \(0.292351\pi\) | ||||
−0.607054 | + | 0.794661i | \(0.707649\pi\) | |||||||
\(602\) | 129.778 | − | 52.7382i | 0.215579 | − | 0.0876050i | ||||
\(603\) | 32.9607 | − | 32.9607i | 0.0546612 | − | 0.0546612i | ||||
\(604\) | −141.018 | − | 144.856i | −0.233473 | − | 0.239827i | ||||
\(605\) | 576.734 | − | 576.734i | 0.953279 | − | 0.953279i | ||||
\(606\) | −209.533 | + | 496.407i | −0.345765 | + | 0.819154i | ||||
\(607\) | − | 291.885i | − | 0.480865i | −0.970666 | − | 0.240432i | \(-0.922711\pi\) | ||
0.970666 | − | 0.240432i | \(-0.0772892\pi\) | |||||||
\(608\) | −107.446 | + | 40.3371i | −0.176720 | + | 0.0663440i | ||||
\(609\) | −55.5881 | −0.0912777 | ||||||||
\(610\) | −648.940 | − | 273.917i | −1.06384 | − | 0.449045i | ||||
\(611\) | 674.238 | + | 674.238i | 1.10350 | + | 1.10350i | ||||
\(612\) | −40.5544 | + | 39.4800i | −0.0662654 | + | 0.0645097i | ||||
\(613\) | −332.933 | − | 332.933i | −0.543121 | − | 0.543121i | 0.381322 | − | 0.924442i | \(-0.375469\pi\) |
−0.924442 | + | 0.381322i | \(0.875469\pi\) | |||||||
\(614\) | −147.257 | − | 362.371i | −0.239833 | − | 0.590181i | ||||
\(615\) | −271.107 | −0.440825 | ||||||||
\(616\) | −56.3287 | − | 24.6724i | −0.0914427 | − | 0.0400526i | ||||
\(617\) | 970.864i | 1.57352i | 0.617257 | + | 0.786762i | \(0.288244\pi\) | ||||
−0.617257 | + | 0.786762i | \(0.711756\pi\) | |||||||
\(618\) | 226.002 | + | 556.146i | 0.365699 | + | 0.899913i | ||||
\(619\) | −696.761 | + | 696.761i | −1.12562 | + | 1.12562i | −0.134744 | + | 0.990881i | \(0.543021\pi\) |
−0.990881 | + | 0.134744i | \(0.956979\pi\) | |||||||
\(620\) | −759.773 | − | 10.2003i | −1.22544 | − | 0.0164520i | ||||
\(621\) | −46.2455 | + | 46.2455i | −0.0744694 | + | 0.0744694i | ||||
\(622\) | −379.183 | − | 160.053i | −0.609619 | − | 0.257320i | ||||
\(623\) | 1359.11i | 2.18156i | ||||||||
\(624\) | 18.1852 | − | 677.146i | 0.0291430 | − | 1.08517i | ||||
\(625\) | 711.432 | 1.13829 | ||||||||
\(626\) | −174.108 | + | 412.481i | −0.278128 | + | 0.658915i | ||||
\(627\) | −3.26856 | − | 3.26856i | −0.00521301 | − | 0.00521301i | ||||
\(628\) | −542.355 | − | 7.28135i | −0.863623 | − | 0.0115945i | ||||
\(629\) | −151.460 | − | 151.460i | −0.240795 | − | 0.240795i | ||||
\(630\) | 388.839 | − | 158.013i | 0.617205 | − | 0.250815i | ||||
\(631\) | −377.591 | −0.598401 | −0.299200 | − | 0.954190i | \(-0.596720\pi\) | ||||
−0.299200 | + | 0.954190i | \(0.596720\pi\) | |||||||
\(632\) | −420.695 | + | 164.413i | −0.665657 | + | 0.260148i | ||||
\(633\) | 32.8571i | 0.0519069i | ||||||||
\(634\) | 462.457 | − | 187.929i | 0.729427 | − | 0.296418i | ||||
\(635\) | 195.582 | − | 195.582i | 0.308003 | − | 0.308003i | ||||
\(636\) | −196.413 | + | 191.209i | −0.308826 | + | 0.300644i | ||||
\(637\) | 997.527 | − | 997.527i | 1.56598 | − | 1.56598i | ||||
\(638\) | −1.79801 | + | 4.25968i | −0.00281820 | + | 0.00667661i | ||||
\(639\) | 157.981i | 0.247232i | ||||||||
\(640\) | −784.333 | − | 368.947i | −1.22552 | − | 0.576480i | ||||
\(641\) | 729.200 | 1.13760 | 0.568799 | − | 0.822477i | \(-0.307408\pi\) | ||||
0.568799 | + | 0.822477i | \(0.307408\pi\) | |||||||
\(642\) | −114.977 | − | 48.5317i | −0.179092 | − | 0.0755946i | ||||
\(643\) | 243.958 | + | 243.958i | 0.379406 | + | 0.379406i | 0.870888 | − | 0.491482i | \(-0.163545\pi\) |
−0.491482 | + | 0.870888i | \(0.663545\pi\) | |||||||
\(644\) | 362.785 | + | 372.659i | 0.563331 | + | 0.578663i | ||||
\(645\) | 56.2332 | + | 56.2332i | 0.0871832 | + | 0.0871832i | ||||
\(646\) | 12.7366 | + | 31.3423i | 0.0197161 | + | 0.0485176i | ||||
\(647\) | −281.594 | −0.435230 | −0.217615 | − | 0.976035i | \(-0.569828\pi\) | ||||
−0.217615 | + | 0.976035i | \(0.569828\pi\) | |||||||
\(648\) | 26.2082 | + | 67.0606i | 0.0404448 | + | 0.103489i | ||||
\(649\) | 84.0331i | 0.129481i | ||||||||
\(650\) | −383.838 | − | 944.549i | −0.590520 | − | 1.45315i | ||||
\(651\) | 354.913 | − | 354.913i | 0.545182 | − | 0.545182i | ||||
\(652\) | 10.6986 | − | 796.893i | 0.0164089 | − | 1.22223i | ||||
\(653\) | 323.704 | − | 323.704i | 0.495718 | − | 0.495718i | −0.414384 | − | 0.910102i | \(-0.636003\pi\) |
0.910102 | + | 0.414384i | \(0.136003\pi\) | |||||||
\(654\) | 149.215 | + | 62.9834i | 0.228157 | + | 0.0963049i | ||||
\(655\) | 718.407i | 1.09680i | ||||||||
\(656\) | −369.698 | − | 9.92850i | −0.563564 | − | 0.0151349i | ||||
\(657\) | −203.418 | −0.309617 | ||||||||
\(658\) | −313.417 | + | 742.519i | −0.476317 | + | 1.12845i | ||||
\(659\) | 507.811 | + | 507.811i | 0.770578 | + | 0.770578i | 0.978208 | − | 0.207629i | \(-0.0665748\pi\) |
−0.207629 | + | 0.978208i | \(0.566575\pi\) | |||||||
\(660\) | 0.468647 | − | 34.9075i | 0.000710071 | − | 0.0528901i | ||||
\(661\) | 57.1593 | + | 57.1593i | 0.0864741 | + | 0.0864741i | 0.749021 | − | 0.662547i | \(-0.230524\pi\) |
−0.662547 | + | 0.749021i | \(0.730524\pi\) | |||||||
\(662\) | 481.981 | − | 195.863i | 0.728068 | − | 0.295866i | ||||
\(663\) | −199.682 | −0.301179 | ||||||||
\(664\) | −264.949 | + | 604.897i | −0.399020 | + | 0.910990i | ||||
\(665\) | − | 250.887i | − | 0.377274i | ||||||
\(666\) | −252.439 | + | 102.584i | −0.379037 | + | 0.154030i | ||||
\(667\) | 27.6502 | − | 27.6502i | 0.0414546 | − | 0.0414546i | ||||
\(668\) | −300.919 | − | 309.109i | −0.450478 | − | 0.462739i | ||||
\(669\) | 362.010 | − | 362.010i | 0.541121 | − | 0.541121i | ||||
\(670\) | 81.8329 | − | 193.871i | 0.122139 | − | 0.289360i | ||||
\(671\) | − | 38.7009i | − | 0.0576765i | ||||||
\(672\) | 536.031 | − | 201.236i | 0.797666 | − | 0.299458i | ||||
\(673\) | 1110.84 | 1.65059 | 0.825293 | − | 0.564705i | \(-0.191010\pi\) | ||||
0.825293 | + | 0.564705i | \(0.191010\pi\) | |||||||
\(674\) | −23.4307 | − | 9.89007i | −0.0347636 | − | 0.0146737i | ||||
\(675\) | 76.6288 | + | 76.6288i | 0.113524 | + | 0.113524i | ||||
\(676\) | 1228.06 | − | 1195.52i | 1.81665 | − | 1.76852i | ||||
\(677\) | 397.465 | + | 397.465i | 0.587097 | + | 0.587097i | 0.936844 | − | 0.349747i | \(-0.113732\pi\) |
−0.349747 | + | 0.936844i | \(0.613732\pi\) | |||||||
\(678\) | 182.787 | + | 449.803i | 0.269597 | + | 0.663426i | ||||
\(679\) | −629.539 | −0.927156 | ||||||||
\(680\) | −102.512 | + | 234.043i | −0.150754 | + | 0.344181i | ||||
\(681\) | 237.782i | 0.349166i | ||||||||
\(682\) | −15.7170 | − | 38.6765i | −0.0230455 | − | 0.0567104i | ||||
\(683\) | −238.015 | + | 238.015i | −0.348485 | + | 0.348485i | −0.859545 | − | 0.511060i | \(-0.829253\pi\) |
0.511060 | + | 0.859545i | \(0.329253\pi\) | |||||||
\(684\) | 43.0341 | + | 0.577751i | 0.0629153 | + | 0.000844665i | ||||
\(685\) | −641.768 | + | 641.768i | −0.936887 | + | 0.936887i | ||||
\(686\) | 165.866 | + | 70.0120i | 0.241787 | + | 0.102058i | ||||
\(687\) | − | 83.9109i | − | 0.122141i | ||||||
\(688\) | 74.6236 | + | 78.7423i | 0.108464 | + | 0.114451i | ||||
\(689\) | −967.099 | −1.40363 | ||||||||
\(690\) | −114.816 | + | 272.011i | −0.166400 | + | 0.394219i | ||||
\(691\) | −685.172 | − | 685.172i | −0.991565 | − | 0.991565i | 0.00839951 | − | 0.999965i | \(-0.497326\pi\) |
−0.999965 | + | 0.00839951i | \(0.997326\pi\) | |||||||
\(692\) | −304.789 | − | 4.09192i | −0.440447 | − | 0.00591318i | ||||
\(693\) | 16.3064 | + | 16.3064i | 0.0235301 | + | 0.0235301i | ||||
\(694\) | 297.528 | − | 120.907i | 0.428714 | − | 0.174217i | ||||
\(695\) | −219.111 | −0.315267 | ||||||||
\(696\) | −15.6699 | − | 40.0956i | −0.0225142 | − | 0.0576086i | ||||
\(697\) | 109.019i | 0.156412i | ||||||||
\(698\) | −238.359 | + | 96.8624i | −0.341489 | + | 0.138771i | ||||
\(699\) | 76.9356 | − | 76.9356i | 0.110065 | − | 0.110065i | ||||
\(700\) | 617.495 | − | 601.135i | 0.882136 | − | 0.858764i | ||||
\(701\) | 543.074 | − | 543.074i | 0.774713 | − | 0.774713i | −0.204214 | − | 0.978926i | \(-0.565464\pi\) |
0.978926 | + | 0.204214i | \(0.0654637\pi\) | |||||||
\(702\) | −98.7828 | + | 234.027i | −0.140716 | + | 0.333372i | ||||
\(703\) | 162.879i | 0.231691i | ||||||||
\(704\) | 1.91746 | − | 47.5847i | 0.00272366 | − | 0.0675919i | ||||
\(705\) | −457.538 | −0.648991 | ||||||||
\(706\) | −66.7398 | − | 28.1708i | −0.0945323 | − | 0.0399020i | ||||
\(707\) | −1136.18 | − | 1136.18i | −1.60704 | − | 1.60704i | ||||
\(708\) | −545.767 | − | 560.621i | −0.770857 | − | 0.791837i | ||||
\(709\) | −488.019 | − | 488.019i | −0.688320 | − | 0.688320i | 0.273541 | − | 0.961860i | \(-0.411805\pi\) |
−0.961860 | + | 0.273541i | \(0.911805\pi\) | |||||||
\(710\) | 268.501 | + | 660.729i | 0.378171 | + | 0.930604i | ||||
\(711\) | 169.381 | 0.238229 | ||||||||
\(712\) | −980.322 | + | 383.123i | −1.37686 | + | 0.538094i | ||||
\(713\) | 353.076i | 0.495198i | ||||||||
\(714\) | −63.5412 | − | 156.362i | −0.0889933 | − | 0.218995i | ||||
\(715\) | 87.0923 | − | 87.0923i | 0.121807 | − | 0.121807i | ||||
\(716\) | −7.91118 | + | 589.269i | −0.0110491 | + | 0.823002i | ||||
\(717\) | 435.899 | − | 435.899i | 0.607948 | − | 0.607948i | ||||
\(718\) | −261.869 | − | 110.535i | −0.364721 | − | 0.153948i | ||||
\(719\) | − | 297.369i | − | 0.413587i | −0.978385 | − | 0.206793i | \(-0.933697\pi\) | ||
0.978385 | − | 0.206793i | \(-0.0663028\pi\) | |||||||
\(720\) | 223.586 | + | 235.926i | 0.310535 | + | 0.327675i | ||||
\(721\) | −1790.18 | −2.48292 | ||||||||
\(722\) | −270.764 | + | 641.470i | −0.375020 | + | 0.888463i | ||||
\(723\) | −81.1449 | − | 81.1449i | −0.112234 | − | 0.112234i | ||||
\(724\) | 15.6053 | − | 1162.37i | 0.0215542 | − | 1.60548i | ||||
\(725\) | −45.8164 | − | 45.8164i | −0.0631950 | − | 0.0631950i | ||||
\(726\) | −386.541 | + | 157.079i | −0.532425 | + | 0.216362i | ||||
\(727\) | 1158.85 | 1.59402 | 0.797009 | − | 0.603967i | \(-0.206414\pi\) | ||||
0.797009 | + | 0.603967i | \(0.206414\pi\) | |||||||
\(728\) | 1850.33 | + | 810.456i | 2.54166 | + | 1.11326i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | −850.759 | + | 345.724i | −1.16542 | + | 0.473595i | ||||
\(731\) | 22.6128 | − | 22.6128i | 0.0309341 | − | 0.0309341i | ||||
\(732\) | 251.349 | + | 258.190i | 0.343373 | + | 0.352719i | ||||
\(733\) | −348.835 | + | 348.835i | −0.475901 | + | 0.475901i | −0.903818 | − | 0.427917i | \(-0.859248\pi\) |
0.427917 | + | 0.903818i | \(0.359248\pi\) | |||||||
\(734\) | 508.819 | − | 1205.45i | 0.693215 | − | 1.64230i | ||||
\(735\) | 676.923i | 0.920983i | ||||||||
\(736\) | −166.531 | + | 366.726i | −0.226265 | + | 0.498269i | ||||
\(737\) | 11.5619 | 0.0156878 | ||||||||
\(738\) | 127.771 | + | 53.9320i | 0.173131 | + | 0.0730786i | ||||
\(739\) | 825.489 | + | 825.489i | 1.11703 | + | 1.11703i | 0.992174 | + | 0.124860i | \(0.0398482\pi\) |
0.124860 | + | 0.992174i | \(0.460152\pi\) | |||||||
\(740\) | −881.430 | + | 858.076i | −1.19112 | + | 1.15956i | ||||
\(741\) | 107.368 | + | 107.368i | 0.144896 | + | 0.144896i | ||||
\(742\) | −307.743 | − | 757.295i | −0.414748 | − | 1.02061i | ||||
\(743\) | −899.725 | −1.21094 | −0.605468 | − | 0.795870i | \(-0.707014\pi\) | ||||
−0.605468 | + | 0.795870i | \(0.707014\pi\) | |||||||
\(744\) | 356.046 | + | 155.951i | 0.478556 | + | 0.209611i | ||||
\(745\) | 89.2659i | 0.119820i | ||||||||
\(746\) | −357.013 | − | 878.538i | −0.478569 | − | 1.17767i | ||||
\(747\) | 175.109 | − | 175.109i | 0.234416 | − | 0.234416i | ||||
\(748\) | −14.0372 | − | 0.188455i | −0.0187663 | − | 0.000251945i | ||||
\(749\) | 263.160 | − | 263.160i | 0.351348 | − | 0.351348i | ||||
\(750\) | −89.5638 | − | 37.8048i | −0.119418 | − | 0.0504065i | ||||
\(751\) | 80.4386i | 0.107109i | 0.998565 | + | 0.0535543i | \(0.0170550\pi\) | ||||
−0.998565 | + | 0.0535543i | \(0.982945\pi\) | |||||||
\(752\) | −623.927 | − | 16.7560i | −0.829690 | − | 0.0222819i | ||||
\(753\) | −797.052 | −1.05850 | ||||||||
\(754\) | 59.0623 | − | 139.925i | 0.0783319 | − | 0.185577i | ||||
\(755\) | 242.003 | + | 242.003i | 0.320533 | + | 0.320533i | ||||
\(756\) | −214.691 | − | 2.88231i | −0.283983 | − | 0.00381258i | ||||
\(757\) | 233.298 | + | 233.298i | 0.308187 | + | 0.308187i | 0.844206 | − | 0.536019i | \(-0.180072\pi\) |
−0.536019 | + | 0.844206i | \(0.680072\pi\) | |||||||
\(758\) | 258.757 | − | 105.151i | 0.341368 | − | 0.138722i | ||||
\(759\) | −16.2220 | −0.0213728 | ||||||||
\(760\) | 180.964 | − | 70.7233i | 0.238111 | − | 0.0930569i | ||||
\(761\) | 56.1906i | 0.0738378i | 0.999318 | + | 0.0369189i | \(0.0117543\pi\) | ||||
−0.999318 | + | 0.0369189i | \(0.988246\pi\) | |||||||
\(762\) | −131.084 | + | 53.2687i | −0.172026 | + | 0.0699064i | ||||
\(763\) | −341.523 | + | 341.523i | −0.447606 | + | 0.447606i | ||||
\(764\) | 711.535 | − | 692.682i | 0.931328 | − | 0.906652i | ||||
\(765\) | 67.7521 | − | 67.7521i | 0.0885648 | − | 0.0885648i | ||||
\(766\) | −121.441 | + | 287.708i | −0.158540 | + | 0.375598i | ||||
\(767\) | − | 2760.38i | − | 3.59893i | ||||||
\(768\) | 296.255 | + | 329.911i | 0.385748 | + | 0.429572i | ||||
\(769\) | 517.343 | 0.672748 | 0.336374 | − | 0.941728i | \(-0.390799\pi\) | ||||
0.336374 | + | 0.941728i | \(0.390799\pi\) | |||||||
\(770\) | 95.9122 | + | 40.4845i | 0.124561 | + | 0.0525773i | ||||
\(771\) | 382.134 | + | 382.134i | 0.495635 | + | 0.495635i | ||||
\(772\) | −362.506 | − | 372.372i | −0.469567 | − | 0.482347i | ||||
\(773\) | −523.925 | − | 523.925i | −0.677781 | − | 0.677781i | 0.281716 | − | 0.959498i | \(-0.409096\pi\) |
−0.959498 | + | 0.281716i | \(0.909096\pi\) | |||||||
\(774\) | −15.3157 | − | 37.6888i | −0.0197877 | − | 0.0486936i | ||||
\(775\) | 585.048 | 0.754900 | ||||||||
\(776\) | −177.463 | − | 454.085i | −0.228689 | − | 0.585161i | ||||
\(777\) | − | 812.578i | − | 1.04579i | ||||||
\(778\) | 416.397 | + | 1024.67i | 0.535215 | + | 1.31706i | ||||
\(779\) | 58.6192 | − | 58.6192i | 0.0752492 | − | 0.0752492i | ||||
\(780\) | −15.3944 | + | 1146.66i | −0.0197365 | + | 1.47008i | ||||
\(781\) | −27.7083 | + | 27.7083i | −0.0354780 | + | 0.0354780i | ||||
\(782\) | 109.383 | + | 46.1704i | 0.139876 | + | 0.0590414i | ||||
\(783\) | 16.1433i | 0.0206173i | ||||||||
\(784\) | −24.7903 | + | 923.092i | −0.0316202 | + | 1.17741i | ||||
\(785\) | 918.248 | 1.16974 | ||||||||
\(786\) | 142.914 | − | 338.579i | 0.181825 | − | 0.430763i | ||||
\(787\) | −46.6965 | − | 46.6965i | −0.0593348 | − | 0.0593348i | 0.676817 | − | 0.736152i | \(-0.263359\pi\) |
−0.736152 | + | 0.676817i | \(0.763359\pi\) | |||||||
\(788\) | −17.9975 | + | 1340.56i | −0.0228395 | + | 1.70122i | ||||
\(789\) | 205.957 | + | 205.957i | 0.261035 | + | 0.261035i | ||||
\(790\) | 708.403 | − | 287.875i | 0.896713 | − | 0.364398i | ||||
\(791\) | −1447.87 | −1.83044 | ||||||||
\(792\) | −7.16509 | + | 16.3584i | −0.00904683 | + | 0.0206545i | ||||
\(793\) | 1271.27i | 1.60312i | ||||||||
\(794\) | −639.000 | + | 259.671i | −0.804786 | + | 0.327042i | ||||
\(795\) | 328.137 | − | 328.137i | 0.412751 | − | 0.412751i | ||||
\(796\) | 687.806 | + | 706.526i | 0.864078 | + | 0.887595i | ||||
\(797\) | 127.126 | − | 127.126i | 0.159505 | − | 0.159505i | −0.622842 | − | 0.782348i | \(-0.714022\pi\) |
0.782348 | + | 0.622842i | \(0.214022\pi\) | |||||||
\(798\) | −49.9095 | + | 118.241i | −0.0625432 | + | 0.148172i | ||||
\(799\) | 183.988i | 0.230273i | ||||||||
\(800\) | 607.665 | + | 275.942i | 0.759581 | + | 0.344928i | ||||
\(801\) | 394.698 | 0.492756 | ||||||||
\(802\) | 322.932 | + | 136.309i | 0.402658 | + | 0.169962i | ||||
\(803\) | −35.6774 | − | 35.6774i | −0.0444302 | − | 0.0444302i | ||||
\(804\) | −77.1344 | + | 75.0908i | −0.0959384 | + | 0.0933965i | ||||
\(805\) | −622.580 | − | 622.580i | −0.773392 | − | 0.773392i | ||||
\(806\) | 516.284 | + | 1270.47i | 0.640551 | + | 1.57627i | ||||
\(807\) | −519.576 | −0.643836 | ||||||||
\(808\) | 499.243 | − | 1139.80i | 0.617874 | − | 1.41065i | ||||
\(809\) | − | 1047.16i | − | 1.29439i | −0.762325 | − | 0.647194i | \(-0.775942\pi\) | ||
0.762325 | − | 0.647194i | \(-0.224058\pi\) | |||||||
\(810\) | −45.8885 | − | 112.923i | −0.0566524 | − | 0.139411i | ||||
\(811\) | −112.206 | + | 112.206i | −0.138356 | + | 0.138356i | −0.772893 | − | 0.634537i | \(-0.781191\pi\) |
0.634537 | + | 0.772893i | \(0.281191\pi\) | |||||||
\(812\) | 128.364 | + | 1.72334i | 0.158083 | + | 0.00212234i | ||||
\(813\) | −212.432 | + | 212.432i | −0.261294 | + | 0.261294i | ||||
\(814\) | −62.2672 | − | 26.2830i | −0.0764954 | − | 0.0322887i | ||||
\(815\) | 1349.20i | 1.65546i | ||||||||
\(816\) | 94.8720 | − | 89.9096i | 0.116265 | − | 0.110183i | ||||
\(817\) | −24.3176 | −0.0297645 | ||||||||
\(818\) | 34.5714 | − | 81.9035i | 0.0422633 | − | 0.100126i | ||||
\(819\) | −535.643 | − | 535.643i | −0.654020 | − | 0.654020i | ||||
\(820\) | 626.039 | + | 8.40484i | 0.763463 | + | 0.0102498i | ||||
\(821\) | −7.63080 | − | 7.63080i | −0.00929452 | − | 0.00929452i | 0.702444 | − | 0.711739i | \(-0.252092\pi\) |
−0.711739 | + | 0.702444i | \(0.752092\pi\) | |||||||
\(822\) | 430.128 | − | 174.792i | 0.523271 | − | 0.212642i | ||||
\(823\) | 1316.28 | 1.59937 | 0.799687 | − | 0.600417i | \(-0.204999\pi\) | ||||
0.799687 | + | 0.600417i | \(0.204999\pi\) | |||||||
\(824\) | −504.640 | − | 1291.26i | −0.612427 | − | 1.56706i | ||||
\(825\) | 26.8798i | 0.0325816i | ||||||||
\(826\) | 2161.54 | − | 878.387i | 2.61687 | − | 1.06342i | ||||
\(827\) | 341.515 | − | 341.515i | 0.412957 | − | 0.412957i | −0.469810 | − | 0.882767i | \(-0.655678\pi\) |
0.882767 | + | 0.469810i | \(0.155678\pi\) | |||||||
\(828\) | 108.224 | − | 105.356i | 0.130705 | − | 0.127242i | ||||
\(829\) | −621.672 | + | 621.672i | −0.749905 | + | 0.749905i | −0.974461 | − | 0.224556i | \(-0.927907\pi\) |
0.224556 | + | 0.974461i | \(0.427907\pi\) | |||||||
\(830\) | 434.751 | − | 1029.97i | 0.523796 | − | 1.24093i | ||||
\(831\) | 94.0725i | 0.113204i | ||||||||
\(832\) | −62.9859 | + | 1563.10i | −0.0757042 | + | 1.87872i | ||||
\(833\) | 272.208 | 0.326781 | ||||||||
\(834\) | 103.265 | + | 43.5882i | 0.123819 | + | 0.0522640i | ||||
\(835\) | 516.412 | + | 516.412i | 0.618457 | + | 0.618457i | ||||
\(836\) | 7.44640 | + | 7.64906i | 0.00890717 | + | 0.00914959i | ||||
\(837\) | −103.070 | − | 103.070i | −0.123142 | − | 0.123142i | ||||
\(838\) | −15.9708 | − | 39.3010i | −0.0190582 | − | 0.0468986i | ||||
\(839\) | 1440.49 | 1.71692 | 0.858459 | − | 0.512883i | \(-0.171422\pi\) | ||||
0.858459 | + | 0.512883i | \(0.171422\pi\) | |||||||
\(840\) | −902.804 | + | 352.828i | −1.07477 | + | 0.420033i | ||||
\(841\) | 831.348i | 0.988523i | ||||||||
\(842\) | −333.192 | − | 819.921i | −0.395715 | − | 0.973778i | ||||
\(843\) | 273.820 | − | 273.820i | 0.324816 | − | 0.324816i | ||||
\(844\) | 1.01863 | − | 75.8734i | 0.00120691 | − | 0.0898974i | ||||
\(845\) | −2051.65 | + | 2051.65i | −2.42798 | + | 2.42798i | ||||
\(846\) | 215.634 | + | 91.0191i | 0.254887 | + | 0.107588i | ||||
\(847\) | − | 1244.24i | − | 1.46900i | ||||||
\(848\) | 459.484 | − | 435.450i | 0.541845 | − | 0.513503i | ||||
\(849\) | −606.873 | −0.714809 | ||||||||
\(850\) | 76.5043 | − | 181.247i | 0.0900051 | − | 0.213232i | ||||
\(851\) | 404.186 | + | 404.186i | 0.474954 | + | 0.474954i | ||||
\(852\) | 4.89772 | − | 364.810i | 0.00574850 | − | 0.428180i | ||||
\(853\) | −625.193 | − | 625.193i | −0.732934 | − | 0.732934i | 0.238266 | − | 0.971200i | \(-0.423421\pi\) |
−0.971200 | + | 0.238266i | \(0.923421\pi\) | |||||||
\(854\) | −995.482 | + | 404.535i | −1.16567 | + | 0.473695i | ||||
\(855\) | −72.8599 | −0.0852163 | ||||||||
\(856\) | 264.000 | + | 115.634i | 0.308411 | + | 0.135086i | ||||
\(857\) | − | 1105.18i | − | 1.28959i | −0.764356 | − | 0.644794i | \(-0.776943\pi\) | ||
0.764356 | − | 0.644794i | \(-0.223057\pi\) | |||||||
\(858\) | −58.3714 | + | 23.7205i | −0.0680319 | + | 0.0276462i | ||||
\(859\) | 379.841 | − | 379.841i | 0.442190 | − | 0.442190i | −0.450558 | − | 0.892747i | \(-0.648775\pi\) |
0.892747 | + | 0.450558i | \(0.148775\pi\) | |||||||
\(860\) | −128.110 | − | 131.597i | −0.148965 | − | 0.153019i | ||||
\(861\) | −292.442 | + | 292.442i | −0.339654 | + | 0.339654i | ||||
\(862\) | −414.075 | + | 980.989i | −0.480365 | + | 1.13804i | ||||
\(863\) | 381.969i | 0.442606i | 0.975205 | + | 0.221303i | \(0.0710311\pi\) | ||||
−0.975205 | + | 0.221303i | \(0.928969\pi\) | |||||||
\(864\) | −58.4408 | − | 155.668i | −0.0676398 | − | 0.180172i | ||||
\(865\) | 516.031 | 0.596567 | ||||||||
\(866\) | −1019.78 | − | 430.448i | −1.17757 | − | 0.497053i | ||||
\(867\) | 326.706 | + | 326.706i | 0.376824 | + | 0.376824i | ||||
\(868\) | −830.567 | + | 808.561i | −0.956874 | + | 0.931521i | ||||
\(869\) | 29.7076 | + | 29.7076i | 0.0341859 | + | 0.0341859i | ||||
\(870\) | 27.4367 | + | 67.5164i | 0.0315365 | + | 0.0776051i | ||||
\(871\) | −379.794 | −0.436044 | ||||||||
\(872\) | −342.613 | − | 150.067i | −0.392904 | − | 0.172095i | ||||
\(873\) | 182.824i | 0.209420i | ||||||||
\(874\) | −33.9890 | − | 83.6401i | −0.0388890 | − | 0.0956981i | ||||
\(875\) | 204.994 | − | 204.994i | 0.234279 | − | 0.234279i | ||||
\(876\) | 469.732 | + | 6.30634i | 0.536224 | + | 0.00719902i | ||||
\(877\) | 638.602 | − | 638.602i | 0.728166 | − | 0.728166i | −0.242088 | − | 0.970254i | \(-0.577832\pi\) |
0.970254 | + | 0.242088i | \(0.0778323\pi\) | |||||||
\(878\) | −1189.00 | − | 501.877i | −1.35421 | − | 0.571614i | ||||
\(879\) | 250.489i | 0.284971i | ||||||||
\(880\) | −2.16439 | + | 80.5935i | −0.00245954 | + | 0.0915835i | ||||
\(881\) | −1362.97 | −1.54707 | −0.773533 | − | 0.633756i | \(-0.781512\pi\) | ||||
−0.773533 | + | 0.633756i | \(0.781512\pi\) | |||||||
\(882\) | 134.662 | − | 319.028i | 0.152678 | − | 0.361710i | ||||
\(883\) | −897.988 | − | 897.988i | −1.01697 | − | 1.01697i | −0.999853 | − | 0.0171209i | \(-0.994550\pi\) |
−0.0171209 | − | 0.999853i | \(-0.505450\pi\) | |||||||
\(884\) | 461.104 | + | 6.19051i | 0.521610 | + | 0.00700284i | ||||
\(885\) | 936.598 | + | 936.598i | 1.05830 | + | 1.05830i | ||||
\(886\) | −827.587 | + | 336.308i | −0.934071 | + | 0.379580i | ||||
\(887\) | 1343.56 | 1.51472 | 0.757359 | − | 0.652998i | \(-0.226489\pi\) | ||||
0.757359 | + | 0.652998i | \(0.226489\pi\) | |||||||
\(888\) | 586.110 | − | 229.060i | 0.660034 | − | 0.257950i | ||||
\(889\) | − | 421.947i | − | 0.474631i | ||||||
\(890\) | 1650.75 | − | 670.818i | 1.85478 | − | 0.753728i | ||||
\(891\) | 4.73552 | − | 4.73552i | 0.00531483 | − | 0.00531483i | ||||
\(892\) | −847.174 | + | 824.728i | −0.949746 | + | 0.924583i | ||||
\(893\) | 98.9295 | − | 98.9295i | 0.110783 | − | 0.110783i | ||||
\(894\) | 17.7579 | − | 42.0703i | 0.0198634 | − | 0.0470585i | ||||
\(895\) | − | 997.676i | − | 1.11472i | ||||||
\(896\) | −1244.04 | + | 448.075i | −1.38844 | + | 0.500084i | ||||
\(897\) | 532.870 | 0.594058 | ||||||||
\(898\) | −402.767 | − | 170.008i | −0.448516 | − | 0.189318i | ||||
\(899\) | 61.6257 | + | 61.6257i | 0.0685491 | + | 0.0685491i | ||||
\(900\) | −174.575 | − | 179.326i | −0.193972 | − | 0.199252i | ||||
\(901\) | −131.952 | − | 131.952i | −0.146451 | − | 0.146451i | ||||
\(902\) | 12.9506 | + | 31.8688i | 0.0143576 | + | 0.0353312i | ||||
\(903\) | 121.317 | 0.134349 | ||||||||
\(904\) | −408.146 | − | 1044.35i | −0.451488 | − | 1.15525i | ||||
\(905\) | 1967.97i | 2.17456i | ||||||||
\(906\) | −65.9118 | − | 162.196i | −0.0727503 | − | 0.179024i | ||||
\(907\) | −671.651 | + | 671.651i | −0.740519 | + | 0.740519i | −0.972678 | − | 0.232159i | \(-0.925421\pi\) |
0.232159 | + | 0.972678i | \(0.425421\pi\) | |||||||
\(908\) | 7.37170 | − | 549.085i | 0.00811861 | − | 0.604720i | ||||
\(909\) | −329.957 | + | 329.957i | −0.362989 | + | 0.362989i | ||||
\(910\) | −3150.59 | − | 1329.86i | −3.46219 | − | 1.46139i | ||||
\(911\) | 770.729i | 0.846025i | 0.906124 | + | 0.423012i | \(0.139027\pi\) | ||||
−0.906124 | + | 0.423012i | \(0.860973\pi\) | |||||||
\(912\) | −99.3561 | − | 2.66828i | −0.108943 | − | 0.00292574i | ||||
\(913\) | 61.4246 | 0.0672778 | ||||||||
\(914\) | −230.651 | + | 546.438i | −0.252354 | + | 0.597853i | ||||
\(915\) | −431.344 | − | 431.344i | −0.471414 | − | 0.471414i | ||||
\(916\) | −2.60140 | + | 193.767i | −0.00283995 | + | 0.211536i | ||||
\(917\) | 774.942 | + | 774.942i | 0.845084 | + | 0.845084i | ||||
\(918\) | −45.4091 | + | 18.4530i | −0.0494652 | + | 0.0201013i | ||||
\(919\) | −1153.98 | −1.25569 | −0.627843 | − | 0.778340i | \(-0.716062\pi\) | ||||
−0.627843 | + | 0.778340i | \(0.716062\pi\) | |||||||
\(920\) | 273.565 | − | 624.567i | 0.297353 | − | 0.678877i | ||||
\(921\) | − | 338.745i | − | 0.367801i | ||||||
\(922\) | −309.358 | + | 125.714i | −0.335529 | + | 0.136350i | ||||
\(923\) | 910.182 | − | 910.182i | 0.986112 | − | 0.986112i | ||||
\(924\) | −37.1490 | − | 38.1601i | −0.0402045 | − | 0.0412988i | ||||
\(925\) | 669.736 | − | 669.736i | 0.724039 | − | 0.724039i | ||||
\(926\) | −318.453 | + | 754.450i | −0.343902 | + | 0.814741i | ||||
\(927\) | 519.886i | 0.560826i | ||||||||
\(928\) | 34.9418 | + | 93.0742i | 0.0376528 | + | 0.100296i | ||||
\(929\) | −652.736 | −0.702622 | −0.351311 | − | 0.936259i | \(-0.614264\pi\) | ||||
−0.351311 | + | 0.936259i | \(0.614264\pi\) | |||||||
\(930\) | −606.247 | − | 255.897i | −0.651879 | − | 0.275158i | ||||
\(931\) | −146.365 | − | 146.365i | −0.157213 | − | 0.157213i | ||||
\(932\) | −180.044 | + | 175.274i | −0.193180 | + | 0.188062i | ||||
\(933\) | −252.039 | − | 252.039i | −0.270139 | − | 0.270139i | ||||
\(934\) | −526.838 | − | 1296.45i | −0.564067 | − | 1.38806i | ||||
\(935\) | 23.7660 | 0.0254182 | ||||||||
\(936\) | 235.364 | − | 537.352i | 0.251457 | − | 0.574094i | ||||
\(937\) | − | 644.074i | − | 0.687378i | −0.939083 | − | 0.343689i | \(-0.888323\pi\) | ||
0.939083 | − | 0.343689i | \(-0.111677\pi\) | |||||||
\(938\) | −120.855 | − | 297.401i | −0.128843 | − | 0.317059i | ||||
\(939\) | −274.172 | + | 274.172i | −0.291983 | + | 0.291983i | ||||
\(940\) | 1056.54 | + | 14.1845i | 1.12398 | + | 0.0150899i | ||||
\(941\) | 171.348 | − | 171.348i | 0.182092 | − | 0.182092i | −0.610175 | − | 0.792267i | \(-0.708901\pi\) |
0.792267 | + | 0.610175i | \(0.208901\pi\) | |||||||
\(942\) | −432.763 | − | 182.669i | −0.459409 | − | 0.193916i | ||||
\(943\) | − | 290.929i | − | 0.308514i | ||||||
\(944\) | 1242.90 | + | 1311.50i | 1.31663 | + | 1.38930i | ||||
\(945\) | 363.487 | 0.384643 | ||||||||
\(946\) | 3.92402 | − | 9.29644i | 0.00414801 | − | 0.00982710i | ||||
\(947\) | 731.249 | + | 731.249i | 0.772174 | + | 0.772174i | 0.978486 | − | 0.206312i | \(-0.0661461\pi\) |
−0.206312 | + | 0.978486i | \(0.566146\pi\) | |||||||
\(948\) | −391.132 | − | 5.25111i | −0.412587 | − | 0.00553915i | ||||
\(949\) | 1171.96 | + | 1171.96i | 1.23494 | + | 1.23494i | ||||
\(950\) | −138.592 | + | 56.3197i | −0.145886 | + | 0.0592839i | ||||
\(951\) | 432.305 | 0.454580 | ||||||||
\(952\) | 141.881 | + | 363.041i | 0.149035 | + | 0.381345i | ||||
\(953\) | − | 1745.08i | − | 1.83115i | −0.402152 | − | 0.915573i | \(-0.631738\pi\) | ||
0.402152 | − | 0.915573i | \(-0.368262\pi\) | |||||||
\(954\) | −219.925 | + | 89.3714i | −0.230530 | + | 0.0936807i | ||||
\(955\) | −1188.72 | + | 1188.72i | −1.24473 | + | 1.24473i | ||||
\(956\) | −1020.09 | + | 993.060i | −1.06704 | + | 1.03877i | ||||
\(957\) | −2.83137 | + | 2.83137i | −0.00295859 | + | 0.00295859i | ||||
\(958\) | 434.612 | − | 1029.64i | 0.453666 | − | 1.07479i | ||||
\(959\) | 1384.54i | 1.44374i | ||||||||
\(960\) | −508.988 | − | 551.730i | −0.530196 | − | 0.574719i | ||||
\(961\) | 174.077 | 0.181142 | ||||||||
\(962\) | 2045.40 | + | 863.362i | 2.12619 | + | 0.897465i | ||||
\(963\) | −76.4241 | − | 76.4241i | −0.0793604 | − | 0.0793604i | ||||
\(964\) | 184.864 | + | 189.895i | 0.191767 | + | 0.196986i | ||||
\(965\) | 622.102 | + | 622.102i | 0.644665 | + | 0.644665i | ||||
\(966\) | 169.566 | + | 417.269i | 0.175534 | + | 0.431955i | ||||
\(967\) | 904.237 | 0.935095 | 0.467548 | − | 0.883968i | \(-0.345138\pi\) | ||||
0.467548 | + | 0.883968i | \(0.345138\pi\) | |||||||
\(968\) | 897.467 | − | 350.743i | 0.927136 | − | 0.362337i | ||||
\(969\) | 29.2989i | 0.0302362i | ||||||||
\(970\) | 310.723 | + | 764.628i | 0.320333 | + | 0.788276i | ||||
\(971\) | −1010.37 | + | 1010.37i | −1.04055 | + | 1.04055i | −0.0414029 | + | 0.999143i | \(0.513183\pi\) |
−0.999143 | + | 0.0414029i | \(0.986817\pi\) | |||||||
\(972\) | −0.837051 | + | 62.3482i | −0.000861163 | + | 0.0641442i | ||||
\(973\) | −236.354 | + | 236.354i | −0.242913 | + | 0.242913i | ||||
\(974\) | 665.775 | + | 281.023i | 0.683547 | + | 0.288525i | ||||
\(975\) | − | 882.966i | − | 0.905606i | ||||||
\(976\) | −572.410 | − | 604.003i | −0.586485 | − | 0.618856i | ||||
\(977\) | −396.922 | −0.406266 | −0.203133 | − | 0.979151i | \(-0.565112\pi\) | ||||
−0.203133 | + | 0.979151i | \(0.565112\pi\) | |||||||
\(978\) | 268.399 | − | 635.867i | 0.274437 | − | 0.650171i | ||||
\(979\) | 69.2259 | + | 69.2259i | 0.0707108 | + | 0.0707108i | ||||
\(980\) | 20.9859 | − | 1563.14i | 0.0214142 | − | 1.59505i | ||||
\(981\) | 99.1815 | + | 99.1815i | 0.101102 | + | 0.101102i | ||||
\(982\) | 1281.28 | − | 520.675i | 1.30476 | − | 0.530218i | ||||
\(983\) | 1672.52 | 1.70145 | 0.850724 | − | 0.525612i | \(-0.176164\pi\) | ||||
0.850724 | + | 0.525612i | \(0.176164\pi\) | |||||||
\(984\) | −293.375 | − | 128.501i | −0.298146 | − | 0.130590i | ||||
\(985\) | − | 2269.66i | − | 2.30423i | ||||||
\(986\) | 27.1501 | − | 11.0330i | 0.0275356 | − | 0.0111897i | ||||
\(987\) | −493.545 | + | 493.545i | −0.500045 | + | 0.500045i | ||||
\(988\) | −244.604 | − | 251.262i | −0.247575 | − | 0.254313i | ||||
\(989\) | −60.3446 | + | 60.3446i | −0.0610157 | + | 0.0610157i | ||||
\(990\) | 11.7571 | − | 27.8538i | 0.0118758 | − | 0.0281351i | ||||
\(991\) | 775.801i | 0.782847i | 0.920211 | + | 0.391423i | \(0.128017\pi\) | ||||
−0.920211 | + | 0.391423i | \(0.871983\pi\) | |||||||
\(992\) | −817.343 | − | 371.158i | −0.823935 | − | 0.374151i | ||||
\(993\) | 450.556 | 0.453732 | ||||||||
\(994\) | 1002.36 | + | 423.094i | 1.00841 | + | 0.425648i | ||||
\(995\) | −1180.35 | − | 1180.35i | −1.18629 | − | 1.18629i | ||||
\(996\) | −409.789 | + | 398.932i | −0.411435 | + | 0.400534i | ||||
\(997\) | 201.495 | + | 201.495i | 0.202101 | + | 0.202101i | 0.800900 | − | 0.598799i | \(-0.204355\pi\) |
−0.598799 | + | 0.800900i | \(0.704355\pi\) | |||||||
\(998\) | 109.566 | + | 269.620i | 0.109786 | + | 0.270161i | ||||
\(999\) | −235.980 | −0.236216 |
(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 | 48.3.l.a.43.1 | yes | 16 | |
3.2 | odd | 2 | 144.3.m.c.91.8 | 16 | |||
4.3 | odd | 2 | 192.3.l.a.79.5 | 16 | |||
8.3 | odd | 2 | 384.3.l.b.31.4 | 16 | |||
8.5 | even | 2 | 384.3.l.a.31.8 | 16 | |||
12.11 | even | 2 | 576.3.m.c.271.7 | 16 | |||
16.3 | odd | 4 | inner | 48.3.l.a.19.1 | ✓ | 16 | |
16.5 | even | 4 | 384.3.l.b.223.4 | 16 | |||
16.11 | odd | 4 | 384.3.l.a.223.8 | 16 | |||
16.13 | even | 4 | 192.3.l.a.175.5 | 16 | |||
24.5 | odd | 2 | 1152.3.m.f.415.2 | 16 | |||
24.11 | even | 2 | 1152.3.m.c.415.2 | 16 | |||
48.5 | odd | 4 | 1152.3.m.c.991.2 | 16 | |||
48.11 | even | 4 | 1152.3.m.f.991.2 | 16 | |||
48.29 | odd | 4 | 576.3.m.c.559.7 | 16 | |||
48.35 | even | 4 | 144.3.m.c.19.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.1 | ✓ | 16 | 16.3 | odd | 4 | inner | |
48.3.l.a.43.1 | yes | 16 | 1.1 | even | 1 | trivial | |
144.3.m.c.19.8 | 16 | 48.35 | even | 4 | |||
144.3.m.c.91.8 | 16 | 3.2 | odd | 2 | |||
192.3.l.a.79.5 | 16 | 4.3 | odd | 2 | |||
192.3.l.a.175.5 | 16 | 16.13 | even | 4 | |||
384.3.l.a.31.8 | 16 | 8.5 | even | 2 | |||
384.3.l.a.223.8 | 16 | 16.11 | odd | 4 | |||
384.3.l.b.31.4 | 16 | 8.3 | odd | 2 | |||
384.3.l.b.223.4 | 16 | 16.5 | even | 4 | |||
576.3.m.c.271.7 | 16 | 12.11 | even | 2 | |||
576.3.m.c.559.7 | 16 | 48.29 | odd | 4 | |||
1152.3.m.c.415.2 | 16 | 24.11 | even | 2 | |||
1152.3.m.c.991.2 | 16 | 48.5 | odd | 4 | |||
1152.3.m.f.415.2 | 16 | 24.5 | odd | 2 | |||
1152.3.m.f.991.2 | 16 | 48.11 | even | 4 |