Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.4481.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 17x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 232) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.86388\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | 8.72775 | 1.67966 | 0.839828 | − | 0.542852i | \(-0.182656\pi\) | ||||
0.839828 | + | 0.542852i | \(0.182656\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.8591 | −0.971266 | −0.485633 | − | 0.874163i | \(-0.661411\pi\) | ||||
−0.485633 | + | 0.874163i | \(0.661411\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 35.3146 | 1.90681 | 0.953404 | − | 0.301696i | \(-0.0975527\pi\) | ||||
0.953404 | + | 0.301696i | \(0.0975527\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 49.1737 | 1.82125 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.0096 | 0.411415 | 0.205707 | − | 0.978614i | \(-0.434050\pi\) | ||||
0.205707 | + | 0.978614i | \(0.434050\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −63.2256 | −1.34889 | −0.674447 | − | 0.738323i | \(-0.735618\pi\) | ||||
−0.674447 | + | 0.738323i | \(0.735618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −94.7754 | −1.63139 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 89.5964 | 1.27825 | 0.639127 | − | 0.769101i | \(-0.279296\pi\) | ||||
0.639127 | + | 0.769101i | \(0.279296\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 150.367 | 1.81560 | 0.907801 | − | 0.419401i | \(-0.137760\pi\) | ||||
0.907801 | + | 0.419401i | \(0.137760\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 308.217 | 3.20278 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 91.3993 | 0.828611 | 0.414306 | − | 0.910138i | \(-0.364024\pi\) | ||||
0.414306 | + | 0.910138i | \(0.364024\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.08037 | −0.0566429 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 193.526 | 1.37941 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.11646 | −0.0238496 | −0.0119248 | − | 0.999929i | \(-0.503796\pi\) | ||||
−0.0119248 | + | 0.999929i | \(0.503796\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 131.000 | 0.691036 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −383.484 | −1.85202 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 59.1187 | 0.262677 | 0.131339 | − | 0.991338i | \(-0.458072\pi\) | ||||
0.131339 | + | 0.991338i | \(0.458072\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −551.817 | −2.26568 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −346.113 | −1.31839 | −0.659193 | − | 0.751974i | \(-0.729102\pi\) | ||||
−0.659193 | + | 0.751974i | \(0.729102\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −483.285 | −1.71396 | −0.856979 | − | 0.515351i | \(-0.827662\pi\) | ||||
−0.856979 | + | 0.515351i | \(0.827662\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −533.981 | −1.76891 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 75.7902 | 0.235216 | 0.117608 | − | 0.993060i | \(-0.462477\pi\) | ||||
0.117608 | + | 0.993060i | \(0.462477\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 904.120 | 2.63592 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 781.975 | 2.14703 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 191.660 | 0.496726 | 0.248363 | − | 0.968667i | \(-0.420107\pi\) | ||||
0.248363 | + | 0.968667i | \(0.420107\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −162.990 | −0.399593 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1312.36 | 3.04959 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −774.911 | −1.70991 | −0.854956 | − | 0.518700i | \(-0.826416\pi\) | ||||
−0.854956 | + | 0.518700i | \(0.826416\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 277.199 | 0.581832 | 0.290916 | − | 0.956749i | \(-0.406040\pi\) | ||||
0.290916 | + | 0.956749i | \(0.406040\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1736.55 | 3.47277 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 686.572 | 1.31013 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.54382 | 0.0155790 | 0.00778950 | − | 0.999970i | \(-0.497520\pi\) | ||||
0.00778950 | + | 0.999970i | \(0.497520\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 797.710 | 1.39178 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −72.4644 | −0.121126 | −0.0605629 | − | 0.998164i | \(-0.519290\pi\) | ||||
−0.0605629 | + | 0.998164i | \(0.519290\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 775.045 | 1.24263 | 0.621316 | − | 0.783560i | \(-0.286598\pi\) | ||||
0.621316 | + | 0.783560i | \(0.286598\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −61.7957 | −0.0951407 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 530.058 | 0.784489 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 694.941 | 0.989708 | 0.494854 | − | 0.868976i | \(-0.335222\pi\) | ||||
0.494854 | + | 0.868976i | \(0.335222\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 361.361 | 0.495693 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 483.553 | 0.639480 | 0.319740 | − | 0.947505i | \(-0.396405\pi\) | ||||
0.319740 | + | 0.947505i | \(0.396405\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −972.935 | −1.24152 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 253.105 | 0.311904 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1026.96 | −1.22312 | −0.611560 | − | 0.791198i | \(-0.709458\pi\) | ||||
−0.611560 | + | 0.791198i | \(0.709458\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2232.79 | −2.57208 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −35.9274 | −0.0400591 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1632.84 | −1.76343 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 933.115 | 0.976737 | 0.488369 | − | 0.872637i | \(-0.337592\pi\) | ||||
0.488369 | + | 0.872637i | \(0.337592\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 738.077 | 0.749288 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −386.547 | −0.380821 | −0.190410 | − | 0.981705i | \(-0.560982\pi\) | ||||
−0.190410 | + | 0.981705i | \(0.560982\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 79.7090 | 0.0762520 | 0.0381260 | − | 0.999273i | \(-0.487861\pi\) | ||||
0.0381260 | + | 0.999273i | \(0.487861\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3346.95 | −3.11075 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 584.929 | 0.528479 | 0.264239 | − | 0.964457i | \(-0.414879\pi\) | ||||
0.264239 | + | 0.964457i | \(0.414879\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1077.96 | 0.947243 | 0.473621 | − | 0.880729i | \(-0.342947\pi\) | ||||
0.473621 | + | 0.880729i | \(0.342947\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 515.974 | 0.441208 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 724.967 | 0.603532 | 0.301766 | − | 0.953382i | \(-0.402424\pi\) | ||||
0.301766 | + | 0.953382i | \(0.402424\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −992.512 | −0.804802 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3109.03 | −2.45667 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3164.06 | 2.43739 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1105.71 | −0.830738 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3020.79 | −2.21443 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1434.27 | 1.02628 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 141.196 | 0.0986542 | 0.0493271 | − | 0.998783i | \(-0.484292\pi\) | ||||
0.0493271 | + | 0.998783i | \(0.484292\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4217.99 | −2.87886 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 355.950 | 0.237401 | 0.118700 | − | 0.992930i | \(-0.462127\pi\) | ||||
0.118700 | + | 0.992930i | \(0.462127\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5310.13 | 3.46201 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2101.52 | −1.33978 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1699.52 | 1.05986 | 0.529928 | − | 0.848043i | \(-0.322219\pi\) | ||||
0.529928 | + | 0.848043i | \(0.322219\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 689.933 | 0.421003 | 0.210501 | − | 0.977594i | \(-0.432490\pi\) | ||||
0.210501 | + | 0.977594i | \(0.432490\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 661.478 | 0.395082 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −948.990 | −0.554955 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −314.913 | −0.180360 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7890.94 | 4.42744 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1970.49 | −1.08341 | −0.541706 | − | 0.840568i | \(-0.682222\pi\) | ||||
−0.541706 | + | 0.840568i | \(0.682222\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1438.10 | −0.775039 | −0.387520 | − | 0.921861i | \(-0.626668\pi\) | ||||
−0.387520 | + | 0.921861i | \(0.626668\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4405.78 | 2.32802 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 44.7009 | 0.0231643 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1320.69 | 0.671353 | 0.335676 | − | 0.941977i | \(-0.391035\pi\) | ||||
0.335676 | + | 0.941977i | \(0.391035\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1672.76 | 0.834329 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3227.73 | 1.58000 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3812.83 | −1.83217 | −0.916086 | − | 0.400982i | \(-0.868669\pi\) | ||||
−0.916086 | + | 0.400982i | \(0.868669\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1422.54 | −0.671179 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −940.119 | −0.435620 | −0.217810 | − | 0.975991i | \(-0.569891\pi\) | ||||
−0.217810 | + | 0.975991i | \(0.569891\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1800.48 | 0.819516 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7394.07 | 3.30666 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2691.33 | −1.18276 | −0.591381 | − | 0.806392i | \(-0.701417\pi\) | ||||
−0.591381 | + | 0.806392i | \(0.701417\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −250.040 | −0.108007 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6763.23 | −2.87207 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3915.79 | 1.63508 | 0.817541 | − | 0.575870i | \(-0.195336\pi\) | ||||
0.817541 | + | 0.575870i | \(0.195336\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3607.97 | −1.48165 | −0.740824 | − | 0.671699i | \(-0.765565\pi\) | ||||
−0.740824 | + | 0.671699i | \(0.765565\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2419.33 | 0.977278 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −641.975 | −0.255129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1344.81 | 0.525893 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6834.30 | 2.63028 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3158.69 | 1.19662 | 0.598311 | − | 0.801264i | \(-0.295839\pi\) | ||||
0.598311 | + | 0.801264i | \(0.295839\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2845.74 | 1.06135 | 0.530675 | − | 0.847575i | \(-0.321938\pi\) | ||||
0.530675 | + | 0.847575i | \(0.321938\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5992.23 | 2.20058 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −456.198 | −0.164989 | −0.0824943 | − | 0.996592i | \(-0.526289\pi\) | ||||
−0.0824943 | + | 0.996592i | \(0.526289\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2123.49 | 0.756434 | 0.378217 | − | 0.925717i | \(-0.376537\pi\) | ||||
0.378217 | + | 0.925717i | \(0.376537\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 74.5683 | 0.0261674 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1024.12 | 0.354085 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3758.47 | 1.28050 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4494.44 | 1.50911 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2256.94 | 0.746966 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2684.61 | −0.875905 | −0.437952 | − | 0.898998i | \(-0.644296\pi\) | ||||
−0.437952 | + | 0.898998i | \(0.644296\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −632.451 | −0.203450 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5248.03 | 1.66471 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −145.371 | −0.0454766 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6764.40 | 2.08719 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5664.79 | −1.72423 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4442.57 | 1.33407 | 0.667033 | − | 0.745028i | \(-0.267564\pi\) | ||||
0.667033 | + | 0.745028i | \(0.267564\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −348.168 | −0.103161 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 394.373 | 0.115310 | 0.0576551 | − | 0.998337i | \(-0.481638\pi\) | ||||
0.0576551 | + | 0.998337i | \(0.481638\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1426.84 | −0.411740 | −0.205870 | − | 0.978579i | \(-0.566002\pi\) | ||||
−0.205870 | + | 0.978579i | \(0.566002\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4626.21 | 1.31767 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −483.144 | −0.135845 | −0.0679223 | − | 0.997691i | \(-0.521637\pi\) | ||||
−0.0679223 | + | 0.997691i | \(0.521637\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −823.012 | −0.228457 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6065.27 | 1.66237 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −665.454 | −0.180103 | −0.0900516 | − | 0.995937i | \(-0.528703\pi\) | ||||
−0.0900516 | + | 0.995937i | \(0.528703\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 722.879 | 0.193215 | 0.0966073 | − | 0.995323i | \(-0.469201\pi\) | ||||
0.0966073 | + | 0.995323i | \(0.469201\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2071.34 | −0.546818 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9817.91 | −2.56018 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9507.01 | −2.44906 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4220.33 | 1.07411 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4416.87 | −1.11072 | −0.555359 | − | 0.831610i | \(-0.687419\pi\) | ||||
−0.555359 | + | 0.831610i | \(0.687419\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1371.87 | 0.340903 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8491.53 | −2.08534 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1069.36 | −0.259551 | −0.129776 | − | 0.991543i | \(-0.541426\pi\) | ||||
−0.129776 | + | 0.991543i | \(0.541426\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2087.75 | 0.500875 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1426.04 | 0.338197 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4059.01 | −0.951671 | −0.475835 | − | 0.879534i | \(-0.657854\pi\) | ||||
−0.475835 | + | 0.879534i | \(0.657854\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2081.25 | −0.482453 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8963.06 | −2.05442 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6169.01 | 1.39826 | 0.699128 | − | 0.714996i | \(-0.253572\pi\) | ||||
0.699128 | + | 0.714996i | \(0.253572\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −475.127 | −0.106501 | −0.0532507 | − | 0.998581i | \(-0.516958\pi\) | ||||
−0.0532507 | + | 0.998581i | \(0.516958\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −19487.2 | −4.32022 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −106.273 | −0.0233037 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3182.94 | 0.690414 | 0.345207 | − | 0.938527i | \(-0.387809\pi\) | ||||
0.345207 | + | 0.938527i | \(0.387809\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −202.421 | −0.0434360 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6286.93 | −1.33469 | −0.667343 | − | 0.744751i | \(-0.732568\pi\) | ||||
−0.667343 | + | 0.744751i | \(0.732568\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5170.76 | 1.08611 | 0.543056 | − | 0.839697i | \(-0.317267\pi\) | ||||
0.543056 | + | 0.839697i | \(0.317267\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14251.0 | −2.96196 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12222.8 | −2.51391 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3114.52 | 0.633934 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8144.00 | 1.64058 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4967.68 | 0.990495 | 0.495248 | − | 0.868752i | \(-0.335077\pi\) | ||||
0.495248 | + | 0.868752i | \(0.335077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8414.82 | 1.66078 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2904.75 | 0.567511 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5778.77 | −1.11771 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17067.0 | −3.26819 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3373.69 | −0.639648 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3010.13 | −0.565114 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3533.68 | 0.656931 | 0.328465 | − | 0.944516i | \(-0.393469\pi\) | ||||
0.328465 | + | 0.944516i | \(0.393469\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 695.680 | 0.128077 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2787.67 | 0.508278 | 0.254139 | − | 0.967168i | \(-0.418208\pi\) | ||||
0.254139 | + | 0.967168i | \(0.418208\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4644.65 | −0.838758 | −0.419379 | − | 0.907811i | \(-0.637752\pi\) | ||||
−0.419379 | + | 0.907811i | \(0.637752\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −18857.3 | −3.37298 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 83.0639 | 0.0147171 | 0.00735857 | − | 0.999973i | \(-0.497658\pi\) | ||||
0.00735857 | + | 0.999973i | \(0.497658\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 435.278 | 0.0763978 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5105.11 | 0.887663 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13472.3 | 2.32080 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 447.660 | 0.0764053 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9408.13 | 1.59104 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2676.50 | 0.448511 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8782.18 | −1.45834 | −0.729172 | − | 0.684330i | \(-0.760095\pi\) | ||||
−0.729172 | + | 0.684330i | \(0.760095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2907.08 | 0.478400 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −92.7780 | −0.0151314 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2006.52 | −0.324339 | −0.162169 | − | 0.986763i | \(-0.551849\pi\) | ||||
−0.162169 | + | 0.986763i | \(0.551849\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6327.33 | 1.01373 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −61.7863 | −0.00981208 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19815.7 | 3.11938 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8662.40 | −1.35179 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6333.56 | 0.979836 | 0.489918 | − | 0.871769i | \(-0.337027\pi\) | ||||
0.489918 | + | 0.871769i | \(0.337027\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5109.62 | 0.783701 | 0.391851 | − | 0.920029i | \(-0.371835\pi\) | ||||
0.391851 | + | 0.920029i | \(0.371835\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12235.8 | −1.86068 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3692.69 | −0.556776 | −0.278388 | − | 0.960469i | \(-0.589800\pi\) | ||||
−0.278388 | + | 0.960469i | \(0.589800\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 786.896 | 0.117645 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 27615.1 | 4.09397 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10348.9 | −1.52144 | −0.760719 | − | 0.649082i | \(-0.775153\pi\) | ||||
−0.760719 | + | 0.649082i | \(0.775153\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15751.1 | 2.29641 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9650.38 | −1.39535 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8416.27 | −1.20693 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3939.11 | 0.560272 | 0.280136 | − | 0.959960i | \(-0.409620\pi\) | ||||
0.280136 | + | 0.959960i | \(0.409620\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17019.7 | −2.40110 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6768.38 | 0.947161 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2464.89 | −0.342164 | −0.171082 | − | 0.985257i | \(-0.554726\pi\) | ||||
−0.171082 | + | 0.985257i | \(0.554726\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12518.0 | 1.72380 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1833.54 | −0.250483 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11748.7 | 1.59232 | 0.796161 | − | 0.605085i | \(-0.206861\pi\) | ||||
0.796161 | + | 0.605085i | \(0.206861\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1232.32 | 0.165705 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13496.5 | −1.80063 | −0.900313 | − | 0.435243i | \(-0.856662\pi\) | ||||
−0.900313 | + | 0.435243i | \(0.856662\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5755.94 | −0.761947 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23764.9 | −3.12154 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −560.330 | −0.0730330 | −0.0365165 | − | 0.999333i | \(-0.511626\pi\) | ||||
−0.0365165 | + | 0.999333i | \(0.511626\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8189.05 | 1.05918 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3106.65 | 0.398752 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7546.42 | −0.961269 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11464.1 | −1.44928 | −0.724642 | − | 0.689125i | \(-0.757995\pi\) | ||||
−0.724642 | + | 0.689125i | \(0.757995\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 46345.5 | 5.81498 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6943.53 | 0.864697 | 0.432348 | − | 0.901707i | \(-0.357685\pi\) | ||||
0.432348 | + | 0.901707i | \(0.357685\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 260.265 | 0.0321706 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3924.04 | −0.481450 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 887.348 | 0.108069 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −950.076 | −0.114861 | −0.0574306 | − | 0.998350i | \(-0.518291\pi\) | ||||
−0.0574306 | + | 0.998350i | \(0.518291\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14833.0 | 1.78019 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27365.7 | −3.26047 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5250.94 | −0.621105 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6021.57 | 0.707140 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2429.81 | 0.283303 | 0.141651 | − | 0.989917i | \(-0.454759\pi\) | ||||
0.141651 | + | 0.989917i | \(0.454759\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5879.81 | −0.680676 | −0.340338 | − | 0.940303i | \(-0.610541\pi\) | ||||
−0.340338 | + | 0.940303i | \(0.610541\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3726.88 | 0.428386 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −634.375 | −0.0724041 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9789.19 | 1.10944 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8282.55 | −0.932134 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15127.1 | −1.69060 | −0.845300 | − | 0.534292i | \(-0.820578\pi\) | ||||
−0.845300 | + | 0.534292i | \(0.820578\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4474.46 | −0.496602 | −0.248301 | − | 0.968683i | \(-0.579872\pi\) | ||||
−0.248301 | + | 0.968683i | \(0.579872\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2748.49 | −0.302942 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13743.4 | 1.50443 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8016.32 | 0.871522 | 0.435761 | − | 0.900062i | \(-0.356479\pi\) | ||||
0.435761 | + | 0.900062i | \(0.356479\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 44458.9 | 4.80066 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14409.7 | −1.54543 | −0.772714 | − | 0.634755i | \(-0.781101\pi\) | ||||
−0.772714 | + | 0.634755i | \(0.781101\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11151.9 | 1.18797 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17197.9 | −1.81976 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4952.41 | 0.520532 | 0.260266 | − | 0.965537i | \(-0.416190\pi\) | ||||
0.260266 | + | 0.965537i | \(0.416190\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5195.02 | −0.542403 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12551.4 | −1.30180 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24246.0 | 2.49818 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15852.6 | 1.62265 | 0.811326 | − | 0.584594i | \(-0.198746\pi\) | ||||
0.811326 | + | 0.584594i | \(0.198746\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17339.3 | 1.76324 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4825.97 | −0.487566 | −0.243783 | − | 0.969830i | \(-0.578388\pi\) | ||||
−0.243783 | + | 0.969830i | \(0.578388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2052.70 | 0.206042 | 0.103021 | − | 0.994679i | \(-0.467149\pi\) | ||||
0.103021 | + | 0.994679i | \(0.467149\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 390.139 | 0.0389081 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6460.13 | 0.640127 | 0.320063 | − | 0.947396i | \(-0.396296\pi\) | ||||
0.320063 | + | 0.947396i | \(0.396296\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 301.721 | 0.0297062 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11526.6 | 1.12764 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7253.91 | −0.705148 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1064.65 | −0.102841 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9424.60 | 0.904660 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6211.92 | −0.592547 | −0.296273 | − | 0.955103i | \(-0.595744\pi\) | ||||
−0.296273 | + | 0.955103i | \(0.595744\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3737.82 | −0.354324 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28170.8 | 2.65386 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10132.8 | −0.948671 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14172.0 | −1.31867 | −0.659336 | − | 0.751848i | \(-0.729163\pi\) | ||||
−0.659336 | + | 0.751848i | \(0.729163\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −33277.4 | −3.07742 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4875.68 | 0.448140 | 0.224070 | − | 0.974573i | \(-0.428066\pi\) | ||||
0.224070 | + | 0.974573i | \(0.428066\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2598.30 | 0.237366 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8014.83 | −0.727758 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2559.05 | −0.230964 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5020.87 | 0.450431 | 0.225215 | − | 0.974309i | \(-0.427691\pi\) | ||||
0.225215 | + | 0.974309i | \(0.427691\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8205.13 | −0.731693 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10619.4 | −0.941339 | −0.470669 | − | 0.882310i | \(-0.655988\pi\) | ||||
−0.470669 | + | 0.882310i | \(0.655988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4197.55 | 0.369878 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15714.1 | 1.37651 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3280.05 | −0.285630 | −0.142815 | − | 0.989749i | \(-0.545615\pi\) | ||||
−0.142815 | + | 0.989749i | \(0.545615\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27370.4 | 2.36946 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 29099.9 | 2.50447 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −865.566 | −0.0740610 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1137.58 | 0.0967712 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23489.3 | −1.98664 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21762.9 | −1.83004 | −0.915020 | − | 0.403408i | \(-0.867825\pi\) | ||||
−0.915020 | + | 0.403408i | \(0.867825\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20790.2 | −1.73822 | −0.869112 | − | 0.494615i | \(-0.835309\pi\) | ||||
−0.869112 | + | 0.494615i | \(0.835309\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2182.29 | −0.181415 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −368.820 | −0.0304859 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3813.17 | −0.313403 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −38105.2 | −3.11417 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21883.2 | 1.77836 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6351.79 | −0.513293 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34176.0 | 2.74638 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13570.5 | 1.08446 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23195.8 | 1.84338 | 0.921688 | − | 0.387933i | \(-0.126811\pi\) | ||||
0.921688 | + | 0.387933i | \(0.126811\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −31489.5 | −2.48866 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11705.6 | −0.920024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3748.76 | 0.293026 | 0.146513 | − | 0.989209i | \(-0.453195\pi\) | ||||
0.146513 | + | 0.989209i | \(0.453195\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13630.9 | 1.05966 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4360.63 | 0.337149 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24541.5 | 1.88718 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5603.00 | −0.428530 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9464.95 | 0.720005 | 0.360003 | − | 0.932951i | \(-0.382776\pi\) | ||||
0.360003 | + | 0.932951i | \(0.382776\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30556.0 | 2.31195 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11737.1 | 0.883319 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −759.432 | −0.0568495 | −0.0284247 | − | 0.999596i | \(-0.509049\pi\) | ||||
−0.0284247 | + | 0.999596i | \(0.509049\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7872.47 | −0.586190 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12761.3 | 0.945192 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6609.15 | 0.486942 | 0.243471 | − | 0.969908i | \(-0.421714\pi\) | ||||
0.243471 | + | 0.969908i | \(0.421714\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6972.10 | 0.510986 | 0.255493 | − | 0.966811i | \(-0.417762\pi\) | ||||
0.255493 | + | 0.966811i | \(0.417762\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27568.3 | 2.00992 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −647.140 | −0.0469350 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1569.50 | 0.113239 | 0.0566196 | − | 0.998396i | \(-0.481968\pi\) | ||||
0.0566196 | + | 0.998396i | \(0.481968\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24836.9 | 1.78271 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17076.5 | 1.21937 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2876.73 | 0.204360 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 33761.3 | 2.38608 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25741.0 | −1.80996 | −0.904979 | − | 0.425457i | \(-0.860113\pi\) | ||||
−0.904979 | + | 0.425457i | \(0.860113\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −618.977 | −0.0433014 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3981.58 | −0.277124 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11222.8 | 0.777177 | 0.388588 | − | 0.921411i | \(-0.372963\pi\) | ||||
0.388588 | + | 0.921411i | \(0.372963\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −34358.8 | −2.36735 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18533.3 | 1.27055 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25777.2 | −1.75831 | −0.879156 | − | 0.476533i | \(-0.841893\pi\) | ||||
−0.879156 | + | 0.476533i | \(0.841893\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11855.1 | −0.804624 | −0.402312 | − | 0.915503i | \(-0.631793\pi\) | ||||
−0.402312 | + | 0.915503i | \(0.631793\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 420.131 | 0.0283732 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12007.0 | 0.806867 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7293.09 | −0.487673 | −0.243837 | − | 0.969816i | \(-0.578406\pi\) | ||||
−0.243837 | + | 0.969816i | \(0.578406\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8938.29 | 0.594742 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4791.88 | −0.317281 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28047.6 | 1.84801 | 0.924006 | − | 0.382377i | \(-0.124895\pi\) | ||||
0.924006 | + | 0.382377i | \(0.124895\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32803.0 | 2.15080 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6987.42 | −0.455920 | −0.227960 | − | 0.973670i | \(-0.573206\pi\) | ||||
−0.227960 | + | 0.973670i | \(0.573206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6670.44 | 0.433131 | 0.216565 | − | 0.976268i | \(-0.430515\pi\) | ||||
0.216565 | + | 0.976268i | \(0.430515\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17688.2 | 1.14300 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −36266.7 | −2.33226 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14689.8 | −0.940149 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19698.0 | 1.25465 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5296.83 | 0.335768 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28063.1 | −1.77048 | −0.885240 | − | 0.465135i | \(-0.846006\pi\) | ||||
−0.885240 | + | 0.465135i | \(0.846006\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23430.6 | −1.47122 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1533.26 | −0.0958195 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −57163.5 | −3.55558 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3563.34 | −0.220600 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11554.7 | −0.711989 | −0.355995 | − | 0.934488i | \(-0.615858\pi\) | ||||
−0.355995 | + | 0.934488i | \(0.615858\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6197.60 | −0.380108 | −0.190054 | − | 0.981774i | \(-0.560866\pi\) | ||||
−0.190054 | + | 0.981774i | \(0.560866\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 45803.5 | 2.79614 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4932.29 | −0.299704 | −0.149852 | − | 0.988708i | \(-0.547880\pi\) | ||||
−0.149852 | + | 0.988708i | \(0.547880\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11631.1 | −0.703483 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1268.76 | −0.0763851 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22761.0 | −1.36402 | −0.682012 | − | 0.731341i | \(-0.738895\pi\) | ||||
−0.682012 | + | 0.731341i | \(0.738895\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3865.29 | −0.230579 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 38111.8 | 2.26314 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26751.4 | −1.58131 | −0.790656 | − | 0.612260i | \(-0.790261\pi\) | ||||
−0.790656 | + | 0.612260i | \(0.790261\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2558.77 | 0.150567 | 0.0752833 | − | 0.997162i | \(-0.476014\pi\) | ||||
0.0752833 | + | 0.997162i | \(0.476014\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −49440.9 | −2.89611 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −57663.1 | −3.36253 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2650.58 | 0.153869 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 38773.7 | 2.24077 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4160.65 | 0.239374 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12155.6 | 0.696231 | 0.348116 | − | 0.937452i | \(-0.386822\pi\) | ||||
0.348116 | + | 0.937452i | \(0.386822\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1370.24 | −0.0781340 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28508.5 | −1.61842 | −0.809212 | − | 0.587517i | \(-0.800105\pi\) | ||||
−0.809212 | + | 0.587517i | \(0.800105\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32952.6 | 1.86245 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3441.99 | 0.193682 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25318.0 | 1.41840 | 0.709199 | − | 0.705008i | \(-0.249057\pi\) | ||||
0.709199 | + | 0.705008i | \(0.249057\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18455.3 | −1.02940 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12453.1 | −0.691582 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12117.8 | −0.670030 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4704.87 | −0.259018 | −0.129509 | − | 0.991578i | \(-0.541340\pi\) | ||||
−0.129509 | + | 0.991578i | \(0.541340\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 26064.9 | 1.42875 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7492.04 | −0.408905 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31010.5 | −1.68523 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4216.76 | −0.228172 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1673.98 | −0.0901930 | −0.0450965 | − | 0.998983i | \(-0.514360\pi\) | ||||
−0.0450965 | + | 0.998983i | \(0.514360\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8889.48 | 0.476917 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7183.05 | −0.383729 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13650.8 | −0.726152 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11258.9 | 0.596386 | 0.298193 | − | 0.954506i | \(-0.403616\pi\) | ||||
0.298193 | + | 0.954506i | \(0.403616\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 34172.8 | 1.80250 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −376.241 | −0.0197621 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10305.2 | 0.539009 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5807.92 | −0.302511 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15759.7 | 0.817440 | 0.408720 | − | 0.912660i | \(-0.365975\pi\) | ||||
0.408720 | + | 0.912660i | \(0.365975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2814.89 | 0.145398 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6309.11 | 0.324534 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −205.331 | −0.0105183 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16230.9 | 0.828022 | 0.414011 | − | 0.910272i | \(-0.364127\pi\) | ||||
0.414011 | + | 0.910272i | \(0.364127\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27834.9 | −1.41416 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −43300.6 | −2.19088 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31438.2 | −1.58417 | −0.792086 | − | 0.610410i | \(-0.791005\pi\) | ||||
−0.792086 | + | 0.610410i | \(0.791005\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −85688.3 | −4.30022 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 128.239 | 0.00640943 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16449.5 | 0.818817 | 0.409408 | − | 0.912351i | \(-0.365735\pi\) | ||||
0.409408 | + | 0.912351i | \(0.365735\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −82974.9 | −4.11357 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33179.2 | −1.63826 | −0.819129 | − | 0.573610i | \(-0.805543\pi\) | ||||
−0.819129 | + | 0.573610i | \(0.805543\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21397.7 | 1.05228 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23778.1 | 1.16465 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20656.5 | 1.00771 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3581.31 | −0.174013 | −0.0870065 | − | 0.996208i | \(-0.527730\pi\) | ||||
−0.0870065 | + | 0.996208i | \(0.527730\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −38549.4 | −1.86563 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15616.4 | 0.752769 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1050.27 | 0.0504265 | 0.0252132 | − | 0.999682i | \(-0.491974\pi\) | ||||
0.0252132 | + | 0.999682i | \(0.491974\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11973.3 | 0.572600 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19296.7 | 0.919192 | 0.459596 | − | 0.888128i | \(-0.347994\pi\) | ||||
0.459596 | + | 0.888128i | \(0.347994\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38067.6 | 1.80621 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −47842.8 | −2.26112 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 48994.2 | 2.30649 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17635.2 | 0.826973 | 0.413486 | − | 0.910510i | \(-0.364311\pi\) | ||||
0.413486 | + | 0.910510i | \(0.364311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9333.08 | −0.435957 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6482.52 | 0.301630 | 0.150815 | − | 0.988562i | \(-0.451810\pi\) | ||||
0.150815 | + | 0.988562i | \(0.451810\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.1460 | 0.00135091 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18221.4 | 0.841299 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −52043.8 | −2.39366 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1087.66 | −0.0498330 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5612.26 | 0.256151 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14341.5 | −0.652062 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6515.85 | 0.295127 | 0.147563 | − | 0.989053i | \(-0.452857\pi\) | ||||
0.147563 | + | 0.989053i | \(0.452857\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −35426.0 | −1.59848 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25601.9 | 1.15082 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17526.1 | −0.784830 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18164.6 | −0.810355 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31806.7 | 1.41362 | 0.706809 | − | 0.707405i | \(-0.250134\pi\) | ||||
0.706809 | + | 0.707405i | \(0.250134\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6790.53 | 0.300666 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −50499.4 | −2.22760 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11633.1 | 0.511237 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −35050.1 | −1.53460 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 53841.6 | 2.34859 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36594.8 | −1.59036 | −0.795181 | − | 0.606372i | \(-0.792624\pi\) | ||||
−0.795181 | + | 0.606372i | \(0.792624\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13763.1 | −0.595917 | −0.297958 | − | 0.954579i | \(-0.596306\pi\) | ||||
−0.297958 | + | 0.954579i | \(0.596306\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4146.79 | −0.178886 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 41403.8 | 1.77953 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −72669.8 | −3.11187 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −109794. | −4.68440 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5524.35 | −0.234837 | −0.117419 | − | 0.993083i | \(-0.537462\pi\) | ||||
−0.117419 | + | 0.993083i | \(0.537462\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19038.1 | −0.806352 | −0.403176 | − | 0.915122i | \(-0.632094\pi\) | ||||
−0.403176 | + | 0.915122i | \(0.632094\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −927.528 | −0.0391423 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9157.55 | −0.385053 | −0.192527 | − | 0.981292i | \(-0.561668\pi\) | ||||
−0.192527 | + | 0.981292i | \(0.561668\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4033.20 | 0.168973 | 0.0844867 | − | 0.996425i | \(-0.473075\pi\) | ||||
0.0844867 | + | 0.996425i | \(0.473075\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27779.9 | 1.15966 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 81005.9 | 3.36937 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10208.8 | 0.423103 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −796.643 | −0.0328984 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26260.8 | −1.08060 | −0.540301 | − | 0.841472i | \(-0.681689\pi\) | ||||
−0.540301 | + | 0.841472i | \(0.681689\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −54870.7 | −2.24181 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19551.5 | −0.795968 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39047.8 | −1.58406 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 45129.1 | 1.82429 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5403.41 | 0.217657 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5194.92 | −0.208524 | −0.104262 | − | 0.994550i | \(-0.533248\pi\) | ||||
−0.104262 | + | 0.994550i | \(0.533248\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −80292.8 | −3.21165 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22863.1 | −0.911307 | −0.455654 | − | 0.890157i | \(-0.650594\pi\) | ||||
−0.455654 | + | 0.890157i | \(0.650594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19015.3 | −0.755288 | −0.377644 | − | 0.925951i | \(-0.623266\pi\) | ||||
−0.377644 | + | 0.925951i | \(0.623266\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −106678. | −4.22250 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33368.4 | −1.31619 | −0.658096 | − | 0.752934i | \(-0.728638\pi\) | ||||
−0.658096 | + | 0.752934i | \(0.728638\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29225.4 | 1.14878 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27182.8 | 1.06479 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10430.8 | 0.407180 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −540.188 | −0.0210144 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 45884.7 | 1.77888 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 50650.7 | 1.95692 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33775.9 | 1.30049 | 0.650246 | − | 0.759723i | \(-0.274666\pi\) | ||||
0.650246 | + | 0.759723i | \(0.274666\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 43356.7 | 1.66369 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −417.141 | −0.0159521 | −0.00797606 | − | 0.999968i | \(-0.502539\pi\) | ||||
−0.00797606 | + | 0.999968i | \(0.502539\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41417.9 | −1.57851 | −0.789254 | − | 0.614067i | \(-0.789532\pi\) | ||||
−0.789254 | + | 0.614067i | \(0.789532\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 73442.5 | 2.78954 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40342.4 | −1.52713 | −0.763565 | − | 0.645731i | \(-0.776553\pi\) | ||||
−0.763565 | + | 0.645731i | \(0.776553\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4986.27 | 0.188115 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5423.87 | 0.203936 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11396.3 | 0.427058 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42521.9 | −1.58810 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −50435.7 | −1.87737 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −119.377 | −0.00442876 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17172.0 | 0.634942 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −148957. | −5.48944 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 39179.2 | 1.43907 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30573.6 | 1.11927 | 0.559636 | − | 0.828739i | \(-0.310941\pi\) | ||||
0.559636 | + | 0.828739i | \(0.310941\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19007.9 | −0.693568 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15352.6 | −0.558346 | −0.279173 | − | 0.960241i | \(-0.590060\pi\) | ||||
−0.279173 | + | 0.960241i | \(0.590060\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7257.93 | 0.263091 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −26271.7 | −0.949197 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12570.2 | 0.452678 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8524.83 | −0.305994 | −0.152997 | − | 0.988227i | \(-0.548892\pi\) | ||||
−0.152997 | + | 0.988227i | \(0.548892\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30841.1 | 1.10342 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4581.60 | 0.163386 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −418.582 | −0.0148788 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3919.58 | 0.138874 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20169.6 | −0.712319 | −0.356159 | − | 0.934425i | \(-0.615914\pi\) | ||||
−0.356159 | + | 0.934425i | \(0.615914\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 135949. | 4.78578 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24330.1 | 0.853733 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14603.4 | −0.510782 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17975.4 | 0.626713 | 0.313356 | − | 0.949636i | \(-0.398547\pi\) | ||||
0.313356 | + | 0.949636i | \(0.398547\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −40537.4 | −1.40883 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41436.9 | −1.43550 | −0.717750 | − | 0.696301i | \(-0.754828\pi\) | ||||
−0.717750 | + | 0.696301i | \(0.754828\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31634.5 | −1.09243 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −74214.2 | −2.55470 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44431.8 | 1.52465 | 0.762323 | − | 0.647197i | \(-0.224059\pi\) | ||||
0.762323 | + | 0.647197i | \(0.224059\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49002.7 | −1.67618 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 724.961 | 0.0247197 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35372.8 | −1.20235 | −0.601174 | − | 0.799118i | \(-0.705300\pi\) | ||||
−0.601174 | + | 0.799118i | \(0.705300\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34300.5 | −1.16224 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3799.00 | 0.128322 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 60018.0 | 2.02094 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29774.1 | −0.999431 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 28763.1 | 0.962490 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30902.1 | −1.03085 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37084.4 | 1.23325 | 0.616626 | − | 0.787257i | \(-0.288499\pi\) | ||||
0.616626 | + | 0.787257i | \(0.288499\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 117583. | 3.89815 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21317.9 | −0.704557 | −0.352279 | − | 0.935895i | \(-0.614593\pi\) | ||||
−0.352279 | + | 0.935895i | \(0.614593\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24364.7 | 0.802771 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3907.07 | 0.128335 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17115.5 | 0.560464 | 0.280232 | − | 0.959932i | \(-0.409589\pi\) | ||||
0.280232 | + | 0.959932i | \(0.409589\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15414.3 | −0.503210 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 53007.0 | 1.72516 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2593.88 | 0.0841625 | 0.0420813 | − | 0.999114i | \(-0.486601\pi\) | ||||
0.0420813 | + | 0.999114i | \(0.486601\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4953.89 | 0.160248 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 23359.8 | 0.753345 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44171.9 | −1.42021 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13864.0 | 0.444404 | 0.222202 | − | 0.975001i | \(-0.428676\pi\) | ||||
0.222202 | + | 0.975001i | \(0.428676\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −76648.7 | −2.44952 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23059.2 | −0.734698 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51189.0 | −1.62605 | −0.813026 | − | 0.582228i | \(-0.802181\pi\) | ||||
−0.813026 | + | 0.582228i | \(0.802181\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11441.0 | 0.362340 |
(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 | 1856.4.a.t.1.3 | 3 | ||
4.3 | odd | 2 | 1856.4.a.q.1.1 | 3 | |||
8.3 | odd | 2 | 232.4.a.a.1.3 | ✓ | 3 | ||
8.5 | even | 2 | 464.4.a.h.1.1 | 3 | |||
24.11 | even | 2 | 2088.4.a.a.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.4.a.a.1.3 | ✓ | 3 | 8.3 | odd | 2 | ||
464.4.a.h.1.1 | 3 | 8.5 | even | 2 | |||
1856.4.a.q.1.1 | 3 | 4.3 | odd | 2 | |||
1856.4.a.t.1.3 | 3 | 1.1 | even | 1 | trivial | ||
2088.4.a.a.1.2 | 3 | 24.11 | even | 2 |