Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2496,4,Mod(1,2496)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2496, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2496.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2496 = 2^{6} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2496.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: | \(147.268767374\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 20x^{3} - 33x^{2} + 17x + 40 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 1248) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(5.05502\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2496.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.77633 | −0.248322 | −0.124161 | − | 0.992262i | \(-0.539624\pi\) | ||||
−0.124161 | + | 0.992262i | \(0.539624\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.23038 | −0.282414 | −0.141207 | − | 0.989980i | \(-0.545098\pi\) | ||||
−0.141207 | + | 0.989980i | \(0.545098\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −26.0282 | −0.713435 | −0.356717 | − | 0.934212i | \(-0.616104\pi\) | ||||
−0.356717 | + | 0.934212i | \(0.616104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.32898 | 0.143369 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.06350 | 0.0579731 | 0.0289866 | − | 0.999580i | \(-0.490772\pi\) | ||||
0.0289866 | + | 0.999580i | \(0.490772\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 73.9991 | 0.893503 | 0.446751 | − | 0.894658i | \(-0.352581\pi\) | ||||
0.446751 | + | 0.894658i | \(0.352581\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 15.6911 | 0.163052 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −145.163 | −1.31603 | −0.658013 | − | 0.753006i | \(-0.728603\pi\) | ||||
−0.658013 | + | 0.753006i | \(0.728603\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −117.292 | −0.938336 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 259.573 | 1.66212 | 0.831060 | − | 0.556183i | \(-0.187735\pi\) | ||||
0.831060 | + | 0.556183i | \(0.187735\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 78.5918 | 0.455339 | 0.227669 | − | 0.973738i | \(-0.426889\pi\) | ||||
0.227669 | + | 0.973738i | \(0.426889\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 78.0845 | 0.411902 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.5213 | 0.0701297 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −99.8291 | −0.443562 | −0.221781 | − | 0.975096i | \(-0.571187\pi\) | ||||
−0.221781 | + | 0.975096i | \(0.571187\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 346.320 | 1.31917 | 0.659586 | − | 0.751629i | \(-0.270732\pi\) | ||||
0.659586 | + | 0.751629i | \(0.270732\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 137.732 | 0.488463 | 0.244231 | − | 0.969717i | \(-0.421464\pi\) | ||||
0.244231 | + | 0.969717i | \(0.421464\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −24.9869 | −0.0827741 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 56.7561 | 0.176143 | 0.0880716 | − | 0.996114i | \(-0.471930\pi\) | ||||
0.0880716 | + | 0.996114i | \(0.471930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −315.643 | −0.920242 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.1905 | −0.0334708 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −173.382 | −0.449355 | −0.224677 | − | 0.974433i | \(-0.572133\pi\) | ||||
−0.224677 | + | 0.974433i | \(0.572133\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 72.2627 | 0.177162 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −221.997 | −0.515864 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −675.923 | −1.49149 | −0.745743 | − | 0.666234i | \(-0.767905\pi\) | ||||
−0.745743 | + | 0.666234i | \(0.767905\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 798.265 | 1.67553 | 0.837765 | − | 0.546030i | \(-0.183862\pi\) | ||||
0.837765 | + | 0.546030i | \(0.183862\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −47.0734 | −0.0941380 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −36.0923 | −0.0688722 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 292.584 | 0.533504 | 0.266752 | − | 0.963765i | \(-0.414050\pi\) | ||||
0.266752 | + | 0.963765i | \(0.414050\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 435.489 | 0.759808 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −333.464 | −0.557393 | −0.278697 | − | 0.960379i | \(-0.589902\pi\) | ||||
−0.278697 | + | 0.960379i | \(0.589902\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 243.292 | 0.390072 | 0.195036 | − | 0.980796i | \(-0.437518\pi\) | ||||
0.195036 | + | 0.980796i | \(0.437518\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 351.876 | 0.541749 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 136.137 | 0.201484 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −670.246 | −0.954539 | −0.477270 | − | 0.878757i | \(-0.658373\pi\) | ||||
−0.477270 | + | 0.878757i | \(0.658373\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 786.662 | 1.04033 | 0.520165 | − | 0.854066i | \(-0.325870\pi\) | ||||
0.520165 | + | 0.854066i | \(0.325870\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.2816 | −0.0143960 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −778.719 | −0.959625 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −317.044 | −0.377602 | −0.188801 | − | 0.982015i | \(-0.560460\pi\) | ||||
−0.188801 | + | 0.982015i | \(0.560460\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −67.9950 | −0.0783276 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −235.775 | −0.262890 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −205.446 | −0.221877 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 886.328 | 0.927762 | 0.463881 | − | 0.885897i | \(-0.346456\pi\) | ||||
0.463881 | + | 0.885897i | \(0.346456\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −234.253 | −0.237812 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −207.528 | −0.204454 | −0.102227 | − | 0.994761i | \(-0.532597\pi\) | ||||
−0.102227 | + | 0.994761i | \(0.532597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1738.86 | 1.66345 | 0.831724 | − | 0.555189i | \(-0.187354\pi\) | ||||
0.831724 | + | 0.555189i | \(0.187354\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −43.5638 | −0.0404894 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1248.91 | 1.12838 | 0.564189 | − | 0.825645i | \(-0.309189\pi\) | ||||
0.564189 | + | 0.825645i | \(0.309189\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1775.18 | 1.55992 | 0.779961 | − | 0.625828i | \(-0.215239\pi\) | ||||
0.779961 | + | 0.625828i | \(0.215239\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 299.487 | 0.256091 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1385.03 | −1.15304 | −0.576518 | − | 0.817085i | \(-0.695589\pi\) | ||||
−0.576518 | + | 0.817085i | \(0.695589\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 403.020 | 0.326799 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 117.000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −21.2537 | −0.0163724 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −653.535 | −0.491011 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1038.96 | −0.761624 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 672.682 | 0.481332 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −276.727 | −0.193351 | −0.0966755 | − | 0.995316i | \(-0.530821\pi\) | ||||
−0.0966755 | + | 0.995316i | \(0.530821\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −413.196 | −0.282014 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2293.51 | −1.52966 | −0.764829 | − | 0.644233i | \(-0.777177\pi\) | ||||
−0.764829 | + | 0.644233i | \(0.777177\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −387.043 | −0.252338 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 74.9608 | 0.0477896 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2639.75 | −1.64620 | −0.823098 | − | 0.567900i | \(-0.807756\pi\) | ||||
−0.823098 | + | 0.567900i | \(0.807756\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1371.48 | −0.836888 | −0.418444 | − | 0.908243i | \(-0.637424\pi\) | ||||
−0.418444 | + | 0.908243i | \(0.637424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −170.268 | −0.101696 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −338.366 | −0.197871 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −720.659 | −0.412741 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 946.929 | 0.531302 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1674.18 | 0.920498 | 0.460249 | − | 0.887790i | \(-0.347760\pi\) | ||||
0.460249 | + | 0.887790i | \(0.347760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2426.56 | −1.30775 | −0.653876 | − | 0.756602i | \(-0.726858\pi\) | ||||
−0.653876 | + | 0.756602i | \(0.726858\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 36.5715 | 0.0193244 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −218.197 | −0.113071 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1290.62 | 0.656069 | 0.328035 | − | 0.944666i | \(-0.393614\pi\) | ||||
0.328035 | + | 0.944666i | \(0.393614\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 520.145 | 0.259435 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 759.259 | 0.371664 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3787.85 | −1.82017 | −0.910083 | − | 0.414426i | \(-0.863982\pi\) | ||||
−0.910083 | + | 0.414426i | \(0.863982\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −216.788 | −0.102284 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1004.20 | 0.465314 | 0.232657 | − | 0.972559i | \(-0.425258\pi\) | ||||
0.232657 | + | 0.972559i | \(0.425258\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 665.992 | 0.297834 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.1058 | −0.00532015 | −0.00266008 | − | 0.999996i | \(-0.500847\pi\) | ||||
−0.00266008 | + | 0.999996i | \(0.500847\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 613.482 | 0.264999 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2027.77 | 0.861110 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 263.726 | 0.110122 | 0.0550610 | − | 0.998483i | \(-0.482465\pi\) | ||||
0.0550610 | + | 0.998483i | \(0.482465\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1941.94 | 0.797478 | 0.398739 | − | 0.917064i | \(-0.369448\pi\) | ||||
0.398739 | + | 0.917064i | \(0.369448\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2394.80 | −0.967368 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 277.158 | 0.110146 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −105.765 | −0.0413601 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 141.220 | 0.0543506 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1925.11 | 0.729297 | 0.364649 | − | 0.931145i | \(-0.381189\pi\) | ||||
0.364649 | + | 0.931145i | \(0.381189\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3317.81 | −1.23742 | −0.618708 | − | 0.785621i | \(-0.712343\pi\) | ||||
−0.618708 | + | 0.785621i | \(0.712343\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 108.277 | 0.0397634 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4282.47 | 1.54880 | 0.774399 | − | 0.632697i | \(-0.218052\pi\) | ||||
0.774399 | + | 0.632697i | \(0.218052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1219.10 | −0.434271 | −0.217135 | − | 0.976142i | \(-0.569671\pi\) | ||||
−0.217135 | + | 0.976142i | \(0.569671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −877.751 | −0.308019 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1357.67 | −0.469406 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −961.496 | −0.327580 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1306.47 | −0.438675 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1926.06 | −0.637456 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4956.66 | −1.61721 | −0.808603 | − | 0.588355i | \(-0.799776\pi\) | ||||
−0.808603 | + | 0.588355i | \(0.799776\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1000.39 | 0.321811 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −382.389 | −0.121296 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −411.065 | −0.128594 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −729.877 | −0.225208 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 52.8255 | 0.0160789 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1918.63 | 0.576148 | 0.288074 | − | 0.957608i | \(-0.406985\pi\) | ||||
0.288074 | + | 0.957608i | \(0.406985\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1055.63 | −0.312779 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1268.36 | 0.370853 | 0.185427 | − | 0.982658i | \(-0.440633\pi\) | ||||
0.185427 | + | 0.982658i | \(0.440633\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2481.05 | 0.715950 | 0.357975 | − | 0.933731i | \(-0.383467\pi\) | ||||
0.357975 | + | 0.933731i | \(0.383467\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −408.412 | −0.116327 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5103.45 | 1.43493 | 0.717464 | − | 0.696595i | \(-0.245303\pi\) | ||||
0.717464 | + | 0.696595i | \(0.245303\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −157.574 | −0.0437403 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2010.74 | 0.551103 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6552.57 | −1.77343 | −0.886716 | − | 0.462314i | \(-0.847019\pi\) | ||||
−0.886716 | + | 0.462314i | \(0.847019\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2398.64 | 0.641120 | 0.320560 | − | 0.947228i | \(-0.396129\pi\) | ||||
0.320560 | + | 0.947228i | \(0.396129\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 876.329 | 0.228517 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 961.988 | 0.247813 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2359.99 | −0.600635 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2899.21 | −0.729069 | −0.364535 | − | 0.931190i | \(-0.618772\pi\) | ||||
−0.364535 | + | 0.931190i | \(0.618772\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3778.33 | 0.938899 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 33.8448 | 0.00831155 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5784.67 | −1.40404 | −0.702019 | − | 0.712158i | \(-0.747718\pi\) | ||||
−0.702019 | + | 0.712158i | \(0.747718\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 522.144 | 0.125268 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2336.16 | 0.554040 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5346.03 | −1.25342 | −0.626712 | − | 0.779251i | \(-0.715600\pi\) | ||||
−0.626712 | + | 0.779251i | \(0.715600\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 481.364 | 0.111585 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 951.132 | 0.218009 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5693.67 | −1.29052 | −0.645259 | − | 0.763964i | \(-0.723250\pi\) | ||||
−0.645259 | + | 0.763964i | \(0.723250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −496.345 | −0.111258 | −0.0556288 | − | 0.998452i | \(-0.517716\pi\) | ||||
−0.0556288 | + | 0.998452i | \(0.517716\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 203.985 | 0.0452224 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3052.89 | 0.669442 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2832.42 | −0.614380 | −0.307190 | − | 0.951648i | \(-0.599389\pi\) | ||||
−0.307190 | + | 0.951648i | \(0.599389\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 707.326 | 0.151780 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5362.12 | −1.13835 | −0.569176 | − | 0.822216i | \(-0.692738\pi\) | ||||
−0.569176 | + | 0.822216i | \(0.692738\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3330.32 | −0.699530 | −0.349765 | − | 0.936838i | \(-0.613739\pi\) | ||||
−0.349765 | + | 0.936838i | \(0.613739\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 616.337 | 0.128100 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1811.38 | −0.372553 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4896.49 | −0.996639 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2658.98 | −0.535644 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 939.941 | 0.187413 | 0.0937064 | − | 0.995600i | \(-0.470128\pi\) | ||||
0.0937064 | + | 0.995600i | \(0.470128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1876.58 | 0.370369 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 702.760 | 0.137301 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1887.12 | −0.365000 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −720.390 | −0.137949 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 622.585 | 0.118041 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2216.25 | −0.416072 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −366.403 | −0.0681165 | −0.0340582 | − | 0.999420i | \(-0.510843\pi\) | ||||
−0.0340582 | + | 0.999420i | \(0.510843\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5216.59 | −0.960392 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3116.58 | −0.568247 | −0.284124 | − | 0.958788i | \(-0.591703\pi\) | ||||
−0.284124 | + | 0.958788i | \(0.591703\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2360.35 | 0.426246 | 0.213123 | − | 0.977025i | \(-0.431636\pi\) | ||||
0.213123 | + | 0.977025i | \(0.431636\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 130.691 | 0.0233766 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1279.56 | 0.226711 | 0.113356 | − | 0.993554i | \(-0.463840\pi\) | ||||
0.113356 | + | 0.993554i | \(0.463840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6756.20 | −1.18581 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3746.73 | −0.651470 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 300.695 | 0.0517991 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1524.80 | −0.260248 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5325.54 | −0.900622 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −296.856 | −0.0497453 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10696.4 | −1.77621 | −0.888107 | − | 0.459638i | \(-0.847979\pi\) | ||||
−0.888107 | + | 0.459638i | \(0.847979\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −898.462 | −0.147854 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −812.308 | −0.132481 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1046.80 | −0.169208 | −0.0846038 | − | 0.996415i | \(-0.526962\pi\) | ||||
−0.0846038 | + | 0.996415i | \(0.526962\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4155.10 | 0.665705 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2045.60 | −0.324855 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3444.95 | 0.542303 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1209.06 | −0.188677 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6330.72 | −0.979397 | −0.489698 | − | 0.871892i | \(-0.662893\pi\) | ||||
−0.489698 | + | 0.871892i | \(0.662893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5009.55 | −0.768353 | −0.384176 | − | 0.923260i | \(-0.625515\pi\) | ||||
−0.384176 | + | 0.923260i | \(0.625515\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1846.27 | 0.278376 | 0.139188 | − | 0.990266i | \(-0.455551\pi\) | ||||
0.139188 | + | 0.990266i | \(0.455551\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 925.806 | 0.138413 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 63.7610 | 0.00945263 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2967.18 | −0.436217 | −0.218109 | − | 0.975925i | \(-0.569989\pi\) | ||||
−0.218109 | + | 0.975925i | \(0.569989\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1383.14 | −0.201653 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1960.61 | 0.283485 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −675.459 | −0.0968634 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1714.49 | −0.243858 | −0.121929 | − | 0.992539i | \(-0.538908\pi\) | ||||
−0.121929 | + | 0.992539i | \(0.538908\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3116.88 | 0.439724 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 906.852 | 0.126904 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12101.2 | 1.67983 | 0.839917 | − | 0.542715i | \(-0.182604\pi\) | ||||
0.839917 | + | 0.542715i | \(0.182604\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2018.05 | −0.277897 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3374.45 | 0.460989 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8525.01 | −1.15541 | −0.577705 | − | 0.816245i | \(-0.696052\pi\) | ||||
−0.577705 | + | 0.816245i | \(0.696052\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 830.182 | 0.111631 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2563.79 | −0.342045 | −0.171023 | − | 0.985267i | \(-0.554707\pi\) | ||||
−0.171023 | + | 0.985267i | \(0.554707\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −377.961 | −0.0500330 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1239.59 | 0.162821 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10963.3 | −1.42895 | −0.714475 | − | 0.699661i | \(-0.753334\pi\) | ||||
−0.714475 | + | 0.699661i | \(0.753334\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −589.870 | −0.0762942 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6880.54 | 0.883149 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1860.82 | 0.237033 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7970.57 | −1.00764 | −0.503818 | − | 0.863810i | \(-0.668072\pi\) | ||||
−0.503818 | + | 0.863810i | \(0.668072\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1161.13 | 0.145687 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 972.347 | 0.121089 | 0.0605445 | − | 0.998165i | \(-0.480716\pi\) | ||||
0.0605445 | + | 0.998165i | \(0.480716\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1021.69 | 0.126288 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −224.883 | −0.0275914 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2598.37 | 0.316453 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13183.5 | 1.59384 | 0.796920 | − | 0.604085i | \(-0.206461\pi\) | ||||
0.796920 | + | 0.604085i | \(0.206461\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7919.24 | 0.950431 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3535.33 | 0.421216 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2184.03 | −0.258337 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4114.44 | 0.483177 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4346.49 | 0.506778 | 0.253389 | − | 0.967365i | \(-0.418455\pi\) | ||||
0.253389 | + | 0.967365i | \(0.418455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2930.12 | 0.339205 | 0.169603 | − | 0.985513i | \(-0.445752\pi\) | ||||
0.169603 | + | 0.985513i | \(0.445752\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 510.805 | 0.0587144 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −476.616 | −0.0543983 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4175.23 | −0.473193 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1015.10 | 0.114241 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14506.2 | −1.62121 | −0.810604 | − | 0.585595i | \(-0.800861\pi\) | ||||
−0.810604 | + | 0.585595i | \(0.800861\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3672.96 | 0.407647 | 0.203823 | − | 0.979008i | \(-0.434663\pi\) | ||||
0.203823 | + | 0.979008i | \(0.434663\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2161.98 | 0.238296 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10741.9 | −1.17587 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17003.5 | 1.84860 | 0.924299 | − | 0.381669i | \(-0.124650\pi\) | ||||
0.924299 | + | 0.381669i | \(0.124650\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2840.79 | −0.306747 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14173.8 | 1.52013 | 0.760066 | − | 0.649846i | \(-0.225167\pi\) | ||||
0.760066 | + | 0.649846i | \(0.225167\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 880.218 | 0.0937671 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5022.54 | −0.531450 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12102.9 | −1.27209 | −0.636046 | − | 0.771651i | \(-0.719431\pi\) | ||||
−0.636046 | + | 0.771651i | \(0.719431\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9014.06 | −0.941143 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7279.68 | 0.755031 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 188.776 | 0.0194505 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3341.74 | −0.342056 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −109.714 | −0.0111569 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7857.61 | −0.793851 | −0.396926 | − | 0.917851i | \(-0.629923\pi\) | ||||
−0.396926 | + | 0.917851i | \(0.629923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7149.73 | 0.717659 | 0.358829 | − | 0.933403i | \(-0.383176\pi\) | ||||
0.358829 | + | 0.933403i | \(0.383176\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 654.590 | 0.0652814 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11893.0 | −1.17846 | −0.589230 | − | 0.807965i | \(-0.700569\pi\) | ||||
−0.589230 | + | 0.807965i | \(0.700569\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1530.32 | −0.150669 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3871.87 | −0.378782 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3584.91 | −0.348487 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8679.50 | −0.838406 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1560.43 | −0.149785 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12678.9 | −1.20942 | −0.604710 | − | 0.796446i | \(-0.706711\pi\) | ||||
−0.604710 | + | 0.796446i | \(0.706711\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1297.78 | −0.123022 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2277.78 | −0.214581 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2460.74 | −0.230384 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8701.84 | −0.809688 | −0.404844 | − | 0.914386i | \(-0.632674\pi\) | ||||
−0.404844 | + | 0.914386i | \(0.632674\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11363.5 | 1.05087 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5212.84 | −0.479128 | −0.239564 | − | 0.970881i | \(-0.577005\pi\) | ||||
−0.239564 | + | 0.970881i | \(0.577005\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1054.77 | 0.0963583 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 650.364 | 0.0590539 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1744.14 | 0.157416 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4138.31 | −0.371255 | −0.185627 | − | 0.982620i | \(-0.559432\pi\) | ||||
−0.185627 | + | 0.982620i | \(0.559432\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3012.60 | −0.268649 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17161.5 | −1.52126 | −0.760630 | − | 0.649185i | \(-0.775110\pi\) | ||||
−0.760630 | + | 0.649185i | \(0.775110\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 576.166 | 0.0507704 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −507.000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16707.7 | −1.45492 | −0.727461 | − | 0.686149i | \(-0.759300\pi\) | ||||
−0.727461 | + | 0.686149i | \(0.759300\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1272.51 | −0.110162 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1997.97 | −0.171955 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4827.65 | −0.413071 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1477.26 | −0.125667 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 36.3174 | 0.00307159 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8042.87 | 0.676324 | 0.338162 | − | 0.941088i | \(-0.390195\pi\) | ||||
0.338162 | + | 0.941088i | \(0.390195\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3521.49 | −0.294425 | −0.147212 | − | 0.989105i | \(-0.547030\pi\) | ||||
−0.147212 | + | 0.989105i | \(0.547030\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1840.45 | −0.152997 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 319.358 | 0.0263974 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8905.34 | 0.731926 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6083.30 | −0.497162 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4502.15 | 0.365872 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3467.38 | −0.280202 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −791.179 | −0.0635790 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8215.61 | 0.656533 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20824.9 | −1.65496 | −0.827480 | − | 0.561495i | \(-0.810226\pi\) | ||||
−0.827480 | + | 0.561495i | \(0.810226\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5825.83 | −0.460424 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4928.49 | −0.387363 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8219.38 | −0.642478 | −0.321239 | − | 0.946998i | \(-0.604099\pi\) | ||||
−0.321239 | + | 0.946998i | \(0.604099\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7184.39 | 0.558510 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19208.1 | 1.48511 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3505.64 | 0.269575 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −831.475 | −0.0635931 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 644.376 | 0.0490181 | 0.0245091 | − | 0.999700i | \(-0.492198\pi\) | ||||
0.0245091 | + | 0.999700i | \(0.492198\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1790.51 | 0.135475 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 317.296 | 0.0238792 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4735.04 | 0.354455 | 0.177227 | − | 0.984170i | \(-0.443287\pi\) | ||||
0.177227 | + | 0.984170i | \(0.443287\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3845.31 | 0.286324 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −423.661 | −0.0313793 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3403.32 | 0.250746 | 0.125373 | − | 0.992110i | \(-0.459987\pi\) | ||||
0.125373 | + | 0.992110i | \(0.459987\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12107.4 | −0.887351 | −0.443676 | − | 0.896187i | \(-0.646326\pi\) | ||||
−0.443676 | + | 0.896187i | \(0.646326\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5775.32 | −0.421060 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17026.5 | 1.23488 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3208.73 | 0.231510 | 0.115755 | − | 0.993278i | \(-0.463071\pi\) | ||||
0.115755 | + | 0.993278i | \(0.463071\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9953.43 | 0.714422 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4114.54 | −0.293804 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4512.80 | 0.320585 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −324.830 | −0.0229574 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13630.6 | −0.958427 | −0.479213 | − | 0.877698i | \(-0.659078\pi\) | ||||
−0.479213 | + | 0.877698i | \(0.659078\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5815.72 | 0.406846 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12847.4 | −0.894199 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3392.81 | 0.234951 | 0.117476 | − | 0.993076i | \(-0.462520\pi\) | ||||
0.117476 | + | 0.993076i | \(0.462520\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 59.0071 | 0.00406564 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3657.31 | 0.250726 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2245.25 | −0.153153 | −0.0765763 | − | 0.997064i | \(-0.524399\pi\) | ||||
−0.0765763 | + | 0.997064i | \(0.524399\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7307.86 | −0.495997 | −0.247998 | − | 0.968760i | \(-0.579773\pi\) | ||||
−0.247998 | + | 0.968760i | \(0.579773\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2633.25 | 0.177835 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1814.43 | 0.121929 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8567.55 | 0.572893 | 0.286447 | − | 0.958096i | \(-0.407526\pi\) | ||||
0.286447 | + | 0.958096i | \(0.407526\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4073.00 | 0.271012 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 737.830 | 0.0488533 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20298.2 | −1.33741 | −0.668707 | − | 0.743526i | \(-0.733152\pi\) | ||||
−0.668707 | + | 0.743526i | \(0.733152\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2884.49 | 0.189128 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7172.25 | −0.467980 | −0.233990 | − | 0.972239i | \(-0.575178\pi\) | ||||
−0.233990 | + | 0.972239i | \(0.575178\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2861.42 | −0.185800 | −0.0928998 | − | 0.995675i | \(-0.529614\pi\) | ||||
−0.0928998 | + | 0.995675i | \(0.529614\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3919.40 | 0.253269 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1658.26 | 0.106640 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12793.9 | 0.818811 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5778.18 | 0.368035 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −405.656 | −0.0257147 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30554.9 | 1.92769 | 0.963843 | − | 0.266469i | \(-0.0858570\pi\) | ||||
0.963843 | + | 0.266469i | \(0.0858570\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14870.0 | 0.933694 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 768.285 | 0.0480133 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4103.36 | −0.255229 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3001.18 | −0.185798 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18473.6 | 1.13832 | 0.569161 | − | 0.822226i | \(-0.307268\pi\) | ||||
0.569161 | + | 0.822226i | \(0.307268\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22801.7 | 1.39846 | 0.699232 | − | 0.714895i | \(-0.253526\pi\) | ||||
0.699232 | + | 0.714895i | \(0.253526\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1147.17 | 0.0700304 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11212.0 | −0.681280 | −0.340640 | − | 0.940194i | \(-0.610644\pi\) | ||||
−0.340640 | + | 0.940194i | \(0.610644\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17593.0 | 1.06408 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1233.20 | 0.0742438 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1885.87 | −0.113017 | −0.0565084 | − | 0.998402i | \(-0.517997\pi\) | ||||
−0.0565084 | + | 0.998402i | \(0.517997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6367.55 | 0.379848 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2189.63 | 0.130024 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −525.205 | −0.0310456 | −0.0155228 | − | 0.999880i | \(-0.504941\pi\) | ||||
−0.0155228 | + | 0.999880i | \(0.504941\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8036.59 | 0.472900 | 0.236450 | − | 0.971644i | \(-0.424016\pi\) | ||||
0.236450 | + | 0.971644i | \(0.424016\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −158.476 | −0.00928313 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1074.56 | 0.0626611 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37680.4 | −2.18739 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5755.89 | −0.332639 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20777.4 | −1.19538 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19505.9 | 1.11723 | 0.558616 | − | 0.829426i | \(-0.311332\pi\) | ||||
0.558616 | + | 0.829426i | \(0.311332\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3166.88 | 0.180583 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12847.5 | 0.729347 | 0.364673 | − | 0.931136i | \(-0.381181\pi\) | ||||
0.364673 | + | 0.931136i | \(0.381181\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4635.83 | −0.262013 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3805.07 | −0.214112 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12286.7 | −0.688342 | −0.344171 | − | 0.938907i | \(-0.611840\pi\) | ||||
−0.344171 | + | 0.938907i | \(0.611840\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7328.80 | 0.408787 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7443.15 | −0.413354 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2253.96 | −0.124629 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24058.5 | 1.32450 | 0.662250 | − | 0.749283i | \(-0.269602\pi\) | ||||
0.662250 | + | 0.749283i | \(0.269602\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1225.23 | 0.0671613 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3807.68 | 0.207818 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1407.27 | 0.0764765 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15310.4 | −0.828456 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28829.0 | −1.55329 | −0.776644 | − | 0.629940i | \(-0.783080\pi\) | ||||
−0.776644 | + | 0.629940i | \(0.783080\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7387.26 | −0.396324 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 472.721 | 0.0252535 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1085.45 | 0.0577406 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4146.60 | −0.219646 | −0.109823 | − | 0.993951i | \(-0.535028\pi\) | ||||
−0.109823 | + | 0.993951i | \(0.535028\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6032.22 | −0.318180 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11408.6 | −0.599238 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 939.415 | 0.0491358 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19657.7 | 1.02389 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9681.67 | −0.502177 | −0.251089 | − | 0.967964i | \(-0.580789\pi\) | ||||
−0.251089 | + | 0.967964i | \(0.580789\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9094.91 | −0.469781 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7195.91 | −0.370151 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −30445.8 | −1.55963 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10092.3 | 0.514860 | 0.257430 | − | 0.966297i | \(-0.417124\pi\) | ||||
0.257430 | + | 0.966297i | \(0.417124\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 559.673 | 0.0283177 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7775.50 | 0.391807 | 0.195904 | − | 0.980623i | \(-0.437236\pi\) | ||||
0.195904 | + | 0.980623i | \(0.437236\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2628.99 | −0.131934 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7615.41 | −0.380621 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2699.84 | −0.134392 | −0.0671958 | − | 0.997740i | \(-0.521405\pi\) | ||||
−0.0671958 | + | 0.997740i | \(0.521405\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2885.96 | −0.143075 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14952.1 | −0.738279 | −0.369139 | − | 0.929374i | \(-0.620348\pi\) | ||||
−0.369139 | + | 0.929374i | \(0.620348\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4648.07 | −0.228580 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7079.96 | 0.346777 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6532.27 | −0.318670 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21169.6 | 1.02861 | 0.514307 | − | 0.857606i | \(-0.328049\pi\) | ||||
0.514307 | + | 0.857606i | \(0.328049\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8697.62 | 0.420928 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6736.92 | 0.324744 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10096.0 | 0.484736 | 0.242368 | − | 0.970184i | \(-0.422076\pi\) | ||||
0.242368 | + | 0.970184i | \(0.422076\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11335.0 | −0.542074 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31395.8 | 1.49553 | 0.747764 | − | 0.663965i | \(-0.231127\pi\) | ||||
0.747764 | + | 0.663965i | \(0.231127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9284.88 | −0.440544 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −101.534 | −0.00479867 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8787.00 | −0.413664 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16798.8 | −0.787750 | −0.393875 | − | 0.919164i | \(-0.628866\pi\) | ||||
−0.393875 | + | 0.919164i | \(0.628866\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17354.0 | 0.810622 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18854.0 | 0.877271 | 0.438635 | − | 0.898665i | \(-0.355462\pi\) | ||||
0.438635 | + | 0.898665i | \(0.355462\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9218.19 | −0.427261 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1566.43 | −0.0723237 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25627.3 | 1.17868 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8679.46 | 0.397664 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7008.47 | −0.319875 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3583.19 | −0.162917 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12420.9 | −0.562587 | −0.281294 | − | 0.959622i | \(-0.590763\pi\) | ||||
−0.281294 | + | 0.959622i | \(0.590763\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16038.1 | 0.723665 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7244.25 | 0.325633 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10377.4 | 0.464709 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1444.09 | −0.0644235 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34417.0 | −1.52963 | −0.764814 | − | 0.644251i | \(-0.777169\pi\) | ||||
−0.764814 | + | 0.644251i | \(0.777169\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 230.628 | 0.0102116 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2853.40 | −0.125867 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6332.45 | −0.278291 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2107.95 | −0.0922925 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17081.0 | 0.745081 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21745.5 | −0.945033 | −0.472516 | − | 0.881322i | \(-0.656654\pi\) | ||||
−0.472516 | + | 0.881322i | \(0.656654\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16487.2 | −0.713863 | −0.356932 | − | 0.934131i | \(-0.616177\pi\) | ||||
−0.356932 | + | 0.934131i | \(0.616177\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1489.03 | 0.0642346 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10516.3 | 0.451988 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10192.0 | 0.436443 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −611.955 | −0.0261092 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12274.1 | −0.521767 | −0.260883 | − | 0.965370i | \(-0.584014\pi\) | ||||
−0.260883 | + | 0.965370i | \(0.584014\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25913.7 | 1.09756 | 0.548782 | − | 0.835966i | \(-0.315092\pi\) | ||||
0.548782 | + | 0.835966i | \(0.315092\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9158.68 | −0.386502 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19617.2 | 0.824855 | 0.412428 | − | 0.910990i | \(-0.364681\pi\) | ||||
0.412428 | + | 0.910990i | \(0.364681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40662.5 | 1.70358 | 0.851790 | − | 0.523883i | \(-0.175517\pi\) | ||||
0.851790 | + | 0.523883i | \(0.175517\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8497.25 | 0.354713 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1282.62 | −0.0533493 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2787.99 | −0.115548 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2121.98 | −0.0876300 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16709.7 | 0.687584 | 0.343792 | − | 0.939046i | \(-0.388289\pi\) | ||||
0.343792 | + | 0.939046i | \(0.388289\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42989.1 | 1.76264 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16086.3 | 0.657228 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −469.199 | −0.0191017 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3418.24 | 0.138668 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9990.96 | 0.403874 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14491.5 | 0.583740 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18833.6 | 0.755978 | 0.377989 | − | 0.925810i | \(-0.376616\pi\) | ||||
0.377989 | + | 0.925810i | \(0.376616\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1849.01 | −0.0739589 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26784.6 | −1.06761 | −0.533807 | − | 0.845607i | \(-0.679239\pi\) | ||||
−0.533807 | + | 0.845607i | \(0.679239\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10246.9 | 0.407007 | 0.203504 | − | 0.979074i | \(-0.434767\pi\) | ||||
0.203504 | + | 0.979074i | \(0.434767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5434.15 | 0.215093 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5000.15 | −0.197227 | −0.0986136 | − | 0.995126i | \(-0.531441\pi\) | ||||
−0.0986136 | + | 0.995126i | \(0.531441\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.6096 | 0.00132111 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14689.5 | 0.575410 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17445.3 | 0.681002 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3803.59 | 0.147967 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7976.95 | 0.309254 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3518.38 | −0.135935 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16648.8 | −0.641039 | −0.320519 | − | 0.947242i | \(-0.603857\pi\) | ||||
−0.320519 | + | 0.947242i | \(0.603857\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2819.82 | −0.108203 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16304.0 | −0.623491 | −0.311746 | − | 0.950166i | \(-0.600914\pi\) | ||||
−0.311746 | + | 0.950166i | \(0.600914\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17857.7 | 0.680589 | 0.340295 | − | 0.940319i | \(-0.389473\pi\) | ||||
0.340295 | + | 0.940319i | \(0.389473\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5629.75 | −0.213833 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46797.7 | 1.77149 | 0.885745 | − | 0.464172i | \(-0.153648\pi\) | ||||
0.885745 | + | 0.464172i | \(0.153648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1447.39 | 0.0546050 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2108.28 | −0.0792705 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4199.90 | 0.157384 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −732.191 | −0.0273458 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5661.36 | 0.210733 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20400.3 | 0.756828 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −704.536 | −0.0260505 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2161.17 | 0.0796448 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5391.47 | −0.198032 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52238.0 | 1.91239 | 0.956193 | − | 0.292738i | \(-0.0945662\pi\) | ||||
0.956193 | + | 0.292738i | \(0.0945662\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1867.75 | −0.0681513 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31047.7 | −1.12915 | −0.564576 | − | 0.825381i | \(-0.690960\pi\) | ||||
−0.564576 | + | 0.825381i | \(0.690960\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20475.4 | −0.742208 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6648.74 | 0.240219 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11996.0 | 0.431997 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13876.1 | 0.498075 | 0.249038 | − | 0.968494i | \(-0.419886\pi\) | ||||
0.249038 | + | 0.968494i | \(0.419886\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1099.21 | 0.0393271 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4335.03 | −0.154593 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11709.2 | 0.416211 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15649.8 | 0.554483 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21424.9 | −0.756650 | −0.378325 | − | 0.925673i | \(-0.623500\pi\) | ||||
−0.378325 | + | 0.925673i | \(0.623500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23357.3 | −0.822239 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9349.73 | 0.328078 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 293.639 | 0.0102706 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4812.13 | −0.167775 | −0.0838876 | − | 0.996475i | \(-0.526734\pi\) | ||||
−0.0838876 | + | 0.996475i | \(0.526734\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7081.06 | −0.246093 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48232.7 | 1.67093 | 0.835464 | − | 0.549546i | \(-0.185199\pi\) | ||||
0.835464 | + | 0.549546i | \(0.185199\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −50272.8 | −1.73606 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −392.074 | −0.0134965 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33990.6 | 1.16636 | 0.583181 | − | 0.812342i | \(-0.301808\pi\) | ||||
0.583181 | + | 0.812342i | \(0.301808\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3162.80 | 0.108186 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3838.69 | −0.130892 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12836.1 | −0.436309 | −0.218154 | − | 0.975914i | \(-0.570004\pi\) | ||||
−0.218154 | + | 0.975914i | \(0.570004\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5344.72 | −0.181101 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20268.6 | 0.684630 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13806.9 | 0.464909 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23614.3 | −0.792667 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11240.2 | 0.376126 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9211.32 | 0.307278 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5141.56 | −0.170984 | −0.0854920 | − | 0.996339i | \(-0.527246\pi\) | ||||
−0.0854920 | + | 0.996339i | \(0.527246\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −902.085 | −0.0299063 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5891.05 | 0.194699 | 0.0973496 | − | 0.995250i | \(-0.468964\pi\) | ||||
0.0973496 | + | 0.995250i | \(0.468964\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7173.36 | 0.236349 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4574.39 | 0.150254 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10105.7 | −0.330922 | −0.165461 | − | 0.986216i | \(-0.552911\pi\) | ||||
−0.165461 | + | 0.986216i | \(0.552911\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8252.07 | 0.269395 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15976.6 | 0.519974 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7957.89 | −0.258207 | −0.129103 | − | 0.991631i | \(-0.541210\pi\) | ||||
−0.129103 | + | 0.991631i | \(0.541210\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11889.5 | −0.384601 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 890.568 | 0.0287205 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19993.6 | −0.642830 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16996.7 | −0.544822 | −0.272411 | − | 0.962181i | \(-0.587821\pi\) | ||||
−0.272411 | + | 0.962181i | \(0.587821\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32089.2 | 1.02550 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3384.63 | 0.107839 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46632.0 | −1.48130 | −0.740648 | − | 0.671894i | \(-0.765481\pi\) | ||||
−0.740648 | + | 0.671894i | \(0.765481\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2695.39 | 0.0853636 |
(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 | 2496.4.a.ca.1.2 | 5 | ||
4.3 | odd | 2 | 2496.4.a.cf.1.2 | 5 | |||
8.3 | odd | 2 | 1248.4.a.g.1.4 | ✓ | 5 | ||
8.5 | even | 2 | 1248.4.a.l.1.4 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1248.4.a.g.1.4 | ✓ | 5 | 8.3 | odd | 2 | ||
1248.4.a.l.1.4 | yes | 5 | 8.5 | even | 2 | ||
2496.4.a.ca.1.2 | 5 | 1.1 | even | 1 | trivial | ||
2496.4.a.cf.1.2 | 5 | 4.3 | odd | 2 |