Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, 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("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(130.099211563\) |
Analytic rank: | \(1\) |
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 | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2205.1 |
$q$-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 | \(-0.263376\pi\) | ||||
0.676777 | + | 0.736188i | \(0.263376\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 6.65685 | 0.832107 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −5.14214 | −0.227252 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 19.1421 | 0.605327 | ||||||||
\(11\) | −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 | \(0.345802\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 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 | \(-0.309646\pi\) | ||||
0.563003 | + | 0.826455i | \(0.309646\pi\) | |||||||
\(20\) | 33.2843 | 0.372129 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −185.941 | −1.80194 | ||||||||
\(23\) | 104.167 | 0.944357 | 0.472179 | − | 0.881503i | \(-0.343468\pi\) | ||||
0.472179 | + | 0.881503i | \(0.343468\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 167.137 | 1.26070 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 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 | \(-0.491619\pi\) | ||||
0.0263276 | + | 0.999653i | \(0.491619\pi\) | |||||||
\(32\) | −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 | \(-0.689717\pi\) | ||||
−0.561347 | + | 0.827580i | \(0.689717\pi\) | |||||||
\(38\) | 357.019 | 1.52411 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −25.7107 | −0.101630 | ||||||||
\(41\) | 276.274 | 1.05236 | 0.526180 | − | 0.850373i | \(-0.323624\pi\) | ||||
0.526180 | + | 0.850373i | \(0.323624\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −92.6375 | −0.328537 | −0.164268 | − | 0.986416i | \(-0.552526\pi\) | ||||
−0.164268 | + | 0.986416i | \(0.552526\pi\) | |||||||
\(44\) | −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 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 95.7107 | 0.270711 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 290.617 | 0.775026 | ||||||||
\(53\) | −623.019 | −1.61468 | −0.807342 | − | 0.590083i | \(-0.799095\pi\) | ||||
−0.807342 | + | 0.590083i | \(0.799095\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −242.843 | −0.595362 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 224.863 | 0.509068 | ||||||||
\(59\) | −524.999 | −1.15846 | −0.579229 | − | 0.815165i | \(-0.696646\pi\) | ||||
−0.579229 | + | 0.815165i | \(0.696646\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 352.794 | 0.740502 | 0.370251 | − | 0.928932i | \(-0.379272\pi\) | ||||
0.370251 | + | 0.928932i | \(0.379272\pi\) | |||||||
\(62\) | 34.7939 | 0.0712715 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −328.068 | −0.640758 | ||||||||
\(65\) | 218.284 | 0.416536 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −736.520 | −1.34299 | −0.671494 | − | 0.741010i | \(-0.734347\pi\) | ||||
−0.671494 | + | 0.741010i | \(0.734347\pi\) | |||||||
\(68\) | −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 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −872.195 | −1.24215 | −0.621074 | − | 0.783752i | \(-0.713303\pi\) | ||||
−0.621074 | + | 0.783752i | \(0.713303\pi\) | |||||||
\(80\) | −364.706 | −0.509692 | ||||||||
\(81\) | 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 | ||||||||
\(85\) | −338.284 | −0.431672 | ||||||||
\(86\) | −354.656 | −0.444692 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 249.746 | 0.302534 | ||||||||
\(89\) | −385.216 | −0.458796 | −0.229398 | − | 0.973333i | \(-0.573676\pi\) | ||||
−0.229398 | + | 0.973333i | \(0.573676\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 693.421 | 0.785806 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2231.18 | −2.44818 | ||||||||
\(95\) | 466.274 | 0.503565 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 463.892 | 0.485579 | 0.242789 | − | 0.970079i | \(-0.421938\pi\) | ||||
0.242789 | + | 0.970079i | \(0.421938\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 166.421 | 0.166421 | ||||||||
\(101\) | −432.725 | −0.426314 | −0.213157 | − | 0.977018i | \(-0.568375\pi\) | ||||
−0.213157 | + | 0.977018i | \(0.568375\pi\) | |||||||
\(102\) | 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 | \(-0.847088\pi\) | ||||
−0.886817 | + | 0.462122i | \(0.847088\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 545.176 | 0.479068 | 0.239534 | − | 0.970888i | \(-0.423005\pi\) | ||||
0.239534 | + | 0.970888i | \(0.423005\pi\) | |||||||
\(110\) | −929.706 | −0.805854 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 231.823 | 0.192992 | 0.0964961 | − | 0.995333i | \(-0.469236\pi\) | ||||
0.0964961 | + | 0.995333i | \(0.469236\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 520.833 | 0.422329 | ||||||||
\(116\) | 390.991 | 0.312953 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2009.92 | −1.56804 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1027.90 | 0.772279 | ||||||||
\(122\) | 1350.65 | 1.00231 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 60.4996 | 0.0438147 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2372.90 | 1.65796 | 0.828979 | − | 0.559280i | \(-0.188922\pi\) | ||||
0.828979 | + | 0.559280i | \(0.188922\pi\) | |||||||
\(128\) | 648.917 | 0.448099 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 835.685 | 0.563804 | ||||||||
\(131\) | 1200.04 | 0.800364 | 0.400182 | − | 0.916436i | \(-0.368947\pi\) | ||||
0.400182 | + | 0.916436i | \(0.368947\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2819.71 | −1.81781 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 347.901 | 0.219355 | ||||||||
\(137\) | −2781.25 | −1.73444 | −0.867221 | − | 0.497924i | \(-0.834096\pi\) | ||||
−0.867221 | + | 0.497924i | \(0.834096\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1245.60 | 0.760078 | 0.380039 | − | 0.924971i | \(-0.375911\pi\) | ||||
0.380039 | + | 0.924971i | \(0.375911\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1884.60 | 1.11375 | ||||||||
\(143\) | −2120.35 | −1.23995 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 293.675 | 0.168196 | ||||||||
\(146\) | −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 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 45.4416 | 0.0235481 | ||||||||
\(156\) | 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 | ||||||||
\(160\) | −1190.56 | −0.588264 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1527.54 | 0.734024 | 0.367012 | − | 0.930216i | \(-0.380381\pi\) | ||||
0.367012 | + | 0.930216i | \(0.380381\pi\) | |||||||
\(164\) | 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 | ||||||||
\(170\) | −1295.10 | −0.584290 | ||||||||
\(171\) | 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 | \(-0.702980\pi\) | ||||
−0.595333 | + | 0.803479i | \(0.702980\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −535.638 | −0.214608 | ||||||||
\(185\) | −1263.38 | −0.502084 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3285.99 | 1.28500 | ||||||||
\(188\) | −3879.57 | −1.50504 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1785.10 | 0.681603 | ||||||||
\(191\) | −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 | \(-0.446383\pi\) | ||||
0.167646 | + | 0.985847i | \(0.446383\pi\) | |||||||
\(194\) | 1775.98 | 0.657257 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3063.63 | −1.10799 | −0.553996 | − | 0.832519i | \(-0.686898\pi\) | ||||
−0.553996 | + | 0.832519i | \(0.686898\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 949.522 | 0.338240 | 0.169120 | − | 0.985595i | \(-0.445907\pi\) | ||||
0.169120 | + | 0.985595i | \(0.445907\pi\) | |||||||
\(200\) | −128.553 | −0.0454505 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1656.66 | −0.577039 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1381.37 | 0.470630 | ||||||||
\(206\) | −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 | ||||||||
\(215\) | −463.188 | −0.146926 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2087.17 | 0.648444 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1616.57 | −0.495405 | ||||||||
\(221\) | −2953.69 | −0.899033 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3227.61 | 0.969222 | 0.484611 | − | 0.874730i | \(-0.338961\pi\) | ||||
0.484611 | + | 0.874730i | \(0.338961\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 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 | \(-0.525046\pi\) | ||||
−0.0786019 | + | 0.996906i | \(0.525046\pi\) | |||||||
\(230\) | 1993.97 | 0.571646 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −302.024 | −0.0854691 | ||||||||
\(233\) | 5748.54 | 1.61631 | 0.808154 | − | 0.588972i | \(-0.200467\pi\) | ||||
0.808154 | + | 0.588972i | \(0.200467\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2913.97 | −0.808878 | ||||||||
\(236\) | −3494.84 | −0.963961 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 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 | \(-0.404913\pi\) | ||||
0.294302 | + | 0.955713i | \(0.404913\pi\) | |||||||
\(242\) | 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 | ||||||||
\(250\) | 478.553 | 0.121065 | ||||||||
\(251\) | −5716.90 | −1.43764 | −0.718820 | − | 0.695196i | \(-0.755317\pi\) | ||||
−0.718820 | + | 0.695196i | \(0.755317\pi\) | |||||||
\(252\) | 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 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1453.09 | 0.346602 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4594.25 | 1.08334 | ||||||||
\(263\) | −5975.36 | −1.40097 | −0.700487 | − | 0.713665i | \(-0.747034\pi\) | ||||
−0.700487 | + | 0.713665i | \(0.747034\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3115.10 | −0.722109 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4902.90 | −1.11751 | ||||||||
\(269\) | 4486.11 | 1.01681 | 0.508407 | − | 0.861117i | \(-0.330234\pi\) | ||||
0.508407 | + | 0.861117i | \(0.330234\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3827.68 | −0.857989 | −0.428994 | − | 0.903307i | \(-0.641132\pi\) | ||||
−0.428994 | + | 0.903307i | \(0.641132\pi\) | |||||||
\(272\) | 4934.97 | 1.10010 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10647.8 | −2.34766 | ||||||||
\(275\) | −1214.21 | −0.266254 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3420.54 | −0.741950 | −0.370975 | − | 0.928643i | \(-0.620976\pi\) | ||||
−0.370975 | + | 0.928643i | \(0.620976\pi\) | |||||||
\(278\) | 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 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −335.550 | −0.0682984 | ||||||||
\(290\) | 1124.31 | 0.227662 | ||||||||
\(291\) | 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 | ||||||||
\(295\) | −2625.00 | −0.518078 | ||||||||
\(296\) | 1299.30 | 0.255135 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −74.2892 | −0.0144411 | ||||||||
\(299\) | 4547.58 | 0.879577 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8996.04 | −1.71412 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6802.11 | −1.28332 | ||||||||
\(305\) | 1763.97 | 0.331163 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2668.64 | −0.496116 | −0.248058 | − | 0.968745i | \(-0.579792\pi\) | ||||
−0.248058 | + | 0.968745i | \(0.579792\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 173.970 | 0.0318736 | ||||||||
\(311\) | 6189.25 | 1.12849 | 0.564244 | − | 0.825608i | \(-0.309168\pi\) | ||||
0.564244 | + | 0.825608i | \(0.309168\pi\) | |||||||
\(312\) | 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 | \(-0.836165\pi\) | ||||
−0.870439 | + | 0.492276i | \(0.836165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2852.68 | −0.500687 | ||||||||
\(320\) | −1640.34 | −0.286556 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6309.33 | −1.08687 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1091.42 | 0.186281 | ||||||||
\(326\) | 5848.07 | 0.993541 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1420.64 | −0.239151 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 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 | ||||||||
\(335\) | −3682.60 | −0.600603 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3693.98 | −0.597103 | −0.298552 | − | 0.954394i | \(-0.596503\pi\) | ||||
−0.298552 | + | 0.954394i | \(0.596503\pi\) | |||||||
\(338\) | −1114.38 | −0.179331 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2251.91 | −0.359197 | ||||||||
\(341\) | −441.406 | −0.0700982 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 476.355 | 0.0746608 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2623.44 | 0.407622 | ||||||||
\(347\) | −3832.83 | −0.592960 | −0.296480 | − | 0.955039i | \(-0.595813\pi\) | ||||
−0.296480 | + | 0.955039i | \(0.595813\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8325.22 | −1.27690 | −0.638451 | − | 0.769662i | \(-0.720425\pi\) | ||||
−0.638451 | + | 0.769662i | \(0.720425\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 2461.32 | 0.367981 | ||||||||
\(356\) | −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 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5823.77 | −0.835150 | ||||||||
\(366\) | 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 | ||||||||
\(370\) | −4836.76 | −0.679598 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3523.32 | −0.489090 | −0.244545 | − | 0.969638i | \(-0.578639\pi\) | ||||
−0.244545 | + | 0.969638i | \(0.578639\pi\) | |||||||
\(374\) | 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 | \(0.131490\pi\) | |||||||
\(380\) | 3103.92 | 0.419020 | ||||||||
\(381\) | 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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11728.9 | −1.49973 | ||||||||
\(395\) | −4360.98 | −0.555505 | ||||||||
\(396\) | 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 | ||||||||
\(400\) | −1823.53 | −0.227941 | ||||||||
\(401\) | 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 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12272.1 | 1.49461 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3083.03 | 0.372729 | 0.186364 | − | 0.982481i | \(-0.440330\pi\) | ||||
0.186364 | + | 0.982481i | \(0.440330\pi\) | |||||||
\(410\) | 5288.48 | 0.637023 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3412.47 | −0.408060 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2647.94 | −0.313210 | ||||||||
\(416\) | −10395.3 | −1.22517 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −17339.9 | −2.02900 | ||||||||
\(419\) | −5415.21 | −0.631385 | −0.315692 | − | 0.948862i | \(-0.602237\pi\) | ||||
−0.315692 | + | 0.948862i | \(0.602237\pi\) | |||||||
\(420\) | 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 | ||||||||
\(425\) | −1691.42 | −0.193049 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −13068.0 | −1.47585 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1773.28 | −0.198872 | ||||||||
\(431\) | 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 | \(0.115495\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3629.16 | 0.398635 | ||||||||
\(437\) | 9714.03 | 1.06335 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8434.14 | −0.916946 | −0.458473 | − | 0.888708i | \(-0.651603\pi\) | ||||
−0.458473 | + | 0.888708i | \(0.651603\pi\) | |||||||
\(440\) | 1248.73 | 0.135297 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11308.0 | −1.21689 | ||||||||
\(443\) | 4298.49 | 0.461010 | 0.230505 | − | 0.973071i | \(-0.425962\pi\) | ||||
0.230505 | + | 0.973071i | \(0.425962\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1926.08 | −0.205180 | ||||||||
\(446\) | 12356.7 | 1.31189 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −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 | \(-0.290478\pi\) | ||||
0.611719 | + | 0.791075i | \(0.290478\pi\) | |||||||
\(458\) | −2085.63 | −0.212784 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3467.11 | 0.351423 | ||||||||
\(461\) | −17200.9 | −1.73780 | −0.868900 | − | 0.494988i | \(-0.835173\pi\) | ||||
−0.868900 | + | 0.494988i | \(0.835173\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10368.7 | −1.04076 | −0.520381 | − | 0.853934i | \(-0.674210\pi\) | ||||
−0.520381 | + | 0.853934i | \(0.674210\pi\) | |||||||
\(464\) | −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 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −11155.9 | −1.09486 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2699.62 | 0.263263 | ||||||||
\(473\) | 4499.27 | 0.437371 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2331.37 | 0.225201 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10252.9 | 0.981082 | ||||||||
\(479\) | 7329.12 | 0.699115 | 0.349558 | − | 0.936915i | \(-0.386332\pi\) | ||||
0.349558 | + | 0.936915i | \(0.386332\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11031.0 | −1.04568 | ||||||||
\(482\) | 8430.80 | 0.796706 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6842.60 | 0.642619 | ||||||||
\(485\) | 2319.46 | 0.217157 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17209.5 | −1.60131 | −0.800655 | − | 0.599125i | \(-0.795515\pi\) | ||||
−0.800655 | + | 0.599125i | \(0.795515\pi\) | |||||||
\(488\) | −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 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19079.4 | 1.71164 | 0.855822 | − | 0.517271i | \(-0.173052\pi\) | ||||
0.855822 | + | 0.517271i | \(0.173052\pi\) | |||||||
\(500\) | 832.107 | 0.0744259 | ||||||||
\(501\) | 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 | ||||||||
\(505\) | −2163.62 | −0.190654 | ||||||||
\(506\) | −19368.8 | −1.70168 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15796.0 | 1.37960 | ||||||||
\(509\) | −4328.85 | −0.376960 | −0.188480 | − | 0.982077i | \(-0.560356\pi\) | ||||
−0.188480 | + | 0.982077i | \(0.560356\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 14367.6 | 1.24017 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18086.6 | 1.55207 | ||||||||
\(515\) | −2563.13 | −0.219311 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28305.5 | 2.40788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1122.45 | −0.0946588 | ||||||||
\(521\) | 19395.7 | 1.63098 | 0.815490 | − | 0.578771i | \(-0.196468\pi\) | ||||
0.815490 | + | 0.578771i | \(0.196468\pi\) | |||||||
\(522\) | 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 | ||||||||
\(530\) | −11925.9 | −0.977413 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12061.3 | 0.980171 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9815.43 | −0.793193 | ||||||||
\(536\) | 3787.28 | 0.305197 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17174.8 | 1.37631 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 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 | ||||||||
\(545\) | 2725.88 | 0.214246 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15334.2 | 1.19862 | 0.599308 | − | 0.800518i | \(-0.295442\pi\) | ||||
0.599308 | + | 0.800518i | \(0.295442\pi\) | |||||||
\(548\) | −18514.4 | −1.44324 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4648.53 | −0.360389 | ||||||||
\(551\) | 5477.33 | 0.423488 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13095.3 | −1.00427 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8291.81 | 0.632466 | ||||||||
\(557\) | 8613.78 | 0.655256 | 0.327628 | − | 0.944807i | \(-0.393751\pi\) | ||||
0.327628 | + | 0.944807i | \(0.393751\pi\) | |||||||
\(558\) | 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 | ||||||||
\(565\) | 1159.12 | 0.0863087 | ||||||||
\(566\) | 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 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2604.16 | 0.188871 | ||||||||
\(576\) | 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 | ||||||||
\(580\) | 1954.95 | 0.139957 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 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 | ||||||||
\(590\) | −10049.6 | −0.701247 | ||||||||
\(591\) | 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 | \(-0.501163\pi\) | ||||
−0.00365347 | + | 0.999993i | \(0.501163\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15642.3 | −1.05377 | ||||||||
\(605\) | 5139.52 | 0.345374 | ||||||||
\(606\) | 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 | ||||||||
\(610\) | 6753.23 | 0.448246 | ||||||||
\(611\) | −25443.0 | −1.68463 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1242.60 | 0.0818732 | 0.0409366 | − | 0.999162i | \(-0.486966\pi\) | ||||
0.0409366 | + | 0.999162i | \(0.486966\pi\) | |||||||
\(614\) | −10216.7 | −0.671519 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13170.6 | 0.859367 | 0.429683 | − | 0.902980i | \(-0.358625\pi\) | ||||
0.429683 | + | 0.902980i | \(0.358625\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19774.1 | −1.28399 | −0.641993 | − | 0.766711i | \(-0.721892\pi\) | ||||
−0.641993 | + | 0.766711i | \(0.721892\pi\) | |||||||
\(620\) | 302.498 | 0.0195945 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23695.1 | 1.52747 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 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 | ||||||||
\(635\) | 11864.5 | 0.741461 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10921.3 | −0.677707 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3244.58 | 0.200396 | ||||||||
\(641\) | −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 | \(0.705286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 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 | ||||||||
\(650\) | 4178.43 | 0.252141 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10168.6 | 0.610787 | ||||||||
\(653\) | 2927.33 | 0.175429 | 0.0877145 | − | 0.996146i | \(-0.472044\pi\) | ||||
0.0877145 | + | 0.996146i | \(0.472044\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6000.18 | 0.357934 | ||||||||
\(656\) | −20151.7 | −1.19938 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 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 | \(-0.122305\pi\) | ||||
0.927086 | + | 0.374849i | \(0.122305\pi\) | |||||||
\(662\) | −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 | ||||||||
\(670\) | −14098.6 | −0.812948 | ||||||||
\(671\) | −17134.7 | −0.985808 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8992.15 | −0.515040 | −0.257520 | − | 0.966273i | \(-0.582905\pi\) | ||||
−0.257520 | + | 0.966273i | \(0.582905\pi\) | |||||||
\(674\) | −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 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1739.50 | 0.0980984 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1689.89 | −0.0948816 | ||||||||
\(683\) | 4255.14 | 0.238387 | 0.119194 | − | 0.992871i | \(-0.461969\pi\) | ||||
0.119194 | + | 0.992871i | \(0.461969\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13906.3 | −0.775666 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6757.08 | 0.374435 | ||||||||
\(689\) | −27199.1 | −1.50392 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17505.5 | 0.963733 | 0.481867 | − | 0.876245i | \(-0.339959\pi\) | ||||
0.481867 | + | 0.876245i | \(0.339959\pi\) | |||||||
\(692\) | 4561.63 | 0.250588 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14673.7 | −0.802603 | ||||||||
\(695\) | 6228.02 | 0.339917 | ||||||||
\(696\) | 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 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19949.3 | 1.05672 | 0.528358 | − | 0.849022i | \(-0.322808\pi\) | ||||
0.528358 | + | 0.849022i | \(0.322808\pi\) | |||||||
\(710\) | 9422.99 | 0.498082 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1980.83 | 0.104262 | ||||||||
\(713\) | 946.698 | 0.0497253 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10601.7 | −0.554522 | ||||||||
\(716\) | −6827.17 | −0.356345 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 49362.9 | 2.56575 | ||||||||
\(719\) | −11259.4 | −0.584011 | −0.292006 | − | 0.956417i | \(-0.594323\pi\) | ||||
−0.292006 | + | 0.956417i | \(0.594323\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7034.60 | 0.362605 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19300.9 | −0.990761 | ||||||||
\(725\) | 1468.38 | 0.0752195 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12228.5 | 0.623840 | 0.311920 | − | 0.950108i | \(-0.399028\pi\) | ||||
0.311920 | + | 0.950108i | \(0.399028\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −22295.9 | −1.13042 | ||||||||
\(731\) | 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 | \(0.548306\pi\) | |||||||
\(740\) | −8410.14 | −0.417788 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4016.87 | 0.198337 | 0.0991686 | − | 0.995071i | \(-0.468382\pi\) | ||||
0.0991686 | + | 0.995071i | \(0.468382\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −97.0231 | −0.00477134 | ||||||||
\(746\) | −13488.8 | −0.662010 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21874.4 | 1.06926 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 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 | ||||||||
\(755\) | −11749.0 | −0.566344 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31044.9 | 1.49055 | 0.745275 | − | 0.666758i | \(-0.232318\pi\) | ||||
0.745275 | + | 0.666758i | \(0.232318\pi\) | |||||||
\(758\) | 51742.9 | 2.47940 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2397.65 | −0.114436 | ||||||||
\(761\) | 14011.8 | 0.667446 | 0.333723 | − | 0.942671i | \(-0.391695\pi\) | ||||
0.333723 | + | 0.942671i | \(0.391695\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −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 | \(-0.524972\pi\) | ||||
−0.0783701 | + | 0.996924i | \(0.524972\pi\) | |||||||
\(770\) | 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 | ||||||||
\(775\) | 227.208 | 0.0105310 | ||||||||
\(776\) | −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 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19492.3 | 0.886254 | ||||||||
\(786\) | 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 | ||||||||
\(790\) | −16695.7 | −0.751906 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 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 | ||||||||
\(800\) | −5952.82 | −0.263080 | ||||||||
\(801\) | 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 | \(-0.664550\pi\) | ||||
−0.494230 | + | 0.869331i | \(0.664550\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 46982.9 | 2.02303 | ||||||||
\(815\) | 7637.69 | 0.328266 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8638.90 | −0.369935 | ||||||||
\(818\) | 11803.2 | 0.504508 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9195.58 | 0.391614 | ||||||||
\(821\) | 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 | \(-0.741050\pi\) | ||||
−0.686948 | + | 0.726707i | \(0.741050\pi\) | |||||||
\(824\) | 2635.99 | 0.111443 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12762.6 | 0.536638 | 0.268319 | − | 0.963330i | \(-0.413532\pi\) | ||||
0.268319 | + | 0.963330i | \(0.413532\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30766.7 | 1.28899 | 0.644494 | − | 0.764609i | \(-0.277068\pi\) | ||||
0.644494 | + | 0.764609i | \(0.277068\pi\) | |||||||
\(830\) | −10137.4 | −0.423947 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14322.4 | −0.596804 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4992.59 | −0.206917 | ||||||||
\(836\) | −30150.6 | −1.24734 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20731.7 | −0.854613 | ||||||||
\(839\) | −9779.71 | −0.402423 | −0.201212 | − | 0.979548i | \(-0.564488\pi\) | ||||
−0.201212 | + | 0.979548i | \(0.564488\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20939.2 | −0.858551 | ||||||||
\(842\) | 16034.8 | 0.656288 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15355.0 | 0.626233 | ||||||||
\(845\) | −1455.40 | −0.0592510 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 45443.7 | 1.84026 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6475.48 | −0.261303 | ||||||||
\(851\) | −26320.4 | −1.06023 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24201.5 | −0.971445 | −0.485723 | − | 0.874113i | \(-0.661444\pi\) | ||||
−0.485723 | + | 0.874113i | \(0.661444\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 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 | \(-0.460839\pi\) | ||||
0.122719 | + | 0.992441i | \(0.460839\pi\) | |||||||
\(860\) | −3083.37 | −0.122258 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 34870.9 | 1.37785 | ||||||||
\(863\) | −50256.2 | −1.98232 | −0.991160 | − | 0.132671i | \(-0.957644\pi\) | ||||
−0.991160 | + | 0.132671i | \(0.957644\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3426.27 | 0.134678 | ||||||||
\(866\) | 64497.7 | 2.53085 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 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 | \(-0.556527\pi\) | ||||
−0.176653 | + | 0.984273i | \(0.556527\pi\) | |||||||
\(878\) | −32289.5 | −1.24114 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 17713.2 | 0.678537 | ||||||||
\(881\) | −26172.7 | −1.00089 | −0.500444 | − | 0.865769i | \(-0.666830\pi\) | ||||
−0.500444 | + | 0.865769i | \(0.666830\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18615.5 | 0.709471 | 0.354736 | − | 0.934967i | \(-0.384571\pi\) | ||||
0.354736 | + | 0.934967i | \(0.384571\pi\) | |||||||
\(884\) | −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 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −7373.86 | −0.277722 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21485.7 | 0.806496 | ||||||||
\(893\) | −54348.4 | −2.03662 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5127.92 | −0.191517 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 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 | ||||||||
\(905\) | −14497.0 | −0.532482 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26766.1 | −0.979885 | −0.489942 | − | 0.871755i | \(-0.662982\pi\) | ||||
−0.489942 | + | 0.871755i | \(0.662982\pi\) | |||||||
\(908\) | −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 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9541.79 | 0.342497 | 0.171248 | − | 0.985228i | \(-0.445220\pi\) | ||||
0.171248 | + | 0.985228i | \(0.445220\pi\) | |||||||
\(920\) | −2678.19 | −0.0959754 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −65852.4 | −2.35220 | ||||||||
\(923\) | 21490.7 | 0.766387 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6316.90 | −0.224539 | ||||||||
\(926\) | −39695.7 | −1.40873 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13985.6 | −0.494718 | ||||||||
\(929\) | −25479.6 | −0.899846 | −0.449923 | − | 0.893067i | \(-0.648549\pi\) | ||||
−0.449923 | + | 0.893067i | \(0.648549\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 38267.2 | 1.34494 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −64621.9 | −2.26391 | ||||||||
\(935\) | 16430.0 | 0.574671 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33608.3 | 1.17176 | 0.585878 | − | 0.810399i | \(-0.300750\pi\) | ||||
0.585878 | + | 0.810399i | \(0.300750\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19397.9 | −0.673073 | ||||||||
\(941\) | −19173.6 | −0.664232 | −0.332116 | − | 0.943239i | \(-0.607762\pi\) | ||||
−0.332116 | + | 0.943239i | \(0.607762\pi\) | |||||||
\(942\) | 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 | \(-0.494651\pi\) | ||||
0.0168023 | + | 0.999859i | \(0.494651\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50849.5 | −1.73935 | ||||||||
\(950\) | 8925.48 | 0.304822 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3048.61 | −0.103624 | −0.0518122 | − | 0.998657i | \(-0.516500\pi\) | ||||
−0.0518122 | + | 0.998657i | \(0.516500\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5370.92 | −0.181989 | ||||||||
\(956\) | 17827.7 | 0.603127 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28059.0 | 0.946290 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29708.4 | −0.997227 | ||||||||
\(962\) | −42231.6 | −1.41538 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14659.4 | 0.489781 | ||||||||
\(965\) | 4495.00 | 0.149947 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14467.9 | −0.481133 | −0.240567 | − | 0.970633i | \(-0.577333\pi\) | ||||
−0.240567 | + | 0.970633i | \(0.577333\pi\) | |||||||
\(968\) | −5285.62 | −0.175502 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8879.89 | 0.293934 | ||||||||
\(971\) | 12952.8 | 0.428090 | 0.214045 | − | 0.976824i | \(-0.431336\pi\) | ||||
0.214045 | + | 0.976824i | \(0.431336\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −65885.4 | −2.16746 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −25733.2 | −0.843954 | ||||||||
\(977\) | −47244.2 | −1.54706 | −0.773529 | − | 0.633760i | \(-0.781511\pi\) | ||||
−0.773529 | + | 0.633760i | \(0.781511\pi\) | |||||||
\(978\) | 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 | ||||||||
\(985\) | −15318.1 | −0.495509 | ||||||||
\(986\) | −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 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4747.61 | 0.151266 | ||||||||
\(996\) | 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 | 2205.4.a.bb.1.2 | 2 | ||
3.2 | odd | 2 | 735.4.a.o.1.1 | 2 | |||
7.6 | odd | 2 | 315.4.a.k.1.2 | 2 | |||
21.20 | even | 2 | 105.4.a.e.1.1 | ✓ | 2 | ||
35.34 | odd | 2 | 1575.4.a.q.1.1 | 2 | |||
84.83 | odd | 2 | 1680.4.a.bo.1.1 | 2 | |||
105.62 | odd | 4 | 525.4.d.l.274.1 | 4 | |||
105.83 | odd | 4 | 525.4.d.l.274.4 | 4 | |||
105.104 | even | 2 | 525.4.a.l.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.e.1.1 | ✓ | 2 | 21.20 | even | 2 | ||
315.4.a.k.1.2 | 2 | 7.6 | odd | 2 | |||
525.4.a.l.1.2 | 2 | 105.104 | even | 2 | |||
525.4.d.l.274.1 | 4 | 105.62 | odd | 4 | |||
525.4.d.l.274.4 | 4 | 105.83 | odd | 4 | |||
735.4.a.o.1.1 | 2 | 3.2 | odd | 2 | |||
1575.4.a.q.1.1 | 2 | 35.34 | odd | 2 | |||
1680.4.a.bo.1.1 | 2 | 84.83 | odd | 2 | |||
2205.4.a.bb.1.2 | 2 | 1.1 | even | 1 | trivial |