Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, 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("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.82843 | −1.35355 | −0.676777 | − | 0.736188i | \(-0.736624\pi\) | ||||
−0.676777 | + | 0.736188i | \(0.736624\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 6.65685 | 0.832107 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 5.14214 | 0.227252 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −48.5685 | −1.33127 | −0.665635 | − | 0.746278i | \(-0.731839\pi\) | ||||
−0.665635 | + | 0.746278i | \(0.731839\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 43.6569 | 0.931403 | 0.465701 | − | 0.884942i | \(-0.345802\pi\) | ||||
0.465701 | + | 0.884942i | \(0.345802\pi\) | |||||||
\(14\) | −26.7990 | −0.511595 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −72.9411 | −1.13971 | ||||||||
\(17\) | −67.6569 | −0.965247 | −0.482623 | − | 0.875828i | \(-0.660316\pi\) | ||||
−0.482623 | + | 0.875828i | \(0.660316\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −93.2548 | −1.12601 | −0.563003 | − | 0.826455i | \(-0.690354\pi\) | ||||
−0.563003 | + | 0.826455i | \(0.690354\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 185.941 | 1.80194 | ||||||||
\(23\) | −104.167 | −0.944357 | −0.472179 | − | 0.881503i | \(-0.656532\pi\) | ||||
−0.472179 | + | 0.881503i | \(0.656532\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −167.137 | −1.26070 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 46.5980 | 0.314507 | ||||||||
\(29\) | 58.7351 | 0.376098 | 0.188049 | − | 0.982160i | \(-0.439784\pi\) | ||||
0.188049 | + | 0.982160i | \(0.439784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.08831 | −0.0526551 | −0.0263276 | − | 0.999653i | \(-0.508381\pi\) | ||||
−0.0263276 | + | 0.999653i | \(0.508381\pi\) | |||||||
\(32\) | 238.113 | 1.31540 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 259.019 | 1.30651 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 252.676 | 1.12269 | 0.561347 | − | 0.827580i | \(-0.310283\pi\) | ||||
0.561347 | + | 0.827580i | \(0.310283\pi\) | |||||||
\(38\) | 357.019 | 1.52411 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −276.274 | −1.05236 | −0.526180 | − | 0.850373i | \(-0.676376\pi\) | ||||
−0.526180 | + | 0.850373i | \(0.676376\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 92.6375 | 0.328537 | 0.164268 | − | 0.986416i | \(-0.447474\pi\) | ||||
0.164268 | + | 0.986416i | \(0.447474\pi\) | |||||||
\(44\) | −323.314 | −1.10776 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 398.794 | 1.27824 | ||||||||
\(47\) | −582.794 | −1.80871 | −0.904354 | − | 0.426784i | \(-0.859646\pi\) | ||||
−0.904354 | + | 0.426784i | \(0.859646\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 290.617 | 0.775026 | ||||||||
\(53\) | 623.019 | 1.61468 | 0.807342 | − | 0.590083i | \(-0.200905\pi\) | ||||
0.807342 | + | 0.590083i | \(0.200905\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 35.9949 | 0.0858933 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −224.863 | −0.509068 | ||||||||
\(59\) | 524.999 | 1.15846 | 0.579229 | − | 0.815165i | \(-0.303354\pi\) | ||||
0.579229 | + | 0.815165i | \(0.303354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −352.794 | −0.740502 | −0.370251 | − | 0.928932i | \(-0.620728\pi\) | ||||
−0.370251 | + | 0.928932i | \(0.620728\pi\) | |||||||
\(62\) | 34.7939 | 0.0712715 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −328.068 | −0.640758 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 736.520 | 1.34299 | 0.671494 | − | 0.741010i | \(-0.265653\pi\) | ||||
0.671494 | + | 0.741010i | \(0.265653\pi\) | |||||||
\(68\) | −450.382 | −0.803188 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 492.264 | 0.822831 | 0.411415 | − | 0.911448i | \(-0.365035\pi\) | ||||
0.411415 | + | 0.911448i | \(0.365035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1164.75 | −1.86745 | −0.933727 | − | 0.357987i | \(-0.883463\pi\) | ||||
−0.933727 | + | 0.357987i | \(0.883463\pi\) | |||||||
\(74\) | −967.352 | −1.51963 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −620.784 | −0.936958 | ||||||||
\(77\) | −339.980 | −0.503173 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −872.195 | −1.24215 | −0.621074 | − | 0.783752i | \(-0.713303\pi\) | ||||
−0.621074 | + | 0.783752i | \(0.713303\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1057.70 | 1.42443 | ||||||||
\(83\) | −529.588 | −0.700359 | −0.350180 | − | 0.936683i | \(-0.613879\pi\) | ||||
−0.350180 | + | 0.936683i | \(0.613879\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −354.656 | −0.444692 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −249.746 | −0.302534 | ||||||||
\(89\) | 385.216 | 0.458796 | 0.229398 | − | 0.973333i | \(-0.426324\pi\) | ||||
0.229398 | + | 0.973333i | \(0.426324\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 305.598 | 0.352037 | ||||||||
\(92\) | −693.421 | −0.785806 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2231.18 | 2.44818 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 463.892 | 0.485579 | 0.242789 | − | 0.970079i | \(-0.421938\pi\) | ||||
0.242789 | + | 0.970079i | \(0.421938\pi\) | |||||||
\(98\) | −187.593 | −0.193365 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 432.725 | 0.426314 | 0.213157 | − | 0.977018i | \(-0.431625\pi\) | ||||
0.213157 | + | 0.977018i | \(0.431625\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −512.626 | −0.490393 | −0.245197 | − | 0.969473i | \(-0.578853\pi\) | ||||
−0.245197 | + | 0.969473i | \(0.578853\pi\) | |||||||
\(104\) | 224.489 | 0.211663 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2385.18 | −2.18556 | ||||||||
\(107\) | 1963.09 | 1.77363 | 0.886817 | − | 0.462122i | \(-0.152912\pi\) | ||||
0.886817 | + | 0.462122i | \(0.152912\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 545.176 | 0.479068 | 0.239534 | − | 0.970888i | \(-0.423005\pi\) | ||||
0.239534 | + | 0.970888i | \(0.423005\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −510.588 | −0.430768 | ||||||||
\(113\) | −231.823 | −0.192992 | −0.0964961 | − | 0.995333i | \(-0.530764\pi\) | ||||
−0.0964961 | + | 0.995333i | \(0.530764\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 390.991 | 0.312953 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2009.92 | −1.56804 | ||||||||
\(119\) | −473.598 | −0.364829 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1027.90 | 0.772279 | ||||||||
\(122\) | 1350.65 | 1.00231 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −60.4996 | −0.0438147 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2372.90 | −1.65796 | −0.828979 | − | 0.559280i | \(-0.811078\pi\) | ||||
−0.828979 | + | 0.559280i | \(0.811078\pi\) | |||||||
\(128\) | −648.917 | −0.448099 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1200.04 | −0.800364 | −0.400182 | − | 0.916436i | \(-0.631053\pi\) | ||||
−0.400182 | + | 0.916436i | \(0.631053\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −652.784 | −0.425591 | ||||||||
\(134\) | −2819.71 | −1.81781 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −347.901 | −0.219355 | ||||||||
\(137\) | 2781.25 | 1.73444 | 0.867221 | − | 0.497924i | \(-0.165904\pi\) | ||||
0.867221 | + | 0.497924i | \(0.165904\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1245.60 | −0.760078 | −0.380039 | − | 0.924971i | \(-0.624089\pi\) | ||||
−0.380039 | + | 0.924971i | \(0.624089\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1884.60 | −1.11375 | ||||||||
\(143\) | −2120.35 | −1.23995 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4459.17 | 2.52770 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1682.03 | 0.934202 | ||||||||
\(149\) | −19.4046 | −0.0106690 | −0.00533452 | − | 0.999986i | \(-0.501698\pi\) | ||||
−0.00533452 | + | 0.999986i | \(0.501698\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2349.80 | −1.26638 | −0.633192 | − | 0.773995i | \(-0.718256\pi\) | ||||
−0.633192 | + | 0.773995i | \(0.718256\pi\) | |||||||
\(152\) | −479.529 | −0.255888 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1301.59 | 0.681071 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3898.46 | 1.98172 | 0.990862 | − | 0.134880i | \(-0.0430650\pi\) | ||||
0.990862 | + | 0.134880i | \(0.0430650\pi\) | |||||||
\(158\) | 3339.14 | 1.68131 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −729.166 | −0.356934 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1527.54 | −0.734024 | −0.367012 | − | 0.930216i | \(-0.619619\pi\) | ||||
−0.367012 | + | 0.930216i | \(0.619619\pi\) | |||||||
\(164\) | −1839.12 | −0.875676 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2027.49 | 0.947974 | ||||||||
\(167\) | −998.518 | −0.462681 | −0.231340 | − | 0.972873i | \(-0.574311\pi\) | ||||
−0.231340 | + | 0.972873i | \(0.574311\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −291.079 | −0.132489 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 616.674 | 0.273378 | ||||||||
\(173\) | 685.253 | 0.301149 | 0.150575 | − | 0.988599i | \(-0.451888\pi\) | ||||
0.150575 | + | 0.988599i | \(0.451888\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3542.64 | 1.51725 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1474.77 | −0.621005 | ||||||||
\(179\) | −1025.58 | −0.428245 | −0.214122 | − | 0.976807i | \(-0.568689\pi\) | ||||
−0.214122 | + | 0.976807i | \(0.568689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2899.40 | 1.19067 | 0.595333 | − | 0.803479i | \(-0.297020\pi\) | ||||
0.595333 | + | 0.803479i | \(0.297020\pi\) | |||||||
\(182\) | −1169.96 | −0.476501 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −535.638 | −0.214608 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3285.99 | 1.28500 | ||||||||
\(188\) | −3879.57 | −1.50504 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1074.18 | −0.406939 | −0.203469 | − | 0.979081i | \(-0.565222\pi\) | ||||
−0.203469 | + | 0.979081i | \(0.565222\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −898.999 | −0.335292 | −0.167646 | − | 0.985847i | \(-0.553617\pi\) | ||||
−0.167646 | + | 0.985847i | \(0.553617\pi\) | |||||||
\(194\) | −1775.98 | −0.657257 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 326.186 | 0.118872 | ||||||||
\(197\) | 3063.63 | 1.10799 | 0.553996 | − | 0.832519i | \(-0.313102\pi\) | ||||
0.553996 | + | 0.832519i | \(0.313102\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −949.522 | −0.338240 | −0.169120 | − | 0.985595i | \(-0.554093\pi\) | ||||
−0.169120 | + | 0.985595i | \(0.554093\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1656.66 | −0.577039 | ||||||||
\(203\) | 411.145 | 0.142151 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1962.55 | 0.663774 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3184.38 | −1.06152 | ||||||||
\(209\) | 4529.25 | 1.49902 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2306.64 | 0.752587 | 0.376294 | − | 0.926500i | \(-0.377198\pi\) | ||||
0.376294 | + | 0.926500i | \(0.377198\pi\) | |||||||
\(212\) | 4147.35 | 1.34359 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7515.53 | −2.40071 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −63.6182 | −0.0199018 | ||||||||
\(218\) | −2087.17 | −0.648444 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2953.69 | −0.899033 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3227.61 | 0.969222 | 0.484611 | − | 0.874730i | \(-0.338961\pi\) | ||||
0.484611 | + | 0.874730i | \(0.338961\pi\) | |||||||
\(224\) | 1666.79 | 0.497174 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 887.519 | 0.261225 | ||||||||
\(227\) | −637.820 | −0.186492 | −0.0932458 | − | 0.995643i | \(-0.529724\pi\) | ||||
−0.0932458 | + | 0.995643i | \(0.529724\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 544.774 | 0.157204 | 0.0786019 | − | 0.996906i | \(-0.474954\pi\) | ||||
0.0786019 | + | 0.996906i | \(0.474954\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 302.024 | 0.0854691 | ||||||||
\(233\) | −5748.54 | −1.61631 | −0.808154 | − | 0.588972i | \(-0.799533\pi\) | ||||
−0.808154 | + | 0.588972i | \(0.799533\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3494.84 | 0.963961 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1813.14 | 0.493816 | ||||||||
\(239\) | 2678.10 | 0.724820 | 0.362410 | − | 0.932019i | \(-0.381954\pi\) | ||||
0.362410 | + | 0.932019i | \(0.381954\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2202.16 | −0.588604 | −0.294302 | − | 0.955713i | \(-0.595087\pi\) | ||||
−0.294302 | + | 0.955713i | \(0.595087\pi\) | |||||||
\(242\) | −3935.25 | −1.04532 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2348.50 | −0.616177 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4071.21 | −1.04877 | ||||||||
\(248\) | −46.7333 | −0.0119660 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5716.90 | 1.43764 | 0.718820 | − | 0.695196i | \(-0.244683\pi\) | ||||
0.718820 | + | 0.695196i | \(0.244683\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5059.22 | 1.25719 | ||||||||
\(254\) | 9084.47 | 2.24413 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5108.88 | 1.24728 | ||||||||
\(257\) | 4724.29 | 1.14666 | 0.573332 | − | 0.819323i | \(-0.305650\pi\) | ||||
0.573332 | + | 0.819323i | \(0.305650\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1768.73 | 0.424339 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4594.25 | 1.08334 | ||||||||
\(263\) | 5975.36 | 1.40097 | 0.700487 | − | 0.713665i | \(-0.252966\pi\) | ||||
0.700487 | + | 0.713665i | \(0.252966\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2499.14 | 0.576059 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4902.90 | 1.11751 | ||||||||
\(269\) | −4486.11 | −1.01681 | −0.508407 | − | 0.861117i | \(-0.669766\pi\) | ||||
−0.508407 | + | 0.861117i | \(0.669766\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3827.68 | 0.857989 | 0.428994 | − | 0.903307i | \(-0.358868\pi\) | ||||
0.428994 | + | 0.903307i | \(0.358868\pi\) | |||||||
\(272\) | 4934.97 | 1.10010 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10647.8 | −2.34766 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3420.54 | 0.741950 | 0.370975 | − | 0.928643i | \(-0.379024\pi\) | ||||
0.370975 | + | 0.928643i | \(0.379024\pi\) | |||||||
\(278\) | 4768.71 | 1.02881 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5235.92 | −1.11156 | −0.555781 | − | 0.831329i | \(-0.687581\pi\) | ||||
−0.555781 | + | 0.831329i | \(0.687581\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6985.88 | 1.46738 | 0.733688 | − | 0.679486i | \(-0.237797\pi\) | ||||
0.733688 | + | 0.679486i | \(0.237797\pi\) | |||||||
\(284\) | 3276.93 | 0.684683 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8117.60 | 1.67834 | ||||||||
\(287\) | −1933.92 | −0.397755 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −335.550 | −0.0682984 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7753.59 | −1.55392 | ||||||||
\(293\) | 7399.70 | 1.47541 | 0.737705 | − | 0.675123i | \(-0.235910\pi\) | ||||
0.737705 | + | 0.675123i | \(0.235910\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1299.30 | 0.255135 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 74.2892 | 0.0144411 | ||||||||
\(299\) | −4547.58 | −0.879577 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 648.463 | 0.124175 | ||||||||
\(302\) | 8996.04 | 1.71412 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6802.11 | 1.28332 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2668.64 | −0.496116 | −0.248058 | − | 0.968745i | \(-0.579792\pi\) | ||||
−0.248058 | + | 0.968745i | \(0.579792\pi\) | |||||||
\(308\) | −2263.20 | −0.418693 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6189.25 | −1.12849 | −0.564244 | − | 0.825608i | \(-0.690832\pi\) | ||||
−0.564244 | + | 0.825608i | \(0.690832\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2921.59 | 0.527598 | 0.263799 | − | 0.964578i | \(-0.415024\pi\) | ||||
0.263799 | + | 0.964578i | \(0.415024\pi\) | |||||||
\(314\) | −14925.0 | −2.68237 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5806.08 | −1.03360 | ||||||||
\(317\) | 9825.56 | 1.74088 | 0.870439 | − | 0.492276i | \(-0.163835\pi\) | ||||
0.870439 | + | 0.492276i | \(0.163835\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2852.68 | −0.500687 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2791.56 | 0.483129 | ||||||||
\(323\) | 6309.33 | 1.08687 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5848.07 | 0.993541 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1420.64 | −0.239151 | ||||||||
\(329\) | −4079.56 | −0.683627 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9258.17 | −1.53739 | −0.768693 | − | 0.639618i | \(-0.779093\pi\) | ||||
−0.768693 | + | 0.639618i | \(0.779093\pi\) | |||||||
\(332\) | −3525.39 | −0.582774 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3822.75 | 0.626263 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3693.98 | 0.597103 | 0.298552 | − | 0.954394i | \(-0.403497\pi\) | ||||
0.298552 | + | 0.954394i | \(0.403497\pi\) | |||||||
\(338\) | 1114.38 | 0.179331 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 441.406 | 0.0700982 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 476.355 | 0.0746608 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2623.44 | −0.407622 | ||||||||
\(347\) | 3832.83 | 0.592960 | 0.296480 | − | 0.955039i | \(-0.404187\pi\) | ||||
0.296480 | + | 0.955039i | \(0.404187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8325.22 | 1.27690 | 0.638451 | − | 0.769662i | \(-0.279575\pi\) | ||||
0.638451 | + | 0.769662i | \(0.279575\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11564.8 | −1.75115 | ||||||||
\(353\) | −8991.52 | −1.35572 | −0.677862 | − | 0.735189i | \(-0.737093\pi\) | ||||
−0.677862 | + | 0.735189i | \(0.737093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2564.33 | 0.381767 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3926.38 | 0.579652 | ||||||||
\(359\) | 12893.8 | 1.89557 | 0.947783 | − | 0.318917i | \(-0.103319\pi\) | ||||
0.947783 | + | 0.318917i | \(0.103319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1837.46 | 0.267891 | ||||||||
\(362\) | −11100.1 | −1.61163 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2034.32 | 0.292932 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7480.17 | 1.06393 | 0.531964 | − | 0.846767i | \(-0.321454\pi\) | ||||
0.531964 | + | 0.846767i | \(0.321454\pi\) | |||||||
\(368\) | 7598.02 | 1.07629 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4361.14 | 0.610293 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3523.32 | 0.489090 | 0.244545 | − | 0.969638i | \(-0.421361\pi\) | ||||
0.244545 | + | 0.969638i | \(0.421361\pi\) | |||||||
\(374\) | −12580.2 | −1.73932 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2996.81 | −0.411033 | ||||||||
\(377\) | 2564.19 | 0.350298 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13515.4 | 1.83177 | 0.915886 | − | 0.401438i | \(-0.131490\pi\) | ||||
0.915886 | + | 0.401438i | \(0.131490\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4112.44 | 0.550813 | ||||||||
\(383\) | −657.182 | −0.0876774 | −0.0438387 | − | 0.999039i | \(-0.513959\pi\) | ||||
−0.0438387 | + | 0.999039i | \(0.513959\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3441.75 | 0.453836 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3088.06 | 0.404053 | ||||||||
\(389\) | 9741.87 | 1.26975 | 0.634875 | − | 0.772615i | \(-0.281052\pi\) | ||||
0.634875 | + | 0.772615i | \(0.281052\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7047.58 | 0.911538 | ||||||||
\(392\) | 251.965 | 0.0324646 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11728.9 | −1.49973 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4407.42 | −0.557184 | −0.278592 | − | 0.960410i | \(-0.589868\pi\) | ||||
−0.278592 | + | 0.960410i | \(0.589868\pi\) | |||||||
\(398\) | 3635.18 | 0.457827 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11569.5 | 1.44078 | 0.720391 | − | 0.693568i | \(-0.243963\pi\) | ||||
0.720391 | + | 0.693568i | \(0.243963\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −396.767 | −0.0490431 | ||||||||
\(404\) | 2880.59 | 0.354739 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1574.04 | −0.192410 | ||||||||
\(407\) | −12272.1 | −1.49461 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3083.03 | −0.372729 | −0.186364 | − | 0.982481i | \(-0.559670\pi\) | ||||
−0.186364 | + | 0.982481i | \(0.559670\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3412.47 | −0.408060 | ||||||||
\(413\) | 3674.99 | 0.437856 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10395.3 | 1.22517 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −17339.9 | −2.02900 | ||||||||
\(419\) | 5415.21 | 0.631385 | 0.315692 | − | 0.948862i | \(-0.397763\pi\) | ||||
0.315692 | + | 0.948862i | \(0.397763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4188.34 | 0.484863 | 0.242432 | − | 0.970168i | \(-0.422055\pi\) | ||||
0.242432 | + | 0.970168i | \(0.422055\pi\) | |||||||
\(422\) | −8830.82 | −1.01867 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3203.65 | 0.366941 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2469.56 | −0.279884 | ||||||||
\(428\) | 13068.0 | 1.47585 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9108.41 | 1.01795 | 0.508975 | − | 0.860781i | \(-0.330024\pi\) | ||||
0.508975 | + | 0.860781i | \(0.330024\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16847.0 | 1.86979 | 0.934893 | − | 0.354930i | \(-0.115495\pi\) | ||||
0.934893 | + | 0.354930i | \(0.115495\pi\) | |||||||
\(434\) | 243.558 | 0.0269381 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3629.16 | 0.398635 | ||||||||
\(437\) | 9714.03 | 1.06335 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8434.14 | 0.916946 | 0.458473 | − | 0.888708i | \(-0.348397\pi\) | ||||
0.458473 | + | 0.888708i | \(0.348397\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11308.0 | 1.21689 | ||||||||
\(443\) | −4298.49 | −0.461010 | −0.230505 | − | 0.973071i | \(-0.574038\pi\) | ||||
−0.230505 | + | 0.973071i | \(0.574038\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12356.7 | −1.31189 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2296.48 | −0.242184 | ||||||||
\(449\) | −10545.0 | −1.10835 | −0.554173 | − | 0.832402i | \(-0.686965\pi\) | ||||
−0.554173 | + | 0.832402i | \(0.686965\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13418.2 | 1.40098 | ||||||||
\(452\) | −1543.21 | −0.160590 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2441.85 | 0.252426 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11952.4 | −1.22344 | −0.611719 | − | 0.791075i | \(-0.709522\pi\) | ||||
−0.611719 | + | 0.791075i | \(0.709522\pi\) | |||||||
\(458\) | −2085.63 | −0.212784 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17200.9 | 1.73780 | 0.868900 | − | 0.494988i | \(-0.164827\pi\) | ||||
0.868900 | + | 0.494988i | \(0.164827\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10368.7 | 1.04076 | 0.520381 | − | 0.853934i | \(-0.325790\pi\) | ||||
0.520381 | + | 0.853934i | \(0.325790\pi\) | |||||||
\(464\) | −4284.20 | −0.428640 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22007.9 | 2.18776 | ||||||||
\(467\) | −16879.5 | −1.67257 | −0.836284 | − | 0.548296i | \(-0.815277\pi\) | ||||
−0.836284 | + | 0.548296i | \(0.815277\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5155.64 | 0.507602 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2699.62 | 0.263263 | ||||||||
\(473\) | −4499.27 | −0.437371 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3152.67 | −0.303577 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10252.9 | −0.981082 | ||||||||
\(479\) | −7329.12 | −0.699115 | −0.349558 | − | 0.936915i | \(-0.613668\pi\) | ||||
−0.349558 | + | 0.936915i | \(0.613668\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11031.0 | 1.04568 | ||||||||
\(482\) | 8430.80 | 0.796706 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6842.60 | 0.642619 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17209.5 | 1.60131 | 0.800655 | − | 0.599125i | \(-0.204485\pi\) | ||||
0.800655 | + | 0.599125i | \(0.204485\pi\) | |||||||
\(488\) | −1814.11 | −0.168281 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11392.5 | −1.04712 | −0.523560 | − | 0.851989i | \(-0.675396\pi\) | ||||
−0.523560 | + | 0.851989i | \(0.675396\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3973.83 | −0.363027 | ||||||||
\(494\) | 15586.3 | 1.41956 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 662.912 | 0.0600113 | ||||||||
\(497\) | 3445.85 | 0.311001 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19079.4 | 1.71164 | 0.855822 | − | 0.517271i | \(-0.173052\pi\) | ||||
0.855822 | + | 0.517271i | \(0.173052\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21886.7 | −1.94592 | ||||||||
\(503\) | −13499.4 | −1.19663 | −0.598317 | − | 0.801259i | \(-0.704164\pi\) | ||||
−0.598317 | + | 0.801259i | \(0.704164\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −19368.8 | −1.70168 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15796.0 | −1.37960 | ||||||||
\(509\) | 4328.85 | 0.376960 | 0.188480 | − | 0.982077i | \(-0.439644\pi\) | ||||
0.188480 | + | 0.982077i | \(0.439644\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8153.27 | −0.705831 | ||||||||
\(512\) | −14367.6 | −1.24017 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18086.6 | −1.55207 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28305.5 | 2.40788 | ||||||||
\(518\) | −6771.47 | −0.574365 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19395.7 | −1.63098 | −0.815490 | − | 0.578771i | \(-0.803532\pi\) | ||||
−0.815490 | + | 0.578771i | \(0.803532\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20413.8 | −1.70675 | −0.853377 | − | 0.521294i | \(-0.825450\pi\) | ||||
−0.853377 | + | 0.521294i | \(0.825450\pi\) | |||||||
\(524\) | −7988.47 | −0.665989 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22876.2 | −1.89629 | ||||||||
\(527\) | 614.887 | 0.0508252 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1316.34 | −0.108189 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4345.49 | −0.354137 | ||||||||
\(533\) | −12061.3 | −0.980171 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3787.28 | 0.305197 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17174.8 | 1.37631 | ||||||||
\(539\) | −2379.86 | −0.190181 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4919.18 | −0.390928 | −0.195464 | − | 0.980711i | \(-0.562621\pi\) | ||||
−0.195464 | + | 0.980711i | \(0.562621\pi\) | |||||||
\(542\) | −14654.0 | −1.16133 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16110.0 | −1.26969 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15334.2 | −1.19862 | −0.599308 | − | 0.800518i | \(-0.704558\pi\) | ||||
−0.599308 | + | 0.800518i | \(0.704558\pi\) | |||||||
\(548\) | 18514.4 | 1.44324 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5477.33 | −0.423488 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6105.37 | −0.469487 | ||||||||
\(554\) | −13095.3 | −1.00427 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8291.81 | −0.632466 | ||||||||
\(557\) | −8613.78 | −0.655256 | −0.327628 | − | 0.944807i | \(-0.606249\pi\) | ||||
−0.327628 | + | 0.944807i | \(0.606249\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4044.26 | 0.306000 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20045.3 | 1.50456 | ||||||||
\(563\) | −2320.81 | −0.173731 | −0.0868654 | − | 0.996220i | \(-0.527685\pi\) | ||||
−0.0868654 | + | 0.996220i | \(0.527685\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −26744.9 | −1.98617 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2531.29 | 0.186990 | ||||||||
\(569\) | 1736.04 | 0.127906 | 0.0639529 | − | 0.997953i | \(-0.479629\pi\) | ||||
0.0639529 | + | 0.997953i | \(0.479629\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23897.8 | 1.75148 | 0.875738 | − | 0.482786i | \(-0.160375\pi\) | ||||
0.875738 | + | 0.482786i | \(0.160375\pi\) | |||||||
\(572\) | −14114.9 | −1.03177 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7403.87 | 0.538382 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8029.26 | −0.579311 | −0.289655 | − | 0.957131i | \(-0.593541\pi\) | ||||
−0.289655 | + | 0.957131i | \(0.593541\pi\) | |||||||
\(578\) | 1284.63 | 0.0924455 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3707.12 | −0.264711 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30259.1 | −2.14958 | ||||||||
\(584\) | −5989.32 | −0.424383 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28329.2 | −1.99705 | ||||||||
\(587\) | −8015.14 | −0.563578 | −0.281789 | − | 0.959476i | \(-0.590928\pi\) | ||||
−0.281789 | + | 0.959476i | \(0.590928\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 847.529 | 0.0592900 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −18430.5 | −1.27954 | ||||||||
\(593\) | 12820.3 | 0.887801 | 0.443901 | − | 0.896076i | \(-0.353594\pi\) | ||||
0.443901 | + | 0.896076i | \(0.353594\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −129.174 | −0.00887779 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 17410.1 | 1.19055 | ||||||||
\(599\) | 15330.5 | 1.04572 | 0.522860 | − | 0.852418i | \(-0.324865\pi\) | ||||
0.522860 | + | 0.852418i | \(0.324865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 107.658 | 0.00730694 | 0.00365347 | − | 0.999993i | \(-0.498837\pi\) | ||||
0.00365347 | + | 0.999993i | \(0.498837\pi\) | |||||||
\(602\) | −2482.59 | −0.168078 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15642.3 | −1.05377 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8213.06 | 0.549189 | 0.274595 | − | 0.961560i | \(-0.411456\pi\) | ||||
0.274595 | + | 0.961560i | \(0.411456\pi\) | |||||||
\(608\) | −22205.2 | −1.48115 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25443.0 | −1.68463 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1242.60 | −0.0818732 | −0.0409366 | − | 0.999162i | \(-0.513034\pi\) | ||||
−0.0409366 | + | 0.999162i | \(0.513034\pi\) | |||||||
\(614\) | 10216.7 | 0.671519 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1748.22 | −0.114347 | ||||||||
\(617\) | −13170.6 | −0.859367 | −0.429683 | − | 0.902980i | \(-0.641375\pi\) | ||||
−0.429683 | + | 0.902980i | \(0.641375\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19774.1 | 1.28399 | 0.641993 | − | 0.766711i | \(-0.278108\pi\) | ||||
0.641993 | + | 0.766711i | \(0.278108\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23695.1 | 1.52747 | ||||||||
\(623\) | 2696.51 | 0.173409 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11185.1 | −0.714132 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 25951.5 | 1.64901 | ||||||||
\(629\) | −17095.3 | −1.08368 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14308.8 | −0.902735 | −0.451367 | − | 0.892338i | \(-0.649064\pi\) | ||||
−0.451367 | + | 0.892338i | \(0.649064\pi\) | |||||||
\(632\) | −4484.95 | −0.282281 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −37616.4 | −2.35637 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2139.19 | 0.133058 | ||||||||
\(638\) | 10921.3 | 0.677707 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11537.5 | −0.710925 | −0.355463 | − | 0.934691i | \(-0.615677\pi\) | ||||
−0.355463 | + | 0.934691i | \(0.615677\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19603.0 | −1.20228 | −0.601139 | − | 0.799144i | \(-0.705286\pi\) | ||||
−0.601139 | + | 0.799144i | \(0.705286\pi\) | |||||||
\(644\) | −4853.95 | −0.297007 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24154.8 | −1.47114 | ||||||||
\(647\) | 21650.0 | 1.31553 | 0.657765 | − | 0.753223i | \(-0.271502\pi\) | ||||
0.657765 | + | 0.753223i | \(0.271502\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25498.4 | −1.54222 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10168.6 | −0.610787 | ||||||||
\(653\) | −2927.33 | −0.175429 | −0.0877145 | − | 0.996146i | \(-0.527956\pi\) | ||||
−0.0877145 | + | 0.996146i | \(0.527956\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 20151.7 | 1.19938 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15618.3 | 0.925326 | ||||||||
\(659\) | 4778.76 | 0.282480 | 0.141240 | − | 0.989975i | \(-0.454891\pi\) | ||||
0.141240 | + | 0.989975i | \(0.454891\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31510.3 | −1.85417 | −0.927086 | − | 0.374849i | \(-0.877695\pi\) | ||||
−0.927086 | + | 0.374849i | \(0.877695\pi\) | |||||||
\(662\) | 35444.2 | 2.08093 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2723.21 | −0.159158 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6118.23 | −0.355170 | ||||||||
\(668\) | −6646.99 | −0.385000 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17134.7 | 0.985808 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8992.15 | 0.515040 | 0.257520 | − | 0.966273i | \(-0.417095\pi\) | ||||
0.257520 | + | 0.966273i | \(0.417095\pi\) | |||||||
\(674\) | −14142.1 | −0.808211 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1937.67 | −0.110245 | ||||||||
\(677\) | 19340.8 | 1.09797 | 0.548985 | − | 0.835832i | \(-0.315014\pi\) | ||||
0.548985 | + | 0.835832i | \(0.315014\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3247.25 | 0.183531 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1689.89 | −0.0948816 | ||||||||
\(683\) | −4255.14 | −0.238387 | −0.119194 | − | 0.992871i | \(-0.538031\pi\) | ||||
−0.119194 | + | 0.992871i | \(0.538031\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1313.15 | −0.0730850 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6757.08 | −0.374435 | ||||||||
\(689\) | 27199.1 | 1.50392 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17505.5 | −0.963733 | −0.481867 | − | 0.876245i | \(-0.660041\pi\) | ||||
−0.481867 | + | 0.876245i | \(0.660041\pi\) | |||||||
\(692\) | 4561.63 | 0.250588 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14673.7 | −0.802603 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18691.8 | 1.01579 | ||||||||
\(698\) | −31872.5 | −1.72836 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3240.77 | 0.174611 | 0.0873054 | − | 0.996182i | \(-0.472174\pi\) | ||||
0.0873054 | + | 0.996182i | \(0.472174\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23563.3 | −1.26416 | ||||||||
\(704\) | 15933.8 | 0.853022 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 34423.4 | 1.83504 | ||||||||
\(707\) | 3029.07 | 0.161132 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19949.3 | 1.05672 | 0.528358 | − | 0.849022i | \(-0.322808\pi\) | ||||
0.528358 | + | 0.849022i | \(0.322808\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1980.83 | 0.104262 | ||||||||
\(713\) | 946.698 | 0.0497253 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6827.17 | −0.356345 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −49362.9 | −2.56575 | ||||||||
\(719\) | 11259.4 | 0.584011 | 0.292006 | − | 0.956417i | \(-0.405677\pi\) | ||||
0.292006 | + | 0.956417i | \(0.405677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3588.38 | −0.185351 | ||||||||
\(722\) | −7034.60 | −0.362605 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19300.9 | 0.990761 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12228.5 | 0.623840 | 0.311920 | − | 0.950108i | \(-0.399028\pi\) | ||||
0.311920 | + | 0.950108i | \(0.399028\pi\) | |||||||
\(728\) | 1571.43 | 0.0800013 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6267.56 | −0.317119 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26635.1 | 1.34214 | 0.671072 | − | 0.741392i | \(-0.265834\pi\) | ||||
0.671072 | + | 0.741392i | \(0.265834\pi\) | |||||||
\(734\) | −28637.3 | −1.44008 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24803.4 | −1.24221 | ||||||||
\(737\) | −35771.7 | −1.78788 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6074.00 | −0.302349 | −0.151174 | − | 0.988507i | \(-0.548306\pi\) | ||||
−0.151174 | + | 0.988507i | \(0.548306\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16696.3 | −0.826065 | ||||||||
\(743\) | −4016.87 | −0.198337 | −0.0991686 | − | 0.995071i | \(-0.531618\pi\) | ||||
−0.0991686 | + | 0.995071i | \(0.531618\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13488.8 | −0.662010 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21874.4 | 1.06926 | ||||||||
\(749\) | 13741.6 | 0.670370 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23913.2 | −1.16192 | −0.580962 | − | 0.813931i | \(-0.697324\pi\) | ||||
−0.580962 | + | 0.813931i | \(0.697324\pi\) | |||||||
\(752\) | 42509.6 | 2.06139 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9816.81 | −0.474147 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31044.9 | −1.49055 | −0.745275 | − | 0.666758i | \(-0.767682\pi\) | ||||
−0.745275 | + | 0.666758i | \(0.767682\pi\) | |||||||
\(758\) | −51742.9 | −2.47940 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14011.8 | −0.667446 | −0.333723 | − | 0.942671i | \(-0.608305\pi\) | ||||
−0.333723 | + | 0.942671i | \(0.608305\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3816.23 | 0.181071 | ||||||||
\(764\) | −7150.69 | −0.338616 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2515.97 | 0.118676 | ||||||||
\(767\) | 22919.8 | 1.07899 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3342.49 | 0.156740 | 0.0783701 | − | 0.996924i | \(-0.475028\pi\) | ||||
0.0783701 | + | 0.996924i | \(0.475028\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5984.51 | −0.278999 | ||||||||
\(773\) | −21074.6 | −0.980594 | −0.490297 | − | 0.871555i | \(-0.663112\pi\) | ||||
−0.490297 | + | 0.871555i | \(0.663112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2385.40 | 0.110349 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −37296.0 | −1.71867 | ||||||||
\(779\) | 25763.9 | 1.18496 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23908.5 | −1.09541 | ||||||||
\(782\) | −26981.1 | −1.23382 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3574.12 | −0.162815 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21394.8 | −0.969048 | −0.484524 | − | 0.874778i | \(-0.661007\pi\) | ||||
−0.484524 | + | 0.874778i | \(0.661007\pi\) | |||||||
\(788\) | 20394.1 | 0.921968 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1622.76 | −0.0729442 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15401.9 | −0.689706 | ||||||||
\(794\) | 16873.5 | 0.754179 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6320.83 | −0.281452 | ||||||||
\(797\) | 20645.0 | 0.917547 | 0.458773 | − | 0.888553i | \(-0.348289\pi\) | ||||
0.458773 | + | 0.888553i | \(0.348289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39430.0 | 1.74585 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −44293.0 | −1.95017 | ||||||||
\(803\) | 56570.4 | 2.48608 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1518.99 | 0.0663825 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2225.13 | 0.0968810 | ||||||||
\(809\) | 15939.0 | 0.692688 | 0.346344 | − | 0.938108i | \(-0.387423\pi\) | ||||
0.346344 | + | 0.938108i | \(0.387423\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22829.2 | 0.988460 | 0.494230 | − | 0.869331i | \(-0.335450\pi\) | ||||
0.494230 | + | 0.869331i | \(0.335450\pi\) | |||||||
\(812\) | 2736.94 | 0.118285 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 46982.9 | 2.02303 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8638.90 | −0.369935 | ||||||||
\(818\) | 11803.2 | 0.504508 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5700.22 | 0.242313 | 0.121157 | − | 0.992633i | \(-0.461340\pi\) | ||||
0.121157 | + | 0.992633i | \(0.461340\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32438.0 | 1.37390 | 0.686948 | − | 0.726707i | \(-0.258950\pi\) | ||||
0.686948 | + | 0.726707i | \(0.258950\pi\) | |||||||
\(824\) | −2635.99 | −0.111443 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14069.4 | −0.592662 | ||||||||
\(827\) | −12762.6 | −0.536638 | −0.268319 | − | 0.963330i | \(-0.586468\pi\) | ||||
−0.268319 | + | 0.963330i | \(0.586468\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30766.7 | −1.28899 | −0.644494 | − | 0.764609i | \(-0.722932\pi\) | ||||
−0.644494 | + | 0.764609i | \(0.722932\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14322.4 | −0.596804 | ||||||||
\(833\) | −3315.19 | −0.137892 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 30150.6 | 1.24734 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20731.7 | −0.854613 | ||||||||
\(839\) | 9779.71 | 0.402423 | 0.201212 | − | 0.979548i | \(-0.435512\pi\) | ||||
0.201212 | + | 0.979548i | \(0.435512\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20939.2 | −0.858551 | ||||||||
\(842\) | −16034.8 | −0.656288 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15355.0 | 0.626233 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7195.32 | 0.291894 | ||||||||
\(848\) | −45443.7 | −1.84026 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26320.4 | −1.06023 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24201.5 | −0.971445 | −0.485723 | − | 0.874113i | \(-0.661444\pi\) | ||||
−0.485723 | + | 0.874113i | \(0.661444\pi\) | |||||||
\(854\) | 9454.52 | 0.378837 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10094.5 | 0.403062 | ||||||||
\(857\) | 21036.7 | 0.838507 | 0.419254 | − | 0.907869i | \(-0.362292\pi\) | ||||
0.419254 | + | 0.907869i | \(0.362292\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6179.19 | −0.245438 | −0.122719 | − | 0.992441i | \(-0.539161\pi\) | ||||
−0.122719 | + | 0.992441i | \(0.539161\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −34870.9 | −1.37785 | ||||||||
\(863\) | 50256.2 | 1.98232 | 0.991160 | − | 0.132671i | \(-0.0423555\pi\) | ||||
0.991160 | + | 0.132671i | \(0.0423555\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −64497.7 | −2.53085 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −423.497 | −0.0165604 | ||||||||
\(869\) | 42361.2 | 1.65363 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32154.1 | 1.25086 | ||||||||
\(872\) | 2803.37 | 0.108869 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −37189.5 | −1.43930 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9175.95 | 0.353306 | 0.176653 | − | 0.984273i | \(-0.443473\pi\) | ||||
0.176653 | + | 0.984273i | \(0.443473\pi\) | |||||||
\(878\) | −32289.5 | −1.24114 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26172.7 | 1.00089 | 0.500444 | − | 0.865769i | \(-0.333170\pi\) | ||||
0.500444 | + | 0.865769i | \(0.333170\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18615.5 | −0.709471 | −0.354736 | − | 0.934967i | \(-0.615429\pi\) | ||||
−0.354736 | + | 0.934967i | \(0.615429\pi\) | |||||||
\(884\) | −19662.3 | −0.748092 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16456.4 | 0.624001 | ||||||||
\(887\) | −12837.8 | −0.485964 | −0.242982 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242982 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16610.3 | −0.626649 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21485.7 | 0.806496 | ||||||||
\(893\) | 54348.4 | 2.03662 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4542.42 | −0.169366 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40370.6 | 1.50020 | ||||||||
\(899\) | −533.803 | −0.0198035 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42151.5 | −1.55857 | ||||||||
\(902\) | −51370.7 | −1.89630 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1192.07 | −0.0438579 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26766.1 | 0.979885 | 0.489942 | − | 0.871755i | \(-0.337018\pi\) | ||||
0.489942 | + | 0.871755i | \(0.337018\pi\) | |||||||
\(908\) | −4245.87 | −0.155181 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5022.67 | −0.182666 | −0.0913328 | − | 0.995820i | \(-0.529113\pi\) | ||||
−0.0913328 | + | 0.995820i | \(0.529113\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25721.3 | 0.932367 | ||||||||
\(914\) | 45759.0 | 1.65599 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3626.48 | 0.130810 | ||||||||
\(917\) | −8400.26 | −0.302509 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9541.79 | 0.342497 | 0.171248 | − | 0.985228i | \(-0.445220\pi\) | ||||
0.171248 | + | 0.985228i | \(0.445220\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −65852.4 | −2.35220 | ||||||||
\(923\) | 21490.7 | 0.766387 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −39695.7 | −1.40873 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13985.6 | 0.494718 | ||||||||
\(929\) | 25479.6 | 0.899846 | 0.449923 | − | 0.893067i | \(-0.351451\pi\) | ||||
0.449923 | + | 0.893067i | \(0.351451\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4569.49 | −0.160858 | ||||||||
\(932\) | −38267.2 | −1.34494 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 64621.9 | 2.26391 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33608.3 | 1.17176 | 0.585878 | − | 0.810399i | \(-0.300750\pi\) | ||||
0.585878 | + | 0.810399i | \(0.300750\pi\) | |||||||
\(938\) | −19738.0 | −0.687066 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19173.6 | 0.664232 | 0.332116 | − | 0.943239i | \(-0.392238\pi\) | ||||
0.332116 | + | 0.943239i | \(0.392238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28778.5 | 0.993804 | ||||||||
\(944\) | −38294.0 | −1.32030 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17225.1 | 0.592005 | ||||||||
\(947\) | −979.315 | −0.0336045 | −0.0168023 | − | 0.999859i | \(-0.505349\pi\) | ||||
−0.0168023 | + | 0.999859i | \(0.505349\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50849.5 | −1.73935 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2435.31 | −0.0829083 | ||||||||
\(953\) | 3048.61 | 0.103624 | 0.0518122 | − | 0.998657i | \(-0.483500\pi\) | ||||
0.0518122 | + | 0.998657i | \(0.483500\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 17827.7 | 0.603127 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28059.0 | 0.946290 | ||||||||
\(959\) | 19468.8 | 0.655557 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29708.4 | −0.997227 | ||||||||
\(962\) | −42231.6 | −1.41538 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14659.4 | −0.489781 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14467.9 | 0.481133 | 0.240567 | − | 0.970633i | \(-0.422667\pi\) | ||||
0.240567 | + | 0.970633i | \(0.422667\pi\) | |||||||
\(968\) | 5285.62 | 0.175502 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12952.8 | −0.428090 | −0.214045 | − | 0.976824i | \(-0.568664\pi\) | ||||
−0.214045 | + | 0.976824i | \(0.568664\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8719.23 | −0.287282 | ||||||||
\(974\) | −65885.4 | −2.16746 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25733.2 | 0.843954 | ||||||||
\(977\) | 47244.2 | 1.54706 | 0.773529 | − | 0.633760i | \(-0.218489\pi\) | ||||
0.773529 | + | 0.633760i | \(0.218489\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18709.4 | −0.610781 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 43615.3 | 1.41733 | ||||||||
\(983\) | −1536.84 | −0.0498651 | −0.0249326 | − | 0.999689i | \(-0.507937\pi\) | ||||
−0.0249326 | + | 0.999689i | \(0.507937\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15213.5 | 0.491376 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27101.5 | −0.872685 | ||||||||
\(989\) | −9649.73 | −0.310256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3785.22 | 0.121334 | 0.0606668 | − | 0.998158i | \(-0.480677\pi\) | ||||
0.0606668 | + | 0.998158i | \(0.480677\pi\) | |||||||
\(992\) | −2164.04 | −0.0692625 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13192.2 | −0.420956 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25894.9 | 0.822566 | 0.411283 | − | 0.911508i | \(-0.365081\pi\) | ||||
0.411283 | + | 0.911508i | \(0.365081\pi\) | |||||||
\(998\) | −73044.0 | −2.31680 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1575.4.a.q.1.1 | 2 | ||
3.2 | odd | 2 | 525.4.a.l.1.2 | 2 | |||
5.4 | even | 2 | 315.4.a.k.1.2 | 2 | |||
15.2 | even | 4 | 525.4.d.l.274.4 | 4 | |||
15.8 | even | 4 | 525.4.d.l.274.1 | 4 | |||
15.14 | odd | 2 | 105.4.a.e.1.1 | ✓ | 2 | ||
35.34 | odd | 2 | 2205.4.a.bb.1.2 | 2 | |||
60.59 | even | 2 | 1680.4.a.bo.1.1 | 2 | |||
105.104 | even | 2 | 735.4.a.o.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.e.1.1 | ✓ | 2 | 15.14 | odd | 2 | ||
315.4.a.k.1.2 | 2 | 5.4 | even | 2 | |||
525.4.a.l.1.2 | 2 | 3.2 | odd | 2 | |||
525.4.d.l.274.1 | 4 | 15.8 | even | 4 | |||
525.4.d.l.274.4 | 4 | 15.2 | even | 4 | |||
735.4.a.o.1.1 | 2 | 105.104 | even | 2 | |||
1575.4.a.q.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1680.4.a.bo.1.1 | 2 | 60.59 | even | 2 | |||
2205.4.a.bb.1.2 | 2 | 35.34 | odd | 2 |