Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2020,1,Mod(19,2020)]
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, 48]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2020.19");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2020 = 2^{2} \cdot 5 \cdot 101 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2020.bu (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: | \(20\) |
Coefficient field: | \(\Q(\zeta_{50})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{15} + x^{10} - x^{5} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{25}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{25} - \cdots)\) |
Embedding invariants
Embedding label | 1179.1 | ||
Root | \(-0.0627905 - 0.998027i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2020.1179 |
Dual form | 2020.1.bu.b.759.1 |
$q$-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 \(\left(\mathbb{Z}/2020\mathbb{Z}\right)^\times\).
\(n\) | \(1011\) | \(1617\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{8}{25}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.535827 | − | 0.844328i | −0.535827 | − | 0.844328i | ||||
\(3\) | 1.23480 | + | 0.317042i | 1.23480 | + | 0.317042i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(4\) | −0.425779 | + | 0.904827i | −0.425779 | + | 0.904827i | ||||
\(5\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(6\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | ||||
\(7\) | 0.996398 | − | 0.394502i | 0.996398 | − | 0.394502i | 0.187381 | − | 0.982287i | \(-0.440000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(8\) | 0.992115 | − | 0.125333i | 0.992115 | − | 0.125333i | ||||
\(9\) | 0.547900 | + | 0.301210i | 0.547900 | + | 0.301210i | ||||
\(10\) | −1.00000 | −1.00000 | ||||||||
\(11\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(12\) | −0.812619 | + | 0.982287i | −0.812619 | + | 0.982287i | ||||
\(13\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(14\) | −0.866986 | − | 0.629902i | −0.866986 | − | 0.629902i | ||||
\(15\) | 0.929324 | − | 0.872693i | 0.929324 | − | 0.872693i | ||||
\(16\) | −0.637424 | − | 0.770513i | −0.637424 | − | 0.770513i | ||||
\(17\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(18\) | −0.0392590 | − | 0.624004i | −0.0392590 | − | 0.624004i | ||||
\(19\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(20\) | 0.535827 | + | 0.844328i | 0.535827 | + | 0.844328i | ||||
\(21\) | 1.35542 | − | 0.171230i | 1.35542 | − | 0.171230i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0915446 | + | 1.45506i | −0.0915446 | + | 1.45506i | 0.637424 | + | 0.770513i | \(0.280000\pi\) |
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(24\) | 1.26480 | + | 0.159781i | 1.26480 | + | 0.159781i | ||||
\(25\) | −0.425779 | − | 0.904827i | −0.425779 | − | 0.904827i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.348276 | − | 0.327053i | −0.348276 | − | 0.327053i | ||||
\(28\) | −0.0672897 | + | 1.06954i | −0.0672897 | + | 1.06954i | ||||
\(29\) | −0.996398 | − | 0.394502i | −0.996398 | − | 0.394502i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(30\) | −1.23480 | − | 0.317042i | −1.23480 | − | 0.317042i | ||||
\(31\) | 0 | 0 | 0.929776 | − | 0.368125i | \(-0.120000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(32\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.200808 | − | 1.05267i | 0.200808 | − | 1.05267i | ||||
\(36\) | −0.505828 | + | 0.367505i | −0.505828 | + | 0.367505i | ||||
\(37\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.425779 | − | 0.904827i | 0.425779 | − | 0.904827i | ||||
\(41\) | −0.574633 | − | 1.76854i | −0.574633 | − | 1.76854i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.0627905 | − | 0.998027i | \(-0.480000\pi\) | |||||||
\(42\) | −0.870846 | − | 1.05267i | −0.870846 | − | 1.05267i | ||||
\(43\) | 0.362989 | + | 1.90285i | 0.362989 | + | 1.90285i | 0.425779 | + | 0.904827i | \(0.360000\pi\) |
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.547900 | − | 0.301210i | 0.547900 | − | 0.301210i | ||||
\(46\) | 1.27760 | − | 0.702367i | 1.27760 | − | 0.702367i | ||||
\(47\) | −0.238883 | + | 1.25227i | −0.238883 | + | 1.25227i | 0.637424 | + | 0.770513i | \(0.280000\pi\) |
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(48\) | −0.542804 | − | 1.15352i | −0.542804 | − | 1.15352i | ||||
\(49\) | 0.108209 | − | 0.101615i | 0.108209 | − | 0.101615i | ||||
\(50\) | −0.535827 | + | 0.844328i | −0.535827 | + | 0.844328i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(54\) | −0.0895243 | + | 0.469303i | −0.0895243 | + | 0.469303i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.939097 | − | 0.516273i | 0.939097 | − | 0.516273i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.200808 | + | 1.05267i | 0.200808 | + | 1.05267i | ||||
\(59\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(60\) | 0.393950 | + | 1.21245i | 0.393950 | + | 1.21245i | ||||
\(61\) | −0.746226 | + | 1.58581i | −0.746226 | + | 1.58581i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.664754 | + | 0.0839780i | 0.664754 | + | 0.0839780i | ||||
\(64\) | 0.968583 | − | 0.248690i | 0.968583 | − | 0.248690i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.121636 | + | 0.0312307i | −0.121636 | + | 0.0312307i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.574354 | + | 1.76768i | −0.574354 | + | 1.76768i | ||||
\(70\) | −0.996398 | + | 0.394502i | −0.996398 | + | 0.394502i | ||||
\(71\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(72\) | 0.581331 | + | 0.230165i | 0.581331 | + | 0.230165i | ||||
\(73\) | 0 | 0 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.238883 | − | 1.25227i | −0.238883 | − | 1.25227i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) | ||||
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(80\) | −0.992115 | + | 0.125333i | −0.992115 | + | 0.125333i | ||||
\(81\) | −0.661379 | − | 1.04217i | −0.661379 | − | 1.04217i | ||||
\(82\) | −1.18532 | + | 1.43281i | −1.18532 | + | 1.43281i | ||||
\(83\) | −0.121636 | − | 1.93334i | −0.121636 | − | 1.93334i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.187381 | − | 0.982287i | \(-0.440000\pi\) | |||||||
\(84\) | −0.422178 | + | 1.29933i | −0.422178 | + | 1.29933i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.41213 | − | 1.32608i | 1.41213 | − | 1.32608i | ||||
\(87\) | −1.10528 | − | 0.803030i | −1.10528 | − | 0.803030i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.03137 | − | 1.24672i | 1.03137 | − | 1.24672i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(90\) | −0.547900 | − | 0.301210i | −0.547900 | − | 0.301210i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.27760 | − | 0.702367i | −1.27760 | − | 0.702367i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.18532 | − | 0.469303i | 1.18532 | − | 0.469303i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.683098 | + | 1.07639i | −0.683098 | + | 1.07639i | ||||
\(97\) | 0 | 0 | 0.425779 | − | 0.904827i | \(-0.360000\pi\) | ||||
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(98\) | −0.143778 | − | 0.0369159i | −0.143778 | − | 0.0369159i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 1.00000 | ||||||||
\(101\) | −0.992115 | + | 0.125333i | −0.992115 | + | 0.125333i | ||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.866986 | + | 1.36615i | 0.866986 | + | 1.36615i | 0.929776 | + | 0.368125i | \(0.120000\pi\) |
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.581698 | − | 1.23617i | 0.581698 | − | 1.23617i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.263146 | + | 0.809880i | 0.263146 | + | 0.809880i | 0.992115 | + | 0.125333i | \(0.0400000\pi\) |
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(108\) | 0.444215 | − | 0.175877i | 0.444215 | − | 0.175877i | ||||
\(109\) | 1.26480 | − | 0.159781i | 1.26480 | − | 0.159781i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.939097 | − | 0.516273i | −0.939097 | − | 0.516273i | ||||
\(113\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.17950 | + | 0.856954i | 1.17950 | + | 0.856954i | ||||
\(116\) | 0.781202 | − | 0.733597i | 0.781202 | − | 0.733597i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.812619 | − | 0.982287i | 0.812619 | − | 0.982287i | ||||
\(121\) | 0.535827 | + | 0.844328i | 0.535827 | + | 0.844328i | ||||
\(122\) | 1.73879 | − | 0.219661i | 1.73879 | − | 0.219661i | ||||
\(123\) | −0.148854 | − | 2.36597i | −0.148854 | − | 2.36597i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.992115 | − | 0.125333i | −0.992115 | − | 0.125333i | ||||
\(126\) | −0.285288 | − | 0.606268i | −0.285288 | − | 0.606268i | ||||
\(127\) | −0.303189 | − | 1.58937i | −0.303189 | − | 1.58937i | −0.728969 | − | 0.684547i | \(-0.760000\pi\) |
0.425779 | − | 0.904827i | \(-0.360000\pi\) | |||||||
\(128\) | −0.728969 | − | 0.684547i | −0.728969 | − | 0.684547i | ||||
\(129\) | −0.155067 | + | 2.46472i | −0.155067 | + | 2.46472i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.0915446 | + | 0.0859661i | 0.0915446 | + | 0.0859661i | ||||
\(135\) | −0.462756 | + | 0.118815i | −0.462756 | + | 0.118815i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(138\) | 1.80026 | − | 0.462227i | 1.80026 | − | 0.462227i | ||||
\(139\) | 0 | 0 | −0.992115 | − | 0.125333i | \(-0.960000\pi\) | ||||
0.992115 | + | 0.125333i | \(0.0400000\pi\) | |||||||
\(140\) | 0.866986 | + | 0.629902i | 0.866986 | + | 0.629902i | ||||
\(141\) | −0.691992 | + | 1.47056i | −0.691992 | + | 1.47056i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.117158 | − | 0.614163i | −0.117158 | − | 0.614163i | ||||
\(145\) | −0.866986 | + | 0.629902i | −0.866986 | + | 0.629902i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.165832 | − | 0.0911672i | 0.165832 | − | 0.0911672i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.0534698 | − | 0.113629i | −0.0534698 | − | 0.113629i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(150\) | −0.929324 | + | 0.872693i | −0.929324 | + | 0.872693i | ||||
\(151\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.637424 | + | 0.770513i | 0.637424 | + | 0.770513i | ||||
\(161\) | 0.482809 | + | 1.48593i | 0.482809 | + | 1.48593i | ||||
\(162\) | −0.525546 | + | 1.11684i | −0.525546 | + | 1.11684i | ||||
\(163\) | 0.101597 | + | 0.0738147i | 0.101597 | + | 0.0738147i | 0.637424 | − | 0.770513i | \(-0.280000\pi\) |
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(164\) | 1.84489 | + | 0.233064i | 1.84489 | + | 0.233064i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.56720 | + | 1.13864i | −1.56720 | + | 1.13864i | ||||
\(167\) | 0.273190 | − | 1.43211i | 0.273190 | − | 1.43211i | −0.535827 | − | 0.844328i | \(-0.680000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(168\) | 1.32327 | − | 0.339759i | 1.32327 | − | 0.339759i | ||||
\(169\) | 0.728969 | + | 0.684547i | 0.728969 | + | 0.684547i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.87631 | − | 0.481754i | −1.87631 | − | 0.481754i | ||||
\(173\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(174\) | −0.0857841 | + | 1.36350i | −0.0857841 | + | 1.36350i | ||||
\(175\) | −0.781202 | − | 0.733597i | −0.781202 | − | 0.733597i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.60528 | − | 0.202793i | −1.60528 | − | 0.202793i | ||||
\(179\) | 0 | 0 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(180\) | 0.0392590 | + | 0.624004i | 0.0392590 | + | 0.624004i | ||||
\(181\) | −1.92189 | + | 0.242791i | −1.92189 | + | 0.242791i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.42421 | + | 1.72157i | −1.42421 | + | 1.72157i | ||||
\(184\) | 0.0915446 | + | 1.45506i | 0.0915446 | + | 1.45506i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.03137 | − | 0.749337i | −1.03137 | − | 0.749337i | ||||
\(189\) | −0.476045 | − | 0.188479i | −0.476045 | − | 0.188479i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(192\) | 1.27485 | 1.27485 | ||||||||
\(193\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.0458709 | + | 0.141176i | 0.0458709 | + | 0.141176i | ||||
\(197\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(200\) | −0.535827 | − | 0.844328i | −0.535827 | − | 0.844328i | ||||
\(201\) | −0.160097 | −0.160097 | ||||||||
\(202\) | 0.637424 | + | 0.770513i | 0.637424 | + | 0.770513i | ||||
\(203\) | −1.14844 | −1.14844 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.80113 | − | 0.462452i | −1.80113 | − | 0.462452i | ||||
\(206\) | 0.688925 | − | 1.46404i | 0.688925 | − | 1.46404i | ||||
\(207\) | −0.488437 | + | 0.769653i | −0.488437 | + | 0.769653i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.35542 | + | 0.171230i | −1.35542 | + | 0.171230i | ||||
\(211\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.542804 | − | 0.656137i | 0.542804 | − | 0.656137i | ||||
\(215\) | 1.80113 | + | 0.713118i | 1.80113 | + | 0.713118i | ||||
\(216\) | −0.386520 | − | 0.280823i | −0.386520 | − | 0.280823i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.812619 | − | 0.982287i | −0.812619 | − | 0.982287i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.371808 | + | 0.0469702i | −0.371808 | + | 0.0469702i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(224\) | 0.0672897 | + | 1.06954i | 0.0672897 | + | 1.06954i | ||||
\(225\) | 0.0392590 | − | 0.624004i | 0.0392590 | − | 0.624004i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.0534698 | + | 0.113629i | 0.0534698 | + | 0.113629i | 0.929776 | − | 0.368125i | \(-0.120000\pi\) |
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.450527 | + | 0.423073i | 0.450527 | + | 0.423073i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(230\) | 0.0915446 | − | 1.45506i | 0.0915446 | − | 1.45506i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.03799 | − | 0.266509i | −1.03799 | − | 0.266509i | ||||
\(233\) | 0 | 0 | 0.929776 | − | 0.368125i | \(-0.120000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.929324 | + | 0.872693i | 0.929324 | + | 0.872693i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(240\) | −1.26480 | − | 0.159781i | −1.26480 | − | 0.159781i | ||||
\(241\) | −1.41789 | − | 1.03016i | −1.41789 | − | 1.03016i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.425779 | − | 0.904827i | \(-0.640000\pi\) | |||||||
\(242\) | 0.425779 | − | 0.904827i | 0.425779 | − | 0.904827i | ||||
\(243\) | −0.338621 | − | 1.04217i | −0.338621 | − | 1.04217i | ||||
\(244\) | −1.11716 | − | 1.35041i | −1.11716 | − | 1.35041i | ||||
\(245\) | −0.0278151 | − | 0.145812i | −0.0278151 | − | 0.145812i | ||||
\(246\) | −1.91789 | + | 1.39343i | −1.91789 | + | 1.39343i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.462756 | − | 2.42585i | 0.462756 | − | 2.42585i | ||||
\(250\) | 0.425779 | + | 0.904827i | 0.425779 | + | 0.904827i | ||||
\(251\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(252\) | −0.359024 | + | 0.565732i | −0.359024 | + | 0.565732i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.17950 | + | 1.10762i | −1.17950 | + | 1.10762i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.187381 | + | 0.982287i | −0.187381 | + | 0.982287i | ||||
\(257\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(258\) | 2.16412 | − | 1.18974i | 2.16412 | − | 1.18974i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.427098 | − | 0.516273i | −0.427098 | − | 0.516273i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.844844 | + | 1.79538i | −0.844844 | + | 1.79538i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.66880 | − | 1.21245i | 1.66880 | − | 1.21245i | ||||
\(268\) | 0.0235315 | − | 0.123357i | 0.0235315 | − | 0.123357i | ||||
\(269\) | −0.824805 | + | 0.211774i | −0.824805 | + | 0.211774i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(270\) | 0.348276 | + | 0.327053i | 0.348276 | + | 0.327053i | ||||
\(271\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.35490 | − | 1.27233i | −1.35490 | − | 1.27233i | ||||
\(277\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0672897 | − | 1.06954i | 0.0672897 | − | 1.06954i | ||||
\(281\) | 0.0915446 | + | 1.45506i | 0.0915446 | + | 1.45506i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(282\) | 1.61242 | − | 0.203696i | 1.61242 | − | 0.203696i | ||||
\(283\) | 0.996398 | + | 1.57007i | 0.996398 | + | 1.57007i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.27026 | − | 1.53548i | −1.27026 | − | 1.53548i | ||||
\(288\) | −0.455778 | + | 0.428004i | −0.455778 | + | 0.428004i | ||||
\(289\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(290\) | 0.996398 | + | 0.394502i | 0.996398 | + | 0.394502i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | −0.165832 | − | 0.0911672i | −0.165832 | − | 0.0911672i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.0672897 | + | 0.106032i | −0.0672897 | + | 0.106032i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.23480 | + | 0.317042i | 1.23480 | + | 0.317042i | ||||
\(301\) | 1.11236 | + | 1.75280i | 1.11236 | + | 1.75280i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.26480 | − | 0.159781i | −1.26480 | − | 0.159781i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.939097 | + | 1.47978i | 0.939097 | + | 1.47978i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.456288 | − | 0.969661i | 0.456288 | − | 0.969661i | −0.535827 | − | 0.844328i | \(-0.680000\pi\) |
0.992115 | − | 0.125333i | \(-0.0400000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.637424 | + | 1.96179i | 0.637424 | + | 1.96179i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.427098 | − | 0.516273i | 0.427098 | − | 0.516273i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(321\) | 0.0681659 | + | 1.08347i | 0.0681659 | + | 1.08347i | ||||
\(322\) | 0.995914 | − | 1.20385i | 0.995914 | − | 1.20385i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.22458 | − | 0.154701i | 1.22458 | − | 0.154701i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.00788530 | − | 0.125333i | 0.00788530 | − | 0.125333i | ||||
\(327\) | 1.61242 | + | 0.203696i | 1.61242 | + | 0.203696i | ||||
\(328\) | −0.791759 | − | 1.68257i | −0.791759 | − | 1.68257i | ||||
\(329\) | 0.255999 | + | 1.34200i | 0.255999 | + | 1.34200i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(332\) | 1.80113 | + | 0.713118i | 1.80113 | + | 0.713118i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.35556 | + | 0.536702i | −1.35556 | + | 0.536702i | ||||
\(335\) | −0.0388067 | + | 0.119435i | −0.0388067 | + | 0.119435i | ||||
\(336\) | −0.995914 | − | 0.935225i | −0.995914 | − | 0.935225i | ||||
\(337\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(338\) | 0.187381 | − | 0.982287i | 0.187381 | − | 0.982287i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.388556 | + | 0.825723i | −0.388556 | + | 0.825723i | ||||
\(344\) | 0.598617 | + | 1.84235i | 0.598617 | + | 1.84235i | ||||
\(345\) | 1.18475 | + | 1.43211i | 1.18475 | + | 1.43211i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.688925 | + | 0.500534i | −0.688925 | + | 0.500534i | −0.876307 | − | 0.481754i | \(-0.840000\pi\) |
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(348\) | 1.19721 | − | 0.658170i | 1.19721 | − | 0.658170i | ||||
\(349\) | −0.328407 | + | 0.180543i | −0.328407 | + | 0.180543i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(350\) | −0.200808 | + | 1.05267i | −0.200808 | + | 1.05267i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.688925 | + | 1.46404i | 0.688925 | + | 1.46404i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(360\) | 0.505828 | − | 0.367505i | 0.505828 | − | 0.367505i | ||||
\(361\) | −0.187381 | − | 0.982287i | −0.187381 | − | 0.982287i | ||||
\(362\) | 1.23480 | + | 1.49261i | 1.23480 | + | 1.49261i | ||||
\(363\) | 0.393950 | + | 1.21245i | 0.393950 | + | 1.21245i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.21670 | + | 0.280034i | 2.21670 | + | 0.280034i | ||||
\(367\) | 1.56720 | − | 0.402389i | 1.56720 | − | 0.402389i | 0.637424 | − | 0.770513i | \(-0.280000\pi\) |
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(368\) | 1.17950 | − | 0.856954i | 1.17950 | − | 0.856954i | ||||
\(369\) | 0.217861 | − | 1.14207i | 0.217861 | − | 1.14207i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.929776 | − | 0.368125i | \(-0.120000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.18532 | − | 0.469303i | −1.18532 | − | 0.469303i | ||||
\(376\) | −0.0800484 | + | 1.27233i | −0.0800484 | + | 1.27233i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.0959390 | + | 0.502930i | 0.0959390 | + | 0.502930i | ||||
\(379\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.129521 | − | 2.05868i | 0.129521 | − | 2.05868i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.96858 | + | 0.248690i | −1.96858 | + | 0.248690i | −0.968583 | + | 0.248690i | \(0.920000\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(384\) | −0.683098 | − | 1.07639i | −0.683098 | − | 1.07639i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.374278 | + | 1.15191i | −0.374278 | + | 1.15191i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.45794 | − | 1.36909i | 1.45794 | − | 1.36909i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.0946201 | − | 0.114376i | 0.0946201 | − | 0.114376i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.929776 | − | 0.368125i | \(-0.120000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.425779 | + | 0.904827i | −0.425779 | + | 0.904827i | ||||
\(401\) | 0.598617 | + | 0.153699i | 0.598617 | + | 0.153699i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(402\) | 0.0857841 | + | 0.135174i | 0.0857841 | + | 0.135174i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(405\) | −1.23432 | −1.23432 | ||||||||
\(406\) | 0.615366 | + | 0.969661i | 0.615366 | + | 0.969661i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.781202 | − | 1.23098i | 0.781202 | − | 1.23098i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(410\) | 0.574633 | + | 1.76854i | 0.574633 | + | 1.76854i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.60528 | + | 0.202793i | −1.60528 | + | 0.202793i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.911557 | 0.911557 | ||||||||
\(415\) | −1.69755 | − | 0.933237i | −1.69755 | − | 0.933237i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(420\) | 0.870846 | + | 1.05267i | 0.870846 | + | 1.05267i | ||||
\(421\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.508080 | + | 0.614163i | −0.508080 | + | 0.614163i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.117933 | + | 1.87449i | −0.117933 | + | 1.87449i | ||||
\(428\) | −0.844844 | − | 0.106729i | −0.844844 | − | 0.106729i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.362989 | − | 1.90285i | −0.362989 | − | 1.90285i | ||||
\(431\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(432\) | −0.0299991 | + | 0.476823i | −0.0299991 | + | 0.476823i | ||||
\(433\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.27026 | + | 0.502930i | −1.27026 | + | 0.502930i | ||||
\(436\) | −0.393950 | + | 1.21245i | −0.393950 | + | 1.21245i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0898953 | − | 0.0230812i | 0.0898953 | − | 0.0230812i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | ||||
\(446\) | 0.238883 | + | 0.288760i | 0.238883 | + | 0.288760i | ||||
\(447\) | −0.0299991 | − | 0.157261i | −0.0299991 | − | 0.157261i | ||||
\(448\) | 0.866986 | − | 0.629902i | 0.866986 | − | 0.629902i | ||||
\(449\) | 1.53583 | − | 0.844328i | 1.53583 | − | 0.844328i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
1.00000 | \(0\) | |||||||||
\(450\) | −0.547900 | + | 0.301210i | −0.547900 | + | 0.301210i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.0672897 | − | 0.106032i | 0.0672897 | − | 0.106032i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(458\) | 0.115808 | − | 0.607087i | 0.115808 | − | 0.607087i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.27760 | + | 0.702367i | −1.27760 | + | 0.702367i | ||||
\(461\) | 0.688925 | − | 0.500534i | 0.688925 | − | 0.500534i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.393950 | + | 0.476203i | 0.393950 | + | 0.476203i | 0.929776 | − | 0.368125i | \(-0.120000\pi\) |
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(464\) | 0.331159 | + | 1.01920i | 0.331159 | + | 1.01920i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.84489 | − | 0.233064i | −1.84489 | − | 0.233064i | −0.876307 | − | 0.481754i | \(-0.840000\pi\) |
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.108877 | + | 0.0791038i | −0.108877 | + | 0.0791038i | ||||
\(470\) | 0.238883 | − | 1.25227i | 0.238883 | − | 1.25227i | ||||
\(471\) | 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 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(480\) | 0.542804 | + | 1.15352i | 0.542804 | + | 1.15352i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.110048 | + | 1.74915i | −0.110048 | + | 1.74915i | ||||
\(483\) | 0.125068 | + | 1.98790i | 0.125068 | + | 1.98790i | ||||
\(484\) | −0.992115 | + | 0.125333i | −0.992115 | + | 0.125333i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.698489 | + | 0.844328i | −0.698489 | + | 0.844328i | ||||
\(487\) | 0.116762 | + | 1.85588i | 0.116762 | + | 1.85588i | 0.425779 | + | 0.904827i | \(0.360000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(488\) | −0.541587 | + | 1.66683i | −0.541587 | + | 1.66683i | ||||
\(489\) | 0.102049 | + | 0.123357i | 0.102049 | + | 0.123357i | ||||
\(490\) | −0.108209 | + | 0.101615i | −0.108209 | + | 0.101615i | ||||
\(491\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(492\) | 2.20417 | + | 0.872693i | 2.20417 | + | 0.872693i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.29617 | + | 0.909118i | −2.29617 | + | 0.909118i | ||||
\(499\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(500\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(501\) | 0.791374 | − | 1.68176i | 0.791374 | − | 1.68176i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.939097 | − | 1.47978i | −0.939097 | − | 1.47978i | −0.876307 | − | 0.481754i | \(-0.840000\pi\) |
−0.0627905 | − | 0.998027i | \(-0.520000\pi\) | |||||||
\(504\) | 0.670038 | 0.670038 | ||||||||
\(505\) | −0.425779 | + | 0.904827i | −0.425779 | + | 0.904827i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.683098 | + | 1.07639i | 0.683098 | + | 1.07639i | ||||
\(508\) | 1.56720 | + | 0.402389i | 1.56720 | + | 0.402389i | ||||
\(509\) | −0.824805 | + | 1.75280i | −0.824805 | + | 1.75280i | −0.187381 | + | 0.982287i | \(0.560000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.929776 | − | 0.368125i | 0.929776 | − | 0.368125i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.61803 | 1.61803 | ||||||||
\(516\) | −2.16412 | − | 1.18974i | −2.16412 | − | 1.18974i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.18532 | + | 1.43281i | 1.18532 | + | 1.43281i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(522\) | −0.207053 | + | 0.637244i | −0.207053 | + | 0.637244i | ||||
\(523\) | −0.110048 | − | 1.74915i | −0.110048 | − | 1.74915i | −0.535827 | − | 0.844328i | \(-0.680000\pi\) |
0.425779 | − | 0.904827i | \(-0.360000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.732044 | − | 1.15352i | −0.732044 | − | 1.15352i | ||||
\(526\) | 1.96858 | − | 0.248690i | 1.96858 | − | 0.248690i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.11671 | − | 0.141073i | −1.11671 | − | 0.141073i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.91789 | − | 0.759348i | −1.91789 | − | 0.759348i | ||||
\(535\) | 0.824805 | + | 0.211774i | 0.824805 | + | 0.211774i | ||||
\(536\) | −0.116762 | + | 0.0462295i | −0.116762 | + | 0.0462295i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.620759 | + | 0.582932i | 0.620759 | + | 0.582932i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.0895243 | − | 0.469303i | 0.0895243 | − | 0.469303i | ||||
\(541\) | 1.50441 | − | 1.09302i | 1.50441 | − | 1.09302i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.45012 | − | 0.309522i | −2.45012 | − | 0.309522i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.542804 | − | 1.15352i | 0.542804 | − | 1.15352i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.542804 | − | 0.656137i | −0.542804 | − | 0.656137i | 0.425779 | − | 0.904827i | \(-0.360000\pi\) |
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.886520 | + | 0.644095i | −0.886520 | + | 0.644095i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.348276 | + | 1.82573i | −0.348276 | + | 1.82573i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.939097 | + | 0.516273i | −0.939097 | + | 0.516273i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.17950 | − | 0.856954i | 1.17950 | − | 0.856954i | ||||
\(563\) | −0.303189 | − | 1.58937i | −0.303189 | − | 1.58937i | −0.728969 | − | 0.684547i | \(-0.760000\pi\) |
0.425779 | − | 0.904827i | \(-0.360000\pi\) | |||||||
\(564\) | −1.03597 | − | 1.25227i | −1.03597 | − | 1.25227i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.791759 | − | 1.68257i | 0.791759 | − | 1.68257i | ||||
\(567\) | −1.07013 | − | 0.777498i | −1.07013 | − | 0.777498i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.87631 | − | 0.481754i | 1.87631 | − | 0.481754i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
1.00000 | \(0\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.615808 | + | 1.89526i | −0.615808 | + | 1.89526i | ||||
\(575\) | 1.35556 | − | 0.536702i | 1.35556 | − | 0.536702i | ||||
\(576\) | 0.605594 | + | 0.155490i | 0.605594 | + | 0.155490i | ||||
\(577\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(578\) | −0.0627905 | + | 0.998027i | −0.0627905 | + | 0.998027i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.200808 | − | 1.05267i | −0.200808 | − | 1.05267i | ||||
\(581\) | −0.883906 | − | 1.87839i | −0.883906 | − | 1.87839i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.26480 | + | 1.52888i | −1.26480 | + | 1.52888i | −0.535827 | + | 0.844328i | \(0.680000\pi\) |
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(588\) | 0.0118825 | + | 0.188867i | 0.0118825 | + | 0.188867i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.125581 | 0.125581 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.929776 | − | 0.368125i | \(-0.120000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(600\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | ||||
\(601\) | 0.331159 | − | 0.521823i | 0.331159 | − | 0.521823i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(602\) | 0.883906 | − | 1.87839i | 0.883906 | − | 1.87839i | ||||
\(603\) | −0.0760512 | − | 0.0195266i | −0.0760512 | − | 0.0195266i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | 1.00000 | ||||||||
\(606\) | 0.542804 | + | 1.15352i | 0.542804 | + | 1.15352i | ||||
\(607\) | 1.98423 | 1.98423 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
0.992115 | + | 0.125333i | \(0.0400000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.41809 | − | 0.364104i | −1.41809 | − | 0.364104i | ||||
\(610\) | 0.746226 | − | 1.58581i | 0.746226 | − | 1.58581i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.929776 | − | 0.368125i | \(-0.120000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(614\) | −1.06320 | + | 0.134314i | −1.06320 | + | 0.134314i | ||||
\(615\) | −2.07741 | − | 1.14207i | −2.07741 | − | 1.14207i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(618\) | 1.31484 | − | 1.58937i | 1.31484 | − | 1.58937i | ||||
\(619\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.507765 | − | 0.476823i | 0.507765 | − | 0.476823i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.535827 | − | 1.64911i | 0.535827 | − | 1.64911i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.637424 | + | 0.770513i | −0.637424 | + | 0.770513i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −0.664754 | − | 0.0839780i | −0.664754 | − | 0.0839780i | ||||
\(631\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.50441 | − | 0.595638i | −1.50441 | − | 0.595638i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.968583 | + | 0.248690i | −0.968583 | + | 0.248690i | ||||
\(641\) | 0.303189 | − | 1.58937i | 0.303189 | − | 1.58937i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(642\) | 0.878275 | − | 0.638104i | 0.878275 | − | 0.638104i | ||||
\(643\) | −1.93717 | + | 0.497380i | −1.93717 | + | 0.497380i | −0.968583 | + | 0.248690i | \(0.920000\pi\) |
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(644\) | −1.55008 | − | 0.195821i | −1.55008 | − | 0.195821i | ||||
\(645\) | 1.99794 | + | 1.45159i | 1.99794 | + | 1.45159i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.115808 | + | 0.356420i | 0.115808 | + | 0.356420i | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) |
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(648\) | −0.786782 | − | 0.951057i | −0.786782 | − | 0.951057i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.110048 | + | 0.0604991i | −0.110048 | + | 0.0604991i | ||||
\(653\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(654\) | −0.691992 | − | 1.47056i | −0.691992 | − | 1.47056i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.996398 | + | 1.57007i | −0.996398 | + | 1.57007i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.995914 | − | 0.935225i | 0.995914 | − | 0.935225i | ||||
\(659\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.73879 | + | 0.955910i | −1.73879 | + | 0.955910i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.362989 | − | 1.90285i | −0.362989 | − | 1.90285i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.665239 | − | 1.41371i | 0.665239 | − | 1.41371i | ||||
\(668\) | 1.17950 | + | 0.856954i | 1.17950 | + | 0.856954i | ||||
\(669\) | −0.473998 | − | 0.0598799i | −0.473998 | − | 0.0598799i | ||||
\(670\) | 0.121636 | − | 0.0312307i | 0.121636 | − | 0.0312307i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.255999 | + | 1.34200i | −0.255999 | + | 1.34200i | ||||
\(673\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.147638 | + | 0.454382i | −0.147638 | + | 0.454382i | ||||
\(676\) | −0.929776 | + | 0.368125i | −0.929776 | + | 0.368125i | ||||
\(677\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0299991 | + | 0.157261i | 0.0299991 | + | 0.157261i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.371808 | − | 0.0469702i | −0.371808 | − | 0.0469702i | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.905380 | − | 0.114376i | 0.905380 | − | 0.114376i | ||||
\(687\) | 0.422178 | + | 0.665245i | 0.422178 | + | 0.665245i | ||||
\(688\) | 1.23480 | − | 1.49261i | 1.23480 | − | 1.49261i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.574354 | − | 1.76768i | 0.574354 | − | 1.76768i | ||||
\(691\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.791759 | + | 0.313480i | 0.791759 | + | 0.313480i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.19721 | − | 0.658170i | −1.19721 | − | 0.658170i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0.328407 | + | 0.180543i | 0.328407 | + | 0.180543i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.996398 | − | 0.394502i | 0.996398 | − | 0.394502i | ||||
\(701\) | −0.574633 | − | 1.76854i | −0.574633 | − | 1.76854i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.0627905 | − | 0.998027i | \(-0.480000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.870846 | + | 1.37223i | 0.870846 | + | 1.37223i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.939097 | + | 0.516273i | −0.939097 | + | 0.516273i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.06320 | − | 1.67534i | −1.06320 | − | 1.67534i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
−0.425779 | − | 0.904827i | \(-0.640000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.866986 | − | 1.36615i | 0.866986 | − | 1.36615i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(720\) | −0.581331 | − | 0.230165i | −0.581331 | − | 0.230165i | ||||
\(721\) | 1.40281 | + | 1.01920i | 1.40281 | + | 1.01920i | ||||
\(722\) | −0.728969 | + | 0.684547i | −0.728969 | + | 0.684547i | ||||
\(723\) | −1.42421 | − | 1.72157i | −1.42421 | − | 1.72157i | ||||
\(724\) | 0.598617 | − | 1.84235i | 0.598617 | − | 1.84235i | ||||
\(725\) | 0.0672897 | + | 1.06954i | 0.0672897 | + | 1.06954i | ||||
\(726\) | 0.812619 | − | 0.982287i | 0.812619 | − | 0.982287i | ||||
\(727\) | −0.331159 | − | 0.521823i | −0.331159 | − | 0.521823i | 0.637424 | − | 0.770513i | \(-0.280000\pi\) |
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.0102136 | − | 0.162341i | −0.0102136 | − | 0.162341i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.951325 | − | 2.02167i | −0.951325 | − | 2.02167i | ||||
\(733\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(734\) | −1.17950 | − | 1.10762i | −1.17950 | − | 1.10762i | ||||
\(735\) | 0.0118825 | − | 0.188867i | 0.0118825 | − | 0.188867i | ||||
\(736\) | −1.35556 | − | 0.536702i | −1.35556 | − | 0.536702i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.08102 | + | 0.428004i | −1.08102 | + | 0.428004i | ||||
\(739\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.101597 | − | 0.0738147i | 0.101597 | − | 0.0738147i | −0.535827 | − | 0.844328i | \(-0.680000\pi\) |
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.124591 | − | 0.0157395i | −0.124591 | − | 0.0157395i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.515699 | − | 1.09592i | 0.515699 | − | 1.09592i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.581698 | + | 0.703152i | 0.581698 | + | 0.703152i | ||||
\(750\) | 0.238883 | + | 1.25227i | 0.238883 | + | 1.25227i | ||||
\(751\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(752\) | 1.11716 | − | 0.614163i | 1.11716 | − | 0.614163i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.373231 | − | 0.350487i | 0.373231 | − | 0.350487i | ||||
\(757\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.371808 | − | 1.94908i | 0.371808 | − | 1.94908i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(762\) | −1.80760 | + | 0.993736i | −1.80760 | + | 0.993736i | ||||
\(763\) | 1.19721 | − | 0.658170i | 1.19721 | − | 0.658170i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.26480 | + | 1.52888i | 1.26480 | + | 1.52888i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.542804 | + | 1.15352i | −0.542804 | + | 1.15352i | ||||
\(769\) | −1.56720 | − | 1.13864i | −1.56720 | − | 1.13864i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
−0.637424 | − | 0.770513i | \(-0.720000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(774\) | 1.17314 | − | 0.301210i | 1.17314 | − | 0.301210i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.93717 | − | 0.497380i | −1.93717 | − | 0.497380i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.217999 | + | 0.463271i | 0.217999 | + | 0.463271i | ||||
\(784\) | −0.147271 | − | 0.0186046i | −0.147271 | − | 0.0186046i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.73879 | − | 0.219661i | 1.73879 | − | 0.219661i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.61242 | + | 1.94908i | −1.61242 | + | 1.94908i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.992115 | − | 0.125333i | 0.992115 | − | 0.125333i | ||||
\(801\) | 0.940613 | − | 0.372415i | 0.940613 | − | 0.372415i | ||||
\(802\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.0681659 | − | 0.144860i | 0.0681659 | − | 0.144860i | ||||
\(805\) | 1.51332 | + | 0.388554i | 1.51332 | + | 0.388554i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.08561 | −1.08561 | ||||||||
\(808\) | −0.968583 | + | 0.248690i | −0.968583 | + | 0.248690i | ||||
\(809\) | 1.07165 | 1.07165 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(810\) | 0.661379 | + | 1.04217i | 0.661379 | + | 1.04217i | ||||
\(811\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(812\) | 0.488983 | − | 1.03914i | 0.488983 | − | 1.03914i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.116762 | − | 0.0462295i | 0.116762 | − | 0.0462295i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −1.45794 | −1.45794 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.18532 | − | 1.43281i | 1.18532 | − | 1.43281i | ||||
\(821\) | −1.35556 | − | 0.536702i | −1.35556 | − | 0.536702i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.06279 | + | 0.998027i | −1.06279 | + | 0.998027i | −0.0627905 | + | 0.998027i | \(0.520000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(824\) | 1.03137 | + | 1.24672i | 1.03137 | + | 1.24672i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.929324 | − | 1.12336i | 0.929324 | − | 1.12336i | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) |
0.992115 | − | 0.125333i | \(-0.0400000\pi\) | |||||||
\(828\) | −0.488437 | − | 0.769653i | −0.488437 | − | 0.769653i | ||||
\(829\) | 0.844844 | − | 0.106729i | 0.844844 | − | 0.106729i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(830\) | 0.121636 | + | 1.93334i | 0.121636 | + | 1.93334i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.06279 | − | 0.998027i | −1.06279 | − | 0.998027i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.929776 | − | 0.368125i | \(-0.120000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(840\) | 0.422178 | − | 1.29933i | 0.422178 | − | 1.29933i | ||||
\(841\) | 0.108209 | + | 0.101615i | 0.108209 | + | 0.101615i | ||||
\(842\) | 1.56720 | − | 0.402389i | 1.56720 | − | 0.402389i | ||||
\(843\) | −0.348276 | + | 1.82573i | −0.348276 | + | 1.82573i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.968583 | − | 0.248690i | 0.968583 | − | 0.248690i | ||||
\(846\) | 0.790797 | + | 0.0999009i | 0.790797 | + | 0.0999009i | ||||
\(847\) | 0.866986 | + | 0.629902i | 0.866986 | + | 0.629902i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.732570 | + | 2.25462i | 0.732570 | + | 2.25462i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(854\) | 1.64587 | − | 0.904827i | 1.64587 | − | 0.904827i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.362576 | + | 0.770513i | 0.362576 | + | 0.770513i | ||||
\(857\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(860\) | −1.41213 | + | 1.32608i | −1.41213 | + | 1.32608i | ||||
\(861\) | −1.08170 | − | 2.29872i | −1.08170 | − | 2.29872i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.62954 | − | 0.895846i | 1.62954 | − | 0.895846i | 0.637424 | − | 0.770513i | \(-0.280000\pi\) |
0.992115 | − | 0.125333i | \(-0.0400000\pi\) | |||||||
\(864\) | 0.418669 | − | 0.230165i | 0.418669 | − | 0.230165i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.812619 | − | 0.982287i | −0.812619 | − | 0.982287i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.10528 | + | 0.803030i | 1.10528 | + | 0.803030i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.23480 | − | 0.317042i | 1.23480 | − | 0.317042i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.03799 | + | 0.266509i | −1.03799 | + | 0.266509i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.116762 | + | 1.85588i | −0.116762 | + | 1.85588i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(882\) | −0.0676564 | − | 0.0635336i | −0.0676564 | − | 0.0635336i | ||||
\(883\) | −0.348445 | − | 1.82662i | −0.348445 | − | 1.82662i | −0.535827 | − | 0.844328i | \(-0.680000\pi\) |
0.187381 | − | 0.982287i | \(-0.440000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.0388067 | − | 0.616814i | 0.0388067 | − | 0.616814i | ||||
\(887\) | −0.0672897 | − | 1.06954i | −0.0672897 | − | 1.06954i | −0.876307 | − | 0.481754i | \(-0.840000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.929109 | − | 1.46404i | −0.929109 | − | 1.46404i | ||||
\(890\) | −1.03137 | + | 1.24672i | −1.03137 | + | 1.24672i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.115808 | − | 0.356420i | 0.115808 | − | 0.356420i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.116705 | + | 0.109594i | −0.116705 | + | 0.109594i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.996398 | − | 0.394502i | −0.996398 | − | 0.394502i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.53583 | − | 0.844328i | −1.53583 | − | 0.844328i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.547900 | + | 0.301210i | 0.547900 | + | 0.301210i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.817828 | + | 2.51702i | 0.817828 | + | 2.51702i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.824805 | + | 1.75280i | −0.824805 | + | 1.75280i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.200808 | + | 0.316423i | 0.200808 | + | 0.316423i | 0.929776 | − | 0.368125i | \(-0.120000\pi\) |
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(908\) | −0.125581 | −0.125581 | ||||||||
\(909\) | −0.581331 | − | 0.230165i | −0.581331 | − | 0.230165i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.690441 | + | 2.12496i | 0.690441 | + | 2.12496i | ||||
\(916\) | −0.574633 | + | 0.227513i | −0.574633 | + | 0.227513i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 1.27760 | + | 0.702367i | 1.27760 | + | 0.702367i | ||||
\(921\) | 0.870846 | − | 1.05267i | 0.870846 | − | 1.05267i | ||||
\(922\) | −0.791759 | − | 0.313480i | −0.791759 | − | 0.313480i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(927\) | 0.0635224 | + | 1.00966i | 0.0635224 | + | 1.00966i | ||||
\(928\) | 0.683098 | − | 0.825723i | 0.683098 | − | 0.825723i | ||||
\(929\) | −0.996398 | − | 1.57007i | −0.996398 | − | 1.57007i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.187381 | − | 0.982287i | \(-0.560000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.791759 | + | 1.68257i | 0.791759 | + | 1.68257i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(938\) | 0.125129 | + | 0.0495420i | 0.125129 | + | 0.0495420i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.18532 | + | 0.469303i | −1.18532 | + | 0.469303i | ||||
\(941\) | 0.0388067 | − | 0.119435i | 0.0388067 | − | 0.119435i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.62594 | − | 0.674226i | 2.62594 | − | 0.674226i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.414216 | + | 0.300945i | −0.414216 | + | 0.300945i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.371808 | − | 0.0469702i | −0.371808 | − | 0.0469702i | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.683098 | − | 1.07639i | 0.683098 | − | 1.07639i | ||||
\(961\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.0997667 | + | 0.522996i | −0.0997667 | + | 0.522996i | ||||
\(964\) | 1.53583 | − | 0.844328i | 1.53583 | − | 0.844328i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.61142 | − | 1.17077i | 1.61142 | − | 1.17077i | ||||
\(967\) | −0.371808 | − | 1.94908i | −0.371808 | − | 1.94908i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−0.0627905 | − | 0.998027i | \(-0.520000\pi\) | |||||||
\(968\) | 0.637424 | + | 0.770513i | 0.637424 | + | 0.770513i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(972\) | 1.08716 | + | 0.137340i | 1.08716 | + | 0.137340i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.50441 | − | 1.09302i | 1.50441 | − | 1.09302i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.69755 | − | 0.435857i | 1.69755 | − | 0.435857i | ||||
\(977\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(978\) | 0.0494726 | − | 0.152261i | 0.0494726 | − | 0.152261i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.143778 | + | 0.0369159i | 0.143778 | + | 0.0369159i | ||||
\(981\) | 0.741109 | + | 0.293426i | 0.741109 | + | 0.293426i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.35556 | + | 1.27295i | 1.35556 | + | 1.27295i | 0.929776 | + | 0.368125i | \(0.120000\pi\) |
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(984\) | −0.444215 | − | 2.32866i | −0.444215 | − | 2.32866i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.109362 | + | 1.73825i | −0.109362 | + | 1.73825i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.80200 | + | 0.353975i | −2.80200 | + | 0.353975i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.99794 | + | 1.45159i | 1.99794 | + | 1.45159i | ||||
\(997\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(998\) | 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.bu.b.1179.1 | yes | 20 | |
4.3 | odd | 2 | 2020.1.bu.a.1179.1 | yes | 20 | ||
5.4 | even | 2 | 2020.1.bu.a.1179.1 | yes | 20 | ||
20.19 | odd | 2 | CM | 2020.1.bu.b.1179.1 | yes | 20 | |
101.52 | even | 25 | inner | 2020.1.bu.b.759.1 | yes | 20 | |
404.355 | odd | 50 | 2020.1.bu.a.759.1 | ✓ | 20 | ||
505.254 | even | 50 | 2020.1.bu.a.759.1 | ✓ | 20 | ||
2020.759 | odd | 50 | inner | 2020.1.bu.b.759.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2020.1.bu.a.759.1 | ✓ | 20 | 404.355 | odd | 50 | ||
2020.1.bu.a.759.1 | ✓ | 20 | 505.254 | even | 50 | ||
2020.1.bu.a.1179.1 | yes | 20 | 4.3 | odd | 2 | ||
2020.1.bu.a.1179.1 | yes | 20 | 5.4 | even | 2 | ||
2020.1.bu.b.759.1 | yes | 20 | 101.52 | even | 25 | inner | |
2020.1.bu.b.759.1 | yes | 20 | 2020.759 | odd | 50 | inner | |
2020.1.bu.b.1179.1 | yes | 20 | 1.1 | even | 1 | trivial | |
2020.1.bu.b.1179.1 | yes | 20 | 20.19 | odd | 2 | CM |