Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2008,1,Mod(51,2008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2008, base_ring=CyclotomicField(50))
chi = DirichletCharacter(H, H._module([25, 25, 18]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2008.51");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2008 = 2^{3} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2008.w (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: | \(1.00212254537\) |
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: | \(\Z[a_1, \ldots, a_{9}]\) |
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 | 1531.1 | ||
Root | \(0.929776 - 0.368125i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2008.1531 |
Dual form | 2008.1.w.a.1747.1 |
$q$-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 \(\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(503\) | \(1005\) |
\(\chi(n)\) | \(e\left(\frac{1}{25}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(3\) | 0.791759 | − | 1.68257i | 0.791759 | − | 1.68257i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(4\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(5\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(6\) | 1.84489 | + | 0.233064i | 1.84489 | + | 0.233064i | ||||
\(7\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(8\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(9\) | −1.56675 | − | 1.89387i | −1.56675 | − | 1.89387i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.328407 | − | 1.72157i | −0.328407 | − | 1.72157i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(12\) | 0.348445 | + | 1.82662i | 0.348445 | + | 1.82662i | ||||
\(13\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(17\) | −1.98423 | + | 0.250666i | −1.98423 | + | 0.250666i | −0.992115 | + | 0.125333i | \(0.960000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(18\) | 1.31703 | − | 2.07531i | 1.31703 | − | 2.07531i | ||||
\(19\) | 0.0388067 | − | 0.616814i | 0.0388067 | − | 0.616814i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.53583 | − | 0.844328i | 1.53583 | − | 0.844328i | ||||
\(23\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(24\) | −1.62954 | + | 0.895846i | −1.62954 | + | 0.895846i | ||||
\(25\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.62594 | + | 0.674226i | −2.62594 | + | 0.674226i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(32\) | 1.00000 | 1.00000 | ||||||||
\(33\) | −3.15669 | − | 0.810500i | −3.15669 | − | 0.810500i | ||||
\(34\) | −0.851559 | − | 1.80965i | −0.851559 | − | 1.80965i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.38072 | + | 0.611264i | 2.38072 | + | 0.611264i | ||||
\(37\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(38\) | 0.598617 | − | 0.153699i | 0.598617 | − | 0.153699i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.69755 | + | 0.933237i | 1.69755 | + | 0.933237i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.84489 | − | 0.730444i | 1.84489 | − | 0.730444i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(44\) | 1.27760 | + | 1.19975i | 1.27760 | + | 1.19975i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(48\) | −1.35556 | − | 1.27295i | −1.35556 | − | 1.27295i | ||||
\(49\) | 0.876307 | − | 0.481754i | 0.876307 | − | 0.481754i | ||||
\(50\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(51\) | −1.14927 | + | 3.53708i | −1.14927 | + | 3.53708i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(54\) | −1.45269 | − | 2.28907i | −1.45269 | − | 2.28907i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00711 | − | 0.553664i | −1.00711 | − | 0.553664i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.371808 | + | 0.0469702i | 0.371808 | + | 0.0469702i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.204639 | − | 3.25265i | −0.204639 | − | 3.25265i | ||||
\(67\) | 0.110048 | + | 0.0604991i | 0.110048 | + | 0.0604991i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(68\) | 1.45794 | − | 1.36909i | 1.45794 | − | 1.36909i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(72\) | 0.154335 | + | 2.45309i | 0.154335 | + | 2.45309i | ||||
\(73\) | −0.263146 | − | 0.559214i | −0.263146 | − | 0.559214i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.84489 | + | 0.233064i | 1.84489 | + | 0.233064i | ||||
\(76\) | 0.331159 | + | 0.521823i | 0.331159 | + | 0.521823i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.484103 | + | 2.53776i | −0.484103 | + | 2.53776i | ||||
\(82\) | −0.362989 | + | 1.90285i | −0.362989 | + | 1.90285i | ||||
\(83\) | −0.620759 | + | 0.582932i | −0.620759 | + | 0.582932i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.26480 | + | 1.52888i | 1.26480 | + | 1.52888i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.746226 | + | 1.58581i | −0.746226 | + | 1.58581i | ||||
\(89\) | −1.06320 | + | 0.134314i | −1.06320 | + | 0.134314i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.791759 | − | 1.68257i | 0.791759 | − | 1.68257i | ||||
\(97\) | 1.41213 | − | 1.32608i | 1.41213 | − | 1.32608i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(98\) | 0.728969 | + | 0.684547i | 0.728969 | + | 0.684547i | ||||
\(99\) | −2.74590 | + | 3.31923i | −2.74590 | + | 3.31923i | ||||
\(100\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(101\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(102\) | −3.71911 | −3.71911 | ||||||||
\(103\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.72897 | − | 0.684547i | 1.72897 | − | 0.684547i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
1.00000 | \(0\) | |||||||||
\(108\) | 1.72813 | − | 2.08895i | 1.72813 | − | 2.08895i | ||||
\(109\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.98423 | −1.98423 | −0.992115 | − | 0.125333i | \(-0.960000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(114\) | 0.215351 | − | 1.12891i | 0.215351 | − | 1.12891i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.0702235 | + | 0.368125i | 0.0702235 | + | 0.368125i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.92617 | + | 0.762627i | −1.92617 | + | 0.762627i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.91429 | − | 2.11736i | 2.91429 | − | 2.11736i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(128\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(129\) | 0.231683 | − | 3.68250i | 0.231683 | − | 3.68250i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.60528 | + | 0.202793i | 1.60528 | + | 0.202793i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(132\) | 3.03021 | − | 1.19975i | 3.03021 | − | 1.19975i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.0235315 | + | 0.123357i | −0.0235315 | + | 0.123357i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.75261 | + | 0.963507i | 1.75261 | + | 0.963507i | ||||
\(137\) | 0.348445 | − | 1.82662i | 0.348445 | − | 1.82662i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0534698 | + | 0.849878i | −0.0534698 | + | 0.849878i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.28533 | + | 0.904827i | −2.28533 | + | 0.904827i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.450527 | − | 0.423073i | 0.450527 | − | 0.423073i | ||||
\(147\) | −0.116762 | − | 1.85588i | −0.116762 | − | 1.85588i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(150\) | 0.348445 | + | 1.82662i | 0.348445 | + | 1.82662i | ||||
\(151\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(152\) | −0.393950 | + | 0.476203i | −0.393950 | + | 0.476203i | ||||
\(153\) | 3.58352 | + | 3.36515i | 3.58352 | + | 3.36515i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.56315 | + | 0.323801i | −2.56315 | + | 0.323801i | ||||
\(163\) | −0.456288 | + | 0.969661i | −0.456288 | + | 0.969661i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(164\) | −1.92189 | + | 0.242791i | −1.92189 | + | 0.242791i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.746226 | − | 0.410241i | −0.746226 | − | 0.410241i | ||||
\(167\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.187381 | + | 0.982287i | −0.187381 | + | 0.982287i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.22897 | + | 0.892898i | −1.22897 | + | 0.892898i | ||||
\(172\) | −1.06320 | + | 1.67534i | −1.06320 | + | 1.67534i | ||||
\(173\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.73879 | − | 0.219661i | −1.73879 | − | 0.219661i | ||||
\(177\) | 0.373413 | − | 0.588404i | 0.373413 | − | 0.588404i | ||||
\(178\) | −0.456288 | − | 0.969661i | −0.456288 | − | 0.969661i | ||||
\(179\) | −0.0800484 | − | 1.27233i | −0.0800484 | − | 1.27233i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.08317 | + | 3.33367i | 1.08317 | + | 3.33367i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.425779 | − | 0.904827i | \(-0.360000\pi\) | ||||
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(192\) | 1.84489 | + | 0.233064i | 1.84489 | + | 0.233064i | ||||
\(193\) | 0.238883 | − | 0.288760i | 0.238883 | − | 0.288760i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(194\) | 1.69755 | + | 0.933237i | 1.69755 | + | 0.933237i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.425779 | + | 0.904827i | −0.425779 | + | 0.904827i | ||||
\(197\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(198\) | −4.00530 | − | 1.58581i | −4.00530 | − | 1.58581i | ||||
\(199\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(200\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(201\) | 0.188925 | − | 0.137262i | 0.188925 | − | 0.137262i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.14927 | − | 3.53708i | −1.14927 | − | 3.53708i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.07463 | + | 0.135758i | −1.07463 | + | 0.135758i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.331159 | + | 1.01920i | 0.331159 | + | 1.01920i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.18532 | + | 1.43281i | 1.18532 | + | 1.43281i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.52073 | + | 0.998027i | 2.52073 | + | 0.998027i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.14927 | −1.14927 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.31703 | − | 2.07531i | 1.31703 | − | 2.07531i | ||||
\(226\) | −0.613161 | − | 1.88711i | −0.613161 | − | 1.88711i | ||||
\(227\) | −1.41789 | + | 0.779494i | −1.41789 | + | 0.779494i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(228\) | 1.14020 | − | 0.144041i | 1.14020 | − | 0.144041i | ||||
\(229\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.06320 | + | 1.67534i | −1.06320 | + | 1.67534i | −0.425779 | + | 0.904827i | \(0.640000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.328407 | + | 0.180543i | −0.328407 | + | 0.180543i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.393950 | + | 1.21245i | −0.393950 | + | 1.21245i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(242\) | −1.32052 | − | 1.59624i | −1.32052 | − | 1.59624i | ||||
\(243\) | 1.69334 | + | 1.23028i | 1.69334 | + | 1.23028i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.91429 | + | 2.11736i | 2.91429 | + | 2.11736i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.489334 | + | 1.50602i | 0.489334 | + | 1.50602i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.968583 | + | 0.248690i | 0.968583 | + | 0.248690i | ||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(257\) | 0.371808 | + | 0.0469702i | 0.371808 | + | 0.0469702i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(258\) | 3.57386 | − | 0.917611i | 3.57386 | − | 0.917611i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.303189 | + | 1.58937i | 0.303189 | + | 1.58937i | ||||
\(263\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(264\) | 2.07741 | + | 2.51116i | 2.07741 | + | 2.51116i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.615808 | + | 1.89526i | −0.615808 | + | 1.89526i | ||||
\(268\) | −0.124591 | + | 0.0157395i | −0.124591 | + | 0.0157395i | ||||
\(269\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −0.374763 | + | 1.96457i | −0.374763 | + | 1.96457i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.84489 | − | 0.233064i | 1.84489 | − | 0.233064i | ||||
\(275\) | 1.53583 | − | 0.844328i | 1.53583 | − | 0.844328i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(278\) | −0.824805 | + | 0.211774i | −0.824805 | + | 0.211774i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.41213 | + | 1.32608i | 1.41213 | + | 1.32608i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.27485 | −1.27485 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.56675 | − | 1.89387i | −1.56675 | − | 1.89387i | ||||
\(289\) | 2.90575 | − | 0.746070i | 2.90575 | − | 0.746070i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.11316 | − | 3.42596i | −1.11316 | − | 3.42596i | ||||
\(292\) | 0.541587 | + | 0.297740i | 0.541587 | + | 0.297740i | ||||
\(293\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(294\) | 1.72897 | − | 0.684547i | 1.72897 | − | 0.684547i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.02310 | + | 4.29931i | 2.02310 | + | 4.29931i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.62954 | + | 0.895846i | −1.62954 | + | 0.895846i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.574633 | − | 0.227513i | −0.574633 | − | 0.227513i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.09308 | + | 4.44802i | −2.09308 | + | 4.44802i | ||||
\(307\) | 1.18532 | + | 0.469303i | 1.18532 | + | 0.469303i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.425779 | − | 0.904827i | \(-0.360000\pi\) | ||||
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.939097 | − | 0.516273i | 0.939097 | − | 0.516273i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) | ||||
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.217126 | − | 3.45111i | 0.217126 | − | 3.45111i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0776134 | + | 1.23363i | 0.0776134 | + | 1.23363i | ||||
\(324\) | −1.10001 | − | 2.33764i | −1.10001 | − | 2.33764i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.06320 | − | 0.134314i | −1.06320 | − | 0.134314i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.824805 | − | 1.75280i | −0.824805 | − | 1.75280i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.303189 | − | 0.220280i | 0.303189 | − | 0.220280i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(332\) | 0.159566 | − | 0.836475i | 0.159566 | − | 0.836475i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.11716 | − | 1.35041i | −1.11716 | − | 1.35041i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
−0.187381 | − | 0.982287i | \(-0.560000\pi\) | |||||||
\(338\) | −0.992115 | + | 0.125333i | −0.992115 | + | 0.125333i | ||||
\(339\) | −1.57103 | + | 3.33861i | −1.57103 | + | 3.33861i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.22897 | − | 0.892898i | −1.22897 | − | 0.892898i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.92189 | − | 0.493458i | −1.92189 | − | 0.493458i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.159566 | − | 0.339095i | 0.159566 | − | 0.339095i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.328407 | − | 1.72157i | −0.328407 | − | 1.72157i | ||||
\(353\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(354\) | 0.674997 | + | 0.173310i | 0.674997 | + | 0.173310i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.781202 | − | 0.733597i | 0.781202 | − | 0.733597i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.18532 | − | 0.469303i | 1.18532 | − | 0.469303i | ||||
\(359\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.613161 | + | 0.0774602i | 0.613161 | + | 0.0774602i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.241891 | + | 3.84475i | −0.241891 | + | 3.84475i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.892204 | − | 4.67710i | −0.892204 | − | 4.67710i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(374\) | −2.83579 | + | 2.06032i | −2.83579 | + | 2.06032i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.101597 | + | 0.0738147i | −0.101597 | + | 0.0738147i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.929776 | − | 0.368125i | \(-0.120000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(384\) | 0.348445 | + | 1.82662i | 0.348445 | + | 1.82662i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.348445 | + | 0.137959i | 0.348445 | + | 0.137959i | ||||
\(387\) | −4.27385 | − | 2.34957i | −4.27385 | − | 2.34957i | ||||
\(388\) | −0.362989 | + | 1.90285i | −0.362989 | + | 1.90285i | ||||
\(389\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.992115 | − | 0.125333i | −0.992115 | − | 0.125333i | ||||
\(393\) | 1.61221 | − | 2.54043i | 1.61221 | − | 2.54043i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.270490 | − | 4.29931i | 0.270490 | − | 4.29931i | ||||
\(397\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 1.00000 | ||||||||
\(401\) | −0.273190 | − | 1.43211i | −0.273190 | − | 1.43211i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(402\) | 0.188925 | + | 0.137262i | 0.188925 | + | 0.137262i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 3.00882 | − | 2.18604i | 3.00882 | − | 2.18604i | ||||
\(409\) | −0.824805 | − | 0.211774i | −0.824805 | − | 0.211774i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.79753 | − | 2.03252i | −2.79753 | − | 2.03252i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.38765 | + | 0.762866i | 1.38765 | + | 0.762866i | ||||
\(418\) | −0.461193 | − | 0.980086i | −0.461193 | − | 0.980086i | ||||
\(419\) | −0.620759 | + | 0.582932i | −0.620759 | + | 0.582932i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(422\) | −0.866986 | + | 0.629902i | −0.866986 | + | 0.629902i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.851559 | − | 1.80965i | −0.851559 | − | 1.80965i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.996398 | + | 1.57007i | −0.996398 | + | 1.57007i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(432\) | −0.170232 | + | 2.70576i | −0.170232 | + | 2.70576i | ||||
\(433\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.355143 | − | 1.09302i | −0.355143 | − | 1.09302i | ||||
\(439\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.28533 | − | 0.904827i | −2.28533 | − | 0.904827i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.98423 | − | 0.250666i | −1.98423 | − | 0.250666i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.992115 | − | 0.125333i | \(-0.960000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.791759 | + | 0.313480i | 0.791759 | + | 0.313480i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(450\) | 2.38072 | + | 0.611264i | 2.38072 | + | 0.611264i | ||||
\(451\) | 1.04914 | − | 3.22894i | 1.04914 | − | 3.22894i | ||||
\(452\) | 1.60528 | − | 1.16630i | 1.60528 | − | 1.16630i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.17950 | − | 1.10762i | −1.17950 | − | 1.10762i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.489334 | + | 1.03989i | 0.489334 | + | 1.03989i | ||||
\(457\) | 0.0388067 | + | 0.616814i | 0.0388067 | + | 0.616814i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.04146 | − | 1.99605i | 5.04146 | − | 1.99605i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.92189 | − | 0.493458i | −1.92189 | − | 0.493458i | ||||
\(467\) | −1.35556 | − | 0.536702i | −1.35556 | − | 0.536702i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.273190 | − | 0.256543i | −0.273190 | − | 0.256543i | ||||
\(473\) | −1.86338 | − | 2.93622i | −1.86338 | − | 2.93622i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.598617 | − | 0.153699i | 0.598617 | − | 0.153699i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.27485 | −1.27485 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.11005 | − | 1.74915i | 1.11005 | − | 1.74915i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.646797 | + | 1.99064i | −0.646797 | + | 1.99064i | ||||
\(487\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.27026 | + | 1.53548i | 1.27026 | + | 1.53548i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.362989 | − | 1.90285i | −0.362989 | − | 1.90285i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.0627905 | − | 0.998027i | \(-0.480000\pi\) | |||||||
\(492\) | −1.11316 | + | 3.42596i | −1.11316 | + | 3.42596i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.28109 | + | 0.930769i | −1.28109 | + | 0.930769i | ||||
\(499\) | −0.0534698 | + | 0.113629i | −0.0534698 | + | 0.113629i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.0627905 | + | 0.998027i | 0.0627905 | + | 0.998027i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.50441 | + | 1.09302i | 1.50441 | + | 1.09302i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(513\) | 0.313968 | + | 1.64588i | 0.313968 | + | 1.64588i | ||||
\(514\) | 0.0702235 | + | 0.368125i | 0.0702235 | + | 0.368125i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.97708 | + | 3.11538i | 1.97708 | + | 3.11538i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.0800484 | + | 1.27233i | −0.0800484 | + | 1.27233i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.273190 | + | 1.43211i | −0.273190 | + | 1.43211i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(524\) | −1.41789 | + | 0.779494i | −1.41789 | + | 0.779494i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.74630 | + | 2.75173i | −1.74630 | + | 2.75173i | ||||
\(529\) | 0.968583 | − | 0.248690i | 0.968583 | − | 0.248690i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.493573 | − | 0.777747i | −0.493573 | − | 0.777747i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.99280 | −1.99280 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.0534698 | − | 0.113629i | −0.0534698 | − | 0.113629i | ||||
\(537\) | −2.20417 | − | 0.872693i | −2.20417 | − | 0.872693i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.11716 | − | 1.35041i | −1.11716 | − | 1.35041i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.98423 | + | 0.250666i | −1.98423 | + | 0.250666i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.00788530 | + | 0.125333i | 0.00788530 | + | 0.125333i | 1.00000 | \(0\) | ||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(548\) | 0.791759 | + | 1.68257i | 0.791759 | + | 1.68257i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.27760 | + | 1.19975i | 1.27760 | + | 1.19975i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.456288 | − | 0.718995i | −0.456288 | − | 0.718995i | ||||
\(557\) | 0 | 0 | 0.425779 | − | 0.904827i | \(-0.360000\pi\) | ||||
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.46676 | + | 0.816941i | 6.46676 | + | 0.816941i | ||||
\(562\) | −0.824805 | + | 1.75280i | −0.824805 | + | 1.75280i | ||||
\(563\) | 1.50441 | + | 0.595638i | 1.50441 | + | 0.595638i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.328407 | − | 0.180543i | −0.328407 | − | 0.180543i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.541587 | − | 1.66683i | 0.541587 | − | 1.66683i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.31703 | − | 2.07531i | 1.31703 | − | 2.07531i | ||||
\(577\) | −0.124591 | − | 0.0157395i | −0.124591 | − | 0.0157395i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(578\) | 1.60748 | + | 2.53298i | 1.60748 | + | 2.53298i | ||||
\(579\) | −0.296722 | − | 0.630566i | −0.296722 | − | 0.630566i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.91429 | − | 2.11736i | 2.91429 | − | 2.11736i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.115808 | + | 0.607087i | −0.115808 | + | 0.607087i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.939097 | + | 0.516273i | 0.939097 | + | 0.516273i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(588\) | 1.18532 | + | 1.43281i | 1.18532 | + | 1.43281i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.50441 | + | 1.09302i | 1.50441 | + | 1.09302i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(594\) | −3.46372 | + | 3.25265i | −3.46372 | + | 3.25265i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(600\) | −1.35556 | − | 1.27295i | −1.35556 | − | 1.27295i | ||||
\(601\) | −0.393950 | + | 0.476203i | −0.393950 | + | 0.476203i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.0578390 | − | 0.303203i | −0.0578390 | − | 0.303203i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(608\) | 0.0388067 | − | 0.616814i | 0.0388067 | − | 0.616814i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4.87711 | − | 0.616122i | −4.87711 | − | 0.616122i | ||||
\(613\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(614\) | −0.0800484 | + | 1.27233i | −0.0800484 | + | 1.27233i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.328407 | − | 0.180543i | −0.328407 | − | 0.180543i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.371808 | − | 1.94908i | 0.371808 | − | 1.94908i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(626\) | 0.781202 | + | 0.733597i | 0.781202 | + | 0.733597i | ||||
\(627\) | −0.622428 | + | 1.91564i | −0.622428 | + | 1.91564i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.97708 | + | 0.249764i | 1.97708 | + | 0.249764i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.101597 | + | 1.61484i | −0.101597 | + | 1.61484i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(642\) | 3.34930 | − | 0.859954i | 3.34930 | − | 0.859954i | ||||
\(643\) | −1.44644 | − | 0.182728i | −1.44644 | − | 0.182728i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.14927 | + | 0.455027i | −1.14927 | + | 0.455027i | ||||
\(647\) | 0 | 0 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(648\) | 1.88330 | − | 1.76854i | 1.88330 | − | 1.76854i | ||||
\(649\) | −0.0412417 | − | 0.655518i | −0.0412417 | − | 0.655518i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.200808 | − | 1.05267i | −0.200808 | − | 1.05267i | ||||
\(653\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.41213 | − | 1.32608i | 1.41213 | − | 1.32608i | ||||
\(657\) | −0.646797 | + | 1.37451i | −0.646797 | + | 1.37451i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
1.00000 | \(0\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(662\) | 0.303189 | + | 0.220280i | 0.303189 | + | 0.220280i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.844844 | − | 0.106729i | 0.844844 | − | 0.106729i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.866986 | + | 0.629902i | −0.866986 | + | 0.629902i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(674\) | 0.939097 | − | 1.47978i | 0.939097 | − | 1.47978i | ||||
\(675\) | −1.45269 | − | 2.28907i | −1.45269 | − | 2.28907i | ||||
\(676\) | −0.425779 | − | 0.904827i | −0.425779 | − | 0.904827i | ||||
\(677\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(678\) | −3.66068 | − | 0.462452i | −3.66068 | − | 0.462452i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.188925 | + | 3.00288i | 0.188925 | + | 3.00288i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.110048 | − | 1.74915i | 0.110048 | − | 1.74915i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(684\) | 0.469424 | − | 1.44474i | 0.469424 | − | 1.44474i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.124591 | − | 1.98031i | −0.124591 | − | 1.98031i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.69755 | − | 0.933237i | 1.69755 | − | 0.933237i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.371808 | + | 0.0469702i | 0.371808 | + | 0.0469702i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.60226 | − | 1.42624i | −3.60226 | − | 1.42624i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.97708 | + | 3.11538i | 1.97708 | + | 3.11538i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.53583 | − | 0.844328i | 1.53583 | − | 0.844328i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.0437581 | + | 0.695516i | 0.0437581 | + | 0.695516i | ||||
\(709\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.939097 | + | 0.516273i | 0.939097 | + | 0.516273i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.812619 | + | 0.982287i | 0.812619 | + | 0.982287i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.115808 | + | 0.607087i | 0.115808 | + | 0.607087i | ||||
\(723\) | 1.72813 | + | 1.62282i | 1.72813 | + | 1.62282i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.73132 | + | 0.958040i | −3.73132 | + | 0.958040i | ||||
\(727\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.14680 | − | 0.630457i | 1.14680 | − | 0.630457i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.47759 | + | 1.91182i | −3.47759 | + | 1.91182i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.0680131 | − | 0.209323i | 0.0680131 | − | 0.209323i | ||||
\(738\) | 4.17248 | − | 2.29384i | 4.17248 | − | 2.29384i | ||||
\(739\) | 0.939097 | + | 1.47978i | 0.939097 | + | 1.47978i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.07657 | + | 0.262332i | 2.07657 | + | 0.262332i | ||||
\(748\) | −2.83579 | − | 2.06032i | −2.83579 | − | 2.06032i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.18532 | − | 1.43281i | 1.18532 | − | 1.43281i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(758\) | −0.101597 | − | 0.0738147i | −0.101597 | − | 0.0738147i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.688925 | + | 0.500534i | 0.688925 | + | 0.500534i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.62954 | + | 0.895846i | −1.62954 | + | 0.895846i | ||||
\(769\) | 0.541587 | − | 1.66683i | 0.541587 | − | 1.66683i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.373413 | − | 0.588404i | 0.373413 | − | 0.588404i | ||||
\(772\) | −0.0235315 | + | 0.374023i | −0.0235315 | + | 0.374023i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0.913880 | − | 4.79072i | 0.913880 | − | 4.79072i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.92189 | + | 0.242791i | −1.92189 | + | 0.242791i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.641510 | − | 1.01086i | 0.641510 | − | 1.01086i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.187381 | − | 0.982287i | −0.187381 | − | 0.982287i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.91429 | + | 0.748263i | 2.91429 | + | 0.748263i | ||||
\(787\) | 0.844844 | + | 1.79538i | 0.844844 | + | 1.79538i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.17248 | − | 1.07131i | 4.17248 | − | 1.07131i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(801\) | 1.92015 | + | 1.80314i | 1.92015 | + | 1.80314i | ||||
\(802\) | 1.27760 | − | 0.702367i | 1.27760 | − | 0.702367i | ||||
\(803\) | −0.876307 | + | 0.636674i | −0.876307 | + | 0.636674i | ||||
\(804\) | −0.0721631 | + | 0.222095i | −0.0721631 | + | 0.222095i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.62954 | − | 0.645180i | −1.62954 | − | 0.645180i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.683098 | + | 0.825723i | −0.683098 | + | 0.825723i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.00882 | + | 2.18604i | 3.00882 | + | 2.18604i | ||||
\(817\) | −0.378954 | − | 1.16630i | −0.378954 | − | 1.16630i | ||||
\(818\) | −0.0534698 | − | 0.849878i | −0.0534698 | − | 0.849878i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(822\) | 1.06856 | − | 3.28869i | 1.06856 | − | 3.28869i | ||||
\(823\) | 0 | 0 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.204639 | − | 3.25265i | −0.204639 | − | 3.25265i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.781202 | − | 1.23098i | 0.781202 | − | 1.23098i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.61803 | + | 1.17557i | −1.61803 | + | 1.17557i | ||||
\(834\) | −0.296722 | + | 1.55547i | −0.296722 | + | 1.55547i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.789600 | − | 0.741484i | 0.789600 | − | 0.741484i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.746226 | − | 0.410241i | −0.746226 | − | 0.410241i | ||||
\(839\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.425779 | + | 0.904827i | −0.425779 | + | 0.904827i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.34930 | − | 1.32608i | 3.34930 | − | 1.32608i | ||||
\(844\) | −0.866986 | − | 0.629902i | −0.866986 | − | 0.629902i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.00937 | + | 2.14503i | −1.00937 | + | 2.14503i | ||||
\(850\) | 1.45794 | − | 1.36909i | 1.45794 | − | 1.36909i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.80113 | − | 0.462452i | −1.80113 | − | 0.462452i | ||||
\(857\) | 0.0672897 | + | 1.06954i | 0.0672897 | + | 1.06954i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.0672897 | − | 1.06954i | 0.0672897 | − | 1.06954i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.992115 | − | 0.125333i | \(-0.960000\pi\) | ||||
0.992115 | + | 0.125333i | \(0.0400000\pi\) | |||||||
\(864\) | −2.62594 | + | 0.674226i | −2.62594 | + | 0.674226i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.61803 | −1.61803 | ||||||||
\(867\) | 1.04534 | − | 5.47985i | 1.04534 | − | 5.47985i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.72389 | − | 0.596766i | −4.72389 | − | 0.596766i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.929776 | − | 0.675522i | 0.929776 | − | 0.675522i | ||||
\(877\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.41789 | + | 1.03016i | −1.41789 | + | 1.03016i | −0.425779 | + | 0.904827i | \(0.640000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(882\) | 0.154335 | − | 2.45309i | 0.154335 | − | 2.45309i | ||||
\(883\) | −0.574633 | + | 0.227513i | −0.574633 | + | 0.227513i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.374763 | − | 1.96457i | −0.374763 | − | 1.96457i | ||||
\(887\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.52791 | 4.52791 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.0534698 | + | 0.849878i | −0.0534698 | + | 0.849878i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.154335 | + | 2.45309i | 0.154335 | + | 2.45309i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 3.39510 | 3.39510 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.60528 | + | 1.16630i | 1.60528 | + | 1.16630i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.06279 | − | 0.998027i | 1.06279 | − | 0.998027i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
1.00000 | \(0\) | |||||||||
\(908\) | 0.688925 | − | 1.46404i | 0.688925 | − | 1.46404i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(912\) | −0.837780 | + | 0.786727i | −0.837780 | + | 0.786727i | ||||
\(913\) | 1.20742 | + | 0.877242i | 1.20742 | + | 0.877242i | ||||
\(914\) | −0.574633 | + | 0.227513i | −0.574633 | + | 0.227513i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.45626 | + | 4.17789i | 3.45626 | + | 4.17789i | ||||
\(919\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.72813 | − | 1.62282i | 1.72813 | − | 1.62282i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.26480 | + | 0.159781i | 1.26480 | + | 0.159781i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.263146 | − | 0.559214i | −0.263146 | − | 0.559214i | ||||
\(932\) | −0.124591 | − | 1.98031i | −0.124591 | − | 1.98031i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.0915446 | − | 1.45506i | 0.0915446 | − | 1.45506i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.53583 | + | 0.844328i | 1.53583 | + | 0.844328i | 1.00000 | \(0\) | ||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.125129 | − | 1.98886i | −0.125129 | − | 1.98886i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.159566 | − | 0.339095i | 0.159566 | − | 0.339095i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.21670 | − | 2.67953i | 2.21670 | − | 2.67953i | ||||
\(947\) | 0.541587 | + | 0.297740i | 0.541587 | + | 0.297740i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.331159 | + | 0.521823i | 0.331159 | + | 0.521823i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.613161 | + | 1.88711i | −0.613161 | + | 1.88711i | −0.187381 | + | 0.982287i | \(0.560000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.929776 | + | 0.368125i | −0.929776 | + | 0.368125i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.00530 | − | 2.20193i | −4.00530 | − | 2.20193i | ||||
\(964\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(968\) | 2.00657 | + | 0.515199i | 2.00657 | + | 0.515199i | ||||
\(969\) | 2.13712 | + | 0.846147i | 2.13712 | + | 0.846147i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.598617 | + | 0.153699i | 0.598617 | + | 0.153699i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(972\) | −2.09308 | −2.09308 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.824805 | + | 0.211774i | −0.824805 | + | 0.211774i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(978\) | −1.06779 | + | 1.68257i | −1.06779 | + | 1.68257i | ||||
\(979\) | 0.580394 | + | 1.78627i | 0.580394 | + | 1.78627i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.69755 | − | 0.933237i | 1.69755 | − | 0.933237i | ||||
\(983\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(984\) | −3.60226 | −3.60226 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.130584 | − | 0.684547i | −0.130584 | − | 0.684547i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.28109 | − | 0.930769i | −1.28109 | − | 0.930769i | ||||
\(997\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(998\) | −0.124591 | − | 0.0157395i | −0.124591 | − | 0.0157395i | ||||
\(999\) | 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 | 2008.1.w.a.1531.1 | ✓ | 20 | |
8.3 | odd | 2 | CM | 2008.1.w.a.1531.1 | ✓ | 20 | |
251.241 | even | 25 | inner | 2008.1.w.a.1747.1 | yes | 20 | |
2008.1747 | odd | 50 | inner | 2008.1.w.a.1747.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.1.w.a.1531.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
2008.1.w.a.1531.1 | ✓ | 20 | 8.3 | odd | 2 | CM | |
2008.1.w.a.1747.1 | yes | 20 | 251.241 | even | 25 | inner | |
2008.1.w.a.1747.1 | yes | 20 | 2008.1747 | odd | 50 | inner |