Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(53,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([0, 10, 10, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.bp (of order \(20\), degree \(8\), 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: | \(4.79102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{20})\) |
Coefficient field: | 16.0.6879707136000000000000.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 9x^{12} + 81x^{8} - 729x^{4} + 6561 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{20}]$ |
Embedding invariants
Embedding label | 533.2 | ||
Root | \(0.786335 - 1.54327i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.533 |
Dual form | 600.2.bp.b.197.2 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{20}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.26007 | − | 0.642040i | −0.891007 | − | 0.453990i | ||||
\(3\) | 1.71073 | + | 0.270952i | 0.987688 | + | 0.156434i | ||||
\(4\) | 1.17557 | + | 1.61803i | 0.587785 | + | 0.809017i | ||||
\(5\) | −2.18531 | + | 0.473739i | −0.977299 | + | 0.211862i | ||||
\(6\) | −1.98168 | − | 1.43977i | −0.809017 | − | 0.587785i | ||||
\(7\) | 1.93871 | − | 1.93871i | 0.732762 | − | 0.732762i | −0.238404 | − | 0.971166i | \(-0.576624\pi\) |
0.971166 | + | 0.238404i | \(0.0766241\pi\) | |||||||
\(8\) | −0.442463 | − | 2.79360i | −0.156434 | − | 0.987688i | ||||
\(9\) | 2.85317 | + | 0.927051i | 0.951057 | + | 0.309017i | ||||
\(10\) | 3.05781 | + | 0.806108i | 0.966964 | + | 0.254914i | ||||
\(11\) | 1.74740 | + | 5.37793i | 0.526860 | + | 1.62151i | 0.760608 | + | 0.649211i | \(0.224901\pi\) |
−0.233748 | + | 0.972297i | \(0.575099\pi\) | |||||||
\(12\) | 1.57267 | + | 3.08654i | 0.453990 | + | 0.891007i | ||||
\(13\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(14\) | −3.68764 | + | 1.19819i | −0.985563 | + | 0.320229i | ||||
\(15\) | −3.86682 | + | 0.218323i | −0.998410 | + | 0.0563708i | ||||
\(16\) | −1.23607 | + | 3.80423i | −0.309017 | + | 0.951057i | ||||
\(17\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.707107 | − | 0.707107i | ||||
\(19\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(20\) | −3.33551 | − | 2.97899i | −0.745843 | − | 0.666122i | ||||
\(21\) | 3.84189 | − | 2.79130i | 0.838370 | − | 0.609112i | ||||
\(22\) | 1.25100 | − | 7.89849i | 0.266714 | − | 1.68396i | ||||
\(23\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(24\) | − | 4.89898i | − | 1.00000i | ||||||
\(25\) | 4.55114 | − | 2.07053i | 0.910229 | − | 0.414106i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.62981 | + | 2.35900i | 0.891007 | + | 0.453990i | ||||
\(28\) | 5.41598 | + | 0.857807i | 1.02352 | + | 0.162110i | ||||
\(29\) | −3.14375 | − | 4.32700i | −0.583780 | − | 0.803504i | 0.410323 | − | 0.911940i | \(-0.365416\pi\) |
−0.994103 | + | 0.108436i | \(0.965416\pi\) | |||||||
\(30\) | 5.01266 | + | 2.20755i | 0.915182 | + | 0.403042i | ||||
\(31\) | 7.96171 | + | 5.78452i | 1.42996 | + | 1.03893i | 0.990023 | + | 0.140904i | \(0.0450008\pi\) |
0.439941 | + | 0.898027i | \(0.354999\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.707107 | − | 0.707107i | ||||
\(33\) | 1.53215 | + | 9.67364i | 0.266714 | + | 1.68396i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.31823 | + | 5.15511i | −0.560883 | + | 0.871373i | ||||
\(36\) | 1.85410 | + | 5.70634i | 0.309017 | + | 0.951057i | ||||
\(37\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.29036 | + | 5.89527i | 0.362137 | + | 0.932125i | ||||
\(41\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(42\) | −6.63319 | + | 1.05059i | −1.02352 | + | 0.162110i | ||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | −6.64749 | + | 9.14949i | −1.00215 | + | 1.37934i | ||||
\(45\) | −6.67423 | − | 0.674235i | −0.994936 | − | 0.100509i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(48\) | −3.14534 | + | 6.17307i | −0.453990 | + | 0.891007i | ||||
\(49\) | − | 0.517171i | − | 0.0738815i | ||||||
\(50\) | −7.06414 | − | 0.312992i | −0.999020 | − | 0.0442638i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14.3417 | + | 2.27150i | 1.96998 | + | 0.312014i | 0.996546 | + | 0.0830438i | \(0.0264641\pi\) |
0.973433 | + | 0.228970i | \(0.0735359\pi\) | |||||||
\(54\) | −4.31932 | − | 5.94504i | −0.587785 | − | 0.809017i | ||||
\(55\) | −6.36634 | − | 10.9246i | −0.858437 | − | 1.47308i | ||||
\(56\) | −6.27379 | − | 4.55817i | −0.838370 | − | 0.609112i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.18325 | + | 7.47075i | 0.155368 | + | 0.980958i | ||||
\(59\) | 5.10012 | + | 1.65713i | 0.663979 | + | 0.215740i | 0.621568 | − | 0.783360i | \(-0.286496\pi\) |
0.0424110 | + | 0.999100i | \(0.486496\pi\) | |||||||
\(60\) | −4.89898 | − | 6.00000i | −0.632456 | − | 0.774597i | ||||
\(61\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(62\) | −6.31845 | − | 12.4006i | −0.802443 | − | 1.57488i | ||||
\(63\) | 7.32874 | − | 3.73418i | 0.923335 | − | 0.470462i | ||||
\(64\) | −7.60845 | + | 2.47214i | −0.951057 | + | 0.309017i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.28023 | − | 13.1732i | 0.526860 | − | 1.62151i | ||||
\(67\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.49100 | − | 4.36539i | 0.895346 | − | 0.521763i | ||||
\(71\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(72\) | 1.32739 | − | 8.38081i | 0.156434 | − | 0.987688i | ||||
\(73\) | −7.63962 | + | 14.9936i | −0.894149 | + | 1.75487i | −0.292145 | + | 0.956374i | \(0.594369\pi\) |
−0.602004 | + | 0.798493i | \(0.705631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.34678 | − | 2.30897i | 0.963803 | − | 0.266617i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.8139 | + | 7.03855i | 1.57424 | + | 0.802117i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.25966 | − | 11.3684i | −0.929284 | − | 1.27905i | −0.960138 | − | 0.279526i | \(-0.909823\pi\) |
0.0308541 | − | 0.999524i | \(-0.490177\pi\) | |||||||
\(80\) | 0.898979 | − | 8.89898i | 0.100509 | − | 0.994936i | ||||
\(81\) | 7.28115 | + | 5.29007i | 0.809017 | + | 0.587785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.876698 | − | 5.53525i | −0.0962301 | − | 0.607573i | −0.987925 | − | 0.154935i | \(-0.950483\pi\) |
0.891695 | − | 0.452638i | \(-0.149517\pi\) | |||||||
\(84\) | 9.03284 | + | 2.93495i | 0.985563 | + | 0.320229i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.20569 | − | 8.25412i | −0.450897 | − | 0.884935i | ||||
\(88\) | 14.2507 | − | 7.26108i | 1.51913 | − | 0.774033i | ||||
\(89\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(90\) | 7.97714 | + | 5.13471i | 0.840864 | + | 0.541246i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.0530 | + | 12.0530i | 1.24983 | + | 1.24983i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.92672 | − | 5.75910i | 0.809017 | − | 0.587785i | ||||
\(97\) | 2.97879 | − | 18.8074i | 0.302451 | − | 1.90960i | −0.101535 | − | 0.994832i | \(-0.532375\pi\) |
0.403985 | − | 0.914766i | \(-0.367625\pi\) | |||||||
\(98\) | −0.332044 | + | 0.651673i | −0.0335415 | + | 0.0658289i | ||||
\(99\) | 16.9641i | 1.70495i | ||||||||
\(100\) | 8.70038 | + | 4.92985i | 0.870038 | + | 0.492985i | ||||
\(101\) | −19.2137 | −1.91183 | −0.955917 | − | 0.293636i | \(-0.905135\pi\) | ||||
−0.955917 | + | 0.293636i | \(0.905135\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.1742 | − | 1.92820i | −1.19956 | − | 0.189991i | −0.475489 | − | 0.879721i | \(-0.657729\pi\) |
−0.724066 | + | 0.689730i | \(0.757729\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.07338 | + | 7.91991i | −0.690291 | + | 0.772904i | ||||
\(106\) | −16.6132 | − | 12.0702i | −1.61361 | − | 1.17236i | ||||
\(107\) | 14.1202 | − | 14.1202i | 1.36505 | − | 1.36505i | 0.497694 | − | 0.867353i | \(-0.334180\pi\) |
0.867353 | − | 0.497694i | \(-0.165820\pi\) | |||||||
\(108\) | 1.62571 | + | 10.2644i | 0.156434 | + | 0.987688i | ||||
\(109\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(110\) | 1.00801 | + | 17.8533i | 0.0961096 | + | 1.70224i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.97891 | + | 9.77165i | 0.470462 | + | 0.923335i | ||||
\(113\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.30554 | − | 10.1734i | 0.306911 | − | 0.944576i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.36258 | − | 5.36258i | −0.493666 | − | 0.493666i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.32084 | + | 10.7058i | 0.211862 | + | 0.977299i | ||||
\(121\) | −16.9696 | + | 12.3291i | −1.54269 | + | 1.12083i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 19.6824i | 1.76753i | ||||||||
\(125\) | −8.96476 | + | 6.68080i | −0.801832 | + | 0.597549i | ||||
\(126\) | −11.6322 | −1.03628 | ||||||||
\(127\) | −15.4840 | − | 7.88947i | −1.37398 | − | 0.700077i | −0.397887 | − | 0.917434i | \(-0.630256\pi\) |
−0.976092 | + | 0.217357i | \(0.930256\pi\) | |||||||
\(128\) | 11.1744 | + | 1.76985i | 0.987688 | + | 0.156434i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.9260 | − | 10.8443i | −1.30409 | − | 0.947474i | −0.304100 | − | 0.952640i | \(-0.598356\pi\) |
−0.999987 | + | 0.00516600i | \(0.998356\pi\) | |||||||
\(132\) | −13.8511 | + | 13.8511i | −1.20559 | + | 1.20559i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.2351 | − | 2.96183i | −0.966964 | − | 0.254914i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(140\) | −12.2420 | + | 0.691188i | −1.03463 | + | 0.0584161i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.05342 | + | 9.70820i | −0.587785 | + | 0.809017i | ||||
\(145\) | 8.91993 | + | 7.96652i | 0.740760 | + | 0.661583i | ||||
\(146\) | 19.2530 | − | 13.9881i | 1.59339 | − | 1.15766i | ||||
\(147\) | 0.140129 | − | 0.884738i | 0.0115576 | − | 0.0729719i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.48854i | 0.695408i | 0.937604 | + | 0.347704i | \(0.113039\pi\) | ||||
−0.937604 | + | 0.347704i | \(0.886961\pi\) | |||||||
\(150\) | −12.0000 | − | 2.44949i | −0.979796 | − | 0.200000i | ||||
\(151\) | −16.0158 | −1.30335 | −0.651673 | − | 0.758500i | \(-0.725932\pi\) | ||||
−0.651673 | + | 0.758500i | \(0.725932\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.8875 | − | 17.7382i | −1.03851 | − | 1.42938i | ||||
\(155\) | −20.1391 | − | 8.86918i | −1.61761 | − | 0.712390i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 3.10879 | + | 19.6281i | 0.247322 | + | 1.56153i | ||||
\(159\) | 23.9192 | + | 7.77182i | 1.89692 | + | 0.616345i | ||||
\(160\) | −6.84628 | + | 10.6362i | −0.541246 | + | 0.840864i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.77836 | − | 11.3407i | −0.453990 | − | 0.891007i | ||||
\(163\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.93101 | − | 20.4140i | −0.617428 | − | 1.58923i | ||||
\(166\) | −2.44915 | + | 7.53770i | −0.190091 | + | 0.585039i | ||||
\(167\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(168\) | −9.49769 | − | 9.49769i | −0.732762 | − | 0.732762i | ||||
\(169\) | 7.64121 | − | 10.5172i | 0.587785 | − | 0.809017i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.64993 | − | 5.20079i | 0.201471 | − | 0.395409i | −0.768060 | − | 0.640378i | \(-0.778778\pi\) |
0.969531 | + | 0.244969i | \(0.0787778\pi\) | |||||||
\(174\) | 13.1010i | 0.993186i | ||||||||
\(175\) | 4.80918 | − | 12.8375i | 0.363540 | − | 0.970423i | ||||
\(176\) | −22.6188 | −1.70495 | ||||||||
\(177\) | 8.27590 | + | 4.21678i | 0.622055 | + | 0.316953i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.0373 | − | 17.9443i | −0.974451 | − | 1.34122i | −0.939766 | − | 0.341818i | \(-0.888957\pi\) |
−0.0346846 | − | 0.999398i | \(-0.511043\pi\) | |||||||
\(180\) | −6.75510 | − | 11.5917i | −0.503495 | − | 0.863998i | ||||
\(181\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.44915 | − | 22.9261i | −0.546198 | − | 1.68102i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.5493 | − | 4.40242i | 0.985563 | − | 0.320229i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(192\) | −13.6858 | + | 2.16762i | −0.987688 | + | 0.156434i | ||||
\(193\) | −3.96689 | − | 3.96689i | −0.285543 | − | 0.285543i | 0.549772 | − | 0.835315i | \(-0.314715\pi\) |
−0.835315 | + | 0.549772i | \(0.814715\pi\) | |||||||
\(194\) | −15.8286 | + | 21.7861i | −1.13642 | + | 1.56415i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.836800 | − | 0.607971i | 0.0597714 | − | 0.0434265i | ||||
\(197\) | −4.36924 | + | 27.5863i | −0.311295 | + | 1.96544i | −0.0567145 | + | 0.998390i | \(0.518062\pi\) |
−0.254581 | + | 0.967051i | \(0.581938\pi\) | |||||||
\(198\) | 10.8916 | − | 21.3760i | 0.774033 | − | 1.51913i | ||||
\(199\) | 18.9698i | 1.34473i | 0.740218 | + | 0.672367i | \(0.234722\pi\) | ||||
−0.740218 | + | 0.672367i | \(0.765278\pi\) | |||||||
\(200\) | −7.79796 | − | 11.7980i | −0.551399 | − | 0.834242i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24.2107 | + | 12.3360i | 1.70346 | + | 0.867955i | ||||
\(203\) | −14.4836 | − | 2.29398i | −1.01655 | − | 0.161006i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 14.1024 | + | 10.2460i | 0.982558 | + | 0.713870i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 13.9979 | − | 5.43828i | 0.965945 | − | 0.375277i | ||||
\(211\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(212\) | 13.1843 | + | 25.8756i | 0.905500 | + | 1.77714i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −26.8581 | + | 8.72673i | −1.83598 | + | 0.596547i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.54160 | − | 13.9776i | 0.309017 | − | 0.951057i | ||||
\(217\) | 26.6499 | − | 4.22093i | 1.80911 | − | 0.286535i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.1318 | + | 23.5800i | −1.15766 | + | 1.59339i | ||||
\(220\) | 10.1924 | − | 23.1436i | 0.687168 | − | 1.56034i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.586245 | − | 1.15057i | 0.0392579 | − | 0.0770479i | −0.870544 | − | 0.492090i | \(-0.836233\pi\) |
0.909802 | + | 0.415042i | \(0.136233\pi\) | |||||||
\(224\) | − | 15.5097i | − | 1.03628i | ||||||
\(225\) | 14.9047 | − | 1.68843i | 0.993645 | − | 0.112562i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.1066 | − | 10.7544i | −1.40090 | − | 0.713793i | −0.419856 | − | 0.907591i | \(-0.637919\pi\) |
−0.981041 | + | 0.193798i | \(0.937919\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.7247 | + | 15.7840i | 1.42938 | + | 1.03851i | ||||
\(232\) | −10.6969 | + | 10.6969i | −0.702288 | + | 0.702288i | ||||
\(233\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.31426 | + | 10.2002i | 0.215740 | + | 0.663979i | ||||
\(237\) | −11.0497 | − | 21.6863i | −0.717756 | − | 1.40867i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(240\) | 3.94911 | − | 14.9801i | 0.254914 | − | 0.966964i | ||||
\(241\) | −9.16483 | + | 28.2064i | −0.590358 | + | 1.81694i | −0.0137643 | + | 0.999905i | \(0.504381\pi\) |
−0.576594 | + | 0.817031i | \(0.695619\pi\) | |||||||
\(242\) | 29.2987 | − | 4.64046i | 1.88339 | − | 0.298300i | ||||
\(243\) | 11.0227 | + | 11.0227i | 0.707107 | + | 0.707107i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.245004 | + | 1.13018i | 0.0156527 | + | 0.0722044i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 12.6369 | − | 24.8013i | 0.802443 | − | 1.57488i | ||||
\(249\) | − | 9.70684i | − | 0.615146i | ||||||
\(250\) | 15.5856 | − | 2.66257i | 0.985719 | − | 0.168396i | ||||
\(251\) | 31.6780 | 1.99950 | 0.999749 | − | 0.0224095i | \(-0.00713375\pi\) | ||||
0.999749 | + | 0.0224095i | \(0.00713375\pi\) | |||||||
\(252\) | 14.6575 | + | 7.46836i | 0.923335 | + | 0.470462i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 14.4456 | + | 19.8826i | 0.906396 | + | 1.24755i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9443 | − | 9.40456i | −0.809017 | − | 0.587785i | ||||
\(257\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.95830 | − | 15.2601i | −0.306911 | − | 0.944576i | ||||
\(262\) | 11.8453 | + | 23.2477i | 0.731805 | + | 1.43625i | ||||
\(263\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(264\) | 26.3464 | − | 8.56046i | 1.62151 | − | 0.526860i | ||||
\(265\) | −32.4171 | + | 1.83028i | −1.99136 | + | 0.112434i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.1069 | − | 23.5456i | 1.04302 | − | 1.43560i | 0.148320 | − | 0.988939i | \(-0.452613\pi\) |
0.894704 | − | 0.446660i | \(-0.147387\pi\) | |||||||
\(270\) | 12.2554 | + | 10.9455i | 0.745843 | + | 0.666122i | ||||
\(271\) | 26.0472 | − | 18.9244i | 1.58225 | − | 1.14958i | 0.668202 | − | 0.743980i | \(-0.267064\pi\) |
0.914052 | − | 0.405596i | \(-0.132936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.0878 | + | 20.8577i | 1.15104 | + | 1.25777i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.3536 | + | 23.8851i | 1.03893 | + | 1.42996i | ||||
\(280\) | 15.8695 | + | 6.98888i | 0.948387 | + | 0.417665i | ||||
\(281\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 15.1209 | − | 7.70447i | 0.891007 | − | 0.453990i | ||||
\(289\) | 16.1680 | − | 5.25329i | 0.951057 | − | 0.309017i | ||||
\(290\) | −6.12496 | − | 15.7653i | −0.359670 | − | 0.925773i | ||||
\(291\) | 10.1918 | − | 31.3671i | 0.597454 | − | 1.83877i | ||||
\(292\) | −33.2410 | + | 5.26486i | −1.94528 | + | 0.308103i | ||||
\(293\) | −2.69816 | − | 2.69816i | −0.157628 | − | 0.157628i | 0.623887 | − | 0.781515i | \(-0.285553\pi\) |
−0.781515 | + | 0.623887i | \(0.785553\pi\) | |||||||
\(294\) | −0.744609 | + | 1.02487i | −0.0434265 | + | 0.0597714i | ||||
\(295\) | −11.9304 | − | 1.20521i | −0.694613 | − | 0.0701702i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.59646 | + | 29.0209i | −0.266714 | + | 1.68396i | ||||
\(298\) | 5.44998 | − | 10.6962i | 0.315709 | − | 0.619613i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 13.5482 | + | 10.7910i | 0.782206 | + | 0.623019i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 20.1811 | + | 10.2828i | 1.16129 | + | 0.591706i | ||||
\(303\) | −32.8694 | − | 5.20600i | −1.88830 | − | 0.299077i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | 4.85064 | + | 30.6257i | 0.276391 | + | 1.74506i | ||||
\(309\) | −20.3042 | − | 6.59724i | −1.15507 | − | 0.375304i | ||||
\(310\) | 19.6824 | + | 24.1059i | 1.11789 | + | 1.36913i | ||||
\(311\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.97476 | + | 3.04429i | −0.337713 | + | 0.172074i | −0.614620 | − | 0.788823i | \(-0.710691\pi\) |
0.276907 | + | 0.960897i | \(0.410691\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.2465 | + | 11.6322i | −0.802701 | + | 0.655403i | ||||
\(316\) | 8.68472 | − | 26.7288i | 0.488554 | − | 1.50361i | ||||
\(317\) | −6.77399 | + | 1.07289i | −0.380465 | + | 0.0602598i | −0.343738 | − | 0.939066i | \(-0.611693\pi\) |
−0.0367271 | + | 0.999325i | \(0.511693\pi\) | |||||||
\(318\) | −25.1501 | − | 25.1501i | −1.41035 | − | 1.41035i | ||||
\(319\) | 17.7770 | − | 24.4679i | 0.995318 | − | 1.36994i | ||||
\(320\) | 15.4557 | − | 9.00680i | 0.863998 | − | 0.503495i | ||||
\(321\) | 27.9816 | − | 20.3298i | 1.56178 | − | 1.13470i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 18.0000i | 1.00000i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.11297 | + | 30.8152i | −0.171363 | + | 1.69632i | ||||
\(331\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(332\) | 7.92560 | − | 7.92560i | 0.434974 | − | 0.434974i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.86989 | + | 18.0657i | 0.320229 | + | 0.985563i | ||||
\(337\) | −14.7427 | − | 28.9341i | −0.803085 | − | 1.57614i | −0.817278 | − | 0.576244i | \(-0.804518\pi\) |
0.0141927 | − | 0.999899i | \(-0.495482\pi\) | |||||||
\(338\) | −16.3810 | + | 8.34651i | −0.891007 | + | 0.453990i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.1965 | + | 52.9254i | −0.931243 | + | 2.86607i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.5683 | + | 12.5683i | 0.678625 | + | 0.678625i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.67822 | + | 4.85201i | −0.359023 | + | 0.260846i | ||||
\(347\) | 5.38028 | − | 33.9698i | 0.288829 | − | 1.82359i | −0.235264 | − | 0.971931i | \(-0.575596\pi\) |
0.524093 | − | 0.851661i | \(-0.324404\pi\) | |||||||
\(348\) | 8.41137 | − | 16.5082i | 0.450897 | − | 0.884935i | ||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | −14.3021 | + | 13.0885i | −0.764479 | + | 0.699609i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 28.5013 | + | 14.5222i | 1.51913 | + | 0.774033i | ||||
\(353\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(354\) | −7.72090 | − | 10.6269i | −0.410361 | − | 0.564814i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.90699 | + | 30.9815i | 0.259342 | + | 1.63742i | ||||
\(359\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(360\) | 1.06956 | + | 18.9435i | 0.0563708 | + | 0.998410i | ||||
\(361\) | −5.87132 | − | 18.0701i | −0.309017 | − | 0.951057i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −32.3710 | + | 16.4938i | −1.69903 | + | 0.865701i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.59187 | − | 36.3848i | 0.502061 | − | 1.90447i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.09223 | − | 0.172992i | 0.0570139 | − | 0.00903012i | −0.127862 | − | 0.991792i | \(-0.540812\pi\) |
0.184876 | + | 0.982762i | \(0.440812\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32.2081 | − | 23.4005i | 1.67216 | − | 1.21489i | ||||
\(372\) | −5.33300 | + | 33.6712i | −0.276503 | + | 1.74577i | ||||
\(373\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.1464 | + | 9.00000i | −0.885438 | + | 0.464758i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −19.8996 | − | 3.15178i | −1.02352 | − | 0.162110i | ||||
\(379\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.3511 | − | 17.6921i | −1.24755 | − | 0.906396i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(384\) | 18.6368 | + | 6.05547i | 0.951057 | + | 0.309017i | ||||
\(385\) | −33.5221 | − | 8.83720i | −1.70845 | − | 0.450386i | ||||
\(386\) | 2.45167 | + | 7.54548i | 0.124787 | + | 0.384055i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 33.9327 | − | 17.2896i | 1.72267 | − | 0.877746i | ||||
\(389\) | 7.11475 | − | 2.31172i | 0.360732 | − | 0.117209i | −0.123043 | − | 0.992401i | \(-0.539265\pi\) |
0.483775 | + | 0.875192i | \(0.339265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.44477 | + | 0.228829i | −0.0729719 | + | 0.0115576i | ||||
\(393\) | −22.5959 | − | 22.5959i | −1.13981 | − | 1.13981i | ||||
\(394\) | 23.2171 | − | 31.9555i | 1.16966 | − | 1.60990i | ||||
\(395\) | 23.4356 | + | 20.9306i | 1.17917 | + | 1.05313i | ||||
\(396\) | −27.4485 | + | 19.9425i | −1.37934 | + | 1.00215i | ||||
\(397\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(398\) | 12.1794 | − | 23.9033i | 0.610496 | − | 1.19817i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.25125 | + | 19.8729i | 0.112562 | + | 0.993645i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −22.5871 | − | 31.0884i | −1.12375 | − | 1.54671i | ||||
\(405\) | −18.4177 | − | 8.11106i | −0.915182 | − | 0.403042i | ||||
\(406\) | 16.7776 | + | 12.1896i | 0.832657 | + | 0.604961i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.5633 | + | 6.68141i | 1.01679 | + | 0.330375i | 0.769554 | − | 0.638581i | \(-0.220478\pi\) |
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.1917 | − | 21.9649i | −0.551375 | − | 1.08213i | ||||
\(413\) | 13.1003 | − | 6.67495i | 0.644625 | − | 0.328453i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.53812 | + | 11.6809i | 0.222767 | + | 0.573393i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.9441 | + | 32.9563i | −1.16975 | + | 1.61002i | −0.504447 | + | 0.863443i | \(0.668303\pi\) |
−0.665300 | + | 0.746576i | \(0.731697\pi\) | |||||||
\(420\) | −21.1299 | − | 2.13456i | −1.03103 | − | 0.104156i | ||||
\(421\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 41.0700i | − | 1.99454i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 39.4461 | + | 6.24765i | 1.90670 | + | 0.301992i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(432\) | −14.6969 | + | 14.6969i | −0.707107 | + | 0.707107i | ||||
\(433\) | 6.45700 | + | 40.7679i | 0.310303 | + | 1.95918i | 0.281377 | + | 0.959597i | \(0.409209\pi\) |
0.0289266 | + | 0.999582i | \(0.490791\pi\) | |||||||
\(434\) | −36.2908 | − | 11.7916i | −1.74202 | − | 0.566015i | ||||
\(435\) | 13.1010 | + | 16.0454i | 0.628146 | + | 0.769318i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 36.7266 | − | 18.7132i | 1.75487 | − | 0.894149i | ||||
\(439\) | −12.1635 | + | 3.95216i | −0.580532 | + | 0.188626i | −0.584539 | − | 0.811366i | \(-0.698725\pi\) |
0.00400696 | + | 0.999992i | \(0.498725\pi\) | |||||||
\(440\) | −27.7022 | + | 22.6188i | −1.32065 | + | 1.07831i | ||||
\(441\) | 0.479444 | − | 1.47558i | 0.0228306 | − | 0.0702655i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.5908 | − | 29.5908i | −1.40590 | − | 1.40590i | −0.779501 | − | 0.626401i | \(-0.784527\pi\) |
−0.626401 | − | 0.779501i | \(-0.715473\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.47742 | + | 1.07341i | −0.0699580 | + | 0.0508275i | ||||
\(447\) | −2.29999 | + | 14.5216i | −0.108786 | + | 0.686846i | ||||
\(448\) | −9.95781 | + | 19.5433i | −0.470462 | + | 0.923335i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | −19.8650 | − | 7.44184i | −0.936446 | − | 0.350812i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −27.3986 | − | 4.33951i | −1.28730 | − | 0.203888i | ||||
\(454\) | 19.6912 | + | 27.1026i | 0.924153 | + | 1.27199i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.6507 | − | 17.6507i | 0.825666 | − | 0.825666i | −0.161248 | − | 0.986914i | \(-0.551552\pi\) |
0.986914 | + | 0.161248i | \(0.0515519\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.20086 | + | 12.9289i | 0.195654 | + | 0.602160i | 0.999968 | + | 0.00795653i | \(0.00253267\pi\) |
−0.804315 | + | 0.594204i | \(0.797467\pi\) | |||||||
\(462\) | −17.2409 | − | 33.8371i | −0.802117 | − | 1.57424i | ||||
\(463\) | 5.22480 | − | 2.66217i | 0.242817 | − | 0.123722i | −0.328348 | − | 0.944557i | \(-0.606492\pi\) |
0.571165 | + | 0.820835i | \(0.306492\pi\) | |||||||
\(464\) | 20.3468 | − | 6.61107i | 0.944576 | − | 0.306911i | ||||
\(465\) | −32.0494 | − | 20.6295i | −1.48626 | − | 0.956670i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.3558 | + | 4.49111i | −1.31215 | + | 0.207824i | −0.773010 | − | 0.634393i | \(-0.781250\pi\) |
−0.539138 | + | 0.842217i | \(0.681250\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.37275 | − | 14.9809i | 0.109214 | − | 0.689553i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 34.4206i | 1.58099i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 38.8134 | + | 19.7764i | 1.77714 | + | 0.905500i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(480\) | −14.5940 | + | 16.3406i | −0.666122 | + | 0.745843i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 29.6580 | − | 29.6580i | 1.35088 | − | 1.35088i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −39.8979 | − | 12.9636i | −1.81354 | − | 0.589255i | ||||
\(485\) | 2.40020 | + | 42.5110i | 0.108987 | + | 1.93033i | ||||
\(486\) | −6.81241 | − | 20.9664i | −0.309017 | − | 0.951057i | ||||
\(487\) | 9.89646 | + | 19.4229i | 0.448451 | + | 0.880135i | 0.998973 | + | 0.0453143i | \(0.0144289\pi\) |
−0.550521 | + | 0.834821i | \(0.685571\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.416896 | − | 1.58141i | 0.0188334 | − | 0.0714408i | ||||
\(491\) | −12.7240 | + | 39.1604i | −0.574226 | + | 1.76728i | 0.0645759 | + | 0.997913i | \(0.479431\pi\) |
−0.638801 | + | 0.769372i | \(0.720569\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.03655 | − | 37.0718i | −0.361216 | − | 1.66625i | ||||
\(496\) | −31.8468 | + | 23.1381i | −1.42996 | + | 1.03893i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.23218 | + | 12.2313i | −0.279271 | + | 0.548099i | ||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | −21.3485 | − | 6.65153i | −0.954733 | − | 0.297465i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −39.9166 | − | 20.3385i | −1.78157 | − | 0.907753i | ||||
\(503\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(504\) | −13.6745 | − | 18.8214i | −0.609112 | − | 0.838370i | ||||
\(505\) | 41.9879 | − | 9.10228i | 1.86843 | − | 0.405046i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.9217 | − | 15.9217i | 0.707107 | − | 0.707107i | ||||
\(508\) | −5.43705 | − | 34.3282i | −0.241230 | − | 1.52307i | ||||
\(509\) | 39.3824 | + | 12.7961i | 1.74559 | + | 0.567177i | 0.995552 | − | 0.0942147i | \(-0.0300340\pi\) |
0.750040 | + | 0.661392i | \(0.230034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.2572 | + | 43.8792i | 0.630701 | + | 1.94110i | ||||
\(512\) | 10.2726 | + | 20.1612i | 0.453990 | + | 0.891007i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 27.5178 | − | 1.55367i | 1.21258 | − | 0.0684628i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.94248 | − | 8.17912i | 0.260846 | − | 0.359023i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(522\) | −3.54975 | + | 22.4123i | −0.155368 | + | 0.980958i | ||||
\(523\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(524\) | − | 36.8990i | − | 1.61194i | ||||||
\(525\) | 11.7055 | − | 20.6584i | 0.510872 | − | 0.901605i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −38.6945 | − | 6.12861i | −1.68396 | − | 0.266714i | ||||
\(529\) | −13.5191 | − | 18.6074i | −0.587785 | − | 0.809017i | ||||
\(530\) | 42.0230 | + | 18.5067i | 1.82536 | + | 0.803881i | ||||
\(531\) | 13.0153 | + | 9.45614i | 0.564814 | + | 0.410361i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.1676 | + | 37.5461i | −1.04486 | + | 1.62326i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.4411 | − | 34.2302i | −0.752641 | − | 1.47714i | ||||
\(538\) | −36.6731 | + | 18.6859i | −1.58109 | + | 0.805605i | ||||
\(539\) | 2.78131 | − | 0.903702i | 0.119800 | − | 0.0389252i | ||||
\(540\) | −8.41531 | − | 21.6606i | −0.362137 | − | 0.932125i | ||||
\(541\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(542\) | −44.9716 | + | 7.12280i | −1.93170 | + | 0.305951i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.6606 | − | 38.5374i | −0.454569 | − | 1.64324i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −38.0531 | − | 6.02703i | −1.61818 | − | 0.256295i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.8840 | + | 19.8840i | −0.842511 | + | 0.842511i | −0.989185 | − | 0.146674i | \(-0.953143\pi\) |
0.146674 | + | 0.989185i | \(0.453143\pi\) | |||||||
\(558\) | −6.53156 | − | 41.2387i | −0.276503 | − | 1.74577i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −15.5097 | − | 18.9954i | −0.655403 | − | 0.802701i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.6546 | − | 6.44785i | 0.533329 | − | 0.271744i | −0.166517 | − | 0.986039i | \(-0.553252\pi\) |
0.699846 | + | 0.714294i | \(0.253252\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.3719 | − | 3.86013i | 1.02352 | − | 0.162110i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −1.00000 | ||||||||
\(577\) | −29.3444 | − | 14.9517i | −1.22162 | − | 0.622447i | −0.280285 | − | 0.959917i | \(-0.590429\pi\) |
−0.941336 | + | 0.337470i | \(0.890429\pi\) | |||||||
\(578\) | −23.7456 | − | 3.76094i | −0.987688 | − | 0.156434i | ||||
\(579\) | −5.71143 | − | 7.86111i | −0.237359 | − | 0.326696i | ||||
\(580\) | −2.40408 | + | 23.7980i | −0.0998241 | + | 0.988156i | ||||
\(581\) | −12.4309 | − | 9.03157i | −0.515720 | − | 0.374693i | ||||
\(582\) | −32.9813 | + | 32.9813i | −1.36712 | + | 1.36712i | ||||
\(583\) | 12.8446 | + | 81.0977i | 0.531970 | + | 3.35873i | ||||
\(584\) | 45.2664 | + | 14.7079i | 1.87314 | + | 0.608619i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.66755 | + | 5.13220i | 0.0688860 | + | 0.212009i | ||||
\(587\) | −1.12965 | − | 2.21706i | −0.0466257 | − | 0.0915080i | 0.866518 | − | 0.499146i | \(-0.166353\pi\) |
−0.913144 | + | 0.407638i | \(0.866353\pi\) | |||||||
\(588\) | 1.59627 | − | 0.813338i | 0.0658289 | − | 0.0335415i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 14.2594 | + | 9.17843i | 0.587048 | + | 0.377870i | ||||
\(591\) | −14.9491 | + | 46.0087i | −0.614926 | + | 1.89255i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(594\) | 24.4244 | − | 33.6174i | 1.00215 | − | 1.37934i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.7347 | + | 9.97887i | −0.562597 | + | 0.408751i | ||||
\(597\) | −5.13991 | + | 32.4521i | −0.210363 | + | 1.32818i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | −10.1435 | − | 22.2960i | −0.414106 | − | 0.910229i | ||||
\(601\) | 47.2101 | 1.92574 | 0.962870 | − | 0.269965i | \(-0.0870123\pi\) | ||||
0.962870 | + | 0.269965i | \(0.0870123\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −18.8277 | − | 25.9141i | −0.766087 | − | 1.05443i | ||||
\(605\) | 31.2430 | − | 34.9821i | 1.27021 | − | 1.42223i | ||||
\(606\) | 38.0754 | + | 27.6634i | 1.54671 | + | 1.12375i | ||||
\(607\) | 34.8413 | − | 34.8413i | 1.41416 | − | 1.41416i | 0.701131 | − | 0.713032i | \(-0.252679\pi\) |
0.713032 | − | 0.701131i | \(-0.247321\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.1559 | − | 7.84874i | −0.978847 | − | 0.318047i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.5508 | − | 41.7050i | 0.545976 | − | 1.68034i | ||||
\(617\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(618\) | 21.3491 | + | 21.3491i | 0.858787 | + | 0.858787i | ||||
\(619\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(620\) | −9.32433 | − | 43.0122i | −0.374474 | − | 1.72741i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.4258 | − | 18.8466i | 0.657032 | − | 0.753863i | ||||
\(626\) | 9.48320 | 0.379025 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 25.4200 | − | 5.51065i | 1.01276 | − | 0.219549i | ||||
\(631\) | −3.96336 | − | 2.87955i | −0.157779 | − | 0.114633i | 0.506095 | − | 0.862478i | \(-0.331089\pi\) |
−0.663873 | + | 0.747845i | \(0.731089\pi\) | |||||||
\(632\) | −28.1043 | + | 28.1043i | −1.11793 | + | 1.11793i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.22457 | + | 2.99724i | 0.366354 | + | 0.119036i | ||||
\(635\) | 37.5748 | + | 9.90557i | 1.49111 | + | 0.393091i | ||||
\(636\) | 15.5436 | + | 47.8384i | 0.616345 | + | 1.89692i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −38.1096 | + | 19.4178i | −1.50877 | + | 0.768759i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −25.2580 | + | 1.42608i | −0.998410 | + | 0.0563708i | ||||
\(641\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(642\) | −48.3114 | + | 7.65178i | −1.90670 | + | 0.301992i | ||||
\(643\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(648\) | 11.5567 | − | 22.6813i | 0.453990 | − | 0.891007i | ||||
\(649\) | 30.3238i | 1.19031i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 46.7344 | 1.83166 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.3659 | + | 4.49271i | 1.11004 | + | 0.175813i | 0.684420 | − | 0.729088i | \(-0.260055\pi\) |
0.425622 | + | 0.904901i | \(0.360055\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37.7552 | + | 16.6272i | 1.47522 | + | 0.649679i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −35.6969 | + | 35.6969i | −1.39267 | + | 1.39267i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 46.1177 | + | 14.9845i | 1.79649 | + | 0.583715i | 0.999787 | − | 0.0206555i | \(-0.00657532\pi\) |
0.796703 | + | 0.604371i | \(0.206575\pi\) | |||||||
\(660\) | 23.7071 | − | 36.8308i | 0.922799 | − | 1.43364i | ||||
\(661\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.0754 | + | 4.89829i | −0.585039 | + | 0.190091i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.31465 | − | 1.80947i | 0.0508275 | − | 0.0699580i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.20238 | − | 26.5328i | 0.162110 | − | 1.02352i | ||||
\(673\) | 12.4622 | − | 24.4585i | 0.480384 | − | 0.942807i | −0.515897 | − | 0.856650i | \(-0.672541\pi\) |
0.996282 | − | 0.0861567i | \(-0.0274586\pi\) | |||||||
\(674\) | 45.9245i | 1.76895i | ||||||||
\(675\) | 25.9553 | + | 1.15001i | 0.999020 | + | 0.0442638i | ||||
\(676\) | 26.0000 | 1.00000 | ||||||||
\(677\) | −25.1745 | − | 12.8270i | −0.967534 | − | 0.492983i | −0.102520 | − | 0.994731i | \(-0.532690\pi\) |
−0.865014 | + | 0.501748i | \(0.832690\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.6869 | − | 42.2370i | −1.17766 | − | 1.62091i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.1938 | − | 24.1167i | −1.27199 | − | 0.924153i | ||||
\(682\) | 55.6490 | − | 55.6490i | 2.13091 | − | 2.13091i | ||||
\(683\) | −8.00419 | − | 50.5365i | −0.306272 | − | 1.93372i | −0.354893 | − | 0.934907i | \(-0.615483\pi\) |
0.0486213 | − | 0.998817i | \(-0.484517\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.76764 | − | 23.9063i | −0.296570 | − | 0.912748i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(692\) | 11.5302 | − | 1.82621i | 0.438314 | − | 0.0694221i | ||||
\(693\) | 32.8884 | + | 32.8884i | 1.24933 | + | 1.24933i | ||||
\(694\) | −28.5895 | + | 39.3500i | −1.08524 | + | 1.49371i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −21.1979 | + | 15.4012i | −0.803504 | + | 0.583780i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 26.4250 | − | 7.30995i | 0.998772 | − | 0.276290i | ||||
\(701\) | 52.9444 | 1.99968 | 0.999841 | − | 0.0178345i | \(-0.00567720\pi\) | ||||
0.999841 | + | 0.0178345i | \(0.00567720\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −26.5900 | − | 36.5980i | −1.00215 | − | 1.37934i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −37.2497 | + | 37.2497i | −1.40092 | + | 1.40092i | ||||
\(708\) | 2.90601 | + | 18.3478i | 0.109214 | + | 0.689553i | ||||
\(709\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.0271 | − | 40.0932i | −0.488554 | − | 1.50361i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.7082 | − | 42.1895i | 0.512299 | − | 1.57669i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(720\) | 10.8147 | − | 24.5569i | 0.403042 | − | 0.915182i | ||||
\(721\) | −27.3403 | + | 19.8639i | −1.01821 | + | 0.739771i | ||||
\(722\) | −4.20340 | + | 26.5392i | −0.156434 | + | 0.987688i | ||||
\(723\) | −23.3211 | + | 45.7703i | −0.867321 | + | 1.70221i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.2669 | − | 13.1836i | −0.864109 | − | 0.489626i | ||||
\(726\) | 51.3795 | 1.90687 | ||||||||
\(727\) | −35.2120 | − | 17.9414i | −1.30594 | − | 0.665410i | −0.344077 | − | 0.938941i | \(-0.611808\pi\) |
−0.961863 | + | 0.273532i | \(0.911808\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.8702 | + | 21.8435i | 0.587785 | + | 0.809017i | ||||
\(730\) | −35.4469 | + | 39.6892i | −1.31195 | + | 1.46896i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(734\) | −1.48736 | − | 0.483272i | −0.0548994 | − | 0.0178379i | ||||
\(735\) | 0.112910 | + | 1.99981i | 0.00416476 | + | 0.0737640i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −55.6086 | + | 8.80753i | −2.04146 | + | 0.323335i | ||||
\(743\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | 28.3382 | − | 39.0042i | 1.03893 | − | 1.42996i | ||||
\(745\) | −4.02135 | − | 18.5501i | −0.147331 | − | 0.679622i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.63009 | − | 16.6058i | 0.0962301 | − | 0.607573i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 54.7497i | − | 2.00051i | ||||||
\(750\) | 27.3841 | − | 0.331977i | 0.999927 | − | 0.0121221i | ||||
\(751\) | −49.4748 | −1.80536 | −0.902680 | − | 0.430312i | \(-0.858404\pi\) | ||||
−0.902680 | + | 0.430312i | \(0.858404\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 54.1924 | + | 8.58323i | 1.97488 | + | 0.312790i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.9994 | − | 7.58729i | 1.27376 | − | 0.276130i | ||||
\(756\) | 23.0514 | + | 16.7478i | 0.838370 | + | 0.609112i | ||||
\(757\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(762\) | 19.3252 | + | 37.9278i | 0.700077 | + | 1.37398i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −19.5959 | − | 19.5959i | −0.707107 | − | 0.707107i | ||||
\(769\) | 4.56182 | − | 6.27881i | 0.164504 | − | 0.226420i | −0.718805 | − | 0.695212i | \(-0.755311\pi\) |
0.883309 | + | 0.468792i | \(0.155311\pi\) | |||||||
\(770\) | 36.5665 | + | 32.6581i | 1.31777 | + | 1.17691i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.75521 | − | 11.0819i | 0.0631712 | − | 0.398847i | ||||
\(773\) | −25.2131 | + | 49.4834i | −0.906851 | + | 1.77980i | −0.408993 | + | 0.912538i | \(0.634120\pi\) |
−0.497859 | + | 0.867258i | \(0.665880\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 48.2119 | + | 9.84121i | 1.73182 | + | 0.353507i | ||||
\(776\) | −53.8583 | −1.93340 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.4493 | − | 1.65501i | −0.374626 | − | 0.0593350i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.34754 | − | 27.4493i | −0.155368 | − | 0.980958i | ||||
\(784\) | 1.96743 | + | 0.639258i | 0.0702655 | + | 0.0228306i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.9650 | + | 42.9800i | 0.498117 | + | 1.53305i | ||||
\(787\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(788\) | −49.7719 | + | 25.3601i | −1.77305 | + | 0.903414i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.0922 | − | 41.4207i | −0.572537 | − | 1.47368i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 47.3909 | − | 7.50599i | 1.68396 | − | 0.266714i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −55.9526 | − | 5.65236i | −1.98444 | − | 0.200469i | ||||
\(796\) | −30.6938 | + | 22.3003i | −1.08791 | + | 0.790414i | ||||
\(797\) | −5.17476 | + | 32.6721i | −0.183299 | + | 1.15731i | 0.708781 | + | 0.705429i | \(0.249246\pi\) |
−0.892080 | + | 0.451877i | \(0.850754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 9.92245 | − | 26.4867i | 0.350812 | − | 0.936446i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −93.9840 | − | 14.8856i | −3.31662 | − | 0.525301i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.6449 | − | 35.6449i | 1.25476 | − | 1.25476i | ||||
\(808\) | 8.50136 | + | 53.6755i | 0.299077 | + | 1.88830i | ||||
\(809\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(810\) | 18.0000 | + | 22.0454i | 0.632456 | + | 0.774597i | ||||
\(811\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(812\) | −13.3148 | − | 26.1317i | −0.467257 | − | 0.917043i | ||||
\(813\) | 49.6872 | − | 25.3169i | 1.74261 | − | 0.887903i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −21.6215 | − | 21.6215i | −0.755978 | − | 0.755978i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.3669 | + | 30.7814i | −1.47862 | + | 1.07428i | −0.500617 | + | 0.865669i | \(0.666894\pi\) |
−0.977999 | + | 0.208609i | \(0.933106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.6754 | − | 50.3908i | 0.894988 | − | 1.75651i | 0.297301 | − | 0.954784i | \(-0.403913\pi\) |
0.597687 | − | 0.801730i | \(-0.296087\pi\) | |||||||
\(824\) | 34.8629i | 1.21451i | ||||||||
\(825\) | 27.0026 | + | 40.8537i | 0.940110 | + | 1.42234i | ||||
\(826\) | −20.7929 | −0.723479 | ||||||||
\(827\) | −37.1173 | − | 18.9122i | −1.29069 | − | 0.657642i | −0.332323 | − | 0.943166i | \(-0.607832\pi\) |
−0.958372 | + | 0.285524i | \(0.907832\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(830\) | 1.78124 | − | 17.6324i | 0.0618277 | − | 0.612031i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.2155 | + | 45.5629i | 0.802443 | + | 1.57488i | ||||
\(838\) | 51.3306 | − | 26.1542i | 1.77319 | − | 0.903483i | ||||
\(839\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(840\) | 25.2548 | + | 16.2559i | 0.871373 | + | 0.560883i | ||||
\(841\) | 0.121715 | − | 0.374599i | 0.00419706 | − | 0.0129172i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.7160 | + | 26.6033i | −0.403042 | + | 0.915182i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.99650 | + | 56.8017i | −0.309123 | + | 1.95173i | ||||
\(848\) | −26.3686 | + | 51.7512i | −0.905500 | + | 1.77714i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −45.6938 | − | 33.1985i | −1.56178 | − | 1.13470i | ||||
\(857\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(864\) | 27.9552 | − | 9.08321i | 0.951057 | − | 0.309017i | ||||
\(865\) | −3.32711 | + | 12.6207i | −0.113125 | + | 0.429117i | ||||
\(866\) | 18.0383 | − | 55.5162i | 0.612966 | − | 1.88652i | ||||
\(867\) | 29.0823 | − | 4.60619i | 0.987688 | − | 0.156434i | ||||
\(868\) | 38.1584 | + | 38.1584i | 1.29518 | + | 1.29518i | ||||
\(869\) | 46.7058 | − | 64.2851i | 1.58439 | − | 2.18072i | ||||
\(870\) | −6.20646 | − | 28.6298i | −0.210419 | − | 0.970640i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 25.9344 | − | 50.8991i | 0.877746 | − | 1.72267i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.42792 | + | 30.3322i | −0.149691 | + | 1.02541i | ||||
\(876\) | −58.2929 | −1.96953 | ||||||||
\(877\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(878\) | 17.8643 | + | 2.82943i | 0.602892 | + | 0.0954887i | ||||
\(879\) | −3.88474 | − | 5.34689i | −0.131029 | − | 0.180346i | ||||
\(880\) | 49.4290 | − | 10.7154i | 1.66625 | − | 0.361216i | ||||
\(881\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(882\) | −1.55151 | + | 1.55151i | −0.0522421 | + | 0.0522421i | ||||
\(883\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.0830 | − | 5.29435i | −0.675084 | − | 0.177968i | ||||
\(886\) | 18.2881 | + | 56.2851i | 0.614402 | + | 1.89093i | ||||
\(887\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.3142 | + | 14.7235i | −1.51979 | + | 0.493810i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.7266 | + | 48.4014i | −0.526860 | + | 1.62151i | ||||
\(892\) | 2.55083 | − | 0.404012i | 0.0854082 | − | 0.0135273i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 12.2216 | − | 16.8216i | 0.408751 | − | 0.562597i | ||||
\(895\) | 36.9913 | + | 33.0375i | 1.23648 | + | 1.10432i | ||||
\(896\) | 25.0952 | − | 18.2327i | 0.838370 | − | 0.609112i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 52.6354i | − | 1.75549i | ||||||
\(900\) | 20.2534 | + | 22.1314i | 0.675114 | + | 0.737713i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 31.7381 | + | 23.0591i | 1.05443 | + | 0.766087i | ||||
\(907\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(908\) | −7.41141 | − | 46.7938i | −0.245956 | − | 1.55291i | ||||
\(909\) | −54.8199 | − | 17.8121i | −1.81826 | − | 0.590789i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.2363 | − | 14.3871i | 0.934484 | − | 0.476144i | ||||
\(914\) | −33.5737 | + | 10.9087i | −1.11052 | + | 0.360829i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49.9610 | + | 7.91305i | −1.64986 | + | 0.261312i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.1568 | + | 27.7435i | −0.664913 | + | 0.915174i | −0.999632 | − | 0.0271443i | \(-0.991359\pi\) |
0.334719 | + | 0.942318i | \(0.391359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.00749 | − | 18.9885i | 0.0990463 | − | 0.625354i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 53.7065i | 1.76681i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.29286 | −0.272520 | ||||||||
\(927\) | −32.9474 | − | 16.7875i | −1.08213 | − | 0.551375i | ||||
\(928\) | −29.8830 | − | 4.73300i | −0.980958 | − | 0.155368i | ||||
\(929\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(930\) | 27.1397 | + | 46.5717i | 0.889945 | + | 1.52715i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 38.6138 | + | 12.5464i | 1.26348 | + | 0.410531i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.3990 | + | 53.7735i | 0.895085 | + | 1.75670i | 0.597178 | + | 0.802108i | \(0.296288\pi\) |
0.297907 | + | 0.954595i | \(0.403712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.0460 | + | 3.58908i | −0.360474 | + | 0.117125i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.30577 | + | 28.6402i | −0.303359 | + | 0.933644i | 0.676925 | + | 0.736052i | \(0.263312\pi\) |
−0.980284 | + | 0.197592i | \(0.936688\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −12.6082 | + | 17.3537i | −0.410361 | + | 0.564814i | ||||
\(945\) | −27.5237 | + | 16.0395i | −0.895346 | + | 0.521763i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.13260 | − | 13.4647i | 0.0693001 | − | 0.437544i | −0.928505 | − | 0.371321i | \(-0.878905\pi\) |
0.997805 | − | 0.0662232i | \(-0.0210949\pi\) | |||||||
\(948\) | 22.0994 | − | 43.3725i | 0.717756 | − | 1.40867i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.8791 | −0.385208 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(954\) | −36.2105 | − | 49.8395i | −1.17236 | − | 1.61361i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37.0411 | − | 37.0411i | 1.19737 | − | 1.19737i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 28.8808 | − | 11.2204i | 0.932125 | − | 0.362137i | ||||
\(961\) | 20.3486 | + | 62.6265i | 0.656406 | + | 2.02021i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 53.3773 | − | 27.1971i | 1.72006 | − | 0.876414i | ||||
\(964\) | −56.4129 | + | 18.3297i | −1.81694 | + | 0.590358i | ||||
\(965\) | 10.5482 | + | 6.78961i | 0.339557 | + | 0.218565i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.3586 | + | 2.27418i | −0.461742 | + | 0.0731328i | −0.382972 | − | 0.923760i | \(-0.625099\pi\) |
−0.0787703 | + | 0.996893i | \(0.525099\pi\) | |||||||
\(968\) | 41.9512 | + | 41.9512i | 1.34836 | + | 1.34836i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24.2693 | − | 55.1080i | 0.779242 | − | 1.76941i | ||||
\(971\) | −5.10712 | + | 3.71054i | −0.163895 | + | 0.119077i | −0.666710 | − | 0.745318i | \(-0.732298\pi\) |
0.502814 | + | 0.864394i | \(0.332298\pi\) | |||||||
\(972\) | −4.87714 | + | 30.7931i | −0.156434 | + | 0.987688i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 30.8282i | − | 0.987799i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.54065 | + | 1.72503i | −0.0492141 | + | 0.0551040i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 41.1757 | − | 41.1757i | 1.31397 | − | 1.31397i | ||||
\(983\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.52057 | − | 62.3544i | −0.112175 | − | 1.98678i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −13.6749 | + | 51.8729i | −0.434617 | + | 1.64863i | ||||
\(991\) | 10.0509 | − | 30.9333i | 0.319276 | − | 0.982630i | −0.654683 | − | 0.755904i | \(-0.727198\pi\) |
0.973959 | − | 0.226726i | \(-0.0728023\pi\) | |||||||
\(992\) | 54.9849 | − | 8.70875i | 1.74577 | − | 0.276503i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.98673 | − | 41.4548i | −0.284898 | − | 1.31421i | ||||
\(996\) | 15.7060 | − | 11.4111i | 0.497664 | − | 0.361574i | ||||
\(997\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 600.2.bp.b.533.2 | yes | 16 | |
3.2 | odd | 2 | 600.2.bp.a.533.1 | yes | 16 | ||
8.5 | even | 2 | 600.2.bp.a.533.1 | yes | 16 | ||
24.5 | odd | 2 | CM | 600.2.bp.b.533.2 | yes | 16 | |
25.22 | odd | 20 | inner | 600.2.bp.b.197.2 | yes | 16 | |
75.47 | even | 20 | 600.2.bp.a.197.1 | ✓ | 16 | ||
200.197 | odd | 20 | 600.2.bp.a.197.1 | ✓ | 16 | ||
600.197 | even | 20 | inner | 600.2.bp.b.197.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.2.bp.a.197.1 | ✓ | 16 | 75.47 | even | 20 | ||
600.2.bp.a.197.1 | ✓ | 16 | 200.197 | odd | 20 | ||
600.2.bp.a.533.1 | yes | 16 | 3.2 | odd | 2 | ||
600.2.bp.a.533.1 | yes | 16 | 8.5 | even | 2 | ||
600.2.bp.b.197.2 | yes | 16 | 25.22 | odd | 20 | inner | |
600.2.bp.b.197.2 | yes | 16 | 600.197 | even | 20 | inner | |
600.2.bp.b.533.2 | yes | 16 | 1.1 | even | 1 | trivial | |
600.2.bp.b.533.2 | yes | 16 | 24.5 | odd | 2 | CM |