Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2020,1,Mod(279,2020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2020, base_ring=CyclotomicField(50))
chi = DirichletCharacter(H, H._module([25, 25, 11]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2020.279");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2020 = 2^{2} \cdot 5 \cdot 101 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2020.bt (of order \(50\), degree \(20\), 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: | \(1.00811132552\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{50})\) |
Coefficient field: | \(\Q(\zeta_{100})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{40} - x^{30} + x^{20} - x^{10} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{50}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{50} - \cdots)\) |
Embedding invariants
Embedding label | 1019.1 | ||
Root | \(0.368125 + 0.929776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2020.1019 |
Dual form | 2020.1.bt.c.1459.1 |
$q$-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 \(\left(\mathbb{Z}/2020\mathbb{Z}\right)^\times\).
\(n\) | \(1011\) | \(1617\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{19}{50}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.368125 | − | 0.929776i | −0.368125 | − | 0.929776i | ||||
\(3\) | 0.0967619 | + | 0.0800484i | 0.0967619 | + | 0.0800484i | 0.684547 | − | 0.728969i | \(-0.260000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(4\) | −0.728969 | + | 0.684547i | −0.728969 | + | 0.684547i | ||||
\(5\) | 0.929776 | + | 0.368125i | 0.929776 | + | 0.368125i | ||||
\(6\) | 0.0388067 | − | 0.119435i | 0.0388067 | − | 0.119435i | ||||
\(7\) | 0.462452 | + | 1.80113i | 0.462452 | + | 1.80113i | 0.587785 | + | 0.809017i | \(0.300000\pi\) |
−0.125333 | + | 0.992115i | \(0.540000\pi\) | |||||||
\(8\) | 0.904827 | + | 0.425779i | 0.904827 | + | 0.425779i | ||||
\(9\) | −0.184426 | − | 0.966796i | −0.184426 | − | 0.966796i | ||||
\(10\) | − | 1.00000i | − | 1.00000i | ||||||
\(11\) | 0 | 0 | 0.982287 | − | 0.187381i | \(-0.0600000\pi\) | ||||
−0.982287 | + | 0.187381i | \(0.940000\pi\) | |||||||
\(12\) | −0.125333 | + | 0.00788530i | −0.125333 | + | 0.00788530i | ||||
\(13\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(14\) | 1.50441 | − | 1.09302i | 1.50441 | − | 1.09302i | ||||
\(15\) | 0.0604991 | + | 0.110048i | 0.0604991 | + | 0.110048i | ||||
\(16\) | 0.0627905 | − | 0.998027i | 0.0627905 | − | 0.998027i | ||||
\(17\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(18\) | −0.831012 | + | 0.527376i | −0.831012 | + | 0.527376i | ||||
\(19\) | 0 | 0 | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) | ||||
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(20\) | −0.929776 | + | 0.368125i | −0.929776 | + | 0.368125i | ||||
\(21\) | −0.0994299 | + | 0.211299i | −0.0994299 | + | 0.211299i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.516273 | + | 0.813516i | −0.516273 | + | 0.813516i | −0.998027 | − | 0.0627905i | \(-0.980000\pi\) |
0.481754 | + | 0.876307i | \(0.340000\pi\) | |||||||
\(24\) | 0.0534698 | + | 0.113629i | 0.0534698 | + | 0.113629i | ||||
\(25\) | 0.728969 | + | 0.684547i | 0.728969 | + | 0.684547i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.120044 | − | 0.218359i | 0.120044 | − | 0.218359i | ||||
\(28\) | −1.57007 | − | 0.996398i | −1.57007 | − | 0.996398i | ||||
\(29\) | 0.183098 | − | 0.713118i | 0.183098 | − | 0.713118i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.992115 | − | 0.125333i | \(-0.0400000\pi\) | |||||||
\(30\) | 0.0800484 | − | 0.0967619i | 0.0800484 | − | 0.0967619i | ||||
\(31\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(32\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.233064 | + | 1.84489i | −0.233064 | + | 1.84489i | ||||
\(36\) | 0.796258 | + | 0.578516i | 0.796258 | + | 0.578516i | ||||
\(37\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.684547 | + | 0.728969i | 0.684547 | + | 0.728969i | ||||
\(41\) | 0.473036 | + | 0.153699i | 0.473036 | + | 0.153699i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(42\) | 0.233064 | + | 0.0146631i | 0.233064 | + | 0.0146631i | ||||
\(43\) | −1.52888 | + | 0.193142i | −1.52888 | + | 0.193142i | −0.844328 | − | 0.535827i | \(-0.820000\pi\) |
−0.684547 | + | 0.728969i | \(0.740000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.184426 | − | 0.966796i | 0.184426 | − | 0.966796i | ||||
\(46\) | 0.946441 | + | 0.180543i | 0.946441 | + | 0.180543i | ||||
\(47\) | 1.98031 | + | 0.250172i | 1.98031 | + | 0.250172i | 0.998027 | + | 0.0627905i | \(0.0200000\pi\) |
0.982287 | + | 0.187381i | \(0.0600000\pi\) | |||||||
\(48\) | 0.0859661 | − | 0.0915446i | 0.0859661 | − | 0.0915446i | ||||
\(49\) | −2.15391 | + | 1.18412i | −2.15391 | + | 1.18412i | ||||
\(50\) | 0.368125 | − | 0.929776i | 0.368125 | − | 0.929776i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.684547 | − | 0.728969i | \(-0.260000\pi\) | ||||
−0.684547 | + | 0.728969i | \(0.740000\pi\) | |||||||
\(54\) | −0.247217 | − | 0.0312307i | −0.247217 | − | 0.0312307i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.348445 | + | 1.82662i | −0.348445 | + | 1.82662i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.730444 | + | 0.0922765i | −0.730444 | + | 0.0922765i | ||||
\(59\) | 0 | 0 | −0.998027 | − | 0.0627905i | \(-0.980000\pi\) | ||||
0.998027 | + | 0.0627905i | \(0.0200000\pi\) | |||||||
\(60\) | −0.119435 | − | 0.0388067i | −0.119435 | − | 0.0388067i | ||||
\(61\) | 1.34484 | + | 1.43211i | 1.34484 | + | 1.43211i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.65604 | − | 0.779273i | 1.65604 | − | 0.779273i | ||||
\(64\) | 0.637424 | + | 0.770513i | 0.637424 | + | 0.770513i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.825723 | + | 0.683098i | −0.825723 | + | 0.683098i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.125333 | + | 0.992115i | \(0.460000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.115076 | + | 0.0373905i | −0.115076 | + | 0.0373905i | ||||
\(70\) | 1.80113 | − | 0.462452i | 1.80113 | − | 0.462452i | ||||
\(71\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(72\) | 0.244768 | − | 0.953308i | 0.244768 | − | 0.953308i | ||||
\(73\) | 0 | 0 | −0.844328 | − | 0.535827i | \(-0.820000\pi\) | ||||
0.844328 | + | 0.535827i | \(0.180000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0157395 | + | 0.124591i | 0.0157395 | + | 0.124591i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(80\) | 0.425779 | − | 0.904827i | 0.425779 | − | 0.904827i | ||||
\(81\) | −0.886018 | + | 0.350799i | −0.886018 | + | 0.350799i | ||||
\(82\) | −0.0312307 | − | 0.496398i | −0.0312307 | − | 0.496398i | ||||
\(83\) | 1.07639 | − | 0.683098i | 1.07639 | − | 0.683098i | 0.125333 | − | 0.992115i | \(-0.460000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(84\) | −0.0721631 | − | 0.222095i | −0.0721631 | − | 0.222095i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.742395 | + | 1.35041i | 0.742395 | + | 1.35041i | ||||
\(87\) | 0.0748008 | − | 0.0543460i | 0.0748008 | − | 0.0543460i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.17325 | + | 0.0738147i | −1.17325 | + | 0.0738147i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(90\) | −0.966796 | + | 0.184426i | −0.966796 | + | 0.184426i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.180543 | − | 0.946441i | −0.180543 | − | 0.946441i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.496398 | − | 1.93334i | −0.496398 | − | 1.93334i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.116762 | − | 0.0462295i | −0.116762 | − | 0.0462295i | ||||
\(97\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(98\) | 1.89387 | + | 1.56675i | 1.89387 | + | 1.56675i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −1.00000 | ||||||||
\(101\) | 0.425779 | − | 0.904827i | 0.425779 | − | 0.904827i | ||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.595638 | − | 1.50441i | −0.595638 | − | 1.50441i | −0.844328 | − | 0.535827i | \(-0.820000\pi\) |
0.248690 | − | 0.968583i | \(-0.420000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.170232 | + | 0.159859i | −0.170232 | + | 0.159859i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.423073 | − | 1.30209i | 0.423073 | − | 1.30209i | −0.481754 | − | 0.876307i | \(-0.660000\pi\) |
0.904827 | − | 0.425779i | \(-0.140000\pi\) | |||||||
\(108\) | 0.0619689 | + | 0.241353i | 0.0619689 | + | 0.241353i | ||||
\(109\) | −1.80608 | − | 0.849878i | −1.80608 | − | 0.849878i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
−0.876307 | − | 0.481754i | \(-0.840000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.82662 | − | 0.348445i | 1.82662 | − | 0.348445i | ||||
\(113\) | 0 | 0 | 0.998027 | − | 0.0627905i | \(-0.0200000\pi\) | ||||
−0.998027 | + | 0.0627905i | \(0.980000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.779494 | + | 0.566335i | −0.779494 | + | 0.566335i | ||||
\(116\) | 0.354691 | + | 0.645180i | 0.354691 | + | 0.645180i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.00788530 | + | 0.125333i | 0.00788530 | + | 0.125333i | ||||
\(121\) | 0.929776 | − | 0.368125i | 0.929776 | − | 0.368125i | ||||
\(122\) | 0.836475 | − | 1.77760i | 0.836475 | − | 1.77760i | ||||
\(123\) | 0.0334685 | + | 0.0527380i | 0.0334685 | + | 0.0527380i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.425779 | + | 0.904827i | 0.425779 | + | 0.904827i | ||||
\(126\) | −1.33418 | − | 1.25288i | −1.33418 | − | 1.25288i | ||||
\(127\) | −0.202793 | − | 1.60528i | −0.202793 | − | 1.60528i | −0.684547 | − | 0.728969i | \(-0.740000\pi\) |
0.481754 | − | 0.876307i | \(-0.340000\pi\) | |||||||
\(128\) | 0.481754 | − | 0.876307i | 0.481754 | − | 0.876307i | ||||
\(129\) | −0.163397 | − | 0.103695i | −0.163397 | − | 0.103695i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.939097 | + | 0.516273i | 0.939097 | + | 0.516273i | ||||
\(135\) | 0.191998 | − | 0.158834i | 0.191998 | − | 0.158834i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(138\) | 0.0771272 | + | 0.0932308i | 0.0771272 | + | 0.0932308i | ||||
\(139\) | 0 | 0 | 0.904827 | − | 0.425779i | \(-0.140000\pi\) | ||||
−0.904827 | + | 0.425779i | \(0.860000\pi\) | |||||||
\(140\) | −1.09302 | − | 1.50441i | −1.09302 | − | 1.50441i | ||||
\(141\) | 0.171593 | + | 0.182728i | 0.171593 | + | 0.182728i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.976468 | + | 0.123357i | −0.976468 | + | 0.123357i | ||||
\(145\) | 0.432756 | − | 0.595638i | 0.432756 | − | 0.595638i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.303203 | − | 0.0578390i | −0.303203 | − | 0.0578390i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.15596 | − | 1.23098i | 1.15596 | − | 1.23098i | 0.187381 | − | 0.982287i | \(-0.440000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(150\) | 0.110048 | − | 0.0604991i | 0.110048 | − | 0.0604991i | ||||
\(151\) | 0 | 0 | 0.368125 | − | 0.929776i | \(-0.380000\pi\) | ||||
−0.368125 | + | 0.929776i | \(0.620000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.998027 | − | 0.0627905i | −0.998027 | − | 0.0627905i | ||||
\(161\) | −1.70400 | − | 0.553664i | −1.70400 | − | 0.553664i | ||||
\(162\) | 0.652330 | + | 0.694661i | 0.652330 | + | 0.694661i | ||||
\(163\) | −0.629902 | − | 0.866986i | −0.629902 | − | 0.866986i | 0.368125 | − | 0.929776i | \(-0.380000\pi\) |
−0.998027 | + | 0.0627905i | \(0.980000\pi\) | |||||||
\(164\) | −0.450043 | + | 0.211774i | −0.450043 | + | 0.211774i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.03137 | − | 0.749337i | −1.03137 | − | 0.749337i | ||||
\(167\) | −0.219661 | + | 1.73879i | −0.219661 | + | 1.73879i | 0.368125 | + | 0.929776i | \(0.380000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(168\) | −0.179934 | + | 0.148854i | −0.179934 | + | 0.148854i | ||||
\(169\) | 0.876307 | + | 0.481754i | 0.876307 | + | 0.481754i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.982287 | − | 1.18738i | 0.982287 | − | 1.18738i | ||||
\(173\) | 0 | 0 | 0.248690 | − | 0.968583i | \(-0.420000\pi\) | ||||
−0.248690 | + | 0.968583i | \(0.580000\pi\) | |||||||
\(174\) | −0.0780657 | − | 0.0495420i | −0.0780657 | − | 0.0495420i | ||||
\(175\) | −0.895846 | + | 1.62954i | −0.895846 | + | 1.62954i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.500534 | + | 1.06369i | 0.500534 | + | 1.06369i | ||||
\(179\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(180\) | 0.527376 | + | 0.831012i | 0.527376 | + | 0.831012i | ||||
\(181\) | −0.542804 | + | 1.15352i | −0.542804 | + | 1.15352i | 0.425779 | + | 0.904827i | \(0.360000\pi\) |
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0154913 | + | 0.246226i | 0.0154913 | + | 0.246226i | ||||
\(184\) | −0.813516 | + | 0.516273i | −0.813516 | + | 0.516273i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.61484 | + | 1.17325i | −1.61484 | + | 1.17325i | ||||
\(189\) | 0.448809 | + | 0.115235i | 0.448809 | + | 0.115235i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.982287 | − | 0.187381i | \(-0.0600000\pi\) | ||||
−0.982287 | + | 0.187381i | \(0.940000\pi\) | |||||||
\(192\) | 0.125581i | 0.125581i | ||||||||
\(193\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.759544 | − | 2.33764i | 0.759544 | − | 2.33764i | ||||
\(197\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.770513 | − | 0.637424i | \(-0.780000\pi\) | ||||
0.770513 | + | 0.637424i | \(0.220000\pi\) | |||||||
\(200\) | 0.368125 | + | 0.929776i | 0.368125 | + | 0.929776i | ||||
\(201\) | −0.134579 | −0.134579 | ||||||||
\(202\) | −0.998027 | − | 0.0627905i | −0.998027 | − | 0.0627905i | ||||
\(203\) | 1.36909 | 1.36909 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.383238 | + | 0.317042i | 0.383238 | + | 0.317042i | ||||
\(206\) | −1.17950 | + | 1.10762i | −1.17950 | + | 1.10762i | ||||
\(207\) | 0.881718 | + | 0.349097i | 0.881718 | + | 0.349097i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.211299 | + | 0.0994299i | 0.211299 | + | 0.0994299i | ||||
\(211\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.36639 | + | 0.0859661i | −1.36639 | + | 0.0859661i | ||||
\(215\) | −1.49261 | − | 0.383238i | −1.49261 | − | 0.383238i | ||||
\(216\) | 0.201592 | − | 0.146465i | 0.201592 | − | 0.146465i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.125333 | + | 1.99211i | −0.125333 | + | 1.99211i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.106729 | + | 0.226810i | −0.106729 | + | 0.226810i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.844328 | + | 0.535827i | \(0.180000\pi\) | |||||||
\(224\) | −0.996398 | − | 1.57007i | −0.996398 | − | 1.57007i | ||||
\(225\) | 0.527376 | − | 0.831012i | 0.527376 | − | 0.831012i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.23098 | − | 1.15596i | −1.23098 | − | 1.15596i | −0.982287 | − | 0.187381i | \(-0.940000\pi\) |
−0.248690 | − | 0.968583i | \(-0.580000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.916350 | − | 1.66683i | 0.916350 | − | 1.66683i | 0.187381 | − | 0.982287i | \(-0.440000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(230\) | 0.813516 | + | 0.516273i | 0.813516 | + | 0.516273i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.469303 | − | 0.567290i | 0.469303 | − | 0.567290i | ||||
\(233\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.74915 | + | 0.961606i | 1.74915 | + | 0.961606i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(240\) | 0.113629 | − | 0.0534698i | 0.113629 | − | 0.0534698i | ||||
\(241\) | −1.15475 | − | 1.58937i | −1.15475 | − | 1.58937i | −0.728969 | − | 0.684547i | \(-0.760000\pi\) |
−0.425779 | − | 0.904827i | \(-0.640000\pi\) | |||||||
\(242\) | −0.684547 | − | 0.728969i | −0.684547 | − | 0.728969i | ||||
\(243\) | −0.350799 | − | 0.113982i | −0.350799 | − | 0.113982i | ||||
\(244\) | −1.96070 | − | 0.123357i | −1.96070 | − | 0.123357i | ||||
\(245\) | −2.43856 | + | 0.308061i | −2.43856 | + | 0.308061i | ||||
\(246\) | 0.0367139 | − | 0.0505324i | 0.0367139 | − | 0.0505324i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.158834 | + | 0.0200654i | 0.158834 | + | 0.0200654i | ||||
\(250\) | 0.684547 | − | 0.728969i | 0.684547 | − | 0.728969i | ||||
\(251\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(252\) | −0.673751 | + | 1.70170i | −0.673751 | + | 1.70170i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.41789 | + | 0.779494i | −1.41789 | + | 0.779494i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.992115 | − | 0.125333i | −0.992115 | − | 0.125333i | ||||
\(257\) | 0 | 0 | −0.982287 | − | 0.187381i | \(-0.940000\pi\) | ||||
0.982287 | + | 0.187381i | \(0.0600000\pi\) | |||||||
\(258\) | −0.0362627 | + | 0.190096i | −0.0362627 | + | 0.190096i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.723208 | − | 0.0455004i | −0.723208 | − | 0.0455004i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.582932 | + | 0.620759i | 0.582932 | + | 0.620759i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.368125 | + | 0.929776i | \(0.620000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.119435 | − | 0.0867744i | −0.119435 | − | 0.0867744i | ||||
\(268\) | 0.134314 | − | 1.06320i | 0.134314 | − | 1.06320i | ||||
\(269\) | −1.05491 | + | 0.872693i | −1.05491 | + | 0.872693i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(270\) | −0.218359 | − | 0.120044i | −0.218359 | − | 0.120044i | ||||
\(271\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.0582914 | − | 0.106032i | 0.0582914 | − | 0.106032i | ||||
\(277\) | 0 | 0 | −0.125333 | − | 0.992115i | \(-0.540000\pi\) | ||||
0.125333 | + | 0.992115i | \(0.460000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.996398 | + | 1.57007i | −0.996398 | + | 1.57007i | ||||
\(281\) | 0.939097 | + | 1.47978i | 0.939097 | + | 1.47978i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(282\) | 0.106729 | − | 0.226810i | 0.106729 | − | 0.226810i | ||||
\(283\) | 0.462452 | − | 0.183098i | 0.462452 | − | 0.183098i | −0.125333 | − | 0.992115i | \(-0.540000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0580752 | + | 0.923079i | −0.0580752 | + | 0.923079i | ||||
\(288\) | 0.474156 | + | 0.862487i | 0.474156 | + | 0.862487i | ||||
\(289\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(290\) | −0.713118 | − | 0.183098i | −0.713118 | − | 0.183098i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0.0578390 | + | 0.303203i | 0.0578390 | + | 0.303203i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.57007 | − | 0.621636i | −1.57007 | − | 0.621636i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.0967619 | − | 0.0800484i | −0.0967619 | − | 0.0800484i | ||||
\(301\) | −1.05491 | − | 2.66439i | −1.05491 | − | 2.66439i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.113629 | − | 0.0534698i | 0.113629 | − | 0.0534698i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.723208 | + | 1.82662i | 0.723208 | + | 1.82662i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.536702 | − | 0.503997i | 0.536702 | − | 0.503997i | −0.368125 | − | 0.929776i | \(-0.620000\pi\) |
0.904827 | + | 0.425779i | \(0.140000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0627905 | − | 0.193249i | 0.0627905 | − | 0.193249i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.904827 | − | 0.425779i | \(-0.860000\pi\) | ||||
0.904827 | + | 0.425779i | \(0.140000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.82662 | − | 0.114921i | 1.82662 | − | 0.114921i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(321\) | 0.145167 | − | 0.0921259i | 0.145167 | − | 0.0921259i | ||||
\(322\) | 0.112501 | + | 1.78816i | 0.112501 | + | 1.78816i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.405741 | − | 0.862243i | 0.405741 | − | 0.862243i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.574221 | + | 0.904827i | −0.574221 | + | 0.904827i | ||||
\(327\) | −0.106729 | − | 0.226810i | −0.106729 | − | 0.226810i | ||||
\(328\) | 0.362574 | + | 0.340480i | 0.362574 | + | 0.340480i | ||||
\(329\) | 0.465208 | + | 3.68250i | 0.465208 | + | 3.68250i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.844328 | − | 0.535827i | \(-0.820000\pi\) | ||||
0.844328 | + | 0.535827i | \(0.180000\pi\) | |||||||
\(332\) | −0.317042 | + | 1.23480i | −0.317042 | + | 1.23480i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.69755 | − | 0.435857i | 1.69755 | − | 0.435857i | ||||
\(335\) | −1.01920 | + | 0.331159i | −1.01920 | + | 0.331159i | ||||
\(336\) | 0.204639 | + | 0.112501i | 0.204639 | + | 0.112501i | ||||
\(337\) | 0 | 0 | 0.770513 | − | 0.637424i | \(-0.220000\pi\) | ||||
−0.770513 | + | 0.637424i | \(0.780000\pi\) | |||||||
\(338\) | 0.125333 | − | 0.992115i | 0.125333 | − | 0.992115i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.85588 | − | 1.97632i | −1.85588 | − | 1.97632i | ||||
\(344\) | −1.46560 | − | 0.476203i | −1.46560 | − | 0.476203i | ||||
\(345\) | −0.120759 | − | 0.00759754i | −0.120759 | − | 0.00759754i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.856954 | − | 1.17950i | 0.856954 | − | 1.17950i | −0.125333 | − | 0.992115i | \(-0.540000\pi\) |
0.982287 | − | 0.187381i | \(-0.0600000\pi\) | |||||||
\(348\) | −0.0173251 | + | 0.0908212i | −0.0173251 | + | 0.0908212i | ||||
\(349\) | 0.246226 | + | 0.0469702i | 0.246226 | + | 0.0469702i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(350\) | 1.84489 | + | 0.233064i | 1.84489 | + | 0.233064i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.368125 | − | 0.929776i | \(-0.380000\pi\) | ||||
−0.368125 | + | 0.929776i | \(0.620000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.804733 | − | 0.856954i | 0.804733 | − | 0.856954i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(360\) | 0.578516 | − | 0.796258i | 0.578516 | − | 0.796258i | ||||
\(361\) | −0.992115 | + | 0.125333i | −0.992115 | + | 0.125333i | ||||
\(362\) | 1.27233 | + | 0.0800484i | 1.27233 | + | 0.0800484i | ||||
\(363\) | 0.119435 | + | 0.0388067i | 0.119435 | + | 0.0388067i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.223233 | − | 0.105045i | 0.223233 | − | 0.105045i | ||||
\(367\) | −0.749337 | − | 0.905793i | −0.749337 | − | 0.905793i | 0.248690 | − | 0.968583i | \(-0.420000\pi\) |
−0.998027 | + | 0.0627905i | \(0.980000\pi\) | |||||||
\(368\) | 0.779494 | + | 0.566335i | 0.779494 | + | 0.566335i | ||||
\(369\) | 0.0613551 | − | 0.485676i | 0.0613551 | − | 0.485676i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.0312307 | + | 0.121636i | −0.0312307 | + | 0.121636i | ||||
\(376\) | 1.68532 | + | 1.06954i | 1.68532 | + | 1.06954i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.0580752 | − | 0.459713i | −0.0580752 | − | 0.459713i | ||||
\(379\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.108877 | − | 0.171563i | 0.108877 | − | 0.171563i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.770513 | − | 1.63742i | 0.770513 | − | 1.63742i | − | 1.00000i | \(-0.5\pi\) | |
0.770513 | − | 0.637424i | \(-0.220000\pi\) | |||||||
\(384\) | 0.116762 | − | 0.0462295i | 0.116762 | − | 0.0462295i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.468693 | + | 1.44249i | 0.468693 | + | 1.44249i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.45309 | + | 0.154335i | −2.45309 | + | 0.154335i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.248690 | − | 0.968583i | \(-0.580000\pi\) | ||||
0.248690 | + | 0.968583i | \(0.420000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(401\) | −1.46560 | − | 1.21245i | −1.46560 | − | 1.21245i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
−0.535827 | − | 0.844328i | \(-0.680000\pi\) | |||||||
\(402\) | 0.0495420 | + | 0.125129i | 0.0495420 | + | 0.125129i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(405\) | −0.952937 | −0.952937 | ||||||||
\(406\) | −0.503997 | − | 1.27295i | −0.503997 | − | 1.27295i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.62954 | + | 0.645180i | 1.62954 | + | 0.645180i | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) |
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(410\) | 0.153699 | − | 0.473036i | 0.153699 | − | 0.473036i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.46404 | + | 0.688925i | 1.46404 | + | 0.688925i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 0.948312i | − | 0.948312i | ||||||
\(415\) | 1.25227 | − | 0.238883i | 1.25227 | − | 0.238883i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.481754 | − | 0.876307i | \(-0.660000\pi\) | ||||
0.481754 | + | 0.876307i | \(0.340000\pi\) | |||||||
\(420\) | 0.0146631 | − | 0.233064i | 0.0146631 | − | 0.233064i | ||||
\(421\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.123357 | − | 1.96070i | −0.123357 | − | 1.96070i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.95750 | + | 3.08452i | −1.95750 | + | 3.08452i | ||||
\(428\) | 0.582932 | + | 1.23879i | 0.582932 | + | 1.23879i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.193142 | + | 1.52888i | 0.193142 | + | 1.52888i | ||||
\(431\) | 0 | 0 | 0.481754 | − | 0.876307i | \(-0.340000\pi\) | ||||
−0.481754 | + | 0.876307i | \(0.660000\pi\) | |||||||
\(432\) | −0.210391 | − | 0.133518i | −0.210391 | − | 0.133518i | ||||
\(433\) | 0 | 0 | 0.248690 | − | 0.968583i | \(-0.420000\pi\) | ||||
−0.248690 | + | 0.968583i | \(0.580000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.0895542 | − | 0.0229936i | 0.0895542 | − | 0.0229936i | ||||
\(436\) | 1.89836 | − | 0.616814i | 1.89836 | − | 0.616814i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.125333 | − | 0.992115i | \(-0.460000\pi\) | ||||
−0.125333 | + | 0.992115i | \(0.540000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.54204 | + | 1.86401i | 1.54204 | + | 1.86401i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.11803 | − | 0.363271i | −1.11803 | − | 0.363271i | ||||
\(446\) | 0.250172 | + | 0.0157395i | 0.250172 | + | 0.0157395i | ||||
\(447\) | 0.210391 | − | 0.0265786i | 0.210391 | − | 0.0265786i | ||||
\(448\) | −1.09302 | + | 1.50441i | −1.09302 | + | 1.50441i | ||||
\(449\) | −0.0702235 | + | 0.368125i | −0.0702235 | + | 0.368125i | 0.929776 | + | 0.368125i | \(0.120000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(450\) | −0.966796 | − | 0.184426i | −0.966796 | − | 0.184426i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.621636 | + | 1.57007i | −0.621636 | + | 1.57007i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.684547 | − | 0.728969i | \(-0.260000\pi\) | ||||
−0.684547 | + | 0.728969i | \(0.740000\pi\) | |||||||
\(458\) | −1.88711 | − | 0.238398i | −1.88711 | − | 0.238398i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.180543 | − | 0.946441i | 0.180543 | − | 0.946441i | ||||
\(461\) | 0.804733 | − | 1.10762i | 0.804733 | − | 1.10762i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.992115 | − | 0.125333i | \(-0.0400000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.616814 | − | 0.0388067i | −0.616814 | − | 0.0388067i | −0.248690 | − | 0.968583i | \(-0.580000\pi\) |
−0.368125 | + | 0.929776i | \(0.620000\pi\) | |||||||
\(464\) | −0.700215 | − | 0.227513i | −0.700215 | − | 0.227513i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.75280 | + | 0.824805i | −1.75280 | + | 0.824805i | −0.770513 | + | 0.637424i | \(0.780000\pi\) |
−0.982287 | + | 0.187381i | \(0.940000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.61221 | − | 1.17134i | −1.61221 | − | 1.17134i | ||||
\(470\) | 0.250172 | − | 1.98031i | 0.250172 | − | 1.98031i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.125333 | − | 0.992115i | \(-0.540000\pi\) | ||||
0.125333 | + | 0.992115i | \(0.460000\pi\) | |||||||
\(480\) | −0.0915446 | − | 0.0859661i | −0.0915446 | − | 0.0859661i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.05267 | + | 1.65875i | −1.05267 | + | 1.65875i | ||||
\(483\) | −0.120562 | − | 0.189976i | −0.120562 | − | 0.189976i | ||||
\(484\) | −0.425779 | + | 0.904827i | −0.425779 | + | 0.904827i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.0231604 | + | 0.368125i | 0.0231604 | + | 0.368125i | ||||
\(487\) | −1.63560 | + | 1.03799i | −1.63560 | + | 1.03799i | −0.684547 | + | 0.728969i | \(0.740000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(488\) | 0.607087 | + | 1.86842i | 0.607087 | + | 1.86842i | ||||
\(489\) | 0.00845031 | − | 0.134314i | 0.00845031 | − | 0.134314i | ||||
\(490\) | 1.18412 | + | 2.15391i | 1.18412 | + | 2.15391i | ||||
\(491\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(492\) | −0.0604991 | − | 0.0155335i | −0.0604991 | − | 0.0155335i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.0398144 | − | 0.155067i | −0.0398144 | − | 0.155067i | ||||
\(499\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(500\) | −0.929776 | − | 0.368125i | −0.929776 | − | 0.368125i | ||||
\(501\) | −0.160442 | + | 0.150665i | −0.160442 | + | 0.150665i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.137959 | − | 0.348445i | −0.137959 | − | 0.348445i | 0.844328 | − | 0.535827i | \(-0.180000\pi\) |
−0.982287 | + | 0.187381i | \(0.940000\pi\) | |||||||
\(504\) | 1.83023 | 1.83023 | ||||||||
\(505\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.0462295 | + | 0.116762i | 0.0462295 | + | 0.116762i | ||||
\(508\) | 1.24672 | + | 1.03137i | 1.24672 | + | 1.03137i | ||||
\(509\) | 0.929324 | − | 0.872693i | 0.929324 | − | 0.872693i | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) |
0.992115 | + | 0.125333i | \(0.0400000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.248690 | + | 0.968583i | 0.248690 | + | 0.968583i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 1.61803i | − | 1.61803i | ||||||
\(516\) | 0.190096 | − | 0.0362627i | 0.190096 | − | 0.0362627i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.121636 | + | 1.93334i | −0.121636 | + | 1.93334i | 0.187381 | + | 0.982287i | \(0.440000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(522\) | 0.223925 | + | 0.689172i | 0.223925 | + | 0.689172i | ||||
\(523\) | −0.316423 | + | 0.200808i | −0.316423 | + | 0.200808i | −0.684547 | − | 0.728969i | \(-0.740000\pi\) |
0.368125 | + | 0.929776i | \(0.380000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.217126 | + | 0.0859661i | −0.217126 | + | 0.0859661i | ||||
\(526\) | 0.362576 | − | 0.770513i | 0.362576 | − | 0.770513i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.0305086 | + | 0.0648341i | 0.0305086 | + | 0.0648341i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.0367139 | + | 0.142991i | −0.0367139 | + | 0.142991i | ||||
\(535\) | 0.872693 | − | 1.05491i | 0.872693 | − | 1.05491i | ||||
\(536\) | −1.03799 | + | 0.266509i | −1.03799 | + | 0.266509i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.19975 | + | 0.659566i | 1.19975 | + | 0.659566i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.0312307 | + | 0.247217i | −0.0312307 | + | 0.247217i | ||||
\(541\) | 1.56720 | + | 1.13864i | 1.56720 | + | 1.13864i | 0.929776 | + | 0.368125i | \(0.120000\pi\) |
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.144860 | + | 0.0681659i | −0.144860 | + | 0.0681659i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.36639 | − | 1.45506i | −1.36639 | − | 1.45506i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.45506 | − | 0.0915446i | −1.45506 | − | 0.0915446i | −0.684547 | − | 0.728969i | \(-0.740000\pi\) |
−0.770513 | + | 0.637424i | \(0.780000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.13654 | − | 1.56431i | 1.13654 | − | 1.56431i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.120044 | − | 0.0151651i | −0.120044 | − | 0.0151651i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.82662 | + | 0.348445i | 1.82662 | + | 0.348445i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.03016 | − | 1.41789i | 1.03016 | − | 1.41789i | ||||
\(563\) | 1.16630 | − | 0.147338i | 1.16630 | − | 0.147338i | 0.481754 | − | 0.876307i | \(-0.340000\pi\) |
0.684547 | + | 0.728969i | \(0.260000\pi\) | |||||||
\(564\) | −0.250172 | − | 0.0157395i | −0.250172 | − | 0.0157395i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.340480 | − | 0.362574i | −0.340480 | − | 0.362574i | ||||
\(567\) | −1.04158 | − | 1.43361i | −1.04158 | − | 1.43361i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.812619 | + | 0.982287i | 0.812619 | + | 0.982287i | 1.00000 | \(0\) | ||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.125333 | − | 0.992115i | \(-0.460000\pi\) | ||||
−0.125333 | + | 0.992115i | \(0.540000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.879636 | − | 0.285811i | 0.879636 | − | 0.285811i | ||||
\(575\) | −0.933237 | + | 0.239615i | −0.933237 | + | 0.239615i | ||||
\(576\) | 0.627371 | − | 0.758362i | 0.627371 | − | 0.758362i | ||||
\(577\) | 0 | 0 | 0.248690 | − | 0.968583i | \(-0.420000\pi\) | ||||
−0.248690 | + | 0.968583i | \(0.580000\pi\) | |||||||
\(578\) | 0.844328 | + | 0.535827i | 0.844328 | + | 0.535827i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.0922765 | + | 0.730444i | 0.0922765 | + | 0.730444i | ||||
\(581\) | 1.72813 | + | 1.62282i | 1.72813 | + | 1.62282i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.113629 | − | 1.80608i | −0.113629 | − | 1.80608i | −0.481754 | − | 0.876307i | \(-0.660000\pi\) |
0.368125 | − | 0.929776i | \(-0.380000\pi\) | |||||||
\(588\) | 0.260619 | − | 0.165394i | 0.260619 | − | 0.165394i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.68866i | 1.68866i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.248690 | − | 0.968583i | \(-0.580000\pi\) | ||||
0.248690 | + | 0.968583i | \(0.420000\pi\) | |||||||
\(600\) | −0.0388067 | + | 0.119435i | −0.0388067 | + | 0.119435i | ||||
\(601\) | −0.574633 | − | 0.227513i | −0.574633 | − | 0.227513i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(602\) | −2.08895 | + | 1.96165i | −2.08895 | + | 1.96165i | ||||
\(603\) | 0.812701 | + | 0.672325i | 0.812701 | + | 0.672325i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | 1.00000 | ||||||||
\(606\) | −0.0915446 | − | 0.0859661i | −0.0915446 | − | 0.0859661i | ||||
\(607\) | −1.80965 | −1.80965 | −0.904827 | − | 0.425779i | \(-0.860000\pi\) | ||||
−0.904827 | + | 0.425779i | \(0.860000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.132476 | + | 0.109594i | 0.132476 | + | 0.109594i | ||||
\(610\) | 1.43211 | − | 1.34484i | 1.43211 | − | 1.34484i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.248690 | − | 0.968583i | \(-0.580000\pi\) | ||||
0.248690 | + | 0.968583i | \(0.420000\pi\) | |||||||
\(614\) | −0.666178 | − | 0.313480i | −0.666178 | − | 0.313480i | ||||
\(615\) | 0.0117041 | + | 0.0613551i | 0.0117041 | + | 0.0613551i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.982287 | − | 0.187381i | \(-0.0600000\pi\) | ||||
−0.982287 | + | 0.187381i | \(0.940000\pi\) | |||||||
\(618\) | −0.202793 | + | 0.0127587i | −0.202793 | + | 0.0127587i | ||||
\(619\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.115663 | + | 0.210391i | 0.115663 | + | 0.210391i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.675522 | − | 2.07904i | −0.675522 | − | 2.07904i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.0627905 | + | 0.998027i | 0.0627905 | + | 0.998027i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −0.779273 | − | 1.65604i | −0.779273 | − | 1.65604i | ||||
\(631\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.402389 | − | 1.56720i | 0.402389 | − | 1.56720i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.770513 | − | 0.637424i | 0.770513 | − | 0.637424i | ||||
\(641\) | −0.147338 | + | 1.16630i | −0.147338 | + | 1.16630i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(642\) | −0.139096 | − | 0.101059i | −0.139096 | − | 0.101059i | ||||
\(643\) | 0 | 0 | 0.770513 | − | 0.637424i | \(-0.220000\pi\) | ||||
−0.770513 | + | 0.637424i | \(0.780000\pi\) | |||||||
\(644\) | 1.62117 | − | 0.762866i | 1.62117 | − | 0.762866i | ||||
\(645\) | −0.113750 | − | 0.156564i | −0.113750 | − | 0.156564i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.88711 | + | 0.613161i | 1.88711 | + | 0.613161i | 0.982287 | + | 0.187381i | \(0.0600000\pi\) |
0.904827 | + | 0.425779i | \(0.140000\pi\) | |||||||
\(648\) | −0.951057 | − | 0.0598354i | −0.951057 | − | 0.0598354i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.05267 | + | 0.200808i | 1.05267 | + | 0.200808i | ||||
\(653\) | 0 | 0 | −0.992115 | − | 0.125333i | \(-0.960000\pi\) | ||||
0.992115 | + | 0.125333i | \(0.0400000\pi\) | |||||||
\(654\) | −0.171593 | + | 0.182728i | −0.171593 | + | 0.182728i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.183098 | − | 0.462452i | 0.183098 | − | 0.462452i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.25265 | − | 1.78816i | 3.25265 | − | 1.78816i | ||||
\(659\) | 0 | 0 | 0.684547 | − | 0.728969i | \(-0.260000\pi\) | ||||
−0.684547 | + | 0.728969i | \(0.740000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.77760 | − | 0.339095i | −1.77760 | − | 0.339095i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.26480 | − | 0.159781i | 1.26480 | − | 0.159781i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.485605 | + | 0.517117i | 0.485605 | + | 0.517117i | ||||
\(668\) | −1.03016 | − | 1.41789i | −1.03016 | − | 1.41789i | ||||
\(669\) | −0.0284830 | + | 0.0134031i | −0.0284830 | + | 0.0134031i | ||||
\(670\) | 0.683098 | + | 0.825723i | 0.683098 | + | 0.825723i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.0292684 | − | 0.231683i | 0.0292684 | − | 0.231683i | ||||
\(673\) | 0 | 0 | 0.770513 | − | 0.637424i | \(-0.220000\pi\) | ||||
−0.770513 | + | 0.637424i | \(0.780000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.236986 | − | 0.0770013i | 0.236986 | − | 0.0770013i | ||||
\(676\) | −0.968583 | + | 0.248690i | −0.968583 | + | 0.248690i | ||||
\(677\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.0265786 | − | 0.210391i | −0.0265786 | − | 0.210391i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.106729 | + | 0.226810i | 0.106729 | + | 0.226810i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.844328 | + | 0.535827i | \(0.820000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.15434 | + | 2.45309i | −1.15434 | + | 2.45309i | ||||
\(687\) | 0.222095 | − | 0.0879337i | 0.222095 | − | 0.0879337i | ||||
\(688\) | 0.0967619 | + | 1.53799i | 0.0967619 | + | 1.53799i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.0373905 | + | 0.115076i | 0.0373905 | + | 0.115076i | ||||
\(691\) | 0 | 0 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.41213 | − | 0.362574i | −1.41213 | − | 0.362574i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.0908212 | − | 0.0173251i | 0.0908212 | − | 0.0173251i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −0.0469702 | − | 0.246226i | −0.0469702 | − | 0.246226i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.462452 | − | 1.80113i | −0.462452 | − | 1.80113i | ||||
\(701\) | 0.598617 | − | 1.84235i | 0.598617 | − | 1.84235i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.0922765 | + | 0.233064i | 0.0922765 | + | 0.233064i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.82662 | + | 0.348445i | 1.82662 | + | 0.348445i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.666178 | − | 1.68257i | −0.666178 | − | 1.68257i | −0.728969 | − | 0.684547i | \(-0.760000\pi\) |
0.0627905 | − | 0.998027i | \(-0.480000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.09302 | − | 0.432756i | −1.09302 | − | 0.432756i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.998027 | − | 0.0627905i | \(-0.0200000\pi\) | ||||
−0.998027 | + | 0.0627905i | \(0.980000\pi\) | |||||||
\(720\) | −0.953308 | − | 0.244768i | −0.953308 | − | 0.244768i | ||||
\(721\) | 2.43419 | − | 1.76854i | 2.43419 | − | 1.76854i | ||||
\(722\) | 0.481754 | + | 0.876307i | 0.481754 | + | 0.876307i | ||||
\(723\) | 0.0154913 | − | 0.246226i | 0.0154913 | − | 0.246226i | ||||
\(724\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | ||||
\(725\) | 0.621636 | − | 0.394502i | 0.621636 | − | 0.394502i | ||||
\(726\) | −0.00788530 | − | 0.125333i | −0.00788530 | − | 0.125333i | ||||
\(727\) | 1.76854 | − | 0.700215i | 1.76854 | − | 0.700215i | 0.770513 | − | 0.637424i | \(-0.220000\pi\) |
0.998027 | − | 0.0627905i | \(-0.0200000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.485789 | + | 0.765481i | 0.485789 | + | 0.765481i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.179846 | − | 0.168887i | −0.179846 | − | 0.168887i | ||||
\(733\) | 0 | 0 | −0.125333 | − | 0.992115i | \(-0.540000\pi\) | ||||
0.125333 | + | 0.992115i | \(0.460000\pi\) | |||||||
\(734\) | −0.566335 | + | 1.03016i | −0.566335 | + | 1.03016i | ||||
\(735\) | −0.260619 | − | 0.165394i | −0.260619 | − | 0.165394i | ||||
\(736\) | 0.239615 | − | 0.933237i | 0.239615 | − | 0.933237i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.474156 | + | 0.121743i | −0.474156 | + | 0.121743i | ||||
\(739\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.36615 | − | 0.992567i | −1.36615 | − | 0.992567i | −0.998027 | − | 0.0627905i | \(-0.980000\pi\) |
−0.368125 | − | 0.929776i | \(-0.620000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.52794 | − | 0.718995i | 1.52794 | − | 0.718995i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.858931 | − | 0.914668i | −0.858931 | − | 0.914668i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.54088 | + | 0.159859i | 2.54088 | + | 0.159859i | ||||
\(750\) | 0.124591 | − | 0.0157395i | 0.124591 | − | 0.0157395i | ||||
\(751\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(752\) | 0.374023 | − | 1.96070i | 0.374023 | − | 1.96070i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.406051 | + | 0.223228i | −0.406051 | + | 0.223228i | ||||
\(757\) | 0 | 0 | 0.368125 | − | 0.929776i | \(-0.380000\pi\) | ||||
−0.368125 | + | 0.929776i | \(0.620000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.844844 | − | 0.106729i | −0.844844 | − | 0.106729i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(762\) | −0.199595 | − | 0.0380748i | −0.199595 | − | 0.0380748i | ||||
\(763\) | 0.695516 | − | 3.64602i | 0.695516 | − | 3.64602i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.80608 | − | 0.113629i | −1.80608 | − | 0.113629i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.0859661 | − | 0.0915446i | −0.0859661 | − | 0.0915446i | ||||
\(769\) | 0.905793 | + | 1.24672i | 0.905793 | + | 1.24672i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.125333 | − | 0.992115i | \(-0.460000\pi\) | ||||
−0.125333 | + | 0.992115i | \(0.540000\pi\) | |||||||
\(774\) | 1.16866 | − | 0.966796i | 1.16866 | − | 0.966796i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.133736 | − | 0.125587i | −0.133736 | − | 0.125587i | ||||
\(784\) | 1.04654 | + | 2.22401i | 1.04654 | + | 2.22401i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.836475 | − | 1.77760i | 0.836475 | − | 1.77760i | 0.248690 | − | 0.968583i | \(-0.420000\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.00671479 | + | 0.106729i | 0.00671479 | + | 0.106729i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.982287 | − | 0.187381i | \(-0.0600000\pi\) | ||||
−0.982287 | + | 0.187381i | \(0.940000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.904827 | − | 0.425779i | −0.904827 | − | 0.425779i | ||||
\(801\) | 0.287742 | + | 1.12068i | 0.287742 | + | 1.12068i | ||||
\(802\) | −0.587785 | + | 1.80902i | −0.587785 | + | 1.80902i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.0981041 | − | 0.0921259i | 0.0981041 | − | 0.0921259i | ||||
\(805\) | −1.38052 | − | 1.14207i | −1.38052 | − | 1.14207i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.171932 | −0.171932 | ||||||||
\(808\) | 0.770513 | − | 0.637424i | 0.770513 | − | 0.637424i | ||||
\(809\) | −1.85955 | −1.85955 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(810\) | 0.350799 | + | 0.886018i | 0.350799 | + | 0.886018i | ||||
\(811\) | 0 | 0 | −0.770513 | − | 0.637424i | \(-0.780000\pi\) | ||||
0.770513 | + | 0.637424i | \(0.220000\pi\) | |||||||
\(812\) | −0.998027 | + | 0.937209i | −0.998027 | + | 0.937209i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.266509 | − | 1.03799i | −0.266509 | − | 1.03799i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 1.75261i | − | 1.75261i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.496398 | + | 0.0312307i | −0.496398 | + | 0.0312307i | ||||
\(821\) | 1.69755 | + | 0.435857i | 1.69755 | + | 0.435857i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.844328 | + | 1.53583i | 0.844328 | + | 1.53583i | 0.844328 | + | 0.535827i | \(0.180000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | 0.101597 | − | 1.61484i | 0.101597 | − | 1.61484i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.0604991 | − | 0.961606i | −0.0604991 | − | 0.961606i | −0.904827 | − | 0.425779i | \(-0.860000\pi\) |
0.844328 | − | 0.535827i | \(-0.180000\pi\) | |||||||
\(828\) | −0.881718 | + | 0.349097i | −0.881718 | + | 0.349097i | ||||
\(829\) | −0.620759 | + | 1.31918i | −0.620759 | + | 1.31918i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(830\) | −0.683098 | − | 1.07639i | −0.683098 | − | 1.07639i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.844328 | + | 1.53583i | −0.844328 | + | 1.53583i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(840\) | −0.222095 | + | 0.0721631i | −0.222095 | + | 0.0721631i | ||||
\(841\) | 0.401293 | + | 0.220613i | 0.401293 | + | 0.220613i | ||||
\(842\) | −1.24672 | + | 1.03137i | −1.24672 | + | 1.03137i | ||||
\(843\) | −0.0275852 | + | 0.218359i | −0.0275852 | + | 0.218359i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.637424 | + | 0.770513i | 0.637424 | + | 0.770513i | ||||
\(846\) | −1.77760 | + | 0.836475i | −1.77760 | + | 0.836475i | ||||
\(847\) | 1.09302 | + | 1.50441i | 1.09302 | + | 1.50441i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.0594044 | + | 0.0193017i | 0.0594044 | + | 0.0193017i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(854\) | 3.58852 | + | 0.684547i | 3.58852 | + | 0.684547i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.937209 | − | 0.998027i | 0.937209 | − | 0.998027i | ||||
\(857\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.368125 | − | 0.929776i | \(-0.380000\pi\) | ||||
−0.368125 | + | 0.929776i | \(0.620000\pi\) | |||||||
\(860\) | 1.35041 | − | 0.742395i | 1.35041 | − | 0.742395i | ||||
\(861\) | −0.0795104 | + | 0.0846700i | −0.0795104 | + | 0.0846700i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.90285 | + | 0.362989i | 1.90285 | + | 0.362989i | 0.998027 | − | 0.0627905i | \(-0.0200000\pi\) |
0.904827 | + | 0.425779i | \(0.140000\pi\) | |||||||
\(864\) | −0.0466920 | + | 0.244768i | −0.0466920 | + | 0.244768i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.125333 | − | 0.00788530i | −0.125333 | − | 0.00788530i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.0543460 | − | 0.0748008i | −0.0543460 | − | 0.0748008i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.27233 | − | 1.53799i | −1.27233 | − | 1.53799i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.43281 | + | 1.18532i | −1.43281 | + | 1.18532i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.419952 | − | 0.266509i | −0.419952 | − | 0.266509i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(882\) | 1.16545 | − | 2.11994i | 1.16545 | − | 2.11994i | ||||
\(883\) | 0.242791 | + | 1.92189i | 0.242791 | + | 1.92189i | 0.368125 | + | 0.929776i | \(0.380000\pi\) |
−0.125333 | + | 0.992115i | \(0.540000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.331159 | + | 0.521823i | −0.331159 | + | 0.521823i | ||||
\(887\) | 0.394502 | + | 0.621636i | 0.394502 | + | 0.621636i | 0.982287 | − | 0.187381i | \(-0.0600000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.79753 | − | 1.10762i | 2.79753 | − | 1.10762i | ||||
\(890\) | 0.0738147 | + | 1.17325i | 0.0738147 | + | 1.17325i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.0774602 | − | 0.238398i | −0.0774602 | − | 0.238398i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.102162 | − | 0.185832i | −0.102162 | − | 0.185832i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.80113 | + | 0.462452i | 1.80113 | + | 0.462452i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.368125 | − | 0.0702235i | 0.368125 | − | 0.0702235i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.184426 | + | 0.966796i | 0.184426 | + | 0.966796i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.111205 | − | 0.342254i | 0.111205 | − | 0.342254i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.929324 | + | 0.872693i | −0.929324 | + | 0.872693i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.730444 | + | 1.84489i | 0.730444 | + | 1.84489i | 0.481754 | + | 0.876307i | \(0.340000\pi\) |
0.248690 | + | 0.968583i | \(0.420000\pi\) | |||||||
\(908\) | 1.68866 | 1.68866 | ||||||||
\(909\) | −0.953308 | − | 0.244768i | −0.953308 | − | 0.244768i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.368125 | − | 0.929776i | \(-0.620000\pi\) | ||||
0.368125 | + | 0.929776i | \(0.380000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0762386 | + | 0.234638i | −0.0762386 | + | 0.234638i | ||||
\(916\) | 0.473036 | + | 1.84235i | 0.473036 | + | 1.84235i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | −0.946441 | + | 0.180543i | −0.946441 | + | 0.180543i | ||||
\(921\) | 0.0922765 | − | 0.00580554i | 0.0922765 | − | 0.00580554i | ||||
\(922\) | −1.32608 | − | 0.340480i | −1.32608 | − | 0.340480i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(927\) | −1.34461 | + | 0.853313i | −1.34461 | + | 0.853313i | ||||
\(928\) | 0.0462295 | + | 0.734796i | 0.0462295 | + | 0.734796i | ||||
\(929\) | −1.80113 | + | 0.713118i | −1.80113 | + | 0.713118i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.41213 | + | 1.32608i | 1.41213 | + | 1.32608i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.844328 | − | 0.535827i | \(-0.820000\pi\) | ||||
0.844328 | + | 0.535827i | \(0.180000\pi\) | |||||||
\(938\) | −0.495588 | + | 1.93019i | −0.495588 | + | 1.93019i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.93334 | + | 0.496398i | −1.93334 | + | 0.496398i | ||||
\(941\) | −1.60601 | + | 0.521823i | −1.60601 | + | 0.521823i | −0.968583 | − | 0.248690i | \(-0.920000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.369252 | + | 0.305472i | −0.369252 | + | 0.305472i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.374871 | + | 0.272360i | 0.374871 | + | 0.272360i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.79538 | − | 0.844844i | 1.79538 | − | 0.844844i | 0.844328 | − | 0.535827i | \(-0.180000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.0462295 | + | 0.116762i | −0.0462295 | + | 0.116762i | ||||
\(961\) | 0.876307 | − | 0.481754i | 0.876307 | − | 0.481754i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.33688 | − | 0.168887i | −1.33688 | − | 0.168887i | ||||
\(964\) | 1.92978 | + | 0.368125i | 1.92978 | + | 0.368125i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.132253 | + | 0.182031i | −0.132253 | + | 0.182031i | ||||
\(967\) | −1.79538 | + | 0.226810i | −1.79538 | + | 0.226810i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.844328 | + | 0.535827i | \(0.820000\pi\) | |||||||
\(968\) | 0.998027 | + | 0.0627905i | 0.998027 | + | 0.0627905i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(972\) | 0.333748 | − | 0.157050i | 0.333748 | − | 0.157050i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.56720 | + | 1.13864i | 1.56720 | + | 1.13864i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.51373 | − | 1.25227i | 1.51373 | − | 1.25227i | ||||
\(977\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(978\) | −0.127993 | + | 0.0415873i | −0.127993 | + | 0.0415873i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.56675 | − | 1.89387i | 1.56675 | − | 1.89387i | ||||
\(981\) | −0.488570 | + | 1.90285i | −0.488570 | + | 1.90285i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.933237 | + | 1.69755i | −0.933237 | + | 1.69755i | −0.248690 | + | 0.968583i | \(0.580000\pi\) |
−0.684547 | + | 0.728969i | \(0.740000\pi\) | |||||||
\(984\) | 0.00782850 | + | 0.0619689i | 0.00782850 | + | 0.0619689i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.249764 | + | 0.393565i | −0.249764 | + | 0.393565i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.632193 | − | 1.34348i | 0.632193 | − | 1.34348i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) | ||||
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.129521 | + | 0.0941025i | −0.129521 | + | 0.0941025i | ||||
\(997\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(998\) | 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 | 2020.1.bt.c.1019.1 | ✓ | 40 | |
4.3 | odd | 2 | inner | 2020.1.bt.c.1019.2 | yes | 40 | |
5.4 | even | 2 | inner | 2020.1.bt.c.1019.2 | yes | 40 | |
20.19 | odd | 2 | CM | 2020.1.bt.c.1019.1 | ✓ | 40 | |
101.45 | even | 50 | inner | 2020.1.bt.c.1459.1 | yes | 40 | |
404.247 | odd | 50 | inner | 2020.1.bt.c.1459.2 | yes | 40 | |
505.449 | even | 50 | inner | 2020.1.bt.c.1459.2 | yes | 40 | |
2020.1459 | odd | 50 | inner | 2020.1.bt.c.1459.1 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2020.1.bt.c.1019.1 | ✓ | 40 | 1.1 | even | 1 | trivial | |
2020.1.bt.c.1019.1 | ✓ | 40 | 20.19 | odd | 2 | CM | |
2020.1.bt.c.1019.2 | yes | 40 | 4.3 | odd | 2 | inner | |
2020.1.bt.c.1019.2 | yes | 40 | 5.4 | even | 2 | inner | |
2020.1.bt.c.1459.1 | yes | 40 | 101.45 | even | 50 | inner | |
2020.1.bt.c.1459.1 | yes | 40 | 2020.1459 | odd | 50 | inner | |
2020.1.bt.c.1459.2 | yes | 40 | 404.247 | odd | 50 | inner | |
2020.1.bt.c.1459.2 | yes | 40 | 505.449 | even | 50 | inner |