Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [736,4,Mod(1,736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(736, 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("736.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 736 = 2^{5} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 736.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: | \(43.4254057642\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 137x^{6} + 344x^{5} + 6175x^{4} - 7924x^{3} - 89643x^{2} + 45072x + 51084 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-6.70977\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 736.1 |
$q$-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 | ||||||||
\(3\) | −8.70977 | −1.67620 | −0.838098 | − | 0.545520i | \(-0.816332\pi\) | ||||
−0.838098 | + | 0.545520i | \(0.816332\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −18.2706 | −1.63417 | −0.817085 | − | 0.576517i | \(-0.804412\pi\) | ||||
−0.817085 | + | 0.576517i | \(0.804412\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.7096 | −0.632259 | −0.316130 | − | 0.948716i | \(-0.602383\pi\) | ||||
−0.316130 | + | 0.948716i | \(0.602383\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 48.8601 | 1.80963 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.01666 | 0.0552768 | 0.0276384 | − | 0.999618i | \(-0.491201\pi\) | ||||
0.0276384 | + | 0.999618i | \(0.491201\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −23.3256 | −0.497643 | −0.248821 | − | 0.968549i | \(-0.580043\pi\) | ||||
−0.248821 | + | 0.968549i | \(0.580043\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 159.133 | 2.73919 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 55.7210 | 0.794960 | 0.397480 | − | 0.917611i | \(-0.369885\pi\) | ||||
0.397480 | + | 0.917611i | \(0.369885\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −105.455 | −1.27332 | −0.636658 | − | 0.771146i | \(-0.719684\pi\) | ||||
−0.636658 | + | 0.771146i | \(0.719684\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 101.988 | 1.05979 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 208.814 | 1.67051 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −190.396 | −1.35710 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 275.935 | 1.76689 | 0.883446 | − | 0.468532i | \(-0.155217\pi\) | ||||
0.883446 | + | 0.468532i | \(0.155217\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 282.019 | 1.63394 | 0.816970 | − | 0.576680i | \(-0.195652\pi\) | ||||
0.816970 | + | 0.576680i | \(0.195652\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −17.5646 | −0.0926547 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 213.941 | 1.03322 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 229.974 | 1.02183 | 0.510913 | − | 0.859632i | \(-0.329307\pi\) | ||||
0.510913 | + | 0.859632i | \(0.329307\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 203.161 | 0.834147 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −75.0934 | −0.286039 | −0.143020 | − | 0.989720i | \(-0.545681\pi\) | ||||
−0.143020 | + | 0.989720i | \(0.545681\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −125.927 | −0.446598 | −0.223299 | − | 0.974750i | \(-0.571683\pi\) | ||||
−0.223299 | + | 0.974750i | \(0.571683\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −892.702 | −2.95725 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −349.795 | −1.08559 | −0.542796 | − | 0.839864i | \(-0.682634\pi\) | ||||
−0.542796 | + | 0.839864i | \(0.682634\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −205.885 | −0.600248 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −485.317 | −1.33251 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 682.616 | 1.76914 | 0.884571 | − | 0.466406i | \(-0.154451\pi\) | ||||
0.884571 | + | 0.466406i | \(0.154451\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −36.8455 | −0.0903317 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 918.487 | 2.13433 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −604.301 | −1.33345 | −0.666723 | − | 0.745305i | \(-0.732304\pi\) | ||||
−0.666723 | + | 0.745305i | \(0.732304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −502.787 | −1.05533 | −0.527666 | − | 0.849452i | \(-0.676933\pi\) | ||||
−0.527666 | + | 0.849452i | \(0.676933\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −572.132 | −1.14416 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 426.172 | 0.813233 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −120.360 | −0.219467 | −0.109734 | − | 0.993961i | \(-0.535000\pi\) | ||||
−0.109734 | + | 0.993961i | \(0.535000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −200.325 | −0.349511 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −381.204 | −0.637191 | −0.318595 | − | 0.947891i | \(-0.603211\pi\) | ||||
−0.318595 | + | 0.947891i | \(0.603211\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 583.989 | 0.936312 | 0.468156 | − | 0.883646i | \(-0.344919\pi\) | ||||
0.468156 | + | 0.883646i | \(0.344919\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1818.72 | −2.80011 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −23.6143 | −0.0349493 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −714.302 | −1.01728 | −0.508641 | − | 0.860979i | \(-0.669852\pi\) | ||||
−0.508641 | + | 0.860979i | \(0.669852\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 339.085 | 0.465137 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −26.3693 | −0.0348724 | −0.0174362 | − | 0.999848i | \(-0.505550\pi\) | ||||
−0.0174362 | + | 0.999848i | \(0.505550\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1018.05 | −1.29910 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2403.33 | −2.96166 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −108.995 | −0.129814 | −0.0649069 | − | 0.997891i | \(-0.520675\pi\) | ||||
−0.0649069 | + | 0.997891i | \(0.520675\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 273.134 | 0.314639 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2456.32 | −2.73880 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1926.72 | 2.08082 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1365.94 | 1.42979 | 0.714897 | − | 0.699229i | \(-0.246473\pi\) | ||||
0.714897 | + | 0.699229i | \(0.246473\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 98.5340 | 0.100031 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 228.537 | 0.225151 | 0.112576 | − | 0.993643i | \(-0.464090\pi\) | ||||
0.112576 | + | 0.993643i | \(0.464090\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1580.80 | 1.51224 | 0.756121 | − | 0.654431i | \(-0.227092\pi\) | ||||
0.756121 | + | 0.654431i | \(0.227092\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1863.38 | −1.73188 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 319.446 | 0.288617 | 0.144309 | − | 0.989533i | \(-0.453904\pi\) | ||||
0.144309 | + | 0.989533i | \(0.453904\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −554.358 | −0.487136 | −0.243568 | − | 0.969884i | \(-0.578318\pi\) | ||||
−0.243568 | + | 0.969884i | \(0.578318\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2003.02 | −1.71278 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −636.882 | −0.530202 | −0.265101 | − | 0.964221i | \(-0.585405\pi\) | ||||
−0.265101 | + | 0.964221i | \(0.585405\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −420.223 | −0.340748 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1139.69 | −0.900551 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −652.471 | −0.502621 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1326.93 | −0.996944 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 654.046 | 0.479458 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1531.33 | −1.09573 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2634.23 | 1.84055 | 0.920277 | − | 0.391267i | \(-0.127963\pi\) | ||||
0.920277 | + | 0.391267i | \(0.127963\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1096.80 | 0.748585 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −605.725 | −0.403988 | −0.201994 | − | 0.979387i | \(-0.564742\pi\) | ||||
−0.201994 | + | 0.979387i | \(0.564742\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1234.84 | 0.805066 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3478.65 | 2.21774 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −262.980 | −0.163999 | −0.0819996 | − | 0.996632i | \(-0.526131\pi\) | ||||
−0.0819996 | + | 0.996632i | \(0.526131\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1428.75 | −0.871835 | −0.435917 | − | 0.899987i | \(-0.643576\pi\) | ||||
−0.435917 | + | 0.899987i | \(0.643576\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3046.63 | 1.81967 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −47.0397 | −0.0275081 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5041.50 | −2.88740 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1793.21 | 1.00613 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1255.23 | 0.690152 | 0.345076 | − | 0.938575i | \(-0.387853\pi\) | ||||
0.345076 | + | 0.938575i | \(0.387853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 552.311 | 0.297658 | 0.148829 | − | 0.988863i | \(-0.452450\pi\) | ||||
0.148829 | + | 0.988863i | \(0.452450\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2722.53 | 1.43859 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5152.65 | −2.67014 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2800.10 | 1.42339 | 0.711695 | − | 0.702488i | \(-0.247928\pi\) | ||||
0.711695 | + | 0.702488i | \(0.247928\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5945.43 | −2.96543 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −269.321 | −0.131835 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3701.73 | 1.77879 | 0.889393 | − | 0.457144i | \(-0.151127\pi\) | ||||
0.889393 | + | 0.457144i | \(0.151127\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 320.916 | 0.151414 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3038.22 | −1.40781 | −0.703905 | − | 0.710294i | \(-0.748562\pi\) | ||||
−0.703905 | + | 0.710294i | \(0.748562\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1652.92 | −0.752352 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5152.53 | −2.30423 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2984.30 | −1.31152 | −0.655758 | − | 0.754971i | \(-0.727651\pi\) | ||||
−0.655758 | + | 0.754971i | \(0.727651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2445.13 | −1.05620 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5263.33 | 2.23512 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −897.226 | −0.374647 | −0.187323 | − | 0.982298i | \(-0.559981\pi\) | ||||
−0.187323 | + | 0.982298i | \(0.559981\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2049.03 | −0.841453 | −0.420726 | − | 0.907188i | \(-0.638225\pi\) | ||||
−0.420726 | + | 0.907188i | \(0.638225\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4379.16 | 1.76894 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4201.77 | −1.66984 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 112.370 | 0.0439429 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2229.46 | 0.858041 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1024.04 | 0.387941 | 0.193971 | − | 0.981007i | \(-0.437863\pi\) | ||||
0.193971 | + | 0.981007i | \(0.437863\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1616.95 | −0.603061 | −0.301530 | − | 0.953457i | \(-0.597497\pi\) | ||||
−0.301530 | + | 0.953457i | \(0.597497\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3711.86 | −1.36314 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1786.83 | 0.646224 | 0.323112 | − | 0.946361i | \(-0.395271\pi\) | ||||
0.323112 | + | 0.946361i | \(0.395271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3092.49 | 1.10161 | 0.550805 | − | 0.834634i | \(-0.314321\pi\) | ||||
0.550805 | + | 0.834634i | \(0.314321\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1048.31 | 0.367870 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3231.09 | −1.11713 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1372.00 | 0.467437 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1123.78 | 0.377334 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −212.666 | −0.0703848 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3733.03 | 1.21797 | 0.608987 | − | 0.793180i | \(-0.291576\pi\) | ||||
0.608987 | + | 0.793180i | \(0.291576\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3320.19 | 1.06806 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2300.76 | 0.729817 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3302.33 | −1.03307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5086.41 | −1.56944 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1299.73 | −0.395606 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1145.85 | −0.344090 | −0.172045 | − | 0.985089i | \(-0.555037\pi\) | ||||
−0.172045 | + | 0.985089i | \(0.555037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10202.7 | 3.02302 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5916.71 | −1.72998 | −0.864990 | − | 0.501789i | \(-0.832676\pi\) | ||||
−0.864990 | + | 0.501789i | \(0.832676\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4894.62 | 1.41243 | 0.706214 | − | 0.707999i | \(-0.250402\pi\) | ||||
0.706214 | + | 0.707999i | \(0.250402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 205.675 | 0.0585818 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1921.15 | 0.540167 | 0.270083 | − | 0.962837i | \(-0.412949\pi\) | ||||
0.270083 | + | 0.962837i | \(0.412949\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6390.96 | 1.77404 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6221.41 | 1.70516 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3806.42 | 1.03020 | 0.515098 | − | 0.857131i | \(-0.327756\pi\) | ||||
0.515098 | + | 0.857131i | \(0.327756\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6887.20 | 1.84085 | 0.920423 | − | 0.390925i | \(-0.127845\pi\) | ||||
0.920423 | + | 0.390925i | \(0.127845\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2187.35 | 0.577442 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3761.64 | 0.980908 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2459.80 | 0.633657 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 229.671 | 0.0584529 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3961.61 | 0.996234 | 0.498117 | − | 0.867110i | \(-0.334025\pi\) | ||||
0.498117 | + | 0.867110i | \(0.334025\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 46.3831 | 0.0115260 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8867.02 | 2.17755 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6821.86 | −1.65578 | −0.827891 | − | 0.560890i | \(-0.810459\pi\) | ||||
−0.827891 | + | 0.560890i | \(0.810459\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2692.91 | −0.646059 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13482.2 | 3.19743 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5109.63 | −1.19800 | −0.598999 | − | 0.800750i | \(-0.704435\pi\) | ||||
−0.598999 | + | 0.800750i | \(0.704435\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12471.8 | −2.89108 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 949.320 | 0.217593 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2427.02 | −0.550105 | −0.275052 | − | 0.961429i | \(-0.588695\pi\) | ||||
−0.275052 | + | 0.961429i | \(0.588695\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6618.07 | −1.48346 | −0.741732 | − | 0.670696i | \(-0.765996\pi\) | ||||
−0.741732 | + | 0.670696i | \(0.765996\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2378.93 | −0.527397 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 421.107 | 0.0923406 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5142.17 | −1.11539 | −0.557695 | − | 0.830046i | \(-0.688314\pi\) | ||||
−0.557695 | + | 0.830046i | \(0.688314\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13779.5 | 2.95683 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6603.95 | −1.40199 | −0.700994 | − | 0.713167i | \(-0.747260\pi\) | ||||
−0.700994 | + | 0.713167i | \(0.747260\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6283.79 | 1.31990 | 0.659951 | − | 0.751309i | \(-0.270577\pi\) | ||||
0.659951 | + | 0.751309i | \(0.270577\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16781.3 | −3.48785 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 879.314 | 0.180851 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1808.17 | −0.368038 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11897.0 | −2.39662 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5960.96 | 1.18854 | 0.594272 | − | 0.804264i | \(-0.297440\pi\) | ||||
0.594272 | + | 0.804264i | \(0.297440\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11040.9 | 2.17908 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −383.964 | −0.0750163 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −536.489 | −0.103766 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1474.56 | 0.282366 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1990.51 | −0.377398 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9186.21 | 1.72459 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4006.77 | −0.744881 | −0.372440 | − | 0.928056i | \(-0.621479\pi\) | ||||
−0.372440 | + | 0.928056i | \(0.621479\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13768.4 | −2.53481 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3461.38 | 0.631115 | 0.315558 | − | 0.948906i | \(-0.397808\pi\) | ||||
0.315558 | + | 0.948906i | \(0.397808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4013.93 | −0.724858 | −0.362429 | − | 0.932011i | \(-0.618053\pi\) | ||||
−0.362429 | + | 0.932011i | \(0.618053\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10453.2 | 1.86975 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8418.82 | −1.49164 | −0.745818 | − | 0.666150i | \(-0.767941\pi\) | ||||
−0.745818 | + | 0.666150i | \(0.767941\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 556.467 | 0.0976682 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2782.30 | −0.483779 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5876.05 | −1.01224 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4870.72 | −0.831319 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4828.33 | 0.816535 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4095.96 | 0.686376 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7515.07 | 1.24793 | 0.623966 | − | 0.781452i | \(-0.285520\pi\) | ||||
0.623966 | + | 0.781452i | \(0.285520\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11236.6 | 1.84913 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2199.05 | 0.358647 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 402.803 | 0.0651100 | 0.0325550 | − | 0.999470i | \(-0.489636\pi\) | ||||
0.0325550 | + | 0.999470i | \(0.489636\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5547.10 | 0.888723 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 568.736 | 0.0903190 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6427.23 | 1.01177 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3660.05 | 0.571161 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9222.48 | −1.42677 | −0.713384 | − | 0.700773i | \(-0.752839\pi\) | ||||
−0.713384 | + | 0.700773i | \(0.752839\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2246.37 | −0.344542 | −0.172271 | − | 0.985050i | \(-0.555111\pi\) | ||||
−0.172271 | + | 0.985050i | \(0.555111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4441.10 | 0.675352 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2710.12 | 0.408626 | 0.204313 | − | 0.978906i | \(-0.434504\pi\) | ||||
0.204313 | + | 0.978906i | \(0.434504\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6964.81 | 1.04128 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5682.87 | 0.842491 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −325.575 | −0.0478641 | −0.0239320 | − | 0.999714i | \(-0.507619\pi\) | ||||
−0.0239320 | + | 0.999714i | \(0.507619\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4261.73 | 0.621334 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11557.3 | 1.67107 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10669.8 | −1.53009 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5863.03 | −0.833917 | −0.416959 | − | 0.908926i | \(-0.636904\pi\) | ||||
−0.416959 | + | 0.908926i | \(0.636904\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3669.07 | −0.517626 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7993.17 | −1.11856 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8236.61 | 1.14337 | 0.571683 | − | 0.820474i | \(-0.306291\pi\) | ||||
0.571683 | + | 0.820474i | \(0.306291\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13337.6 | 1.83666 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6436.35 | −0.879282 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9815.24 | −1.33028 | −0.665139 | − | 0.746720i | \(-0.731628\pi\) | ||||
−0.665139 | + | 0.746720i | \(0.731628\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22943.6 | −3.08513 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9650.81 | 1.28755 | 0.643777 | − | 0.765213i | \(-0.277366\pi\) | ||||
0.643777 | + | 0.765213i | \(0.277366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 431.446 | 0.0571131 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6152.81 | −0.808178 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4957.68 | 0.646181 | 0.323090 | − | 0.946368i | \(-0.395278\pi\) | ||||
0.323090 | + | 0.946368i | \(0.395278\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1281.58 | 0.165761 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5275.72 | 0.677163 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13050.7 | 1.66241 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11698.5 | −1.47892 | −0.739460 | − | 0.673201i | \(-0.764919\pi\) | ||||
−0.739460 | + | 0.673201i | \(0.764919\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10755.1 | −1.34945 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8186.66 | −1.01951 | −0.509753 | − | 0.860321i | \(-0.670263\pi\) | ||||
−0.509753 | + | 0.860321i | \(0.670263\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6578.27 | −0.813118 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6195.27 | −0.760113 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 463.780 | 0.0564833 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6292.14 | 0.760700 | 0.380350 | − | 0.924843i | \(-0.375803\pi\) | ||||
0.380350 | + | 0.924843i | \(0.375803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2290.49 | 0.274895 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7076.13 | 0.843084 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 481.783 | 0.0569874 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12444.1 | 1.46137 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2333.57 | −0.272082 | −0.136041 | − | 0.990703i | \(-0.543438\pi\) | ||||
−0.136041 | + | 0.990703i | \(0.543438\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −636.134 | −0.0736420 | −0.0368210 | − | 0.999322i | \(-0.511723\pi\) | ||||
−0.0368210 | + | 0.999322i | \(0.511723\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17091.0 | −1.96452 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11635.3 | 1.32799 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5887.44 | 0.667244 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 409.705 | 0.0461090 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15664.1 | −1.75061 | −0.875307 | − | 0.483568i | \(-0.839340\pi\) | ||||
−0.875307 | + | 0.483568i | \(0.839340\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7695.84 | −0.854130 | −0.427065 | − | 0.904221i | \(-0.640453\pi\) | ||||
−0.427065 | + | 0.904221i | \(0.640453\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 43910.3 | 4.83985 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2425.46 | −0.265505 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17864.3 | −1.94218 | −0.971088 | − | 0.238723i | \(-0.923271\pi\) | ||||
−0.971088 | + | 0.238723i | \(0.923271\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10059.6 | −1.08623 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14239.6 | 1.52719 | 0.763593 | − | 0.645698i | \(-0.223434\pi\) | ||||
0.763593 | + | 0.645698i | \(0.223434\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1991.40 | 0.212138 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10932.8 | −1.15683 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17765.1 | −1.86723 | −0.933613 | − | 0.358282i | \(-0.883363\pi\) | ||||
−0.933613 | + | 0.358282i | \(0.883363\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −151.438 | −0.0158113 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4810.50 | −0.498934 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4990.31 | −0.514174 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16774.3 | 1.71700 | 0.858500 | − | 0.512814i | \(-0.171397\pi\) | ||||
0.858500 | + | 0.512814i | \(0.171397\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10609.1 | −1.07884 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10129.7 | −1.02340 | −0.511699 | − | 0.859165i | \(-0.670984\pi\) | ||||
−0.511699 | + | 0.859165i | \(0.670984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6375.12 | 0.639907 | 0.319954 | − | 0.947433i | \(-0.396333\pi\) | ||||
0.319954 | + | 0.947433i | \(0.396333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 44878.4 | 4.47567 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −287.766 | −0.0285144 | −0.0142572 | − | 0.999898i | \(-0.504538\pi\) | ||||
−0.0142572 | + | 0.999898i | \(0.504538\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1409.37 | 0.138760 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24388.2 | −2.38588 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −253.952 | −0.0246865 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22020.5 | −2.12709 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33352.7 | 3.20150 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7525.38 | 0.717836 | 0.358918 | − | 0.933369i | \(-0.383146\pi\) | ||||
0.358918 | + | 0.933369i | \(0.383146\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5364.29 | −0.508505 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2345.72 | 0.220982 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −24956.5 | −2.33653 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.7238 | −0.00248659 | −0.00124330 | − | 0.999999i | \(-0.500396\pi\) | ||||
−0.00124330 | + | 0.999999i | \(0.500396\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −32241.2 | −2.98159 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11096.8 | 1.01994 | 0.509970 | − | 0.860192i | \(-0.329657\pi\) | ||||
0.509970 | + | 0.860192i | \(0.329657\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15375.4 | 1.40461 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1800.27 | −0.163467 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4463.74 | 0.402870 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 243.921 | 0.0218826 | 0.0109413 | − | 0.999940i | \(-0.496517\pi\) | ||||
0.0109413 | + | 0.999940i | \(0.496517\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26462.2 | 2.35977 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5095.04 | −0.451643 | −0.225822 | − | 0.974169i | \(-0.572507\pi\) | ||||
−0.225822 | + | 0.974169i | \(0.572507\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4175.51 | −0.367936 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14396.5 | 1.26109 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −434.330 | −0.0378219 | −0.0189109 | − | 0.999821i | \(-0.506020\pi\) | ||||
−0.0189109 | + | 0.999821i | \(0.506020\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6838.28 | −0.591992 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20078.2 | 1.72802 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28882.2 | −2.47126 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −705.417 | −0.0600081 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25992.6 | 2.19836 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4903.38 | 0.412325 | 0.206162 | − | 0.978518i | \(-0.433902\pi\) | ||||
0.206162 | + | 0.978518i | \(0.433902\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6138.01 | −0.513186 | −0.256593 | − | 0.966520i | \(-0.582600\pi\) | ||||
−0.256593 | + | 0.966520i | \(0.582600\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21296.5 | 1.77039 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15714.4 | 1.29892 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29526.2 | −2.41305 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1751.60 | 0.142345 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5836.47 | −0.471650 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7814.63 | 0.627982 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −415.199 | −0.0331798 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1752.95 | 0.139307 | 0.0696535 | − | 0.997571i | \(-0.477811\pi\) | ||||
0.0696535 | + | 0.997571i | \(0.477811\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17846.5 | 1.41044 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10128.4 | 0.796063 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10633.7 | −0.831193 | −0.415597 | − | 0.909549i | \(-0.636427\pi\) | ||||
−0.415597 | + | 0.909549i | \(0.636427\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24566.2 | −1.90976 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29098.7 | −2.24981 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8364.20 | 0.643186 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 36596.4 | 2.79898 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4952.02 | −0.376704 | −0.188352 | − | 0.982102i | \(-0.560315\pi\) | ||||
−0.188352 | + | 0.982102i | \(0.560315\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2937.33 | 0.222246 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −978.718 | −0.0736568 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3532.30 | 0.264421 | 0.132210 | − | 0.991222i | \(-0.457793\pi\) | ||||
0.132210 | + | 0.991222i | \(0.457793\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11636.2 | 0.866441 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3970.55 | −0.294087 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16297.4 | −1.20074 | −0.600372 | − | 0.799721i | \(-0.704981\pi\) | ||||
−0.600372 | + | 0.799721i | \(0.704981\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25981.9 | 1.90422 | 0.952110 | − | 0.305756i | \(-0.0989091\pi\) | ||||
0.952110 | + | 0.305756i | \(0.0989091\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8919.13 | −0.650265 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4802.73 | 0.348326 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22813.0 | −1.64596 | −0.822981 | − | 0.568069i | \(-0.807690\pi\) | ||||
−0.822981 | + | 0.568069i | \(0.807690\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14083.3 | 1.01085 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 308.774 | 0.0220484 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1376.60 | 0.0977925 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 20822.8 | 1.47165 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18286.9 | −1.28583 | −0.642916 | − | 0.765937i | \(-0.722275\pi\) | ||||
−0.642916 | + | 0.765937i | \(0.722275\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29740.3 | −2.08052 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15562.8 | −1.08320 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4978.89 | 0.344786 | 0.172393 | − | 0.985028i | \(-0.444850\pi\) | ||||
0.172393 | + | 0.985028i | \(0.444850\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11921.0 | 0.821369 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26934.8 | −1.84652 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9230.75 | −0.629646 | −0.314823 | − | 0.949150i | \(-0.601945\pi\) | ||||
−0.314823 | + | 0.949150i | \(0.601945\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2956.20 | −0.200642 | −0.100321 | − | 0.994955i | \(-0.531987\pi\) | ||||
−0.100321 | + | 0.994955i | \(0.531987\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5880.80 | −0.397155 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24243.8 | 1.62918 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13356.1 | 0.893093 | 0.446547 | − | 0.894760i | \(-0.352654\pi\) | ||||
0.446547 | + | 0.894760i | \(0.352654\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28142.1 | 1.87254 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8159.18 | 0.540238 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8588.14 | 0.565859 | 0.282930 | − | 0.959141i | \(-0.408694\pi\) | ||||
0.282930 | + | 0.959141i | \(0.408694\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11949.8 | −0.783516 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6308.36 | −0.411612 | −0.205806 | − | 0.978593i | \(-0.565982\pi\) | ||||
−0.205806 | + | 0.978593i | \(0.565982\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9910.23 | 0.643499 | 0.321749 | − | 0.946825i | \(-0.395729\pi\) | ||||
0.321749 | + | 0.946825i | \(0.395729\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4379.11 | −0.282975 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1276.29 | 0.0820760 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1876.59 | 0.120102 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1852.27 | 0.117979 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12814.4 | 0.812311 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8551.40 | 0.539502 | 0.269751 | − | 0.962930i | \(-0.413059\pi\) | ||||
0.269751 | + | 0.962930i | \(0.413059\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32513.8 | −2.04156 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −48129.0 | −3.00778 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4802.39 | 0.298709 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18625.6 | −1.15308 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22921.3 | −1.41238 | −0.706192 | − | 0.708020i | \(-0.749589\pi\) | ||||
−0.706192 | + | 0.708020i | \(0.749589\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29765.5 | −1.82556 | −0.912782 | − | 0.408446i | \(-0.866071\pi\) | ||||
−0.912782 | + | 0.408446i | \(0.866071\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20039.1 | −1.22332 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13184.5 | 0.801139 | 0.400569 | − | 0.916266i | \(-0.368812\pi\) | ||||
0.400569 | + | 0.916266i | \(0.368812\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1218.67 | −0.0737087 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28762.6 | 1.73163 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26389.8 | 1.58149 | 0.790744 | − | 0.612147i | \(-0.209694\pi\) | ||||
0.790744 | + | 0.612147i | \(0.209694\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11066.9 | 0.660185 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 28533.7 | 1.69438 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10789.1 | −0.637761 | −0.318881 | − | 0.947795i | \(-0.603307\pi\) | ||||
−0.318881 | + | 0.947795i | \(0.603307\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12018.5 | 0.707209 | 0.353605 | − | 0.935395i | \(-0.384956\pi\) | ||||
0.353605 | + | 0.935395i | \(0.384956\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11320.3 | 0.663114 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22561.2 | −1.31562 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6346.51 | 0.368423 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9980.13 | 0.576762 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1013.95 | −0.0583354 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28401.4 | −1.62674 | −0.813369 | − | 0.581747i | \(-0.802369\pi\) | ||||
−0.813369 | + | 0.581747i | \(0.802369\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −39757.4 | −2.26706 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15573.7 | 0.884114 | 0.442057 | − | 0.896987i | \(-0.354249\pi\) | ||||
0.442057 | + | 0.896987i | \(0.354249\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15994.6 | −0.904001 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 51533.1 | 2.89979 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3646.89 | −0.204311 | −0.102156 | − | 0.994768i | \(-0.532574\pi\) | ||||
−0.102156 | + | 0.994768i | \(0.532574\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4804.79 | 0.268003 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −42631.0 | −2.36750 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15922.4 | −0.880401 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10621.3 | 0.584736 | 0.292368 | − | 0.956306i | \(-0.405557\pi\) | ||||
0.292368 | + | 0.956306i | \(0.405557\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1153.79 | −0.0632454 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26104.1 | 1.42473 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4184.28 | −0.227390 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16732.8 | −0.905425 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11654.1 | −0.627919 | −0.313959 | − | 0.949436i | \(-0.601656\pi\) | ||||
−0.313959 | + | 0.949436i | \(0.601656\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24251.9 | −1.30111 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −55663.8 | −2.97364 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2676.08 | −0.142354 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26137.6 | −1.38451 | −0.692257 | − | 0.721652i | \(-0.743383\pi\) | ||||
−0.692257 | + | 0.721652i | \(0.743383\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −34900.9 | −1.84091 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6486.44 | 0.340700 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 859.443 | 0.0449529 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −33153.0 | −1.72681 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3021.94 | −0.156744 | −0.0783722 | − | 0.996924i | \(-0.524972\pi\) | ||||
−0.0783722 | + | 0.996924i | \(0.524972\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18510.6 | −0.956130 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −59985.9 | −3.08562 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 57619.2 | 2.95162 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10162.0 | −0.518415 | −0.259208 | − | 0.965822i | \(-0.583461\pi\) | ||||
−0.259208 | + | 0.965822i | \(0.583461\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28206.6 | −1.43304 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7016.78 | −0.355028 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12288.4 | 0.619210 | 0.309605 | − | 0.950865i | \(-0.399803\pi\) | ||||
0.309605 | + | 0.950865i | \(0.399803\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −32763.0 | −1.64419 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −242.725 | −0.0121315 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16349.4 | −0.813834 | −0.406917 | − | 0.913465i | \(-0.633396\pi\) | ||||
−0.406917 | + | 0.913465i | \(0.633396\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21424.3 | −1.06213 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18786.9 | −0.927624 | −0.463812 | − | 0.885934i | \(-0.653519\pi\) | ||||
−0.463812 | + | 0.885934i | \(0.653519\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22933.8 | −1.12783 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1288.41 | −0.0631062 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3740.59 | −0.182481 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32006.4 | −1.55517 | −0.777584 | − | 0.628779i | \(-0.783555\pi\) | ||||
−0.777584 | + | 0.628779i | \(0.783555\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −34504.7 | −1.66988 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10091.0 | −0.486425 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10352.3 | 0.497042 | 0.248521 | − | 0.968627i | \(-0.420055\pi\) | ||||
0.248521 | + | 0.968627i | \(0.420055\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −403.986 | −0.0193199 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14560.4 | 0.693579 | 0.346790 | − | 0.937943i | \(-0.387272\pi\) | ||||
0.346790 | + | 0.937943i | \(0.387272\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6491.31 | 0.307996 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −49742.2 | −2.35089 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14095.7 | 0.663580 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23352.2 | −1.09506 | −0.547529 | − | 0.836786i | \(-0.684432\pi\) | ||||
−0.547529 | + | 0.836786i | \(0.684432\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 59416.8 | 2.77541 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1738.74 | 0.0809032 | 0.0404516 | − | 0.999181i | \(-0.487120\pi\) | ||||
0.0404516 | + | 0.999181i | \(0.487120\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 58889.6 | 2.72952 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23454.6 | 1.08292 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7918.96 | 0.364219 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −768.757 | −0.0352219 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −52537.0 | −2.39785 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −51159.5 | −2.32606 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21512.5 | 0.974380 | 0.487190 | − | 0.873296i | \(-0.338022\pi\) | ||||
0.487190 | + | 0.873296i | \(0.338022\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 44503.7 | 2.00808 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7457.64 | 0.335225 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11727.8 | 0.525178 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 108626. | 4.84602 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6508.32 | −0.289255 | −0.144628 | − | 0.989486i | \(-0.546198\pi\) | ||||
−0.144628 | + | 0.989486i | \(0.546198\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19490.9 | −0.863003 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5325.49 | −0.234915 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1177.71 | 0.0517563 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4920.65 | 0.215441 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21138.8 | 0.922083 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3638.30 | −0.158116 | −0.0790580 | − | 0.996870i | \(-0.525191\pi\) | ||||
−0.0790580 | + | 0.996870i | \(0.525191\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45098.6 | −1.95268 | −0.976341 | − | 0.216237i | \(-0.930621\pi\) | ||||
−0.976341 | + | 0.216237i | \(0.930621\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 57641.8 | 2.48658 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −67632.8 | −2.90684 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13279.6 | 0.568660 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13345.3 | 0.569382 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11064.2 | −0.470332 | −0.235166 | − | 0.971955i | \(-0.575563\pi\) | ||||
−0.235166 | + | 0.971955i | \(0.575563\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41270.8 | −1.74801 | −0.874004 | − | 0.485918i | \(-0.838485\pi\) | ||||
−0.874004 | + | 0.485918i | \(0.838485\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3667.74 | −0.154781 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23569.3 | 0.991035 | 0.495517 | − | 0.868598i | \(-0.334978\pi\) | ||||
0.495517 | + | 0.868598i | \(0.334978\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6327.92 | 0.265112 | 0.132556 | − | 0.991176i | \(-0.457682\pi\) | ||||
0.132556 | + | 0.991176i | \(0.457682\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 44787.1 | 1.86961 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11472.1 | −0.477173 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 55510.0 | 2.30060 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −53695.4 | −2.21742 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45428.3 | −1.86932 | −0.934659 | − | 0.355545i | \(-0.884295\pi\) | ||||
−0.934659 | + | 0.355545i | \(0.884295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51751.3 | 2.12191 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 57518.9 | 2.35001 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30199.7 | 1.22947 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15537.9 | 0.630328 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −54730.3 | −2.21241 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5289.41 | 0.213066 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3650.11 | 0.146515 | 0.0732575 | − | 0.997313i | \(-0.476660\pi\) | ||||
0.0732575 | + | 0.997313i | \(0.476660\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 94139.8 | 3.76551 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21525.6 | 0.857993 | 0.428997 | − | 0.903306i | \(-0.358867\pi\) | ||||
0.428997 | + | 0.903306i | \(0.358867\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20494.7 | −0.814052 | −0.407026 | − | 0.913417i | \(-0.633434\pi\) | ||||
−0.407026 | + | 0.913417i | \(0.633434\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7658.62 | −0.303142 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34600.9 | −1.36481 | −0.682403 | − | 0.730976i | \(-0.739065\pi\) | ||||
−0.682403 | + | 0.730976i | \(0.739065\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54524.9 | 2.14324 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15748.8 | 0.616904 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1440.50 | −0.0562321 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2807.47 | 0.109216 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 66739.9 | 2.58740 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17931.3 | 0.692788 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4815.58 | 0.185417 | 0.0927085 | − | 0.995693i | \(-0.470448\pi\) | ||||
0.0927085 | + | 0.995693i | \(0.470448\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −51918.6 | −1.99223 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45060.2 | 1.72318 | 0.861588 | − | 0.507609i | \(-0.169470\pi\) | ||||
0.861588 | + | 0.507609i | \(0.169470\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30384.6 | −1.15801 | −0.579005 | − | 0.815324i | \(-0.696559\pi\) | ||||
−0.579005 | + | 0.815324i | \(0.696559\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −96164.0 | −3.65256 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22951.5 | 0.868810 | 0.434405 | − | 0.900718i | \(-0.356959\pi\) | ||||
0.434405 | + | 0.900718i | \(0.356959\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30845.8 | −1.16371 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 683.817 | 0.0257113 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36887.6 | 1.38230 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16392.8 | 0.612237 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4672.69 | 0.173932 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 77819.0 | 2.88700 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38036.0 | 1.40640 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12843.1 | −0.473300 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37436.9 | 1.37508 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1091.19 | 0.0399474 | 0.0199737 | − | 0.999801i | \(-0.493642\pi\) | ||||
0.0199737 | + | 0.999801i | \(0.493642\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11166.3 | 0.407441 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10998.3 | −0.399988 | −0.199994 | − | 0.979797i | \(-0.564092\pi\) | ||||
−0.199994 | + | 0.979797i | \(0.564092\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −53.1778 | −0.00192763 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −80009.7 | −2.89075 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7092.80 | 0.255425 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30936.1 | 1.11043 | 0.555217 | − | 0.831706i | \(-0.312635\pi\) | ||||
0.555217 | + | 0.831706i | \(0.312635\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34898.0 | 1.24857 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8891.80 | 0.317093 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48021.9 | 1.70697 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 77238.1 | 2.73660 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28736.7 | 1.01488 | 0.507438 | − | 0.861688i | \(-0.330593\pi\) | ||||
0.507438 | + | 0.861688i | \(0.330593\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21711.6 | 0.764305 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30147.8 | −1.05787 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2053.07 | −0.0718101 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6636.94 | 0.231397 | 0.115699 | − | 0.993284i | \(-0.463089\pi\) | ||||
0.115699 | + | 0.993284i | \(0.463089\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34960.4 | 1.21500 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24771.1 | −0.858145 | −0.429073 | − | 0.903270i | \(-0.641160\pi\) | ||||
−0.429073 | + | 0.903270i | \(0.641160\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1727.15 | −0.0596433 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −40733.6 | −1.40218 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44391.1 | −1.52325 | −0.761625 | − | 0.648018i | \(-0.775598\pi\) | ||||
−0.761625 | + | 0.648018i | \(0.775598\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13621.9 | −0.465949 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 73326.0 | 2.50027 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43327.0 | 1.47272 | 0.736359 | − | 0.676591i | \(-0.236543\pi\) | ||||
0.736359 | + | 0.676591i | \(0.236543\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18709.8 | −0.633962 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4846.70 | −0.163711 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3079.39 | 0.103690 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49743.8 | 1.66976 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15608.2 | 0.522291 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29542.6 | 0.985504 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51071.7 | 1.69840 | 0.849201 | − | 0.528070i | \(-0.177084\pi\) | ||||
0.849201 | + | 0.528070i | \(0.177084\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 51179.0 | 1.69671 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20649.3 | 0.682459 | 0.341229 | − | 0.939980i | \(-0.389157\pi\) | ||||
0.341229 | + | 0.939980i | \(0.389157\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16730.1 | 0.551226 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 42422.8 | 1.39345 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38114.1 | −1.24809 | −0.624043 | − | 0.781390i | \(-0.714511\pi\) | ||||
−0.624043 | + | 0.781390i | \(0.714511\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −219.805 | −0.00717569 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27086.0 | −0.881537 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47799.2 | −1.55092 | −0.775461 | − | 0.631395i | \(-0.782483\pi\) | ||||
−0.775461 | + | 0.631395i | \(0.782483\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32646.4 | −1.05604 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −35674.9 | −1.15050 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2896.32 | −0.0931221 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43820.0 | 1.40463 | 0.702314 | − | 0.711867i | \(-0.252150\pi\) | ||||
0.702314 | + | 0.711867i | \(0.252150\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −65454.5 | −2.09178 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −56501.5 | −1.80022 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11484.4 | 0.364809 | 0.182405 | − | 0.983224i | \(-0.441612\pi\) | ||||
0.182405 | + | 0.983224i | \(0.441612\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −43786.3 | −1.38672 |
(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 | 736.4.a.e.1.1 | ✓ | 8 | |
4.3 | odd | 2 | 736.4.a.f.1.8 | yes | 8 | ||
8.3 | odd | 2 | 1472.4.a.bg.1.1 | 8 | |||
8.5 | even | 2 | 1472.4.a.bh.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
736.4.a.e.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
736.4.a.f.1.8 | yes | 8 | 4.3 | odd | 2 | ||
1472.4.a.bg.1.1 | 8 | 8.3 | odd | 2 | |||
1472.4.a.bh.1.8 | 8 | 8.5 | even | 2 |