Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(1,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, 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("1620.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.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: | \(95.5830942093\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.438516.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 20x^{2} + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 180) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.78794\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.78863 | −0.312557 | −0.156278 | − | 0.987713i | \(-0.549950\pi\) | ||||
−0.156278 | + | 0.987713i | \(0.549950\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.2419 | 0.308140 | 0.154070 | − | 0.988060i | \(-0.450762\pi\) | ||||
0.154070 | + | 0.988060i | \(0.450762\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 39.4377 | 0.841389 | 0.420695 | − | 0.907202i | \(-0.361786\pi\) | ||||
0.420695 | + | 0.907202i | \(0.361786\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 19.6646 | 0.280551 | 0.140275 | − | 0.990113i | \(-0.455201\pi\) | ||||
0.140275 | + | 0.990113i | \(0.455201\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −102.113 | −1.23297 | −0.616483 | − | 0.787368i | \(-0.711443\pi\) | ||||
−0.616483 | + | 0.787368i | \(0.711443\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −175.505 | −1.59110 | −0.795552 | − | 0.605885i | \(-0.792819\pi\) | ||||
−0.795552 | + | 0.605885i | \(0.792819\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −64.6531 | −0.413992 | −0.206996 | − | 0.978342i | \(-0.566369\pi\) | ||||
−0.206996 | + | 0.978342i | \(0.566369\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 193.744 | 1.12250 | 0.561248 | − | 0.827648i | \(-0.310321\pi\) | ||||
0.561248 | + | 0.827648i | \(0.310321\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −28.9432 | −0.139780 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −261.480 | −1.16181 | −0.580906 | − | 0.813970i | \(-0.697302\pi\) | ||||
−0.580906 | + | 0.813970i | \(0.697302\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −207.837 | −0.791677 | −0.395838 | − | 0.918320i | \(-0.629546\pi\) | ||||
−0.395838 | + | 0.918320i | \(0.629546\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 41.1946 | 0.146096 | 0.0730478 | − | 0.997328i | \(-0.476727\pi\) | ||||
0.0730478 | + | 0.997328i | \(0.476727\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 577.877 | 1.79345 | 0.896724 | − | 0.442589i | \(-0.145940\pi\) | ||||
0.896724 | + | 0.442589i | \(0.145940\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −309.492 | −0.902308 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −322.043 | −0.834643 | −0.417321 | − | 0.908759i | \(-0.637031\pi\) | ||||
−0.417321 | + | 0.908759i | \(0.637031\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 56.2093 | 0.137805 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 188.109 | 0.415079 | 0.207540 | − | 0.978227i | \(-0.433454\pi\) | ||||
0.207540 | + | 0.978227i | \(0.433454\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 225.225 | 0.472739 | 0.236369 | − | 0.971663i | \(-0.424042\pi\) | ||||
0.236369 | + | 0.971663i | \(0.424042\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 197.189 | 0.376281 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 419.831 | 0.765531 | 0.382765 | − | 0.923846i | \(-0.374972\pi\) | ||||
0.382765 | + | 0.923846i | \(0.374972\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −361.341 | −0.603990 | −0.301995 | − | 0.953309i | \(-0.597653\pi\) | ||||
−0.301995 | + | 0.953309i | \(0.597653\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −779.176 | −1.24926 | −0.624628 | − | 0.780923i | \(-0.714749\pi\) | ||||
−0.624628 | + | 0.780923i | \(0.714749\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −65.0750 | −0.0963114 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 696.903 | 0.992503 | 0.496252 | − | 0.868179i | \(-0.334709\pi\) | ||||
0.496252 | + | 0.868179i | \(0.334709\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 333.455 | 0.440981 | 0.220491 | − | 0.975389i | \(-0.429234\pi\) | ||||
0.220491 | + | 0.975389i | \(0.429234\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 98.3229 | 0.125466 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −570.655 | −0.679655 | −0.339828 | − | 0.940488i | \(-0.610369\pi\) | ||||
−0.339828 | + | 0.940488i | \(0.610369\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −228.291 | −0.262982 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −510.566 | −0.551399 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1104.42 | −1.15605 | −0.578025 | − | 0.816019i | \(-0.696176\pi\) | ||||
−0.578025 | + | 0.816019i | \(0.696176\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 291.101 | 0.286789 | 0.143394 | − | 0.989666i | \(-0.454198\pi\) | ||||
0.143394 | + | 0.989666i | \(0.454198\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −994.988 | −0.951836 | −0.475918 | − | 0.879490i | \(-0.657884\pi\) | ||||
−0.475918 | + | 0.879490i | \(0.657884\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −90.9192 | −0.0821448 | −0.0410724 | − | 0.999156i | \(-0.513077\pi\) | ||||
−0.0410724 | + | 0.999156i | \(0.513077\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1720.69 | −1.51204 | −0.756018 | − | 0.654551i | \(-0.772858\pi\) | ||||
−0.756018 | + | 0.654551i | \(0.772858\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 658.685 | 0.548353 | 0.274177 | − | 0.961679i | \(-0.411595\pi\) | ||||
0.274177 | + | 0.961679i | \(0.411595\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −877.527 | −0.711563 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −113.831 | −0.0876880 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1204.62 | −0.905049 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1440.57 | −1.00654 | −0.503269 | − | 0.864130i | \(-0.667869\pi\) | ||||
−0.503269 | + | 0.864130i | \(0.667869\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1827.75 | −1.21901 | −0.609507 | − | 0.792781i | \(-0.708633\pi\) | ||||
−0.609507 | + | 0.792781i | \(0.708633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 591.096 | 0.385372 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1903.89 | 1.18730 | 0.593651 | − | 0.804723i | \(-0.297686\pi\) | ||||
0.593651 | + | 0.804723i | \(0.297686\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −282.361 | −0.172299 | −0.0861494 | − | 0.996282i | \(-0.527456\pi\) | ||||
−0.0861494 | + | 0.996282i | \(0.527456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 443.353 | 0.259266 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −323.265 | −0.185143 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1636.50 | 0.899783 | 0.449892 | − | 0.893083i | \(-0.351463\pi\) | ||||
0.449892 | + | 0.893083i | \(0.351463\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1682.35 | −0.906672 | −0.453336 | − | 0.891340i | \(-0.649766\pi\) | ||||
−0.453336 | + | 0.891340i | \(0.649766\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 968.718 | 0.501995 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1959.18 | 0.995920 | 0.497960 | − | 0.867200i | \(-0.334083\pi\) | ||||
0.497960 | + | 0.867200i | \(0.334083\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1015.94 | 0.497311 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −540.779 | −0.259859 | −0.129930 | − | 0.991523i | \(-0.541475\pi\) | ||||
−0.129930 | + | 0.991523i | \(0.541475\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −401.908 | −0.186231 | −0.0931154 | − | 0.995655i | \(-0.529683\pi\) | ||||
−0.0931154 | + | 0.995655i | \(0.529683\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −641.666 | −0.292065 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3244.49 | −1.42586 | −0.712931 | − | 0.701234i | \(-0.752633\pi\) | ||||
−0.712931 | + | 0.701234i | \(0.752633\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −144.716 | −0.0625114 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3845.07 | 1.60555 | 0.802777 | − | 0.596280i | \(-0.203355\pi\) | ||||
0.802777 | + | 0.596280i | \(0.203355\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 883.956 | 0.363005 | 0.181503 | − | 0.983390i | \(-0.441904\pi\) | ||||
0.181503 | + | 0.983390i | \(0.441904\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1307.40 | −0.519578 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 221.066 | 0.0864490 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 409.326 | 0.155067 | 0.0775335 | − | 0.996990i | \(-0.475296\pi\) | ||||
0.0775335 | + | 0.996990i | \(0.475296\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −368.346 | −0.137379 | −0.0686894 | − | 0.997638i | \(-0.521882\pi\) | ||||
−0.0686894 | + | 0.997638i | \(0.521882\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2994.23 | −1.08289 | −0.541447 | − | 0.840735i | \(-0.682123\pi\) | ||||
−0.541447 | + | 0.840735i | \(0.682123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 887.223 | 0.316048 | 0.158024 | − | 0.987435i | \(-0.449488\pi\) | ||||
0.158024 | + | 0.987435i | \(0.449488\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 374.253 | 0.129396 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1039.19 | −0.354049 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1147.94 | −0.379927 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5449.93 | −1.77814 | −0.889072 | − | 0.457767i | \(-0.848649\pi\) | ||||
−0.889072 | + | 0.457767i | \(0.848649\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 205.973 | 0.0653360 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1121.51 | −0.350844 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 775.526 | 0.236052 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3947.57 | −1.18542 | −0.592710 | − | 0.805416i | \(-0.701942\pi\) | ||||
−0.592710 | + | 0.805416i | \(0.701942\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6529.13 | −1.90905 | −0.954523 | − | 0.298138i | \(-0.903634\pi\) | ||||
−0.954523 | + | 0.298138i | \(0.903634\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3645.07 | −1.05185 | −0.525923 | − | 0.850532i | \(-0.676280\pi\) | ||||
−0.525923 | + | 0.850532i | \(0.676280\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1686.19 | −0.474104 | −0.237052 | − | 0.971497i | \(-0.576181\pi\) | ||||
−0.237052 | + | 0.971497i | \(0.576181\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2889.39 | 0.802055 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5899.02 | 1.59655 | 0.798276 | − | 0.602292i | \(-0.205746\pi\) | ||||
0.798276 | + | 0.602292i | \(0.205746\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7053.79 | −1.88537 | −0.942686 | − | 0.333681i | \(-0.891709\pi\) | ||||
−0.942686 | + | 0.333681i | \(0.891709\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1547.46 | −0.403524 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4027.11 | −1.03740 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6617.09 | 1.66401 | 0.832007 | − | 0.554766i | \(-0.187192\pi\) | ||||
0.832007 | + | 0.554766i | \(0.187192\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1973.00 | −0.490284 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5326.18 | 1.29276 | 0.646378 | − | 0.763018i | \(-0.276283\pi\) | ||||
0.646378 | + | 0.763018i | \(0.276283\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1513.61 | 0.363133 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1346.01 | −0.315584 | −0.157792 | − | 0.987472i | \(-0.550438\pi\) | ||||
−0.157792 | + | 0.987472i | \(0.550438\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1610.22 | −0.373264 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6359.78 | −1.44150 | −0.720748 | − | 0.693197i | \(-0.756202\pi\) | ||||
−0.720748 | + | 0.693197i | \(0.756202\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8586.05 | 1.92459 | 0.962297 | − | 0.271999i | \(-0.0876848\pi\) | ||||
0.962297 | + | 0.271999i | \(0.0876848\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 281.046 | 0.0616281 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3757.45 | −0.815030 | −0.407515 | − | 0.913199i | \(-0.633605\pi\) | ||||
−0.407515 | + | 0.913199i | \(0.633605\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5480.33 | 1.16345 | 0.581725 | − | 0.813386i | \(-0.302378\pi\) | ||||
0.581725 | + | 0.813386i | \(0.302378\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5580.88 | −1.17226 | −0.586129 | − | 0.810218i | \(-0.699349\pi\) | ||||
−0.586129 | + | 0.810218i | \(0.699349\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1203.09 | 0.247444 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4526.30 | −0.921291 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3217.92 | −0.641614 | −0.320807 | − | 0.947145i | \(-0.603954\pi\) | ||||
−0.320807 | + | 0.947145i | \(0.603954\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 940.544 | 0.185629 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6921.53 | −1.33874 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −238.460 | −0.0456632 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1126.12 | 0.211415 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8789.12 | −1.63395 | −0.816974 | − | 0.576675i | \(-0.804350\pi\) | ||||
−0.816974 | + | 0.576675i | \(0.804350\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7334.46 | −1.33730 | −0.668648 | − | 0.743579i | \(-0.733127\pi\) | ||||
−0.668648 | + | 0.743579i | \(0.733127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2702.52 | −0.488036 | −0.244018 | − | 0.969771i | \(-0.578466\pi\) | ||||
−0.244018 | + | 0.969771i | \(0.578466\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3581.86 | −0.634629 | −0.317314 | − | 0.948320i | \(-0.602781\pi\) | ||||
−0.317314 | + | 0.948320i | \(0.602781\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −726.820 | −0.127568 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2008.01 | −0.345910 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 985.943 | 0.168278 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3345.12 | −0.560555 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1677.08 | 0.278491 | 0.139245 | − | 0.990258i | \(-0.455532\pi\) | ||||
0.139245 | + | 0.990258i | \(0.455532\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2099.16 | 0.342356 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 481.195 | 0.0777814 | 0.0388907 | − | 0.999243i | \(-0.487618\pi\) | ||||
0.0388907 | + | 0.999243i | \(0.487618\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2178.04 | 0.345886 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3777.04 | 0.594580 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10122.2 | 1.56596 | 0.782980 | − | 0.622047i | \(-0.213699\pi\) | ||||
0.782980 | + | 0.622047i | \(0.213699\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9700.50 | −1.48784 | −0.743920 | − | 0.668269i | \(-0.767035\pi\) | ||||
−0.743920 | + | 0.668269i | \(0.767035\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 918.558 | 0.138498 | 0.0692492 | − | 0.997599i | \(-0.477940\pi\) | ||||
0.0692492 | + | 0.997599i | \(0.477940\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1806.71 | −0.270113 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1178.66 | −0.173279 | −0.0866396 | − | 0.996240i | \(-0.527613\pi\) | ||||
−0.0866396 | + | 0.996240i | \(0.527613\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3568.09 | 0.520206 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3895.88 | −0.558684 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9493.40 | 1.35028 | 0.675139 | − | 0.737691i | \(-0.264084\pi\) | ||||
0.675139 | + | 0.737691i | \(0.264084\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1864.19 | 0.260873 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9529.44 | 1.32283 | 0.661415 | − | 0.750020i | \(-0.269956\pi\) | ||||
0.661415 | + | 0.750020i | \(0.269956\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2549.77 | −0.348329 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7371.67 | −0.999096 | −0.499548 | − | 0.866286i | \(-0.666501\pi\) | ||||
−0.499548 | + | 0.866286i | \(0.666501\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2259.76 | −0.301484 | −0.150742 | − | 0.988573i | \(-0.548166\pi\) | ||||
−0.150742 | + | 0.988573i | \(0.548166\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −325.375 | −0.0430718 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10708.9 | 1.39579 | 0.697896 | − | 0.716199i | \(-0.254120\pi\) | ||||
0.697896 | + | 0.716199i | \(0.254120\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3451.24 | −0.446385 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3484.52 | 0.443861 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14817.3 | −1.87320 | −0.936598 | − | 0.350406i | \(-0.886044\pi\) | ||||
−0.936598 | + | 0.350406i | \(0.886044\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7873.06 | −0.980453 | −0.490227 | − | 0.871595i | \(-0.663086\pi\) | ||||
−0.490227 | + | 0.871595i | \(0.663086\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7640.81 | 0.944456 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2939.52 | −0.358001 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13158.4 | 1.59081 | 0.795403 | − | 0.606081i | \(-0.207259\pi\) | ||||
0.795403 | + | 0.606081i | \(0.207259\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1088.89 | −0.129736 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1667.27 | 0.197213 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12925.7 | −1.50707 | −0.753536 | − | 0.657407i | \(-0.771653\pi\) | ||||
−0.753536 | + | 0.657407i | \(0.771653\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12597.0 | −1.45829 | −0.729144 | − | 0.684360i | \(-0.760081\pi\) | ||||
−0.729144 | + | 0.684360i | \(0.760081\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 491.615 | 0.0561101 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1303.74 | −0.147758 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11443.9 | 1.27896 | 0.639480 | − | 0.768808i | \(-0.279150\pi\) | ||||
0.639480 | + | 0.768808i | \(0.279150\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13890.5 | −1.54165 | −0.770826 | − | 0.637046i | \(-0.780156\pi\) | ||||
−0.770826 | + | 0.637046i | \(0.780156\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17921.4 | 1.96178 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2052.06 | −0.223097 | −0.111548 | − | 0.993759i | \(-0.535581\pi\) | ||||
−0.111548 | + | 0.993759i | \(0.535581\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1686.91 | 0.180920 | 0.0904598 | − | 0.995900i | \(-0.471166\pi\) | ||||
0.0904598 | + | 0.995900i | \(0.471166\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2853.27 | −0.303951 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −579.542 | −0.0609138 | −0.0304569 | − | 0.999536i | \(-0.509696\pi\) | ||||
−0.0304569 | + | 0.999536i | \(0.509696\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2336.48 | −0.243948 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1141.45 | −0.117609 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16306.5 | 1.66912 | 0.834560 | − | 0.550917i | \(-0.185722\pi\) | ||||
0.834560 | + | 0.550917i | \(0.185722\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18894.3 | 1.90888 | 0.954442 | − | 0.298396i | \(-0.0964515\pi\) | ||||
0.954442 | + | 0.298396i | \(0.0964515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 877.924 | 0.0881222 | 0.0440611 | − | 0.999029i | \(-0.485970\pi\) | ||||
0.0440611 | + | 0.999029i | \(0.485970\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1534.76 | −0.152078 | −0.0760388 | − | 0.997105i | \(-0.524227\pi\) | ||||
−0.0760388 | + | 0.997105i | \(0.524227\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2430.25 | −0.239272 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 463.103 | 0.0450180 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2552.83 | −0.246593 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11238.9 | 1.07207 | 0.536033 | − | 0.844197i | \(-0.319922\pi\) | ||||
0.536033 | + | 0.844197i | \(0.319922\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10312.2 | −0.977536 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5522.10 | −0.517001 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −280.487 | −0.0260987 | −0.0130493 | − | 0.999915i | \(-0.504154\pi\) | ||||
−0.0130493 | + | 0.999915i | \(0.504154\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5703.07 | −0.524187 | −0.262094 | − | 0.965042i | \(-0.584413\pi\) | ||||
−0.262094 | + | 0.965042i | \(0.584413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1271.38 | −0.116146 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2091.67 | 0.188781 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14889.4 | 1.33575 | 0.667875 | − | 0.744273i | \(-0.267204\pi\) | ||||
0.667875 | + | 0.744273i | \(0.267204\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20369.3 | −1.80561 | −0.902806 | − | 0.430048i | \(-0.858497\pi\) | ||||
−0.902806 | + | 0.430048i | \(0.858497\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1455.51 | 0.128256 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13531.2 | 1.17831 | 0.589154 | − | 0.808021i | \(-0.299461\pi\) | ||||
0.589154 | + | 0.808021i | \(0.299461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4510.37 | 0.390464 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4974.94 | −0.425674 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6496.41 | 0.552634 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9222.17 | −0.775491 | −0.387745 | − | 0.921766i | \(-0.626746\pi\) | ||||
−0.387745 | + | 0.921766i | \(0.626746\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14246.2 | 1.19109 | 0.595546 | − | 0.803321i | \(-0.296936\pi\) | ||||
0.595546 | + | 0.803321i | \(0.296936\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3809.89 | 0.314917 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18635.1 | 1.53161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8196.63 | −0.666108 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −454.596 | −0.0367363 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3479.26 | −0.278038 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19105.2 | 1.51829 | 0.759145 | − | 0.650922i | \(-0.225617\pi\) | ||||
0.759145 | + | 0.650922i | \(0.225617\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8603.44 | −0.676203 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13200.3 | 1.03182 | 0.515909 | − | 0.856643i | \(-0.327454\pi\) | ||||
0.515909 | + | 0.856643i | \(0.327454\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6601.93 | 0.510439 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4034.12 | −0.310214 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3808.13 | −0.289687 | −0.144844 | − | 0.989455i | \(-0.546268\pi\) | ||||
−0.144844 | + | 0.989455i | \(0.546268\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1624.62 | 0.122923 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18886.7 | −1.41381 | −0.706907 | − | 0.707306i | \(-0.749910\pi\) | ||||
−0.706907 | + | 0.707306i | \(0.749910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3293.43 | 0.245231 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5176.45 | −0.381385 | −0.190693 | − | 0.981650i | \(-0.561073\pi\) | ||||
−0.190693 | + | 0.981650i | \(0.561073\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3393.12 | 0.248683 | 0.124341 | − | 0.992240i | \(-0.460318\pi\) | ||||
0.124341 | + | 0.992240i | \(0.460318\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4387.63 | −0.318221 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3452.26 | −0.249081 | −0.124540 | − | 0.992215i | \(-0.539746\pi\) | ||||
−0.124540 | + | 0.992215i | \(0.539746\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1930.25 | −0.137832 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3620.36 | −0.257187 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8434.27 | 0.593049 | 0.296524 | − | 0.955025i | \(-0.404172\pi\) | ||||
0.296524 | + | 0.955025i | \(0.404172\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19783.8 | −1.38400 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15781.6 | 1.09287 | 0.546437 | − | 0.837500i | \(-0.315984\pi\) | ||||
0.546437 | + | 0.837500i | \(0.315984\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −569.155 | −0.0392153 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18571.8 | 1.26682 | 0.633408 | − | 0.773818i | \(-0.281656\pi\) | ||||
0.633408 | + | 0.773818i | \(0.281656\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4244.55 | −0.288084 | −0.144042 | − | 0.989572i | \(-0.546010\pi\) | ||||
−0.144042 | + | 0.989572i | \(0.546010\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6023.10 | −0.404750 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22200.3 | 1.48448 | 0.742241 | − | 0.670133i | \(-0.233763\pi\) | ||||
0.742241 | + | 0.670133i | \(0.233763\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22790.2 | 1.50899 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20246.2 | −1.33399 | −0.666995 | − | 0.745062i | \(-0.732420\pi\) | ||||
−0.666995 | + | 0.745062i | \(0.732420\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1763.79 | −0.115085 | −0.0575425 | − | 0.998343i | \(-0.518326\pi\) | ||||
−0.0575425 | + | 0.998343i | \(0.518326\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6638.91 | 0.431083 | 0.215542 | − | 0.976495i | \(-0.430848\pi\) | ||||
0.215542 | + | 0.976495i | \(0.430848\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3303.31 | 0.212431 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5141.90 | −0.325947 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9459.54 | 0.596796 | 0.298398 | − | 0.954442i | \(-0.403548\pi\) | ||||
0.298398 | + | 0.954442i | \(0.403548\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7202.87 | −0.450137 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12205.6 | −0.759192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6876.38 | 0.423714 | 0.211857 | − | 0.977301i | \(-0.432049\pi\) | ||||
0.211857 | + | 0.977301i | \(0.432049\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23182.6 | 1.42183 | 0.710913 | − | 0.703280i | \(-0.248282\pi\) | ||||
0.710913 | + | 0.703280i | \(0.248282\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6573.94 | 0.399457 | 0.199728 | − | 0.979851i | \(-0.435994\pi\) | ||||
0.199728 | + | 0.979851i | \(0.435994\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2114.69 | 0.127903 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9591.02 | 0.574771 | 0.287386 | − | 0.957815i | \(-0.407214\pi\) | ||||
0.287386 | + | 0.957815i | \(0.407214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9138.73 | −0.545160 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21843.5 | −1.29120 | −0.645600 | − | 0.763676i | \(-0.723393\pi\) | ||||
−0.645600 | + | 0.763676i | \(0.723393\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15967.9 | 0.939604 | 0.469802 | − | 0.882772i | \(-0.344325\pi\) | ||||
0.469802 | + | 0.882772i | \(0.344325\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2955.48 | 0.172344 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11347.0 | 0.658705 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2531.94 | 0.145670 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10292.5 | 0.589521 | 0.294760 | − | 0.955571i | \(-0.404760\pi\) | ||||
0.294760 | + | 0.955571i | \(0.404760\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10125.7 | −0.574831 | −0.287416 | − | 0.957806i | \(-0.592796\pi\) | ||||
−0.287416 | + | 0.957806i | \(0.592796\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6393.09 | 0.361332 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21430.9 | −1.20063 | −0.600317 | − | 0.799762i | \(-0.704959\pi\) | ||||
−0.600317 | + | 0.799762i | \(0.704959\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9519.45 | 0.530977 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12700.7 | −0.702259 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19890.2 | 1.09502 | 0.547510 | − | 0.836799i | \(-0.315576\pi\) | ||||
0.547510 | + | 0.836799i | \(0.315576\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1411.80 | −0.0770543 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4087.04 | −0.222105 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13792.1 | 0.743112 | 0.371556 | − | 0.928410i | \(-0.378824\pi\) | ||||
0.371556 | + | 0.928410i | \(0.378824\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26700.6 | 1.43248 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1685.08 | −0.0896377 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 839.009 | 0.0444424 | 0.0222212 | − | 0.999753i | \(-0.492926\pi\) | ||||
0.0222212 | + | 0.999753i | \(0.492926\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −34003.0 | −1.78601 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2216.77 | 0.115947 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13911.1 | 0.721554 | 0.360777 | − | 0.932652i | \(-0.382512\pi\) | ||||
0.360777 | + | 0.932652i | \(0.382512\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5759.62 | 0.297503 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1616.33 | −0.0827984 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22702.7 | −1.15818 | −0.579089 | − | 0.815264i | \(-0.696592\pi\) | ||||
−0.579089 | + | 0.815264i | \(0.696592\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 810.074 | 0.0409872 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10727.1 | −0.540536 | −0.270268 | − | 0.962785i | \(-0.587112\pi\) | ||||
−0.270268 | + | 0.962785i | \(0.587112\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4719.68 | 0.235891 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7251.82 | 0.360978 | 0.180489 | − | 0.983577i | \(-0.442232\pi\) | ||||
0.180489 | + | 0.983577i | \(0.442232\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11369.6 | −0.561385 | −0.280693 | − | 0.959798i | \(-0.590564\pi\) | ||||
−0.280693 | + | 0.959798i | \(0.590564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8182.52 | 0.402395 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 526.298 | 0.0256749 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7313.05 | 0.355336 | 0.177668 | − | 0.984091i | \(-0.443145\pi\) | ||||
0.177668 | + | 0.984091i | \(0.443145\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8411.73 | −0.405476 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12759.1 | 0.612601 | 0.306301 | − | 0.951935i | \(-0.400909\pi\) | ||||
0.306301 | + | 0.951935i | \(0.400909\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16085.9 | 0.766247 | 0.383124 | − | 0.923697i | \(-0.374848\pi\) | ||||
0.383124 | + | 0.923697i | \(0.374848\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9960.43 | 0.472597 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7418.58 | 0.349243 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14518.3 | −0.680808 | −0.340404 | − | 0.940279i | \(-0.610564\pi\) | ||||
−0.340404 | + | 0.940279i | \(0.610564\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9065.89 | 0.421834 | 0.210917 | − | 0.977504i | \(-0.432355\pi\) | ||||
0.210917 | + | 0.977504i | \(0.432355\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4843.59 | 0.224499 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21222.9 | 0.976111 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4062.14 | −0.186114 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9795.89 | 0.445389 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13860.6 | 0.627796 | 0.313898 | − | 0.949457i | \(-0.398365\pi\) | ||||
0.313898 | + | 0.949457i | \(0.398365\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3812.89 | −0.171392 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8882.35 | 0.397757 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8384.39 | −0.372635 | −0.186318 | − | 0.982490i | \(-0.559655\pi\) | ||||
−0.186318 | + | 0.982490i | \(0.559655\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11363.7 | 0.503153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8759.38 | −0.384946 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5079.68 | 0.222404 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21047.6 | 0.914704 | 0.457352 | − | 0.889286i | \(-0.348798\pi\) | ||||
0.457352 | + | 0.889286i | \(0.348798\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19804.0 | 0.857474 | 0.428737 | − | 0.903429i | \(-0.358959\pi\) | ||||
0.428737 | + | 0.903429i | \(0.358959\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2703.89 | −0.116213 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4206.51 | −0.180131 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28001.8 | −1.19034 | −0.595170 | − | 0.803600i | \(-0.702915\pi\) | ||||
−0.595170 | + | 0.803600i | \(0.702915\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27449.3 | −1.16260 | −0.581302 | − | 0.813688i | \(-0.697457\pi\) | ||||
−0.581302 | + | 0.813688i | \(0.697457\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 796.827 | 0.0335047 | 0.0167524 | − | 0.999860i | \(-0.494667\pi\) | ||||
0.0167524 | + | 0.999860i | \(0.494667\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39005.0 | 1.63414 | 0.817068 | − | 0.576541i | \(-0.195598\pi\) | ||||
0.817068 | + | 0.576541i | \(0.195598\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6086.02 | −0.253143 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2009.54 | −0.0832850 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31810.5 | −1.30896 | −0.654482 | − | 0.756077i | \(-0.727113\pi\) | ||||
−0.654482 | + | 0.756077i | \(0.727113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20209.0 | −0.828610 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3208.33 | −0.130615 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6973.11 | 0.282879 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45891.2 | 1.84856 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12145.7 | −0.487528 | −0.243764 | − | 0.969835i | \(-0.578382\pi\) | ||||
−0.243764 | + | 0.969835i | \(0.578382\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37821.7 | 1.50754 | 0.753771 | − | 0.657137i | \(-0.228233\pi\) | ||||
0.753771 | + | 0.657137i | \(0.228233\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29061.8 | 1.15434 | 0.577168 | − | 0.816625i | \(-0.304158\pi\) | ||||
0.577168 | + | 0.816625i | \(0.304158\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33579.7 | −1.32452 | −0.662262 | − | 0.749272i | \(-0.730404\pi\) | ||||
−0.662262 | + | 0.749272i | \(0.730404\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16222.5 | −0.637665 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7834.48 | 0.305830 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16557.2 | 0.644109 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −723.579 | −0.0279559 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22286.0 | −0.858091 | −0.429045 | − | 0.903283i | \(-0.641150\pi\) | ||||
−0.429045 | + | 0.903283i | \(0.641150\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29440.6 | 1.12586 | 0.562928 | − | 0.826506i | \(-0.309675\pi\) | ||||
0.562928 | + | 0.826506i | \(0.309675\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25076.6 | 0.955713 | 0.477857 | − | 0.878438i | \(-0.341414\pi\) | ||||
0.477857 | + | 0.878438i | \(0.341414\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3512.01 | 0.132944 | 0.0664722 | − | 0.997788i | \(-0.478826\pi\) | ||||
0.0664722 | + | 0.997788i | \(0.478826\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8338.96 | 0.314600 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −59008.9 | −2.21126 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19225.4 | 0.718025 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12526.1 | −0.464705 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6332.85 | −0.234160 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4419.78 | 0.162341 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9752.72 | 0.357038 | 0.178519 | − | 0.983936i | \(-0.442869\pi\) | ||||
0.178519 | + | 0.983936i | \(0.442869\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38243.9 | 1.39086 | 0.695432 | − | 0.718592i | \(-0.255213\pi\) | ||||
0.695432 | + | 0.718592i | \(0.255213\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3748.65 | 0.135884 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10580.1 | 0.381011 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1523.05 | −0.0546691 | −0.0273345 | − | 0.999626i | \(-0.508702\pi\) | ||||
−0.0273345 | + | 0.999626i | \(0.508702\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14250.5 | −0.508191 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6537.00 | −0.232363 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25605.5 | 0.904294 | 0.452147 | − | 0.891943i | \(-0.350658\pi\) | ||||
0.452147 | + | 0.891943i | \(0.350658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31603.2 | 1.11252 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1105.33 | 0.0386612 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36738.1 | 1.28088 | 0.640439 | − | 0.768009i | \(-0.278752\pi\) | ||||
0.640439 | + | 0.768009i | \(0.278752\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46983.5 | 1.62765 | 0.813824 | − | 0.581111i | \(-0.197382\pi\) | ||||
0.813824 | + | 0.581111i | \(0.197382\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36476.6 | 1.25964 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12024.4 | 0.412607 | 0.206304 | − | 0.978488i | \(-0.433857\pi\) | ||||
0.206304 | + | 0.978488i | \(0.433857\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30728.9 | −1.05111 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35244.7 | −1.19799 | −0.598996 | − | 0.800752i | \(-0.704433\pi\) | ||||
−0.598996 | + | 0.800752i | \(0.704433\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2046.63 | 0.0693480 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11020.9 | −0.371099 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7745.57 | 0.259997 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1841.73 | −0.0614377 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27478.2 | 0.913795 | 0.456898 | − | 0.889519i | \(-0.348961\pi\) | ||||
0.456898 | + | 0.889519i | \(0.348961\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10673.6 | −0.352762 | −0.176381 | − | 0.984322i | \(-0.556439\pi\) | ||||
−0.176381 | + | 0.984322i | \(0.556439\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1634.48 | 0.0538532 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22601.8 | −0.740120 | −0.370060 | − | 0.929008i | \(-0.620663\pi\) | ||||
−0.370060 | + | 0.929008i | \(0.620663\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6415.22 | −0.209429 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2121.82 | −0.0688458 | −0.0344229 | − | 0.999407i | \(-0.510959\pi\) | ||||
−0.0344229 | + | 0.999407i | \(0.510959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14971.1 | −0.484285 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7229.87 | −0.232453 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45219.3 | −1.44948 | −0.724741 | − | 0.689021i | \(-0.758041\pi\) | ||||
−0.724741 | + | 0.689021i | \(0.758041\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4436.11 | 0.141341 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36545.9 | −1.16090 | −0.580452 | − | 0.814295i | \(-0.697124\pi\) | ||||
−0.580452 | + | 0.814295i | \(0.697124\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1620.4.a.h.1.2 | 4 | ||
3.2 | odd | 2 | 1620.4.a.g.1.2 | 4 | |||
9.2 | odd | 6 | 180.4.i.b.121.1 | yes | 8 | ||
9.4 | even | 3 | 540.4.i.b.181.3 | 8 | |||
9.5 | odd | 6 | 180.4.i.b.61.1 | ✓ | 8 | ||
9.7 | even | 3 | 540.4.i.b.361.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.4.i.b.61.1 | ✓ | 8 | 9.5 | odd | 6 | ||
180.4.i.b.121.1 | yes | 8 | 9.2 | odd | 6 | ||
540.4.i.b.181.3 | 8 | 9.4 | even | 3 | |||
540.4.i.b.361.3 | 8 | 9.7 | even | 3 | |||
1620.4.a.g.1.2 | 4 | 3.2 | odd | 2 | |||
1620.4.a.h.1.2 | 4 | 1.1 | even | 1 | trivial |