Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 56x^{7} - 27x^{6} + 945x^{5} + 763x^{4} - 4139x^{3} - 2478x^{2} + 63x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | no (minimal twist has level 507) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.100291\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.34727 | 0.829886 | 0.414943 | − | 0.909848i | \(-0.363802\pi\) | ||||
0.414943 | + | 0.909848i | \(0.363802\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.49032 | −0.311290 | ||||||||
\(5\) | 15.3991 | 1.37734 | 0.688668 | − | 0.725077i | \(-0.258196\pi\) | ||||
0.688668 | + | 0.725077i | \(0.258196\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.1317 | 0.547062 | 0.273531 | − | 0.961863i | \(-0.411808\pi\) | ||||
0.273531 | + | 0.961863i | \(0.411808\pi\) | |||||||
\(8\) | −24.6236 | −1.08822 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 36.1458 | 1.14303 | ||||||||
\(11\) | 15.0669 | 0.412985 | 0.206493 | − | 0.978448i | \(-0.433795\pi\) | ||||
0.206493 | + | 0.978448i | \(0.433795\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 23.7819 | 0.453999 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −37.8757 | −0.591809 | ||||||||
\(17\) | −90.8352 | −1.29593 | −0.647964 | − | 0.761671i | \(-0.724379\pi\) | ||||
−0.647964 | + | 0.761671i | \(0.724379\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −114.640 | −1.38422 | −0.692110 | − | 0.721792i | \(-0.743319\pi\) | ||||
−0.692110 | + | 0.721792i | \(0.743319\pi\) | |||||||
\(20\) | −38.3486 | −0.428751 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 35.3661 | 0.342731 | ||||||||
\(23\) | −75.7635 | −0.686860 | −0.343430 | − | 0.939178i | \(-0.611589\pi\) | ||||
−0.343430 | + | 0.939178i | \(0.611589\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 112.132 | 0.897052 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −25.2313 | −0.170295 | ||||||||
\(29\) | −214.817 | −1.37553 | −0.687767 | − | 0.725931i | \(-0.741409\pi\) | ||||
−0.687767 | + | 0.725931i | \(0.741409\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 284.476 | 1.64817 | 0.824087 | − | 0.566463i | \(-0.191689\pi\) | ||||
0.824087 | + | 0.566463i | \(0.191689\pi\) | |||||||
\(32\) | 108.084 | 0.597087 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −213.215 | −1.07547 | ||||||||
\(35\) | 156.019 | 0.753488 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −358.878 | −1.59457 | −0.797286 | − | 0.603602i | \(-0.793732\pi\) | ||||
−0.797286 | + | 0.603602i | \(0.793732\pi\) | |||||||
\(38\) | −269.091 | −1.14874 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −379.181 | −1.49884 | ||||||||
\(41\) | 313.154 | 1.19284 | 0.596421 | − | 0.802672i | \(-0.296589\pi\) | ||||
0.596421 | + | 0.802672i | \(0.296589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −296.702 | −1.05225 | −0.526123 | − | 0.850409i | \(-0.676355\pi\) | ||||
−0.526123 | + | 0.850409i | \(0.676355\pi\) | |||||||
\(44\) | −37.5214 | −0.128558 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −177.837 | −0.570015 | ||||||||
\(47\) | −316.691 | −0.982854 | −0.491427 | − | 0.870919i | \(-0.663525\pi\) | ||||
−0.491427 | + | 0.870919i | \(0.663525\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −240.348 | −0.700723 | ||||||||
\(50\) | 263.203 | 0.744451 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −163.911 | −0.424810 | −0.212405 | − | 0.977182i | \(-0.568130\pi\) | ||||
−0.212405 | + | 0.977182i | \(0.568130\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 232.016 | 0.568819 | ||||||||
\(56\) | −249.480 | −0.595324 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −504.233 | −1.14154 | ||||||||
\(59\) | 254.149 | 0.560803 | 0.280401 | − | 0.959883i | \(-0.409532\pi\) | ||||
0.280401 | + | 0.959883i | \(0.409532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −935.247 | −1.96305 | −0.981526 | − | 0.191330i | \(-0.938720\pi\) | ||||
−0.981526 | + | 0.191330i | \(0.938720\pi\) | |||||||
\(62\) | 667.742 | 1.36780 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 556.709 | 1.08732 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 240.494 | 0.438522 | 0.219261 | − | 0.975666i | \(-0.429635\pi\) | ||||
0.219261 | + | 0.975666i | \(0.429635\pi\) | |||||||
\(68\) | 226.209 | 0.403409 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 366.220 | 0.625309 | ||||||||
\(71\) | 947.455 | 1.58369 | 0.791847 | − | 0.610720i | \(-0.209120\pi\) | ||||
0.791847 | + | 0.610720i | \(0.209120\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 430.712 | 0.690562 | 0.345281 | − | 0.938499i | \(-0.387784\pi\) | ||||
0.345281 | + | 0.938499i | \(0.387784\pi\) | |||||||
\(74\) | −842.384 | −1.32331 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 285.490 | 0.430894 | ||||||||
\(77\) | 152.654 | 0.225929 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −496.620 | −0.707268 | −0.353634 | − | 0.935384i | \(-0.615054\pi\) | ||||
−0.353634 | + | 0.935384i | \(0.615054\pi\) | |||||||
\(80\) | −583.251 | −0.815119 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 735.058 | 0.989922 | ||||||||
\(83\) | 392.527 | 0.519102 | 0.259551 | − | 0.965729i | \(-0.416425\pi\) | ||||
0.259551 | + | 0.965729i | \(0.416425\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1398.78 | −1.78493 | ||||||||
\(86\) | −696.439 | −0.873244 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −371.002 | −0.449419 | ||||||||
\(89\) | 979.895 | 1.16706 | 0.583532 | − | 0.812090i | \(-0.301670\pi\) | ||||
0.583532 | + | 0.812090i | \(0.301670\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 188.675 | 0.213813 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −743.360 | −0.815656 | ||||||||
\(95\) | −1765.35 | −1.90654 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 553.356 | 0.579225 | 0.289613 | − | 0.957144i | \(-0.406474\pi\) | ||||
0.289613 | + | 0.957144i | \(0.406474\pi\) | |||||||
\(98\) | −564.162 | −0.581520 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −279.243 | −0.279243 | ||||||||
\(101\) | 763.951 | 0.752633 | 0.376317 | − | 0.926491i | \(-0.377190\pi\) | ||||
0.376317 | + | 0.926491i | \(0.377190\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 182.518 | 0.174602 | 0.0873010 | − | 0.996182i | \(-0.472176\pi\) | ||||
0.0873010 | + | 0.996182i | \(0.472176\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −384.744 | −0.352544 | ||||||||
\(107\) | −183.699 | −0.165971 | −0.0829855 | − | 0.996551i | \(-0.526446\pi\) | ||||
−0.0829855 | + | 0.996551i | \(0.526446\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1774.42 | −1.55925 | −0.779627 | − | 0.626244i | \(-0.784592\pi\) | ||||
−0.779627 | + | 0.626244i | \(0.784592\pi\) | |||||||
\(110\) | 544.605 | 0.472055 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −383.747 | −0.323756 | ||||||||
\(113\) | −417.288 | −0.347391 | −0.173695 | − | 0.984799i | \(-0.555571\pi\) | ||||
−0.173695 | + | 0.984799i | \(0.555571\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1166.69 | −0.946037 | ||||||||
\(116\) | 534.963 | 0.428190 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 596.556 | 0.465402 | ||||||||
\(119\) | −920.318 | −0.708953 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1103.99 | −0.829443 | ||||||||
\(122\) | −2195.28 | −1.62911 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −708.436 | −0.513060 | ||||||||
\(125\) | −198.162 | −0.141793 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1951.69 | −1.36366 | −0.681828 | − | 0.731513i | \(-0.738815\pi\) | ||||
−0.681828 | + | 0.731513i | \(0.738815\pi\) | |||||||
\(128\) | 442.072 | 0.305266 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1475.61 | 0.984159 | 0.492080 | − | 0.870550i | \(-0.336237\pi\) | ||||
0.492080 | + | 0.870550i | \(0.336237\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1161.50 | −0.757255 | ||||||||
\(134\) | 564.503 | 0.363923 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2236.69 | 1.41026 | ||||||||
\(137\) | −1900.71 | −1.18532 | −0.592660 | − | 0.805453i | \(-0.701922\pi\) | ||||
−0.592660 | + | 0.805453i | \(0.701922\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2326.76 | −1.41981 | −0.709903 | − | 0.704299i | \(-0.751261\pi\) | ||||
−0.709903 | + | 0.704299i | \(0.751261\pi\) | |||||||
\(140\) | −388.538 | −0.234553 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2223.93 | 1.31428 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3307.98 | −1.89457 | ||||||||
\(146\) | 1011.00 | 0.573088 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 893.721 | 0.496374 | ||||||||
\(149\) | −1370.92 | −0.753761 | −0.376881 | − | 0.926262i | \(-0.623003\pi\) | ||||
−0.376881 | + | 0.926262i | \(0.623003\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1177.57 | −0.634628 | −0.317314 | − | 0.948320i | \(-0.602781\pi\) | ||||
−0.317314 | + | 0.948320i | \(0.602781\pi\) | |||||||
\(152\) | 2822.85 | 1.50634 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 358.320 | 0.187495 | ||||||||
\(155\) | 4380.67 | 2.27009 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1621.57 | 0.824302 | 0.412151 | − | 0.911116i | \(-0.364778\pi\) | ||||
0.412151 | + | 0.911116i | \(0.364778\pi\) | |||||||
\(158\) | −1165.70 | −0.586951 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1664.40 | 0.822389 | ||||||||
\(161\) | −767.616 | −0.375755 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 133.130 | 0.0639727 | 0.0319864 | − | 0.999488i | \(-0.489817\pi\) | ||||
0.0319864 | + | 0.999488i | \(0.489817\pi\) | |||||||
\(164\) | −779.854 | −0.371320 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 921.368 | 0.430795 | ||||||||
\(167\) | −490.724 | −0.227385 | −0.113693 | − | 0.993516i | \(-0.536268\pi\) | ||||
−0.113693 | + | 0.993516i | \(0.536268\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −3283.31 | −1.48129 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 738.882 | 0.327554 | ||||||||
\(173\) | −2008.13 | −0.882518 | −0.441259 | − | 0.897380i | \(-0.645468\pi\) | ||||
−0.441259 | + | 0.897380i | \(0.645468\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1136.09 | 0.490743 | ||||||||
\(176\) | −570.670 | −0.244408 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2300.08 | 0.968529 | ||||||||
\(179\) | 2152.60 | 0.898843 | 0.449421 | − | 0.893320i | \(-0.351630\pi\) | ||||
0.449421 | + | 0.893320i | \(0.351630\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 834.690 | 0.342774 | 0.171387 | − | 0.985204i | \(-0.445175\pi\) | ||||
0.171387 | + | 0.985204i | \(0.445175\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1865.57 | 0.747455 | ||||||||
\(185\) | −5526.39 | −2.19626 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1368.60 | −0.535200 | ||||||||
\(188\) | 788.662 | 0.305953 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4143.75 | −1.58221 | ||||||||
\(191\) | −4464.71 | −1.69139 | −0.845695 | − | 0.533667i | \(-0.820814\pi\) | ||||
−0.845695 | + | 0.533667i | \(0.820814\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3299.84 | 1.23071 | 0.615357 | − | 0.788248i | \(-0.289012\pi\) | ||||
0.615357 | + | 0.788248i | \(0.289012\pi\) | |||||||
\(194\) | 1298.88 | 0.480691 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 598.543 | 0.218128 | ||||||||
\(197\) | 2973.59 | 1.07543 | 0.537714 | − | 0.843127i | \(-0.319288\pi\) | ||||
0.537714 | + | 0.843127i | \(0.319288\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5430.82 | −1.93457 | −0.967287 | − | 0.253684i | \(-0.918358\pi\) | ||||
−0.967287 | + | 0.253684i | \(0.918358\pi\) | |||||||
\(200\) | −2761.08 | −0.976191 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1793.20 | 0.624600 | ||||||||
\(203\) | −2176.47 | −0.752503 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4822.29 | 1.64294 | ||||||||
\(206\) | 428.419 | 0.144900 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1727.27 | −0.571663 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1228.25 | 0.400742 | 0.200371 | − | 0.979720i | \(-0.435785\pi\) | ||||
0.200371 | + | 0.979720i | \(0.435785\pi\) | |||||||
\(212\) | 408.192 | 0.132239 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −431.192 | −0.137737 | ||||||||
\(215\) | −4568.93 | −1.44930 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2882.24 | 0.901654 | ||||||||
\(218\) | −4165.05 | −1.29400 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −577.795 | −0.177068 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 685.256 | 0.205776 | 0.102888 | − | 0.994693i | \(-0.467192\pi\) | ||||
0.102888 | + | 0.994693i | \(0.467192\pi\) | |||||||
\(224\) | 1095.08 | 0.326644 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −979.487 | −0.288294 | ||||||||
\(227\) | 287.067 | 0.0839354 | 0.0419677 | − | 0.999119i | \(-0.486637\pi\) | ||||
0.0419677 | + | 0.999119i | \(0.486637\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2302.23 | 0.664347 | 0.332174 | − | 0.943218i | \(-0.392218\pi\) | ||||
0.332174 | + | 0.943218i | \(0.392218\pi\) | |||||||
\(230\) | −2738.53 | −0.785102 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5289.57 | 1.49688 | ||||||||
\(233\) | 970.620 | 0.272908 | 0.136454 | − | 0.990646i | \(-0.456429\pi\) | ||||
0.136454 | + | 0.990646i | \(0.456429\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4876.75 | −1.35372 | ||||||||
\(236\) | −632.912 | −0.174572 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2160.24 | −0.588350 | ||||||||
\(239\) | −5007.40 | −1.35524 | −0.677619 | − | 0.735413i | \(-0.736988\pi\) | ||||
−0.677619 | + | 0.735413i | \(0.736988\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 540.092 | 0.144358 | 0.0721792 | − | 0.997392i | \(-0.477005\pi\) | ||||
0.0721792 | + | 0.997392i | \(0.477005\pi\) | |||||||
\(242\) | −2591.36 | −0.688343 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2329.07 | 0.611078 | ||||||||
\(245\) | −3701.14 | −0.965130 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7004.83 | −1.79358 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −465.141 | −0.117672 | ||||||||
\(251\) | 6087.80 | 1.53091 | 0.765455 | − | 0.643489i | \(-0.222514\pi\) | ||||
0.765455 | + | 0.643489i | \(0.222514\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1141.52 | −0.283663 | ||||||||
\(254\) | −4581.14 | −1.13168 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3416.01 | −0.833987 | ||||||||
\(257\) | 5096.34 | 1.23697 | 0.618484 | − | 0.785797i | \(-0.287747\pi\) | ||||
0.618484 | + | 0.785797i | \(0.287747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3636.06 | −0.872330 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3463.66 | 0.816739 | ||||||||
\(263\) | −3405.50 | −0.798450 | −0.399225 | − | 0.916853i | \(-0.630721\pi\) | ||||
−0.399225 | + | 0.916853i | \(0.630721\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2524.08 | −0.585106 | ||||||||
\(266\) | −2726.36 | −0.628435 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −598.906 | −0.136507 | ||||||||
\(269\) | 2720.44 | 0.616611 | 0.308306 | − | 0.951287i | \(-0.400238\pi\) | ||||
0.308306 | + | 0.951287i | \(0.400238\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6954.27 | −1.55883 | −0.779413 | − | 0.626511i | \(-0.784482\pi\) | ||||
−0.779413 | + | 0.626511i | \(0.784482\pi\) | |||||||
\(272\) | 3440.45 | 0.766941 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4461.49 | −0.983680 | ||||||||
\(275\) | 1689.47 | 0.370470 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6563.96 | −1.42379 | −0.711895 | − | 0.702286i | \(-0.752163\pi\) | ||||
−0.711895 | + | 0.702286i | \(0.752163\pi\) | |||||||
\(278\) | −5461.53 | −1.17828 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3841.76 | −0.819961 | ||||||||
\(281\) | −652.800 | −0.138586 | −0.0692932 | − | 0.997596i | \(-0.522074\pi\) | ||||
−0.0692932 | + | 0.997596i | \(0.522074\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6010.62 | 1.26252 | 0.631262 | − | 0.775570i | \(-0.282537\pi\) | ||||
0.631262 | + | 0.775570i | \(0.282537\pi\) | |||||||
\(284\) | −2359.47 | −0.492988 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3172.80 | 0.652558 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3338.04 | 0.679430 | ||||||||
\(290\) | −7764.73 | −1.57228 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1072.61 | −0.214965 | ||||||||
\(293\) | −1912.72 | −0.381372 | −0.190686 | − | 0.981651i | \(-0.561071\pi\) | ||||
−0.190686 | + | 0.981651i | \(0.561071\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3913.66 | 0.772413 | ||||||||
\(296\) | 8836.87 | 1.73525 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3217.93 | −0.625535 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3006.10 | −0.575644 | ||||||||
\(302\) | −2764.06 | −0.526669 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4342.07 | 0.819194 | ||||||||
\(305\) | −14401.9 | −2.70378 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1983.07 | 0.368665 | 0.184332 | − | 0.982864i | \(-0.440988\pi\) | ||||
0.184332 | + | 0.982864i | \(0.440988\pi\) | |||||||
\(308\) | −380.157 | −0.0703294 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10282.6 | 1.88391 | ||||||||
\(311\) | −1893.76 | −0.345291 | −0.172645 | − | 0.984984i | \(-0.555231\pi\) | ||||
−0.172645 | + | 0.984984i | \(0.555231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4574.19 | 0.826034 | 0.413017 | − | 0.910723i | \(-0.364475\pi\) | ||||
0.413017 | + | 0.910723i | \(0.364475\pi\) | |||||||
\(314\) | 3806.26 | 0.684076 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1236.74 | 0.220165 | ||||||||
\(317\) | 7594.53 | 1.34559 | 0.672794 | − | 0.739830i | \(-0.265094\pi\) | ||||
0.672794 | + | 0.739830i | \(0.265094\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3236.62 | −0.568076 | ||||||||
\(320\) | 8572.81 | 1.49761 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1801.80 | −0.311834 | ||||||||
\(323\) | 10413.3 | 1.79385 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 312.492 | 0.0530901 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7710.99 | −1.29807 | ||||||||
\(329\) | −3208.63 | −0.537682 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1738.58 | 0.288705 | 0.144352 | − | 0.989526i | \(-0.453890\pi\) | ||||
0.144352 | + | 0.989526i | \(0.453890\pi\) | |||||||
\(332\) | −977.519 | −0.161591 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1151.86 | −0.188704 | ||||||||
\(335\) | 3703.38 | 0.603992 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2710.61 | −0.438149 | −0.219074 | − | 0.975708i | \(-0.570304\pi\) | ||||
−0.219074 | + | 0.975708i | \(0.570304\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3483.41 | 0.555630 | ||||||||
\(341\) | 4286.17 | 0.680672 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5910.33 | −0.930401 | ||||||||
\(344\) | 7305.87 | 1.14508 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4713.63 | −0.732389 | ||||||||
\(347\) | 2506.81 | 0.387817 | 0.193908 | − | 0.981020i | \(-0.437884\pi\) | ||||
0.193908 | + | 0.981020i | \(0.437884\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7536.48 | −1.15593 | −0.577963 | − | 0.816063i | \(-0.696152\pi\) | ||||
−0.577963 | + | 0.816063i | \(0.696152\pi\) | |||||||
\(350\) | 2666.70 | 0.407261 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1628.50 | 0.246588 | ||||||||
\(353\) | −8992.88 | −1.35593 | −0.677964 | − | 0.735095i | \(-0.737138\pi\) | ||||
−0.677964 | + | 0.735095i | \(0.737138\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14589.9 | 2.18128 | ||||||||
\(356\) | −2440.25 | −0.363295 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5052.74 | 0.745937 | ||||||||
\(359\) | −4566.64 | −0.671359 | −0.335679 | − | 0.941976i | \(-0.608966\pi\) | ||||
−0.335679 | + | 0.941976i | \(0.608966\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6283.31 | 0.916068 | ||||||||
\(362\) | 1959.24 | 0.284463 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6632.57 | 0.951136 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6449.50 | −0.917332 | −0.458666 | − | 0.888609i | \(-0.651673\pi\) | ||||
−0.458666 | + | 0.888609i | \(0.651673\pi\) | |||||||
\(368\) | 2869.60 | 0.406490 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12971.9 | −1.82264 | ||||||||
\(371\) | −1660.71 | −0.232398 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7648.89 | 1.06178 | 0.530891 | − | 0.847440i | \(-0.321857\pi\) | ||||
0.530891 | + | 0.847440i | \(0.321857\pi\) | |||||||
\(374\) | −3212.49 | −0.444154 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7798.08 | 1.06956 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10297.8 | 1.39567 | 0.697837 | − | 0.716256i | \(-0.254146\pi\) | ||||
0.697837 | + | 0.716256i | \(0.254146\pi\) | |||||||
\(380\) | 4396.28 | 0.593486 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10479.9 | −1.40366 | ||||||||
\(383\) | 10258.0 | 1.36856 | 0.684282 | − | 0.729217i | \(-0.260116\pi\) | ||||
0.684282 | + | 0.729217i | \(0.260116\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2350.73 | 0.311180 | ||||||||
\(386\) | 7745.63 | 1.02135 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1378.03 | −0.180307 | ||||||||
\(389\) | 4771.57 | 0.621924 | 0.310962 | − | 0.950422i | \(-0.399349\pi\) | ||||
0.310962 | + | 0.950422i | \(0.399349\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6882.00 | 0.890122 | ||||||||
\(392\) | 5918.24 | 0.762541 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6979.82 | 0.892483 | ||||||||
\(395\) | −7647.50 | −0.974145 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2291.22 | −0.289655 | −0.144827 | − | 0.989457i | \(-0.546263\pi\) | ||||
−0.144827 | + | 0.989457i | \(0.546263\pi\) | |||||||
\(398\) | −12747.6 | −1.60548 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4247.07 | −0.530883 | ||||||||
\(401\) | 7534.63 | 0.938308 | 0.469154 | − | 0.883116i | \(-0.344559\pi\) | ||||
0.469154 | + | 0.883116i | \(0.344559\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1902.48 | −0.234287 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5108.76 | −0.624491 | ||||||||
\(407\) | −5407.18 | −0.658535 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1517.97 | 0.183517 | 0.0917587 | − | 0.995781i | \(-0.470751\pi\) | ||||
0.0917587 | + | 0.995781i | \(0.470751\pi\) | |||||||
\(410\) | 11319.2 | 1.36345 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −454.528 | −0.0543519 | ||||||||
\(413\) | 2574.97 | 0.306794 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6044.56 | 0.714978 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4054.36 | −0.474415 | ||||||||
\(419\) | −8080.97 | −0.942199 | −0.471100 | − | 0.882080i | \(-0.656143\pi\) | ||||
−0.471100 | + | 0.882080i | \(0.656143\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8073.13 | −0.934585 | −0.467293 | − | 0.884103i | \(-0.654771\pi\) | ||||
−0.467293 | + | 0.884103i | \(0.654771\pi\) | |||||||
\(422\) | 2883.05 | 0.332570 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4036.09 | 0.462287 | ||||||||
\(425\) | −10185.5 | −1.16252 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9475.68 | −1.07391 | ||||||||
\(428\) | 457.470 | 0.0516651 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10724.5 | −1.20275 | ||||||||
\(431\) | 2241.39 | 0.250496 | 0.125248 | − | 0.992125i | \(-0.460027\pi\) | ||||
0.125248 | + | 0.992125i | \(0.460027\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10237.9 | 1.13626 | 0.568130 | − | 0.822939i | \(-0.307667\pi\) | ||||
0.568130 | + | 0.822939i | \(0.307667\pi\) | |||||||
\(434\) | 6765.39 | 0.748270 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4418.88 | 0.485380 | ||||||||
\(437\) | 8685.52 | 0.950766 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5416.69 | −0.588894 | −0.294447 | − | 0.955668i | \(-0.595135\pi\) | ||||
−0.294447 | + | 0.955668i | \(0.595135\pi\) | |||||||
\(440\) | −5713.08 | −0.619001 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2537.44 | 0.272138 | 0.136069 | − | 0.990699i | \(-0.456553\pi\) | ||||
0.136069 | + | 0.990699i | \(0.456553\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15089.5 | 1.60744 | ||||||||
\(446\) | 1608.48 | 0.170771 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5640.43 | 0.594833 | ||||||||
\(449\) | 7790.61 | 0.818846 | 0.409423 | − | 0.912345i | \(-0.365730\pi\) | ||||
0.409423 | + | 0.912345i | \(0.365730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4718.26 | 0.492626 | ||||||||
\(452\) | 1039.18 | 0.108139 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 673.825 | 0.0696568 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6599.71 | −0.675539 | −0.337770 | − | 0.941229i | \(-0.609672\pi\) | ||||
−0.337770 | + | 0.941229i | \(0.609672\pi\) | |||||||
\(458\) | 5403.95 | 0.551332 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2905.43 | 0.294492 | ||||||||
\(461\) | 4482.57 | 0.452872 | 0.226436 | − | 0.974026i | \(-0.427293\pi\) | ||||
0.226436 | + | 0.974026i | \(0.427293\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3805.86 | 0.382016 | 0.191008 | − | 0.981589i | \(-0.438824\pi\) | ||||
0.191008 | + | 0.981589i | \(0.438824\pi\) | |||||||
\(464\) | 8136.35 | 0.814053 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2278.31 | 0.226482 | ||||||||
\(467\) | −14778.8 | −1.46441 | −0.732207 | − | 0.681082i | \(-0.761510\pi\) | ||||
−0.732207 | + | 0.681082i | \(0.761510\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2436.62 | 0.239899 | ||||||||
\(470\) | −11447.0 | −1.12343 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6258.06 | −0.610277 | ||||||||
\(473\) | −4470.37 | −0.434562 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12854.8 | −1.24172 | ||||||||
\(476\) | 2291.89 | 0.220690 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11753.7 | −1.12469 | ||||||||
\(479\) | 11171.2 | 1.06560 | 0.532801 | − | 0.846240i | \(-0.321139\pi\) | ||||
0.532801 | + | 0.846240i | \(0.321139\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1267.74 | 0.119801 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2749.29 | 0.258197 | ||||||||
\(485\) | 8521.18 | 0.797787 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6046.57 | −0.562621 | −0.281310 | − | 0.959617i | \(-0.590769\pi\) | ||||
−0.281310 | + | 0.959617i | \(0.590769\pi\) | |||||||
\(488\) | 23029.2 | 2.13623 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8687.57 | −0.800948 | ||||||||
\(491\) | 1035.04 | 0.0951338 | 0.0475669 | − | 0.998868i | \(-0.484853\pi\) | ||||
0.0475669 | + | 0.998868i | \(0.484853\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19512.9 | 1.78259 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10774.7 | −0.975404 | ||||||||
\(497\) | 9599.37 | 0.866379 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11698.3 | 1.04947 | 0.524736 | − | 0.851265i | \(-0.324164\pi\) | ||||
0.524736 | + | 0.851265i | \(0.324164\pi\) | |||||||
\(500\) | 493.488 | 0.0441389 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14289.7 | 1.27048 | ||||||||
\(503\) | 13552.0 | 1.20130 | 0.600651 | − | 0.799511i | \(-0.294908\pi\) | ||||
0.600651 | + | 0.799511i | \(0.294908\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11764.1 | 1.03663 | ||||||||
\(506\) | −2679.46 | −0.235408 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4860.33 | 0.424492 | ||||||||
\(509\) | 5076.46 | 0.442064 | 0.221032 | − | 0.975267i | \(-0.429058\pi\) | ||||
0.221032 | + | 0.975267i | \(0.429058\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4363.86 | 0.377781 | ||||||||
\(512\) | −11554.9 | −0.997380 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11962.5 | 1.02654 | ||||||||
\(515\) | 2810.60 | 0.240486 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4771.55 | −0.405904 | ||||||||
\(518\) | −8534.81 | −0.723934 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8493.73 | 0.714236 | 0.357118 | − | 0.934059i | \(-0.383759\pi\) | ||||
0.357118 | + | 0.934059i | \(0.383759\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1384.53 | −0.115758 | −0.0578789 | − | 0.998324i | \(-0.518434\pi\) | ||||
−0.0578789 | + | 0.998324i | \(0.518434\pi\) | |||||||
\(524\) | −3674.75 | −0.306359 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7993.64 | −0.662622 | ||||||||
\(527\) | −25840.4 | −2.13592 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6426.89 | −0.528223 | ||||||||
\(530\) | −5924.71 | −0.485571 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2892.51 | 0.235726 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2828.80 | −0.228598 | ||||||||
\(536\) | −5921.82 | −0.477208 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6385.62 | 0.511717 | ||||||||
\(539\) | −3621.30 | −0.289388 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5026.83 | −0.399483 | −0.199742 | − | 0.979849i | \(-0.564010\pi\) | ||||
−0.199742 | + | 0.979849i | \(0.564010\pi\) | |||||||
\(542\) | −16323.6 | −1.29365 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9817.87 | −0.773782 | ||||||||
\(545\) | −27324.5 | −2.14762 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1540.36 | 0.120404 | 0.0602021 | − | 0.998186i | \(-0.480825\pi\) | ||||
0.0602021 | + | 0.998186i | \(0.480825\pi\) | |||||||
\(548\) | 4733.38 | 0.368978 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3965.65 | 0.307447 | ||||||||
\(551\) | 24626.6 | 1.90404 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5031.63 | −0.386920 | ||||||||
\(554\) | −15407.4 | −1.18158 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5794.38 | 0.441972 | ||||||||
\(557\) | −8550.51 | −0.650443 | −0.325221 | − | 0.945638i | \(-0.605439\pi\) | ||||
−0.325221 | + | 0.945638i | \(0.605439\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −5909.35 | −0.445921 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1532.30 | −0.115011 | ||||||||
\(563\) | 6569.35 | 0.491768 | 0.245884 | − | 0.969299i | \(-0.420922\pi\) | ||||
0.245884 | + | 0.969299i | \(0.420922\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6425.85 | −0.478473 | ||||||||
\(566\) | 14108.5 | 1.04775 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −23329.8 | −1.72341 | ||||||||
\(569\) | −23766.1 | −1.75102 | −0.875508 | − | 0.483204i | \(-0.839473\pi\) | ||||
−0.875508 | + | 0.483204i | \(0.839473\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24971.7 | −1.83018 | −0.915091 | − | 0.403248i | \(-0.867881\pi\) | ||||
−0.915091 | + | 0.403248i | \(0.867881\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7447.41 | 0.541549 | ||||||||
\(575\) | −8495.48 | −0.616150 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16643.4 | 1.20082 | 0.600409 | − | 0.799693i | \(-0.295004\pi\) | ||||
0.600409 | + | 0.799693i | \(0.295004\pi\) | |||||||
\(578\) | 7835.28 | 0.563849 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8237.93 | 0.589761 | ||||||||
\(581\) | 3976.98 | 0.283981 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2469.64 | −0.175441 | ||||||||
\(584\) | −10605.7 | −0.751484 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4489.66 | −0.316495 | ||||||||
\(587\) | −6720.67 | −0.472558 | −0.236279 | − | 0.971685i | \(-0.575928\pi\) | ||||
−0.236279 | + | 0.971685i | \(0.575928\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32612.3 | −2.28144 | ||||||||
\(590\) | 9186.41 | 0.641014 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13592.8 | 0.943681 | ||||||||
\(593\) | 26349.8 | 1.82471 | 0.912357 | − | 0.409395i | \(-0.134260\pi\) | ||||
0.912357 | + | 0.409395i | \(0.134260\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14172.1 | −0.976466 | ||||||||
\(596\) | 3414.04 | 0.234638 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6136.81 | 0.418603 | 0.209302 | − | 0.977851i | \(-0.432881\pi\) | ||||
0.209302 | + | 0.977851i | \(0.432881\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12493.7 | 0.847966 | 0.423983 | − | 0.905670i | \(-0.360632\pi\) | ||||
0.423983 | + | 0.905670i | \(0.360632\pi\) | |||||||
\(602\) | −7056.14 | −0.477719 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2932.51 | 0.197553 | ||||||||
\(605\) | −17000.4 | −1.14242 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18696.6 | 1.25020 | 0.625099 | − | 0.780545i | \(-0.285059\pi\) | ||||
0.625099 | + | 0.780545i | \(0.285059\pi\) | |||||||
\(608\) | −12390.8 | −0.826501 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −33805.3 | −2.24383 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1238.64 | −0.0816123 | −0.0408062 | − | 0.999167i | \(-0.512993\pi\) | ||||
−0.0408062 | + | 0.999167i | \(0.512993\pi\) | |||||||
\(614\) | 4654.81 | 0.305949 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3758.89 | −0.245860 | ||||||||
\(617\) | 16549.5 | 1.07983 | 0.539917 | − | 0.841718i | \(-0.318456\pi\) | ||||
0.539917 | + | 0.841718i | \(0.318456\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13945.4 | −0.905513 | −0.452756 | − | 0.891634i | \(-0.649559\pi\) | ||||
−0.452756 | + | 0.891634i | \(0.649559\pi\) | |||||||
\(620\) | −10909.3 | −0.706656 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4445.17 | −0.286552 | ||||||||
\(623\) | 9928.03 | 0.638456 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17068.0 | −1.09235 | ||||||||
\(626\) | 10736.9 | 0.685513 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4038.23 | −0.256597 | ||||||||
\(629\) | 32598.8 | 2.06645 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15343.1 | −0.967987 | −0.483994 | − | 0.875072i | \(-0.660814\pi\) | ||||
−0.483994 | + | 0.875072i | \(0.660814\pi\) | |||||||
\(632\) | 12228.6 | 0.769663 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17826.4 | 1.11668 | ||||||||
\(635\) | −30054.2 | −1.87821 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7597.23 | −0.471438 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6807.51 | 0.420454 | ||||||||
\(641\) | −11067.7 | −0.681979 | −0.340989 | − | 0.940067i | \(-0.610762\pi\) | ||||
−0.340989 | + | 0.940067i | \(0.610762\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25118.7 | 1.54057 | 0.770284 | − | 0.637701i | \(-0.220115\pi\) | ||||
0.770284 | + | 0.637701i | \(0.220115\pi\) | |||||||
\(644\) | 1911.61 | 0.116969 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24442.9 | 1.48869 | ||||||||
\(647\) | 4447.03 | 0.270217 | 0.135109 | − | 0.990831i | \(-0.456862\pi\) | ||||
0.135109 | + | 0.990831i | \(0.456862\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3829.23 | 0.231603 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −331.537 | −0.0199141 | ||||||||
\(653\) | 19426.2 | 1.16418 | 0.582088 | − | 0.813126i | \(-0.302236\pi\) | ||||
0.582088 | + | 0.813126i | \(0.302236\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22723.1 | 1.35552 | ||||||||
\(656\) | −11861.0 | −0.705934 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7531.52 | −0.446215 | ||||||||
\(659\) | 14099.4 | 0.833438 | 0.416719 | − | 0.909035i | \(-0.363180\pi\) | ||||
0.416719 | + | 0.909035i | \(0.363180\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2754.25 | −0.162070 | −0.0810348 | − | 0.996711i | \(-0.525823\pi\) | ||||
−0.0810348 | + | 0.996711i | \(0.525823\pi\) | |||||||
\(662\) | 4080.93 | 0.239592 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9665.44 | −0.564898 | ||||||||
\(665\) | −17886.0 | −1.04299 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16275.3 | 0.944800 | ||||||||
\(668\) | 1222.06 | 0.0707828 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8692.83 | 0.501244 | ||||||||
\(671\) | −14091.3 | −0.810712 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11936.8 | 0.683700 | 0.341850 | − | 0.939754i | \(-0.388946\pi\) | ||||
0.341850 | + | 0.939754i | \(0.388946\pi\) | |||||||
\(674\) | −6362.53 | −0.363613 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10255.2 | 0.582186 | 0.291093 | − | 0.956695i | \(-0.405981\pi\) | ||||
0.291093 | + | 0.956695i | \(0.405981\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5606.46 | 0.316872 | ||||||||
\(680\) | 34443.0 | 1.94239 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10060.8 | 0.564880 | ||||||||
\(683\) | 10605.7 | 0.594169 | 0.297085 | − | 0.954851i | \(-0.403986\pi\) | ||||
0.297085 | + | 0.954851i | \(0.403986\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29269.2 | −1.63258 | ||||||||
\(686\) | −13873.1 | −0.772127 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11237.8 | 0.622728 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4660.14 | −0.256556 | −0.128278 | − | 0.991738i | \(-0.540945\pi\) | ||||
−0.128278 | + | 0.991738i | \(0.540945\pi\) | |||||||
\(692\) | 5000.90 | 0.274719 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5884.15 | 0.321844 | ||||||||
\(695\) | −35829.9 | −1.95555 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28445.4 | −1.54584 | ||||||||
\(698\) | −17690.2 | −0.959287 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2829.22 | −0.152764 | ||||||||
\(701\) | 24016.9 | 1.29402 | 0.647008 | − | 0.762483i | \(-0.276020\pi\) | ||||
0.647008 | + | 0.762483i | \(0.276020\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41141.7 | 2.20724 | ||||||||
\(704\) | 8387.88 | 0.449048 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21108.7 | −1.12527 | ||||||||
\(707\) | 7740.15 | 0.411737 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7252.56 | 0.384169 | 0.192084 | − | 0.981378i | \(-0.438475\pi\) | ||||
0.192084 | + | 0.981378i | \(0.438475\pi\) | |||||||
\(710\) | 34246.5 | 1.81021 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −24128.6 | −1.27002 | ||||||||
\(713\) | −21552.9 | −1.13207 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5360.66 | −0.279801 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10719.1 | −0.557151 | ||||||||
\(719\) | −10951.7 | −0.568050 | −0.284025 | − | 0.958817i | \(-0.591670\pi\) | ||||
−0.284025 | + | 0.958817i | \(0.591670\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1849.22 | 0.0955182 | ||||||||
\(722\) | 14748.6 | 0.760231 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2078.65 | −0.106702 | ||||||||
\(725\) | −24087.7 | −1.23393 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27856.0 | −1.42108 | −0.710538 | − | 0.703658i | \(-0.751549\pi\) | ||||
−0.710538 | + | 0.703658i | \(0.751549\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15568.4 | 0.789334 | ||||||||
\(731\) | 26951.0 | 1.36364 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31213.8 | 1.57286 | 0.786431 | − | 0.617678i | \(-0.211927\pi\) | ||||
0.786431 | + | 0.617678i | \(0.211927\pi\) | |||||||
\(734\) | −15138.7 | −0.761281 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8188.85 | −0.410116 | ||||||||
\(737\) | 3623.49 | 0.181103 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14423.1 | −0.717946 | −0.358973 | − | 0.933348i | \(-0.616873\pi\) | ||||
−0.358973 | + | 0.933348i | \(0.616873\pi\) | |||||||
\(740\) | 13762.5 | 0.683674 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3898.13 | −0.192864 | ||||||||
\(743\) | 13469.7 | 0.665079 | 0.332539 | − | 0.943089i | \(-0.392095\pi\) | ||||
0.332539 | + | 0.943089i | \(0.392095\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21111.0 | −1.03818 | ||||||||
\(746\) | 17954.0 | 0.881158 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3408.26 | 0.166602 | ||||||||
\(749\) | −1861.19 | −0.0907965 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32033.6 | −1.55649 | −0.778245 | − | 0.627961i | \(-0.783890\pi\) | ||||
−0.778245 | + | 0.627961i | \(0.783890\pi\) | |||||||
\(752\) | 11994.9 | 0.581661 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18133.4 | −0.874096 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26097.2 | −1.25300 | −0.626498 | − | 0.779423i | \(-0.715512\pi\) | ||||
−0.626498 | + | 0.779423i | \(0.715512\pi\) | |||||||
\(758\) | 24171.6 | 1.15825 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 43469.3 | 2.07473 | ||||||||
\(761\) | 18238.2 | 0.868772 | 0.434386 | − | 0.900727i | \(-0.356965\pi\) | ||||
0.434386 | + | 0.900727i | \(0.356965\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17978.0 | −0.853009 | ||||||||
\(764\) | 11118.6 | 0.526513 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24078.4 | 1.13575 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18817.0 | 0.882390 | 0.441195 | − | 0.897411i | \(-0.354555\pi\) | ||||
0.441195 | + | 0.897411i | \(0.354555\pi\) | |||||||
\(770\) | 5517.79 | 0.258243 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8217.67 | −0.383109 | ||||||||
\(773\) | −13795.6 | −0.641904 | −0.320952 | − | 0.947095i | \(-0.604003\pi\) | ||||
−0.320952 | + | 0.947095i | \(0.604003\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31898.7 | 1.47850 | ||||||||
\(776\) | −13625.6 | −0.630325 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11200.2 | 0.516126 | ||||||||
\(779\) | −35900.0 | −1.65116 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14275.2 | 0.654043 | ||||||||
\(782\) | 16153.9 | 0.738699 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9103.36 | 0.414694 | ||||||||
\(785\) | 24970.7 | 1.13534 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40545.4 | 1.83645 | 0.918227 | − | 0.396055i | \(-0.129621\pi\) | ||||
0.918227 | + | 0.396055i | \(0.129621\pi\) | |||||||
\(788\) | −7405.19 | −0.334770 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −17950.7 | −0.808429 | ||||||||
\(791\) | −4227.85 | −0.190044 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5378.11 | −0.240380 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13524.5 | 0.602214 | ||||||||
\(797\) | 31576.4 | 1.40338 | 0.701690 | − | 0.712482i | \(-0.252429\pi\) | ||||
0.701690 | + | 0.712482i | \(0.252429\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28766.7 | 1.27371 | ||||||||
\(800\) | 12119.7 | 0.535619 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17685.8 | 0.778688 | ||||||||
\(803\) | 6489.50 | 0.285192 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11820.6 | −0.517541 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18811.2 | −0.819031 | ||||||||
\(809\) | −31130.1 | −1.35287 | −0.676437 | − | 0.736501i | \(-0.736477\pi\) | ||||
−0.676437 | + | 0.736501i | \(0.736477\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8733.71 | 0.378153 | 0.189076 | − | 0.981962i | \(-0.439451\pi\) | ||||
0.189076 | + | 0.981962i | \(0.439451\pi\) | |||||||
\(812\) | 5420.10 | 0.234247 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12692.1 | −0.546509 | ||||||||
\(815\) | 2050.08 | 0.0881119 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34013.8 | 1.45654 | ||||||||
\(818\) | 3563.08 | 0.152298 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12009.0 | −0.511431 | ||||||||
\(821\) | −36960.1 | −1.57115 | −0.785576 | − | 0.618765i | \(-0.787633\pi\) | ||||
−0.785576 | + | 0.618765i | \(0.787633\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20509.7 | 0.868679 | 0.434340 | − | 0.900749i | \(-0.356982\pi\) | ||||
0.434340 | + | 0.900749i | \(0.356982\pi\) | |||||||
\(824\) | −4494.25 | −0.190006 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6044.15 | 0.254604 | ||||||||
\(827\) | −11533.4 | −0.484952 | −0.242476 | − | 0.970157i | \(-0.577960\pi\) | ||||
−0.242476 | + | 0.970157i | \(0.577960\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34096.4 | 1.42849 | 0.714244 | − | 0.699897i | \(-0.246771\pi\) | ||||
0.714244 | + | 0.699897i | \(0.246771\pi\) | |||||||
\(830\) | 14188.2 | 0.593350 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21832.1 | 0.908087 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7556.69 | −0.313186 | ||||||||
\(836\) | 4301.45 | 0.177953 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18968.2 | −0.781917 | ||||||||
\(839\) | −1855.42 | −0.0763484 | −0.0381742 | − | 0.999271i | \(-0.512154\pi\) | ||||
−0.0381742 | + | 0.999271i | \(0.512154\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21757.3 | 0.892094 | ||||||||
\(842\) | −18949.8 | −0.775599 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3058.75 | −0.124747 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11185.3 | −0.453757 | ||||||||
\(848\) | 6208.26 | 0.251406 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −23908.1 | −0.964755 | ||||||||
\(851\) | 27189.9 | 1.09525 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28668.7 | 1.15076 | 0.575380 | − | 0.817886i | \(-0.304854\pi\) | ||||
0.575380 | + | 0.817886i | \(0.304854\pi\) | |||||||
\(854\) | −22242.0 | −0.891224 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4523.35 | 0.180613 | ||||||||
\(857\) | −449.310 | −0.0179091 | −0.00895457 | − | 0.999960i | \(-0.502850\pi\) | ||||
−0.00895457 | + | 0.999960i | \(0.502850\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33466.9 | 1.32931 | 0.664654 | − | 0.747151i | \(-0.268579\pi\) | ||||
0.664654 | + | 0.747151i | \(0.268579\pi\) | |||||||
\(860\) | 11378.1 | 0.451151 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5261.14 | 0.207883 | ||||||||
\(863\) | −25097.5 | −0.989953 | −0.494976 | − | 0.868906i | \(-0.664823\pi\) | ||||
−0.494976 | + | 0.868906i | \(0.664823\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30923.4 | −1.21552 | ||||||||
\(866\) | 24031.0 | 0.942965 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7177.69 | −0.280676 | ||||||||
\(869\) | −7482.53 | −0.292091 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 43692.7 | 1.69681 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20387.3 | 0.789027 | ||||||||
\(875\) | −2007.73 | −0.0775698 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27015.2 | −1.04018 | −0.520090 | − | 0.854112i | \(-0.674101\pi\) | ||||
−0.520090 | + | 0.854112i | \(0.674101\pi\) | |||||||
\(878\) | −12714.4 | −0.488715 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8787.79 | −0.336632 | ||||||||
\(881\) | −48638.7 | −1.86002 | −0.930010 | − | 0.367534i | \(-0.880202\pi\) | ||||
−0.930010 | + | 0.367534i | \(0.880202\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25479.0 | −0.971048 | −0.485524 | − | 0.874223i | \(-0.661371\pi\) | ||||
−0.485524 | + | 0.874223i | \(0.661371\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5956.05 | 0.225843 | ||||||||
\(887\) | −42359.7 | −1.60350 | −0.801748 | − | 0.597663i | \(-0.796096\pi\) | ||||
−0.801748 | + | 0.597663i | \(0.796096\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19774.0 | −0.746005 | ||||||||
\(890\) | 35419.1 | 1.33399 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1706.51 | −0.0640561 | ||||||||
\(893\) | 36305.4 | 1.36049 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33148.1 | 1.23801 | ||||||||
\(896\) | 4478.96 | 0.167000 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18286.7 | 0.679548 | ||||||||
\(899\) | −61110.3 | −2.26712 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14888.9 | 0.550524 | ||||||||
\(902\) | 11075.0 | 0.408823 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10275.1 | 0.378038 | ||||||||
\(905\) | 12853.5 | 0.472114 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5314.91 | −0.194574 | −0.0972871 | − | 0.995256i | \(-0.531016\pi\) | ||||
−0.0972871 | + | 0.995256i | \(0.531016\pi\) | |||||||
\(908\) | −714.890 | −0.0261283 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2471.71 | −0.0898919 | −0.0449459 | − | 0.998989i | \(-0.514312\pi\) | ||||
−0.0449459 | + | 0.998989i | \(0.514312\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5914.17 | 0.214382 | ||||||||
\(914\) | −15491.3 | −0.560620 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5733.29 | −0.206805 | ||||||||
\(917\) | 14950.5 | 0.538396 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9636.13 | −0.345883 | −0.172942 | − | 0.984932i | \(-0.555327\pi\) | ||||
−0.172942 | + | 0.984932i | \(0.555327\pi\) | |||||||
\(920\) | 28728.1 | 1.02950 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10521.8 | 0.375832 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40241.5 | −1.43041 | ||||||||
\(926\) | 8933.38 | 0.317029 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23218.3 | −0.821314 | ||||||||
\(929\) | −53249.1 | −1.88057 | −0.940283 | − | 0.340394i | \(-0.889439\pi\) | ||||
−0.940283 | + | 0.340394i | \(0.889439\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27553.5 | 0.969955 | ||||||||
\(932\) | −2417.16 | −0.0849534 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34689.8 | −1.21530 | ||||||||
\(935\) | −21075.3 | −0.737149 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41122.6 | −1.43374 | −0.716871 | − | 0.697205i | \(-0.754427\pi\) | ||||
−0.716871 | + | 0.697205i | \(0.754427\pi\) | |||||||
\(938\) | 5719.40 | 0.199088 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12144.7 | 0.421399 | ||||||||
\(941\) | −8005.71 | −0.277342 | −0.138671 | − | 0.990339i | \(-0.544283\pi\) | ||||
−0.138671 | + | 0.990339i | \(0.544283\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23725.7 | −0.819315 | ||||||||
\(944\) | −9626.07 | −0.331888 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10493.2 | −0.360637 | ||||||||
\(947\) | −17468.6 | −0.599424 | −0.299712 | − | 0.954030i | \(-0.596891\pi\) | ||||
−0.299712 | + | 0.954030i | \(0.596891\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −30173.6 | −1.03048 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 22661.6 | 0.771498 | ||||||||
\(953\) | −30681.4 | −1.04288 | −0.521442 | − | 0.853287i | \(-0.674606\pi\) | ||||
−0.521442 | + | 0.853287i | \(0.674606\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −68752.5 | −2.32961 | ||||||||
\(956\) | 12470.0 | 0.421872 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26221.8 | 0.884328 | ||||||||
\(959\) | −19257.5 | −0.648444 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51135.6 | 1.71648 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1345.00 | −0.0449373 | ||||||||
\(965\) | 50814.5 | 1.69511 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15616.0 | −0.519313 | −0.259656 | − | 0.965701i | \(-0.583609\pi\) | ||||
−0.259656 | + | 0.965701i | \(0.583609\pi\) | |||||||
\(968\) | 27184.2 | 0.902617 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 20001.5 | 0.662072 | ||||||||
\(971\) | −7185.98 | −0.237496 | −0.118748 | − | 0.992924i | \(-0.537888\pi\) | ||||
−0.118748 | + | 0.992924i | \(0.537888\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23574.1 | −0.776723 | ||||||||
\(974\) | −14192.9 | −0.466911 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 35423.2 | 1.16175 | ||||||||
\(977\) | 33165.3 | 1.08603 | 0.543015 | − | 0.839723i | \(-0.317283\pi\) | ||||
0.543015 | + | 0.839723i | \(0.317283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14764.0 | 0.481980 | ||||||||
\(980\) | 9217.01 | 0.300435 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2429.52 | 0.0789502 | ||||||||
\(983\) | −11658.7 | −0.378287 | −0.189143 | − | 0.981949i | \(-0.560571\pi\) | ||||
−0.189143 | + | 0.981949i | \(0.560571\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 45790.5 | 1.48123 | ||||||||
\(986\) | 45802.1 | 1.47935 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22479.2 | 0.722746 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1957.32 | −0.0627409 | −0.0313704 | − | 0.999508i | \(-0.509987\pi\) | ||||
−0.0313704 | + | 0.999508i | \(0.509987\pi\) | |||||||
\(992\) | 30747.4 | 0.984104 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 22532.3 | 0.718996 | ||||||||
\(995\) | −83629.5 | −2.66456 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11434.8 | −0.363233 | −0.181617 | − | 0.983369i | \(-0.558133\pi\) | ||||
−0.181617 | + | 0.983369i | \(0.558133\pi\) | |||||||
\(998\) | 27459.0 | 0.870942 | ||||||||
\(999\) | 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 | 1521.4.a.bi.1.6 | 9 | ||
3.2 | odd | 2 | 507.4.a.o.1.4 | ✓ | 9 | ||
13.12 | even | 2 | 1521.4.a.bf.1.4 | 9 | |||
39.5 | even | 4 | 507.4.b.k.337.12 | 18 | |||
39.8 | even | 4 | 507.4.b.k.337.7 | 18 | |||
39.38 | odd | 2 | 507.4.a.p.1.6 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.4 | ✓ | 9 | 3.2 | odd | 2 | ||
507.4.a.p.1.6 | yes | 9 | 39.38 | odd | 2 | ||
507.4.b.k.337.7 | 18 | 39.8 | even | 4 | |||
507.4.b.k.337.12 | 18 | 39.5 | even | 4 | |||
1521.4.a.bf.1.4 | 9 | 13.12 | even | 2 | |||
1521.4.a.bi.1.6 | 9 | 1.1 | even | 1 | trivial |