Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(1,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.a (trivial) |
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: | yes |
Analytic conductor: | \(8.17668116698\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{16})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 512) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.765367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | 0 | ||||||||
\(3\) | 1.08239 | 0.624919 | 0.312460 | − | 0.949931i | \(-0.398847\pi\) | ||||
0.312460 | + | 0.949931i | \(0.398847\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.585786 | 0.261972 | 0.130986 | − | 0.991384i | \(-0.458186\pi\) | ||||
0.130986 | + | 0.991384i | \(0.458186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.69552 | 1.39677 | 0.698387 | − | 0.715720i | \(-0.253901\pi\) | ||||
0.698387 | + | 0.715720i | \(0.253901\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.82843 | −0.609476 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.14386 | 1.24942 | 0.624710 | − | 0.780857i | \(-0.285217\pi\) | ||||
0.624710 | + | 0.780857i | \(0.285217\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.41421 | 0.946932 | 0.473466 | − | 0.880812i | \(-0.343003\pi\) | ||||
0.473466 | + | 0.880812i | \(0.343003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.634051 | 0.163711 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.82843 | 0.685994 | 0.342997 | − | 0.939336i | \(-0.388558\pi\) | ||||
0.342997 | + | 0.939336i | \(0.388558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.30864 | −1.44730 | −0.723651 | − | 0.690166i | \(-0.757538\pi\) | ||||
−0.723651 | + | 0.690166i | \(0.757538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.75699 | −1.40893 | −0.704464 | − | 0.709739i | \(-0.748813\pi\) | ||||
−0.704464 | + | 0.709739i | \(0.748813\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.22625 | −1.00579 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.41421 | 1.37678 | 0.688392 | − | 0.725338i | \(-0.258317\pi\) | ||||
0.688392 | + | 0.725338i | \(0.258317\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.06147 | 0.549856 | 0.274928 | − | 0.961465i | \(-0.411346\pi\) | ||||
0.274928 | + | 0.961465i | \(0.411346\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.48528 | 0.780787 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.16478 | 0.365915 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.07107 | 1.49127 | 0.745637 | − | 0.666352i | \(-0.232145\pi\) | ||||
0.745637 | + | 0.666352i | \(0.232145\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.69552 | 0.591756 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.08239 | −0.165063 | −0.0825316 | − | 0.996588i | \(-0.526301\pi\) | ||||
−0.0825316 | + | 0.996588i | \(0.526301\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.07107 | −0.159665 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.06147 | 0.446561 | 0.223280 | − | 0.974754i | \(-0.428323\pi\) | ||||
0.223280 | + | 0.974754i | \(0.428323\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.65685 | 0.950979 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.06147 | 0.428691 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.58579 | 0.629906 | 0.314953 | − | 0.949107i | \(-0.398011\pi\) | ||||
0.314953 | + | 0.949107i | \(0.398011\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.42742 | 0.327313 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.82843 | −0.904447 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.08239 | 0.140915 | 0.0704577 | − | 0.997515i | \(-0.477554\pi\) | ||||
0.0704577 | + | 0.997515i | \(0.477554\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.07107 | −0.137136 | −0.0685681 | − | 0.997646i | \(-0.521843\pi\) | ||||
−0.0685681 | + | 0.997646i | \(0.521843\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.75699 | −0.851300 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.97908 | 0.241783 | 0.120891 | − | 0.992666i | \(-0.461425\pi\) | ||||
0.120891 | + | 0.992666i | \(0.461425\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.31371 | −0.880467 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.02509 | −0.952403 | −0.476201 | − | 0.879336i | \(-0.657987\pi\) | ||||
−0.476201 | + | 0.879336i | \(0.657987\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.48528 | −0.759045 | −0.379522 | − | 0.925183i | \(-0.623912\pi\) | ||||
−0.379522 | + | 0.925183i | \(0.623912\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.04054 | −0.582032 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.3137 | 1.74516 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.7821 | −1.66311 | −0.831557 | − | 0.555440i | \(-0.812550\pi\) | ||||
−0.831557 | + | 0.555440i | \(0.812550\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.171573 | −0.0190637 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.6997 | 1.50374 | 0.751868 | − | 0.659314i | \(-0.229153\pi\) | ||||
0.751868 | + | 0.659314i | \(0.229153\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.65685 | 0.179711 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.02509 | 0.860380 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.82843 | 0.511812 | 0.255906 | − | 0.966702i | \(-0.417626\pi\) | ||||
0.255906 | + | 0.966702i | \(0.417626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.6173 | 1.32265 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.31371 | 0.343616 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.69552 | −0.379152 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.17157 | 0.525094 | 0.262547 | − | 0.964919i | \(-0.415438\pi\) | ||||
0.262547 | + | 0.964919i | \(0.415438\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.57675 | −0.761492 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.0711 | 1.69863 | 0.849317 | − | 0.527883i | \(-0.177014\pi\) | ||||
0.849317 | + | 0.527883i | \(0.177014\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.1480 | −1.39405 | −0.697023 | − | 0.717049i | \(-0.745492\pi\) | ||||
−0.697023 | + | 0.717049i | \(0.745492\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.34315 | 0.228668 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.97908 | −0.191324 | −0.0956622 | − | 0.995414i | \(-0.530497\pi\) | ||||
−0.0956622 | + | 0.995414i | \(0.530497\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.0711 | −1.25198 | −0.625991 | − | 0.779831i | \(-0.715305\pi\) | ||||
−0.625991 | + | 0.779831i | \(0.715305\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.81845 | 0.931926 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.65685 | −0.720296 | −0.360148 | − | 0.932895i | \(-0.617274\pi\) | ||||
−0.360148 | + | 0.932895i | \(0.617274\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.95815 | −0.369099 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.24264 | −0.577132 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.4525 | 0.958179 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.17157 | 0.561052 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.32957 | −0.390384 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7206 | 1.04004 | 0.520018 | − | 0.854155i | \(-0.325925\pi\) | ||||
0.520018 | + | 0.854155i | \(0.325925\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.17157 | −0.103151 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.5964 | −1.27529 | −0.637645 | − | 0.770330i | \(-0.720091\pi\) | ||||
−0.637645 | + | 0.770330i | \(0.720091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.3137 | −2.02155 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.06147 | −0.263489 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9706 | 1.10815 | 0.554075 | − | 0.832467i | \(-0.313072\pi\) | ||||
0.554075 | + | 0.832467i | \(0.313072\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.1940 | −1.71284 | −0.856418 | − | 0.516283i | \(-0.827315\pi\) | ||||
−0.856418 | + | 0.516283i | \(0.827315\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.31371 | 0.279065 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.1480 | 1.18312 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.34315 | 0.360679 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.20533 | 0.594285 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.75736 | 0.143968 | 0.0719842 | − | 0.997406i | \(-0.477067\pi\) | ||||
0.0719842 | + | 0.997406i | \(0.477067\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.634051 | −0.0515983 | −0.0257992 | − | 0.999667i | \(-0.508213\pi\) | ||||
−0.0257992 | + | 0.999667i | \(0.508213\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.17157 | −0.418097 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.79337 | 0.144047 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.24264 | 0.178982 | 0.0894911 | − | 0.995988i | \(-0.471476\pi\) | ||||
0.0894911 | + | 0.995988i | \(0.471476\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.96362 | 0.393641 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.9706 | −1.96796 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.41196 | 0.423898 | 0.211949 | − | 0.977281i | \(-0.432019\pi\) | ||||
0.211949 | + | 0.977281i | \(0.432019\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.62742 | 0.204544 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.69552 | 0.285968 | 0.142984 | − | 0.989725i | \(-0.454330\pi\) | ||||
0.142984 | + | 0.989725i | \(0.454330\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.34315 | −0.103319 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.5349 | 0.882096 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.2132 | −1.46075 | −0.730376 | − | 0.683045i | \(-0.760655\pi\) | ||||
−0.730376 | + | 0.683045i | \(0.760655\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.2095 | −1.30092 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.17157 | 0.0880608 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.5349 | −0.862159 | −0.431079 | − | 0.902314i | \(-0.641867\pi\) | ||||
−0.431079 | + | 0.902314i | \(0.641867\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2426 | −1.05865 | −0.529324 | − | 0.848420i | \(-0.677554\pi\) | ||||
−0.529324 | + | 0.848420i | \(0.677554\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.15932 | −0.0856991 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.31371 | 0.390672 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.7206 | 0.857096 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −19.3137 | −1.40487 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.7206 | −0.848073 | −0.424037 | − | 0.905645i | \(-0.639387\pi\) | ||||
−0.424037 | + | 0.905645i | \(0.639387\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.485281 | 0.0349313 | 0.0174657 | − | 0.999847i | \(-0.494440\pi\) | ||||
0.0174657 | + | 0.999847i | \(0.494440\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.16478 | 0.155023 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.7279 | −0.764333 | −0.382166 | − | 0.924094i | \(-0.624822\pi\) | ||||
−0.382166 | + | 0.924094i | \(0.624822\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.3547 | 0.875798 | 0.437899 | − | 0.899024i | \(-0.355723\pi\) | ||||
0.437899 | + | 0.899024i | \(0.355723\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.14214 | 0.151095 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 27.3994 | 1.92306 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.34315 | −0.163652 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.3547 | 0.858708 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −26.1421 | −1.80829 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.3283 | −0.917555 | −0.458778 | − | 0.888551i | \(-0.651713\pi\) | ||||
−0.458778 | + | 0.888551i | \(0.651713\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.68629 | −0.595175 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.634051 | −0.0432419 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3137 | 0.768025 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.01962 | −0.474342 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.65685 | 0.649590 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.06147 | 0.205011 | 0.102506 | − | 0.994732i | \(-0.467314\pi\) | ||||
0.102506 | + | 0.994732i | \(0.467314\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.51472 | 0.567648 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.08239 | 0.0718409 | 0.0359204 | − | 0.999355i | \(-0.488564\pi\) | ||||
0.0359204 | + | 0.999355i | \(0.488564\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.89949 | 0.257686 | 0.128843 | − | 0.991665i | \(-0.458874\pi\) | ||||
0.128843 | + | 0.991665i | \(0.458874\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.5754 | 1.09058 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.8284 | 1.36452 | 0.682258 | − | 0.731112i | \(-0.260998\pi\) | ||||
0.682258 | + | 0.731112i | \(0.260998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.79337 | 0.116986 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.0000 | −1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.2459 | −0.792119 | −0.396060 | − | 0.918225i | \(-0.629623\pi\) | ||||
−0.396060 | + | 0.918225i | \(0.629623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.1716 | −0.848456 | −0.424228 | − | 0.905556i | \(-0.639454\pi\) | ||||
−0.424228 | + | 0.905556i | \(0.639454\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.4930 | 0.993879 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.89949 | 0.249130 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.5391 | −1.37050 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.8284 | 0.939713 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0292 | −1.13800 | −0.568998 | − | 0.822339i | \(-0.692669\pi\) | ||||
−0.568998 | + | 0.822339i | \(0.692669\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.0000 | −1.76034 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.79337 | 0.112305 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.9706 | −0.933838 | −0.466919 | − | 0.884300i | \(-0.654636\pi\) | ||||
−0.466919 | + | 0.884300i | \(0.654636\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 33.5223 | 2.08297 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.5563 | −0.839117 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.8799 | 0.794210 | 0.397105 | − | 0.917773i | \(-0.370015\pi\) | ||||
0.397105 | + | 0.917773i | \(0.370015\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.68629 | 0.165018 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.22625 | 0.319841 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.5563 | 1.55820 | 0.779099 | − | 0.626901i | \(-0.215677\pi\) | ||||
0.779099 | + | 0.626901i | \(0.215677\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.59767 | −0.340034 | −0.170017 | − | 0.985441i | \(-0.554382\pi\) | ||||
−0.170017 | + | 0.985441i | \(0.554382\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.6569 | 0.826550 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.2974 | −1.16367 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.41421 | −0.205140 | −0.102570 | − | 0.994726i | \(-0.532707\pi\) | ||||
−0.102570 | + | 0.994726i | \(0.532707\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.59767 | −0.335124 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.7990 | 1.06180 | 0.530899 | − | 0.847435i | \(-0.321854\pi\) | ||||
0.530899 | + | 0.847435i | \(0.321854\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.5964 | −0.867664 | −0.433832 | − | 0.900994i | \(-0.642839\pi\) | ||||
−0.433832 | + | 0.900994i | \(0.642839\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.7821 | −0.872558 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.59767 | 0.328141 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.585786 | 0.0342220 | 0.0171110 | − | 0.999854i | \(-0.494553\pi\) | ||||
0.0171110 | + | 0.999854i | \(0.494553\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.634051 | 0.0369159 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.6569 | −1.25666 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.0698 | −1.33416 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | −0.230556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.4776 | 1.06151 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.627417 | −0.0359258 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.51528 | −0.257701 | −0.128850 | − | 0.991664i | \(-0.541129\pi\) | ||||
−0.128850 | + | 0.991664i | \(0.541129\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.3137 | −0.871166 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.6005 | −1.39497 | −0.697484 | − | 0.716600i | \(-0.745697\pi\) | ||||
−0.697484 | + | 0.716600i | \(0.745697\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.3137 | −1.76996 | −0.884978 | − | 0.465633i | \(-0.845827\pi\) | ||||
−0.884978 | + | 0.465633i | \(0.845827\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.95815 | −0.223017 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.4142 | 0.865748 | 0.432874 | − | 0.901454i | \(-0.357499\pi\) | ||||
0.432874 | + | 0.901454i | \(0.357499\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.7235 | 1.72018 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.14214 | −0.119562 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.8435 | −0.992841 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.8995 | −0.881945 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.1480 | −0.782387 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.3137 | 0.623745 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.47343 | 0.465742 | 0.232871 | − | 0.972508i | \(-0.425188\pi\) | ||||
0.232871 | + | 0.972508i | \(0.425188\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.5858 | −0.908895 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.15932 | 0.0633402 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.00000 | −0.326841 | −0.163420 | − | 0.986557i | \(-0.552253\pi\) | ||||
−0.163420 | + | 0.986557i | \(0.552253\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.28772 | −0.450127 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.6863 | 0.687001 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.26810 | −0.0684710 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.28427 | −0.230657 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.4930 | −0.831710 | −0.415855 | − | 0.909431i | \(-0.636518\pi\) | ||||
−0.415855 | + | 0.909431i | \(0.636518\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.72792 | 0.146022 | 0.0730112 | − | 0.997331i | \(-0.476739\pi\) | ||||
0.0730112 | + | 0.997331i | \(0.476739\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.8435 | −0.952418 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.9706 | 1.22260 | 0.611300 | − | 0.791399i | \(-0.290647\pi\) | ||||
0.611300 | + | 0.791399i | \(0.290647\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.70099 | −0.249502 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.3137 | 0.598785 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.634051 | 0.0334639 | 0.0167320 | − | 0.999860i | \(-0.494674\pi\) | ||||
0.0167320 | + | 0.999860i | \(0.494674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.7990 | 1.09468 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.68006 | 0.350612 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.79899 | −0.198848 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.18440 | −0.479422 | −0.239711 | − | 0.970844i | \(-0.577053\pi\) | ||||
−0.239711 | + | 0.970844i | \(0.577053\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.31371 | 0.380736 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.9469 | 0.879837 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.72792 | −0.348359 | −0.174179 | − | 0.984714i | \(-0.555727\pi\) | ||||
−0.174179 | + | 0.984714i | \(0.555727\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.12293 | −0.316187 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.3137 | 1.30372 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.3170 | 1.35181 | 0.675906 | − | 0.736988i | \(-0.263753\pi\) | ||||
0.675906 | + | 0.736988i | \(0.263753\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.6863 | 0.649938 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.9050 | −1.06820 | −0.534098 | − | 0.845423i | \(-0.679349\pi\) | ||||
−0.534098 | + | 0.845423i | \(0.679349\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.97056 | 0.457182 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.97908 | 0.100602 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.3848 | 1.03355 | 0.516775 | − | 0.856121i | \(-0.327133\pi\) | ||||
0.516775 | + | 0.856121i | \(0.327133\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.1116 | −0.966517 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.7990 | −0.796954 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.65914 | −0.435688 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.07107 | −0.254510 | −0.127255 | − | 0.991870i | \(-0.540617\pi\) | ||||
−0.127255 | + | 0.991870i | \(0.540617\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25.2346 | −1.26331 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.51472 | 0.375267 | 0.187634 | − | 0.982239i | \(-0.439918\pi\) | ||||
0.187634 | + | 0.982239i | \(0.439918\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.4525 | 0.520676 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.100505 | −0.00499414 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 37.5892 | 1.86323 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.3137 | −1.54836 | −0.774182 | − | 0.632964i | \(-0.781838\pi\) | ||||
−0.774182 | + | 0.632964i | \(0.781838\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.0392 | 0.692504 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000 | 0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.02509 | 0.393936 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.8579 | −1.07038 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.4316 | 0.607322 | 0.303661 | − | 0.952780i | \(-0.401791\pi\) | ||||
0.303661 | + | 0.952780i | \(0.401791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.58579 | 0.418446 | 0.209223 | − | 0.977868i | \(-0.432907\pi\) | ||||
0.209223 | + | 0.977868i | \(0.432907\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.59767 | −0.272168 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.1716 | −0.638915 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.95815 | −0.191548 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.3137 | 0.739353 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.4558 | 1.22333 | 0.611665 | − | 0.791117i | \(-0.290500\pi\) | ||||
0.611665 | + | 0.791117i | \(0.290500\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.70099 | 0.225395 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 42.6274 | 2.03915 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.1145 | 1.81911 | 0.909553 | − | 0.415588i | \(-0.136424\pi\) | ||||
0.909553 | + | 0.415588i | \(0.136424\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.1716 | −0.579599 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.97908 | 0.0940287 | 0.0470144 | − | 0.998894i | \(-0.485029\pi\) | ||||
0.0470144 | + | 0.998894i | \(0.485029\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.82843 | 0.134080 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.90215 | 0.0899687 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.14214 | −0.289865 | −0.144933 | − | 0.989442i | \(-0.546297\pi\) | ||||
−0.144933 | + | 0.989442i | \(0.546297\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.5754 | −0.780507 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.686292 | −0.0322448 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.39104 | 0.346497 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.6274 | −1.24558 | −0.622789 | − | 0.782390i | \(-0.714001\pi\) | ||||
−0.622789 | + | 0.782390i | \(0.714001\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.7821 | −0.689968 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.2426 | 1.78114 | 0.890569 | − | 0.454849i | \(-0.150307\pi\) | ||||
0.890569 | + | 0.454849i | \(0.150307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.6871 | 1.65852 | 0.829260 | − | 0.558864i | \(-0.188762\pi\) | ||||
0.829260 | + | 0.558864i | \(0.188762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.94113 | 0.0900175 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 38.0376 | 1.76017 | 0.880084 | − | 0.474817i | \(-0.157486\pi\) | ||||
0.880084 | + | 0.474817i | \(0.157486\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.31371 | 0.337716 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.42742 | 0.111849 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.48528 | −0.206233 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.3784 | 1.34798 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.38478 | −0.383913 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.1618 | 1.60658 | 0.803292 | − | 0.595585i | \(-0.203080\pi\) | ||||
0.803292 | + | 0.595585i | \(0.203080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.9706 | 1.41214 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −27.0279 | −1.22981 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.02944 | 0.137560 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.23172 | 0.282386 | 0.141193 | − | 0.989982i | \(-0.454906\pi\) | ||||
0.141193 | + | 0.989982i | \(0.454906\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.85786 | 0.264902 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.04054 | 0.227477 | 0.113738 | − | 0.993511i | \(-0.463717\pi\) | ||||
0.113738 | + | 0.993511i | \(0.463717\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.9706 | 0.944467 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.43835 | −0.199489 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −29.6569 | −1.33029 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.6578 | −0.790473 | −0.395237 | − | 0.918579i | \(-0.629337\pi\) | ||||
−0.395237 | + | 0.918579i | \(0.629337\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.00000 | 0.178707 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.8072 | 1.01692 | 0.508460 | − | 0.861085i | \(-0.330215\pi\) | ||||
0.508460 | + | 0.861085i | \(0.330215\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.45381 | −0.0645660 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.2426 | 1.16318 | 0.581592 | − | 0.813480i | \(-0.302430\pi\) | ||||
0.581592 | + | 0.813480i | \(0.302430\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.9665 | −1.06021 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.9706 | 1.45569 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.28772 | −0.365201 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.6863 | 0.557942 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.7962 | −0.912853 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.34315 | 0.277898 | 0.138949 | − | 0.990300i | \(-0.455628\pi\) | ||||
0.138949 | + | 0.990300i | \(0.455628\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.2249 | −0.622013 | −0.311007 | − | 0.950408i | \(-0.600666\pi\) | ||||
−0.311007 | + | 0.950408i | \(0.600666\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.6274 | −0.812967 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.65914 | 0.377198 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.6569 | 0.985081 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.97908 | −0.0858846 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.6569 | −0.591544 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.15932 | −0.0501216 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.4853 | −0.538780 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.5851 | 1.18817 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.2426 | 0.440366 | 0.220183 | − | 0.975459i | \(-0.429335\pi\) | ||||
0.220183 | + | 0.975459i | \(0.429335\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.4161 | −0.661569 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.65685 | −0.327984 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.9259 | −0.809214 | −0.404607 | − | 0.914491i | \(-0.632592\pi\) | ||||
−0.404607 | + | 0.914491i | \(0.632592\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.95837 | 0.0835812 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −46.7736 | −1.99262 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −54.6274 | −2.32299 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.75152 | 0.244138 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.4142 | 0.483636 | 0.241818 | − | 0.970322i | \(-0.422256\pi\) | ||||
0.241818 | + | 0.970322i | \(0.422256\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.69552 | −0.156304 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.6863 | 0.535616 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.9678 | −0.630817 | −0.315408 | − | 0.948956i | \(-0.602141\pi\) | ||||
−0.315408 | + | 0.948956i | \(0.602141\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.48528 | −0.188697 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.634051 | −0.0266276 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.6569 | −1.07559 | −0.537796 | − | 0.843075i | \(-0.680743\pi\) | ||||
−0.537796 | + | 0.843075i | \(0.680743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.5851 | −1.15440 | −0.577200 | − | 0.816603i | \(-0.695855\pi\) | ||||
−0.577200 | + | 0.816603i | \(0.695855\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.6863 | −0.529977 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.4663 | 1.31224 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.3137 | 0.720779 | 0.360390 | − | 0.932802i | \(-0.382644\pi\) | ||||
0.360390 | + | 0.932802i | \(0.382644\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.525265 | 0.0218293 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 50.6274 | 2.10038 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.0029 | 0.787018 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.65685 | −0.151192 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.5545 | −0.765827 | −0.382913 | − | 0.923784i | \(-0.625079\pi\) | ||||
−0.382913 | + | 0.923784i | \(0.625079\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.3137 | −0.795807 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.6118 | −0.477646 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.31371 | 0.382468 | 0.191234 | − | 0.981544i | \(-0.438751\pi\) | ||||
0.191234 | + | 0.981544i | \(0.438751\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.12293 | 0.251016 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.3726 | 0.547303 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −45.5055 | −1.85931 | −0.929653 | − | 0.368437i | \(-0.879893\pi\) | ||||
−0.929653 | + | 0.368437i | \(0.879893\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.8284 | 0.849609 | 0.424805 | − | 0.905285i | \(-0.360343\pi\) | ||||
0.424805 | + | 0.905285i | \(0.360343\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.61859 | −0.147361 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.61522 | 0.146980 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.6569 | 1.20176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.4525 | 0.422863 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.4142 | −1.59193 | −0.795963 | − | 0.605346i | \(-0.793035\pi\) | ||||
−0.795963 | + | 0.605346i | \(0.793035\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.53620 | −0.102270 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.4853 | 1.54936 | 0.774680 | − | 0.632354i | \(-0.217911\pi\) | ||||
0.774680 | + | 0.632354i | \(0.217911\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.14386 | 0.166556 | 0.0832779 | − | 0.996526i | \(-0.473461\pi\) | ||||
0.0832779 | + | 0.996526i | \(0.473461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 35.3137 | 1.41709 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.8435 | 0.714886 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −28.2960 | −1.13004 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.6569 | 1.02301 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.1480 | 0.563224 | 0.281612 | − | 0.959528i | \(-0.409131\pi\) | ||||
0.281612 | + | 0.959528i | \(0.409131\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.4264 | −0.573398 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.86577 | 0.272460 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.7279 | 0.900513 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.6733 | 0.580466 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.1421 | −1.50652 | −0.753262 | − | 0.657721i | \(-0.771521\pi\) | ||||
−0.753262 | + | 0.657721i | \(0.771521\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.9259 | −0.746366 | −0.373183 | − | 0.927758i | \(-0.621734\pi\) | ||||
−0.373183 | + | 0.927758i | \(0.621734\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.686292 | −0.0270227 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.5391 | 0.846788 | 0.423394 | − | 0.905946i | \(-0.360839\pi\) | ||||
0.423394 | + | 0.905946i | \(0.360839\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.48528 | 0.176063 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.2459 | 0.479953 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.44365 | −0.252160 | −0.126080 | − | 0.992020i | \(-0.540240\pi\) | ||||
−0.126080 | + | 0.992020i | \(0.540240\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.55035 | −0.334090 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.8579 | 0.462619 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.45381 | 0.0566324 | 0.0283162 | − | 0.999599i | \(-0.490985\pi\) | ||||
0.0283162 | + | 0.999599i | \(0.490985\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.0711 | 1.13073 | 0.565367 | − | 0.824840i | \(-0.308735\pi\) | ||||
0.565367 | + | 0.824840i | \(0.308735\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.4525 | 0.405942 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.6569 | −0.529590 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −50.0977 | −1.93979 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.31371 | 0.128115 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.43835 | −0.171341 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.8284 | −1.03416 | −0.517080 | − | 0.855937i | \(-0.672981\pi\) | ||||
−0.517080 | + | 0.855937i | \(0.672981\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.3379 | 0.936766 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.5563 | −0.521013 | −0.260506 | − | 0.965472i | \(-0.583890\pi\) | ||||
−0.260506 | + | 0.965472i | \(0.583890\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.1116 | 0.733437 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.17157 | 0.0448948 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.8113 | 1.25549 | 0.627745 | − | 0.778419i | \(-0.283978\pi\) | ||||
0.627745 | + | 0.778419i | \(0.283978\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.59798 | 0.290304 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.22078 | 0.161033 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.6569 | 0.596479 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.7276 | 1.54935 | 0.774676 | − | 0.632358i | \(-0.217913\pi\) | ||||
0.774676 | + | 0.632358i | \(0.217913\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −28.0000 | −1.06363 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.8294 | −0.448714 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.3137 | −0.428537 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.5445 | 0.852712 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.8701 | 0.939329 | 0.469665 | − | 0.882845i | \(-0.344375\pi\) | ||||
0.469665 | + | 0.882845i | \(0.344375\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −57.2261 | −2.15832 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.94113 | 0.0731070 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 63.0864 | 2.37261 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.6985 | 0.890015 | 0.445008 | − | 0.895527i | \(-0.353201\pi\) | ||||
0.445008 | + | 0.895527i | \(0.353201\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.0279 | 1.01363 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.6863 | −0.774708 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.28772 | 0.309943 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.2548 | −0.495011 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.5641 | −1.10256 | −0.551278 | − | 0.834321i | \(-0.685860\pi\) | ||||
−0.551278 | + | 0.834321i | \(0.685860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52.2843 | −1.94717 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.2568 | −0.530216 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −34.5269 | −1.28230 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.0643 | −0.818320 | −0.409160 | − | 0.912463i | \(-0.634178\pi\) | ||||
−0.409160 | + | 0.912463i | \(0.634178\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.2843 | 0.640158 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.06147 | −0.113232 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.5269 | −0.684307 | −0.342154 | − | 0.939644i | \(-0.611156\pi\) | ||||
−0.342154 | + | 0.939644i | \(0.611156\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.22078 | 0.155686 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.20101 | 0.302088 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.7582 | 1.83038 | 0.915192 | − | 0.403018i | \(-0.132039\pi\) | ||||
0.915192 | + | 0.403018i | \(0.132039\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.3137 | −0.856450 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.1367 | 0.995550 | 0.497775 | − | 0.867306i | \(-0.334151\pi\) | ||||
0.497775 | + | 0.867306i | \(0.334151\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.02944 | 0.0377157 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −25.0489 | −0.916490 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.31371 | −0.267237 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.7821 | 0.539405 | 0.269703 | − | 0.962944i | \(-0.413075\pi\) | ||||
0.269703 | + | 0.962944i | \(0.413075\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.5147 | −0.711156 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.371418 | −0.0135173 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.9289 | −0.687984 | −0.343992 | − | 0.938973i | \(-0.611779\pi\) | ||||
−0.343992 | + | 0.938973i | \(0.611779\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −30.3070 | −1.10007 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.6274 | 1.25524 | 0.627621 | − | 0.778519i | \(-0.284029\pi\) | ||||
0.627621 | + | 0.778519i | \(0.284029\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −48.3044 | −1.74874 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.02944 | −0.109530 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.69552 | 0.133437 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.17157 | 0.186492 | 0.0932458 | − | 0.995643i | \(-0.470276\pi\) | ||||
0.0932458 | + | 0.995643i | \(0.470276\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.2040 | −0.583574 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.6985 | 1.42786 | 0.713928 | − | 0.700219i | \(-0.246915\pi\) | ||||
0.713928 | + | 0.700219i | \(0.246915\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.2568 | −0.512120 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 36.2843 | 1.30169 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.2346 | 0.904123 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.2548 | −1.18995 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −38.7485 | −1.38476 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.31371 | 0.0468883 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.94816 | −0.283321 | −0.141661 | − | 0.989915i | \(-0.545244\pi\) | ||||
−0.141661 | + | 0.989915i | \(0.545244\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.9411 | 0.496317 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.2960 | −1.00609 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.65685 | −0.129859 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.90762 | 0.103123 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.6985 | −1.40619 | −0.703096 | − | 0.711095i | \(-0.748200\pi\) | ||||
−0.703096 | + | 0.711095i | \(0.748200\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.65914 | 0.306338 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.82843 | −0.311937 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.8741 | −0.948366 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.6274 | −0.515549 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.6620 | 0.973748 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.6863 | −0.867924 | −0.433962 | − | 0.900931i | \(-0.642885\pi\) | ||||
−0.433962 | + | 0.900931i | \(0.642885\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.35049 | 0.0825370 | 0.0412685 | − | 0.999148i | \(-0.486860\pi\) | ||||
0.0412685 | + | 0.999148i | \(0.486860\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.05887 | −0.212494 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.17025 | 0.111049 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.82843 | 0.238896 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −23.0698 | −0.806124 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.5269 | 1.34460 | 0.672299 | − | 0.740279i | \(-0.265307\pi\) | ||||
0.672299 | + | 0.740279i | \(0.265307\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.0643 | −0.769114 | −0.384557 | − | 0.923101i | \(-0.625646\pi\) | ||||
−0.384557 | + | 0.923101i | \(0.625646\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −20.8873 | −0.727203 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.5545 | 0.645204 | 0.322602 | − | 0.946535i | \(-0.395443\pi\) | ||||
0.322602 | + | 0.946535i | \(0.395443\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.3848 | −0.430141 | −0.215071 | − | 0.976599i | \(-0.568998\pi\) | ||||
−0.215071 | + | 0.976599i | \(0.568998\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.69552 | −0.128196 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.8284 | 0.652366 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.16478 | 0.0749155 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.0000 | −0.553041 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.4554 | −1.01691 | −0.508456 | − | 0.861088i | \(-0.669784\pi\) | ||||
−0.508456 | + | 0.861088i | \(0.669784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.9706 | 0.895537 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.2655 | 0.663539 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.786797 | −0.0270666 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.8072 | 0.783663 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.7990 | −0.542220 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −61.2931 | −2.10110 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.1005 | −1.09910 | −0.549550 | − | 0.835461i | \(-0.685201\pi\) | ||||
−0.549550 | + | 0.835461i | \(0.685201\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.75699 | 0.231084 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.2843 | 0.829535 | 0.414767 | − | 0.909927i | \(-0.363863\pi\) | ||||
0.414767 | + | 0.909927i | \(0.363863\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.9063 | −0.406238 | −0.203119 | − | 0.979154i | \(-0.565108\pi\) | ||||
−0.203119 | + | 0.979154i | \(0.565108\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.0000 | −0.545279 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.525265 | 0.0178802 | 0.00894011 | − | 0.999960i | \(-0.497154\pi\) | ||||
0.00894011 | + | 0.999960i | \(0.497154\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.2548 | −0.382676 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.74153 | −0.330840 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −61.2548 | −2.07793 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.75699 | 0.228952 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.45584 | −0.320032 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −20.9050 | −0.706718 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.5563 | 1.67340 | 0.836700 | − | 0.547662i | \(-0.184482\pi\) | ||||
0.836700 | + | 0.547662i | \(0.184482\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.634051 | 0.0213860 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.9411 | −1.34565 | −0.672825 | − | 0.739801i | \(-0.734919\pi\) | ||||
−0.672825 | + | 0.739801i | \(0.734919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.3784 | 0.988663 | 0.494332 | − | 0.869273i | \(-0.335413\pi\) | ||||
0.494332 | + | 0.869273i | \(0.335413\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.686292 | 0.0230694 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.2095 | 0.577838 | 0.288919 | − | 0.957354i | \(-0.406704\pi\) | ||||
0.288919 | + | 0.957354i | \(0.406704\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43.3137 | 1.45270 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.710974 | −0.0238185 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19.3137 | −0.646309 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.75699 | −0.225861 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.9706 | −0.833743 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.6984 | 0.757033 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.9706 | 0.432112 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.32957 | −0.144079 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.34315 | −0.277336 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.0572 | 1.49610 | 0.748050 | − | 0.663643i | \(-0.230990\pi\) | ||||
0.748050 | + | 0.663643i | \(0.230990\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31.2132 | −1.03528 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.9665 | 0.794045 | 0.397022 | − | 0.917809i | \(-0.370044\pi\) | ||||
0.397022 | + | 0.917809i | \(0.370044\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 56.7696 | 1.87880 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.679111 | −0.0224507 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −53.9411 | −1.78129 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.0029 | −0.626846 | −0.313423 | − | 0.949614i | \(-0.601476\pi\) | ||||
−0.313423 | + | 0.949614i | \(0.601476\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.88730 | −0.161042 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27.3994 | −0.901861 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42.2426 | −1.38893 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.8686 | 0.849637 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.8284 | −1.40516 | −0.702578 | − | 0.711607i | \(-0.747968\pi\) | ||||
−0.702578 | + | 0.711607i | \(0.747968\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.9957 | −1.37635 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.6274 | −0.871742 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.86577 | 0.224535 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.4558 | 1.41964 | 0.709820 | − | 0.704383i | \(-0.248776\pi\) | ||||
0.709820 | + | 0.704383i | \(0.248776\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −33.8937 | −1.10608 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.92893 | 0.0954805 | 0.0477402 | − | 0.998860i | \(-0.484798\pi\) | ||||
0.0477402 | + | 0.998860i | \(0.484798\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.0279 | 0.880151 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.3137 | −0.368035 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.4621 | 0.697426 | 0.348713 | − | 0.937230i | \(-0.386619\pi\) | ||||
0.348713 | + | 0.937230i | \(0.386619\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.1421 | −0.718764 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.6842 | 0.541023 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.0294 | 0.357279 | 0.178639 | − | 0.983915i | \(-0.442830\pi\) | ||||
0.178639 | + | 0.983915i | \(0.442830\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.86577 | −0.222171 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.2548 | 1.07498 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 47.9329 | 1.54784 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.6274 | −0.697659 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.61859 | 0.116608 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.284271 | 0.00915102 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.0866 | −0.356520 | −0.178260 | − | 0.983983i | \(-0.557047\pi\) | ||||
−0.178260 | + | 0.983983i | \(0.557047\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19.3137 | −0.620446 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57.6745 | −1.85086 | −0.925431 | − | 0.378916i | \(-0.876297\pi\) | ||||
−0.925431 | + | 0.378916i | \(0.876297\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −74.6274 | −2.39245 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17.2095 | −0.551145 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.1127 | −1.50727 | −0.753634 | − | 0.657294i | \(-0.771701\pi\) | ||||
−0.753634 | + | 0.657294i | \(0.771701\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0083 | 0.639469 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.8995 | 0.763052 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.7736 | 1.49185 | 0.745924 | − | 0.666031i | \(-0.232008\pi\) | ||||
0.745924 | + | 0.666031i | \(0.232008\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.28427 | −0.200234 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.2459 | 0.389790 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.31371 | 0.232562 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.0279 | −0.858571 | −0.429285 | − | 0.903169i | \(-0.641235\pi\) | ||||
−0.429285 | + | 0.903169i | \(0.641235\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.17157 | 0.291051 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.23719 | 0.229434 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.3848 | 0.898955 | 0.449477 | − | 0.893292i | \(-0.351610\pi\) | ||||
0.449477 | + | 0.893292i | \(0.351610\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −47.4077 | −1.49991 |
(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 | 1024.2.a.i.1.3 | 4 | ||
3.2 | odd | 2 | 9216.2.a.w.1.4 | 4 | |||
4.3 | odd | 2 | inner | 1024.2.a.i.1.2 | 4 | ||
8.3 | odd | 2 | 1024.2.a.h.1.3 | 4 | |||
8.5 | even | 2 | 1024.2.a.h.1.2 | 4 | |||
12.11 | even | 2 | 9216.2.a.w.1.3 | 4 | |||
16.3 | odd | 4 | 1024.2.b.g.513.3 | 8 | |||
16.5 | even | 4 | 1024.2.b.g.513.4 | 8 | |||
16.11 | odd | 4 | 1024.2.b.g.513.6 | 8 | |||
16.13 | even | 4 | 1024.2.b.g.513.5 | 8 | |||
24.5 | odd | 2 | 9216.2.a.bp.1.2 | 4 | |||
24.11 | even | 2 | 9216.2.a.bp.1.1 | 4 | |||
32.3 | odd | 8 | 512.2.e.j.129.2 | yes | 8 | ||
32.5 | even | 8 | 512.2.e.i.385.2 | yes | 8 | ||
32.11 | odd | 8 | 512.2.e.j.385.2 | yes | 8 | ||
32.13 | even | 8 | 512.2.e.i.129.2 | ✓ | 8 | ||
32.19 | odd | 8 | 512.2.e.i.129.3 | yes | 8 | ||
32.21 | even | 8 | 512.2.e.j.385.3 | yes | 8 | ||
32.27 | odd | 8 | 512.2.e.i.385.3 | yes | 8 | ||
32.29 | even | 8 | 512.2.e.j.129.3 | yes | 8 | ||
96.5 | odd | 8 | 4608.2.k.bi.3457.2 | 8 | |||
96.11 | even | 8 | 4608.2.k.bd.3457.3 | 8 | |||
96.29 | odd | 8 | 4608.2.k.bd.1153.3 | 8 | |||
96.35 | even | 8 | 4608.2.k.bd.1153.4 | 8 | |||
96.53 | odd | 8 | 4608.2.k.bd.3457.4 | 8 | |||
96.59 | even | 8 | 4608.2.k.bi.3457.1 | 8 | |||
96.77 | odd | 8 | 4608.2.k.bi.1153.1 | 8 | |||
96.83 | even | 8 | 4608.2.k.bi.1153.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
512.2.e.i.129.2 | ✓ | 8 | 32.13 | even | 8 | ||
512.2.e.i.129.3 | yes | 8 | 32.19 | odd | 8 | ||
512.2.e.i.385.2 | yes | 8 | 32.5 | even | 8 | ||
512.2.e.i.385.3 | yes | 8 | 32.27 | odd | 8 | ||
512.2.e.j.129.2 | yes | 8 | 32.3 | odd | 8 | ||
512.2.e.j.129.3 | yes | 8 | 32.29 | even | 8 | ||
512.2.e.j.385.2 | yes | 8 | 32.11 | odd | 8 | ||
512.2.e.j.385.3 | yes | 8 | 32.21 | even | 8 | ||
1024.2.a.h.1.2 | 4 | 8.5 | even | 2 | |||
1024.2.a.h.1.3 | 4 | 8.3 | odd | 2 | |||
1024.2.a.i.1.2 | 4 | 4.3 | odd | 2 | inner | ||
1024.2.a.i.1.3 | 4 | 1.1 | even | 1 | trivial | ||
1024.2.b.g.513.3 | 8 | 16.3 | odd | 4 | |||
1024.2.b.g.513.4 | 8 | 16.5 | even | 4 | |||
1024.2.b.g.513.5 | 8 | 16.13 | even | 4 | |||
1024.2.b.g.513.6 | 8 | 16.11 | odd | 4 | |||
4608.2.k.bd.1153.3 | 8 | 96.29 | odd | 8 | |||
4608.2.k.bd.1153.4 | 8 | 96.35 | even | 8 | |||
4608.2.k.bd.3457.3 | 8 | 96.11 | even | 8 | |||
4608.2.k.bd.3457.4 | 8 | 96.53 | odd | 8 | |||
4608.2.k.bi.1153.1 | 8 | 96.77 | odd | 8 | |||
4608.2.k.bi.1153.2 | 8 | 96.83 | even | 8 | |||
4608.2.k.bi.3457.1 | 8 | 96.59 | even | 8 | |||
4608.2.k.bi.3457.2 | 8 | 96.5 | odd | 8 | |||
9216.2.a.w.1.3 | 4 | 12.11 | even | 2 | |||
9216.2.a.w.1.4 | 4 | 3.2 | odd | 2 | |||
9216.2.a.bp.1.1 | 4 | 24.11 | even | 2 | |||
9216.2.a.bp.1.2 | 4 | 24.5 | odd | 2 |