Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
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: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.100291\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-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 | \(0.363802\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −2.49032 | −0.311290 | ||||||||
\(5\) | 15.3991 | 1.37734 | 0.688668 | − | 0.725077i | \(-0.258196\pi\) | ||||
0.688668 | + | 0.725077i | \(0.258196\pi\) | |||||||
\(6\) | 7.04181 | 0.479135 | ||||||||
\(7\) | −10.1317 | −0.547062 | −0.273531 | − | 0.961863i | \(-0.588192\pi\) | ||||
−0.273531 | + | 0.961863i | \(0.588192\pi\) | |||||||
\(8\) | −24.6236 | −1.08822 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 36.1458 | 1.14303 | ||||||||
\(11\) | 15.0669 | 0.412985 | 0.206493 | − | 0.978448i | \(-0.433795\pi\) | ||||
0.206493 | + | 0.978448i | \(0.433795\pi\) | |||||||
\(12\) | −7.47096 | −0.179723 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −23.7819 | −0.453999 | ||||||||
\(15\) | 46.1972 | 0.795205 | ||||||||
\(16\) | −37.8757 | −0.591809 | ||||||||
\(17\) | 90.8352 | 1.29593 | 0.647964 | − | 0.761671i | \(-0.275621\pi\) | ||||
0.647964 | + | 0.761671i | \(0.275621\pi\) | |||||||
\(18\) | 21.1254 | 0.276629 | ||||||||
\(19\) | 114.640 | 1.38422 | 0.692110 | − | 0.721792i | \(-0.256681\pi\) | ||||
0.692110 | + | 0.721792i | \(0.256681\pi\) | |||||||
\(20\) | −38.3486 | −0.428751 | ||||||||
\(21\) | −30.3952 | −0.315847 | ||||||||
\(22\) | 35.3661 | 0.342731 | ||||||||
\(23\) | 75.7635 | 0.686860 | 0.343430 | − | 0.939178i | \(-0.388411\pi\) | ||||
0.343430 | + | 0.939178i | \(0.388411\pi\) | |||||||
\(24\) | −73.8709 | −0.628284 | ||||||||
\(25\) | 112.132 | 0.897052 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 25.2313 | 0.170295 | ||||||||
\(29\) | 214.817 | 1.37553 | 0.687767 | − | 0.725931i | \(-0.258591\pi\) | ||||
0.687767 | + | 0.725931i | \(0.258591\pi\) | |||||||
\(30\) | 108.437 | 0.659929 | ||||||||
\(31\) | −284.476 | −1.64817 | −0.824087 | − | 0.566463i | \(-0.808311\pi\) | ||||
−0.824087 | + | 0.566463i | \(0.808311\pi\) | |||||||
\(32\) | 108.084 | 0.597087 | ||||||||
\(33\) | 45.2007 | 0.238437 | ||||||||
\(34\) | 213.215 | 1.07547 | ||||||||
\(35\) | −156.019 | −0.753488 | ||||||||
\(36\) | −22.4129 | −0.103763 | ||||||||
\(37\) | 358.878 | 1.59457 | 0.797286 | − | 0.603602i | \(-0.206268\pi\) | ||||
0.797286 | + | 0.603602i | \(0.206268\pi\) | |||||||
\(38\) | 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 | \(0.296589\pi\) | |||||||
\(42\) | −71.3458 | −0.262116 | ||||||||
\(43\) | −296.702 | −1.05225 | −0.526123 | − | 0.850409i | \(-0.676355\pi\) | ||||
−0.526123 | + | 0.850409i | \(0.676355\pi\) | |||||||
\(44\) | −37.5214 | −0.128558 | ||||||||
\(45\) | 138.592 | 0.459112 | ||||||||
\(46\) | 177.837 | 0.570015 | ||||||||
\(47\) | −316.691 | −0.982854 | −0.491427 | − | 0.870919i | \(-0.663525\pi\) | ||||
−0.491427 | + | 0.870919i | \(0.663525\pi\) | |||||||
\(48\) | −113.627 | −0.341681 | ||||||||
\(49\) | −240.348 | −0.700723 | ||||||||
\(50\) | 263.203 | 0.744451 | ||||||||
\(51\) | 272.506 | 0.748204 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 163.911 | 0.424810 | 0.212405 | − | 0.977182i | \(-0.431870\pi\) | ||||
0.212405 | + | 0.977182i | \(0.431870\pi\) | |||||||
\(54\) | 63.3763 | 0.159712 | ||||||||
\(55\) | 232.016 | 0.568819 | ||||||||
\(56\) | 249.480 | 0.595324 | ||||||||
\(57\) | 343.920 | 0.799180 | ||||||||
\(58\) | 504.233 | 1.14154 | ||||||||
\(59\) | 254.149 | 0.560803 | 0.280401 | − | 0.959883i | \(-0.409532\pi\) | ||||
0.280401 | + | 0.959883i | \(0.409532\pi\) | |||||||
\(60\) | −115.046 | −0.247539 | ||||||||
\(61\) | −935.247 | −1.96305 | −0.981526 | − | 0.191330i | \(-0.938720\pi\) | ||||
−0.981526 | + | 0.191330i | \(0.938720\pi\) | |||||||
\(62\) | −667.742 | −1.36780 | ||||||||
\(63\) | −91.1856 | −0.182354 | ||||||||
\(64\) | 556.709 | 1.08732 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 106.098 | 0.197876 | ||||||||
\(67\) | −240.494 | −0.438522 | −0.219261 | − | 0.975666i | \(-0.570365\pi\) | ||||
−0.219261 | + | 0.975666i | \(0.570365\pi\) | |||||||
\(68\) | −226.209 | −0.403409 | ||||||||
\(69\) | 227.291 | 0.396559 | ||||||||
\(70\) | −366.220 | −0.625309 | ||||||||
\(71\) | 947.455 | 1.58369 | 0.791847 | − | 0.610720i | \(-0.209120\pi\) | ||||
0.791847 | + | 0.610720i | \(0.209120\pi\) | |||||||
\(72\) | −221.613 | −0.362740 | ||||||||
\(73\) | −430.712 | −0.690562 | −0.345281 | − | 0.938499i | \(-0.612216\pi\) | ||||
−0.345281 | + | 0.938499i | \(0.612216\pi\) | |||||||
\(74\) | 842.384 | 1.32331 | ||||||||
\(75\) | 336.395 | 0.517913 | ||||||||
\(76\) | −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 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 735.058 | 0.989922 | ||||||||
\(83\) | 392.527 | 0.519102 | 0.259551 | − | 0.965729i | \(-0.416425\pi\) | ||||
0.259551 | + | 0.965729i | \(0.416425\pi\) | |||||||
\(84\) | 75.6938 | 0.0983199 | ||||||||
\(85\) | 1398.78 | 1.78493 | ||||||||
\(86\) | −696.439 | −0.873244 | ||||||||
\(87\) | 644.451 | 0.794165 | ||||||||
\(88\) | −371.002 | −0.449419 | ||||||||
\(89\) | 979.895 | 1.16706 | 0.583532 | − | 0.812090i | \(-0.301670\pi\) | ||||
0.583532 | + | 0.812090i | \(0.301670\pi\) | |||||||
\(90\) | 325.312 | 0.381010 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −188.675 | −0.213813 | ||||||||
\(93\) | −853.428 | −0.951574 | ||||||||
\(94\) | −743.360 | −0.815656 | ||||||||
\(95\) | 1765.35 | 1.90654 | ||||||||
\(96\) | 324.253 | 0.344729 | ||||||||
\(97\) | −553.356 | −0.579225 | −0.289613 | − | 0.957144i | \(-0.593526\pi\) | ||||
−0.289613 | + | 0.957144i | \(0.593526\pi\) | |||||||
\(98\) | −564.162 | −0.581520 | ||||||||
\(99\) | 135.602 | 0.137662 | ||||||||
\(100\) | −279.243 | −0.279243 | ||||||||
\(101\) | −763.951 | −0.752633 | −0.376317 | − | 0.926491i | \(-0.622810\pi\) | ||||
−0.376317 | + | 0.926491i | \(0.622810\pi\) | |||||||
\(102\) | 639.645 | 0.620924 | ||||||||
\(103\) | 182.518 | 0.174602 | 0.0873010 | − | 0.996182i | \(-0.472176\pi\) | ||||
0.0873010 | + | 0.996182i | \(0.472176\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −468.058 | −0.435027 | ||||||||
\(106\) | 384.744 | 0.352544 | ||||||||
\(107\) | 183.699 | 0.165971 | 0.0829855 | − | 0.996551i | \(-0.473554\pi\) | ||||
0.0829855 | + | 0.996551i | \(0.473554\pi\) | |||||||
\(108\) | −67.2386 | −0.0599078 | ||||||||
\(109\) | 1774.42 | 1.55925 | 0.779627 | − | 0.626244i | \(-0.215408\pi\) | ||||
0.779627 | + | 0.626244i | \(0.215408\pi\) | |||||||
\(110\) | 544.605 | 0.472055 | ||||||||
\(111\) | 1076.63 | 0.920627 | ||||||||
\(112\) | 383.747 | 0.323756 | ||||||||
\(113\) | 417.288 | 0.347391 | 0.173695 | − | 0.984799i | \(-0.444429\pi\) | ||||
0.173695 | + | 0.984799i | \(0.444429\pi\) | |||||||
\(114\) | 807.273 | 0.663228 | ||||||||
\(115\) | 1166.69 | 0.946037 | ||||||||
\(116\) | −534.963 | −0.428190 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 596.556 | 0.465402 | ||||||||
\(119\) | −920.318 | −0.708953 | ||||||||
\(120\) | −1137.54 | −0.865358 | ||||||||
\(121\) | −1103.99 | −0.829443 | ||||||||
\(122\) | −2195.28 | −1.62911 | ||||||||
\(123\) | 939.463 | 0.688687 | ||||||||
\(124\) | 708.436 | 0.513060 | ||||||||
\(125\) | −198.162 | −0.141793 | ||||||||
\(126\) | −214.037 | −0.151333 | ||||||||
\(127\) | −1951.69 | −1.36366 | −0.681828 | − | 0.731513i | \(-0.738815\pi\) | ||||
−0.681828 | + | 0.731513i | \(0.738815\pi\) | |||||||
\(128\) | 442.072 | 0.305266 | ||||||||
\(129\) | −890.105 | −0.607514 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1475.61 | −0.984159 | −0.492080 | − | 0.870550i | \(-0.663763\pi\) | ||||
−0.492080 | + | 0.870550i | \(0.663763\pi\) | |||||||
\(132\) | −112.564 | −0.0742231 | ||||||||
\(133\) | −1161.50 | −0.757255 | ||||||||
\(134\) | −564.503 | −0.363923 | ||||||||
\(135\) | 415.775 | 0.265068 | ||||||||
\(136\) | −2236.69 | −1.41026 | ||||||||
\(137\) | −1900.71 | −1.18532 | −0.592660 | − | 0.805453i | \(-0.701922\pi\) | ||||
−0.592660 | + | 0.805453i | \(0.701922\pi\) | |||||||
\(138\) | 533.512 | 0.329099 | ||||||||
\(139\) | −2326.76 | −1.41981 | −0.709903 | − | 0.704299i | \(-0.751261\pi\) | ||||
−0.709903 | + | 0.704299i | \(0.751261\pi\) | |||||||
\(140\) | 388.538 | 0.234553 | ||||||||
\(141\) | −950.073 | −0.567451 | ||||||||
\(142\) | 2223.93 | 1.31428 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −340.882 | −0.197270 | ||||||||
\(145\) | 3307.98 | 1.89457 | ||||||||
\(146\) | −1011.00 | −0.573088 | ||||||||
\(147\) | −721.044 | −0.404563 | ||||||||
\(148\) | −893.721 | −0.496374 | ||||||||
\(149\) | −1370.92 | −0.753761 | −0.376881 | − | 0.926262i | \(-0.623003\pi\) | ||||
−0.376881 | + | 0.926262i | \(0.623003\pi\) | |||||||
\(150\) | 789.609 | 0.429809 | ||||||||
\(151\) | 1177.57 | 0.634628 | 0.317314 | − | 0.948320i | \(-0.397219\pi\) | ||||
0.317314 | + | 0.948320i | \(0.397219\pi\) | |||||||
\(152\) | −2822.85 | −1.50634 | ||||||||
\(153\) | 817.517 | 0.431976 | ||||||||
\(154\) | −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 | ||||||||
\(159\) | 491.734 | 0.245264 | ||||||||
\(160\) | 1664.40 | 0.822389 | ||||||||
\(161\) | −767.616 | −0.375755 | ||||||||
\(162\) | 190.129 | 0.0922095 | ||||||||
\(163\) | −133.130 | −0.0639727 | −0.0319864 | − | 0.999488i | \(-0.510183\pi\) | ||||
−0.0319864 | + | 0.999488i | \(0.510183\pi\) | |||||||
\(164\) | −779.854 | −0.371320 | ||||||||
\(165\) | 696.049 | 0.328408 | ||||||||
\(166\) | 921.368 | 0.430795 | ||||||||
\(167\) | −490.724 | −0.227385 | −0.113693 | − | 0.993516i | \(-0.536268\pi\) | ||||
−0.113693 | + | 0.993516i | \(0.536268\pi\) | |||||||
\(168\) | 748.440 | 0.343711 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3283.31 | 1.48129 | ||||||||
\(171\) | 1031.76 | 0.461407 | ||||||||
\(172\) | 738.882 | 0.327554 | ||||||||
\(173\) | 2008.13 | 0.882518 | 0.441259 | − | 0.897380i | \(-0.354532\pi\) | ||||
0.441259 | + | 0.897380i | \(0.354532\pi\) | |||||||
\(174\) | 1512.70 | 0.659066 | ||||||||
\(175\) | −1136.09 | −0.490743 | ||||||||
\(176\) | −570.670 | −0.244408 | ||||||||
\(177\) | 762.446 | 0.323779 | ||||||||
\(178\) | 2300.08 | 0.968529 | ||||||||
\(179\) | −2152.60 | −0.898843 | −0.449421 | − | 0.893320i | \(-0.648370\pi\) | ||||
−0.449421 | + | 0.893320i | \(0.648370\pi\) | |||||||
\(180\) | −345.138 | −0.142917 | ||||||||
\(181\) | 834.690 | 0.342774 | 0.171387 | − | 0.985204i | \(-0.445175\pi\) | ||||
0.171387 | + | 0.985204i | \(0.445175\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2805.74 | −1.13337 | ||||||||
\(184\) | −1865.57 | −0.747455 | ||||||||
\(185\) | 5526.39 | 2.19626 | ||||||||
\(186\) | −2003.23 | −0.789697 | ||||||||
\(187\) | 1368.60 | 0.535200 | ||||||||
\(188\) | 788.662 | 0.305953 | ||||||||
\(189\) | −273.557 | −0.105282 | ||||||||
\(190\) | 4143.75 | 1.58221 | ||||||||
\(191\) | 4464.71 | 1.69139 | 0.845695 | − | 0.533667i | \(-0.179186\pi\) | ||||
0.845695 | + | 0.533667i | \(0.179186\pi\) | |||||||
\(192\) | 1670.13 | 0.627766 | ||||||||
\(193\) | −3299.84 | −1.23071 | −0.615357 | − | 0.788248i | \(-0.710988\pi\) | ||||
−0.615357 | + | 0.788248i | \(0.710988\pi\) | |||||||
\(194\) | −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 | \(0.319288\pi\) | |||||||
\(198\) | 318.295 | 0.114244 | ||||||||
\(199\) | −5430.82 | −1.93457 | −0.967287 | − | 0.253684i | \(-0.918358\pi\) | ||||
−0.967287 | + | 0.253684i | \(0.918358\pi\) | |||||||
\(200\) | −2761.08 | −0.976191 | ||||||||
\(201\) | −721.481 | −0.253181 | ||||||||
\(202\) | −1793.20 | −0.624600 | ||||||||
\(203\) | −2176.47 | −0.752503 | ||||||||
\(204\) | −678.626 | −0.232909 | ||||||||
\(205\) | 4822.29 | 1.64294 | ||||||||
\(206\) | 428.419 | 0.144900 | ||||||||
\(207\) | 681.872 | 0.228953 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1727.27 | 0.571663 | ||||||||
\(210\) | −1098.66 | −0.361022 | ||||||||
\(211\) | 1228.25 | 0.400742 | 0.200371 | − | 0.979720i | \(-0.435785\pi\) | ||||
0.200371 | + | 0.979720i | \(0.435785\pi\) | |||||||
\(212\) | −408.192 | −0.132239 | ||||||||
\(213\) | 2842.37 | 0.914346 | ||||||||
\(214\) | 431.192 | 0.137737 | ||||||||
\(215\) | −4568.93 | −1.44930 | ||||||||
\(216\) | −664.838 | −0.209428 | ||||||||
\(217\) | 2882.24 | 0.901654 | ||||||||
\(218\) | 4165.05 | 1.29400 | ||||||||
\(219\) | −1292.14 | −0.398696 | ||||||||
\(220\) | −577.795 | −0.177068 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2527.15 | 0.764015 | ||||||||
\(223\) | −685.256 | −0.205776 | −0.102888 | − | 0.994693i | \(-0.532808\pi\) | ||||
−0.102888 | + | 0.994693i | \(0.532808\pi\) | |||||||
\(224\) | −1095.08 | −0.326644 | ||||||||
\(225\) | 1009.18 | 0.299017 | ||||||||
\(226\) | 979.487 | 0.288294 | ||||||||
\(227\) | 287.067 | 0.0839354 | 0.0419677 | − | 0.999119i | \(-0.486637\pi\) | ||||
0.0419677 | + | 0.999119i | \(0.486637\pi\) | |||||||
\(228\) | −856.470 | −0.248777 | ||||||||
\(229\) | −2302.23 | −0.664347 | −0.332174 | − | 0.943218i | \(-0.607782\pi\) | ||||
−0.332174 | + | 0.943218i | \(0.607782\pi\) | |||||||
\(230\) | 2738.53 | 0.785102 | ||||||||
\(231\) | −457.961 | −0.130440 | ||||||||
\(232\) | −5289.57 | −1.49688 | ||||||||
\(233\) | −970.620 | −0.272908 | −0.136454 | − | 0.990646i | \(-0.543571\pi\) | ||||
−0.136454 | + | 0.990646i | \(0.543571\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4876.75 | −1.35372 | ||||||||
\(236\) | −632.912 | −0.174572 | ||||||||
\(237\) | −1489.86 | −0.408341 | ||||||||
\(238\) | −2160.24 | −0.588350 | ||||||||
\(239\) | −5007.40 | −1.35524 | −0.677619 | − | 0.735413i | \(-0.736988\pi\) | ||||
−0.677619 | + | 0.735413i | \(0.736988\pi\) | |||||||
\(240\) | −1749.75 | −0.470609 | ||||||||
\(241\) | −540.092 | −0.144358 | −0.0721792 | − | 0.997392i | \(-0.522995\pi\) | ||||
−0.0721792 | + | 0.997392i | \(0.522995\pi\) | |||||||
\(242\) | −2591.36 | −0.688343 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 2329.07 | 0.611078 | ||||||||
\(245\) | −3701.14 | −0.965130 | ||||||||
\(246\) | 2205.17 | 0.571531 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 7004.83 | 1.79358 | ||||||||
\(249\) | 1177.58 | 0.299704 | ||||||||
\(250\) | −465.141 | −0.117672 | ||||||||
\(251\) | −6087.80 | −1.53091 | −0.765455 | − | 0.643489i | \(-0.777486\pi\) | ||||
−0.765455 | + | 0.643489i | \(0.777486\pi\) | |||||||
\(252\) | 227.081 | 0.0567650 | ||||||||
\(253\) | 1141.52 | 0.283663 | ||||||||
\(254\) | −4581.14 | −1.13168 | ||||||||
\(255\) | 4196.34 | 1.03053 | ||||||||
\(256\) | −3416.01 | −0.833987 | ||||||||
\(257\) | −5096.34 | −1.23697 | −0.618484 | − | 0.785797i | \(-0.712253\pi\) | ||||
−0.618484 | + | 0.785797i | \(0.712253\pi\) | |||||||
\(258\) | −2089.32 | −0.504167 | ||||||||
\(259\) | −3636.06 | −0.872330 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1933.35 | 0.458511 | ||||||||
\(262\) | −3463.66 | −0.816739 | ||||||||
\(263\) | 3405.50 | 0.798450 | 0.399225 | − | 0.916853i | \(-0.369279\pi\) | ||||
0.399225 | + | 0.916853i | \(0.369279\pi\) | |||||||
\(264\) | −1113.00 | −0.259472 | ||||||||
\(265\) | 2524.08 | 0.585106 | ||||||||
\(266\) | −2726.36 | −0.628435 | ||||||||
\(267\) | 2939.68 | 0.673804 | ||||||||
\(268\) | 598.906 | 0.136507 | ||||||||
\(269\) | −2720.44 | −0.616611 | −0.308306 | − | 0.951287i | \(-0.599762\pi\) | ||||
−0.308306 | + | 0.951287i | \(0.599762\pi\) | |||||||
\(270\) | 975.937 | 0.219976 | ||||||||
\(271\) | 6954.27 | 1.55883 | 0.779413 | − | 0.626511i | \(-0.215518\pi\) | ||||
0.779413 | + | 0.626511i | \(0.215518\pi\) | |||||||
\(272\) | −3440.45 | −0.766941 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4461.49 | −0.983680 | ||||||||
\(275\) | 1689.47 | 0.370470 | ||||||||
\(276\) | −566.026 | −0.123445 | ||||||||
\(277\) | −6563.96 | −1.42379 | −0.711895 | − | 0.702286i | \(-0.752163\pi\) | ||||
−0.711895 | + | 0.702286i | \(0.752163\pi\) | |||||||
\(278\) | −5461.53 | −1.17828 | ||||||||
\(279\) | −2560.28 | −0.549392 | ||||||||
\(280\) | 3841.76 | 0.819961 | ||||||||
\(281\) | −652.800 | −0.138586 | −0.0692932 | − | 0.997596i | \(-0.522074\pi\) | ||||
−0.0692932 | + | 0.997596i | \(0.522074\pi\) | |||||||
\(282\) | −2230.08 | −0.470919 | ||||||||
\(283\) | 6010.62 | 1.26252 | 0.631262 | − | 0.775570i | \(-0.282537\pi\) | ||||
0.631262 | + | 0.775570i | \(0.282537\pi\) | |||||||
\(284\) | −2359.47 | −0.492988 | ||||||||
\(285\) | 5296.05 | 1.10074 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3172.80 | −0.652558 | ||||||||
\(288\) | 972.759 | 0.199029 | ||||||||
\(289\) | 3338.04 | 0.679430 | ||||||||
\(290\) | 7764.73 | 1.57228 | ||||||||
\(291\) | −1660.07 | −0.334416 | ||||||||
\(292\) | 1072.61 | 0.214965 | ||||||||
\(293\) | −1912.72 | −0.381372 | −0.190686 | − | 0.981651i | \(-0.561071\pi\) | ||||
−0.190686 | + | 0.981651i | \(0.561071\pi\) | |||||||
\(294\) | −1692.49 | −0.335741 | ||||||||
\(295\) | 3913.66 | 0.772413 | ||||||||
\(296\) | −8836.87 | −1.73525 | ||||||||
\(297\) | 406.806 | 0.0794791 | ||||||||
\(298\) | −3217.93 | −0.625535 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −837.730 | −0.161221 | ||||||||
\(301\) | 3006.10 | 0.575644 | ||||||||
\(302\) | 2764.06 | 0.526669 | ||||||||
\(303\) | −2291.85 | −0.434533 | ||||||||
\(304\) | −4342.07 | −0.819194 | ||||||||
\(305\) | −14401.9 | −2.70378 | ||||||||
\(306\) | 1918.93 | 0.358491 | ||||||||
\(307\) | −1983.07 | −0.368665 | −0.184332 | − | 0.982864i | \(-0.559012\pi\) | ||||
−0.184332 | + | 0.982864i | \(0.559012\pi\) | |||||||
\(308\) | 380.157 | 0.0703294 | ||||||||
\(309\) | 547.553 | 0.100807 | ||||||||
\(310\) | −10282.6 | −1.88391 | ||||||||
\(311\) | 1893.76 | 0.345291 | 0.172645 | − | 0.984984i | \(-0.444769\pi\) | ||||
0.172645 | + | 0.984984i | \(0.444769\pi\) | |||||||
\(312\) | 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 | ||||||||
\(315\) | −1404.17 | −0.251163 | ||||||||
\(316\) | 1236.74 | 0.220165 | ||||||||
\(317\) | 7594.53 | 1.34559 | 0.672794 | − | 0.739830i | \(-0.265094\pi\) | ||||
0.672794 | + | 0.739830i | \(0.265094\pi\) | |||||||
\(318\) | 1154.23 | 0.203541 | ||||||||
\(319\) | 3236.62 | 0.568076 | ||||||||
\(320\) | 8572.81 | 1.49761 | ||||||||
\(321\) | 551.098 | 0.0958234 | ||||||||
\(322\) | −1801.80 | −0.311834 | ||||||||
\(323\) | 10413.3 | 1.79385 | ||||||||
\(324\) | −201.716 | −0.0345878 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −312.492 | −0.0530901 | ||||||||
\(327\) | 5323.27 | 0.900236 | ||||||||
\(328\) | −7710.99 | −1.29807 | ||||||||
\(329\) | 3208.63 | 0.537682 | ||||||||
\(330\) | 1633.82 | 0.272541 | ||||||||
\(331\) | −1738.58 | −0.288705 | −0.144352 | − | 0.989526i | \(-0.546110\pi\) | ||||
−0.144352 | + | 0.989526i | \(0.546110\pi\) | |||||||
\(332\) | −977.519 | −0.161591 | ||||||||
\(333\) | 3229.90 | 0.531524 | ||||||||
\(334\) | −1151.86 | −0.188704 | ||||||||
\(335\) | −3703.38 | −0.603992 | ||||||||
\(336\) | 1151.24 | 0.186921 | ||||||||
\(337\) | −2710.61 | −0.438149 | −0.219074 | − | 0.975708i | \(-0.570304\pi\) | ||||
−0.219074 | + | 0.975708i | \(0.570304\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1251.86 | 0.200566 | ||||||||
\(340\) | −3483.41 | −0.555630 | ||||||||
\(341\) | −4286.17 | −0.680672 | ||||||||
\(342\) | 2421.82 | 0.382915 | ||||||||
\(343\) | 5910.33 | 0.930401 | ||||||||
\(344\) | 7305.87 | 1.14508 | ||||||||
\(345\) | 3500.06 | 0.546195 | ||||||||
\(346\) | 4713.63 | 0.732389 | ||||||||
\(347\) | −2506.81 | −0.387817 | −0.193908 | − | 0.981020i | \(-0.562116\pi\) | ||||
−0.193908 | + | 0.981020i | \(0.562116\pi\) | |||||||
\(348\) | −1604.89 | −0.247216 | ||||||||
\(349\) | 7536.48 | 1.15593 | 0.577963 | − | 0.816063i | \(-0.303848\pi\) | ||||
0.577963 | + | 0.816063i | \(0.303848\pi\) | |||||||
\(350\) | −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 | \(0.737138\pi\) | |||||||
\(354\) | 1789.67 | 0.268700 | ||||||||
\(355\) | 14589.9 | 2.18128 | ||||||||
\(356\) | −2440.25 | −0.363295 | ||||||||
\(357\) | −2760.96 | −0.409314 | ||||||||
\(358\) | −5052.74 | −0.745937 | ||||||||
\(359\) | −4566.64 | −0.671359 | −0.335679 | − | 0.941976i | \(-0.608966\pi\) | ||||
−0.335679 | + | 0.941976i | \(0.608966\pi\) | |||||||
\(360\) | −3412.63 | −0.499615 | ||||||||
\(361\) | 6283.31 | 0.916068 | ||||||||
\(362\) | 1959.24 | 0.284463 | ||||||||
\(363\) | −3311.97 | −0.478879 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6632.57 | −0.951136 | ||||||||
\(366\) | −6585.84 | −0.940566 | ||||||||
\(367\) | −6449.50 | −0.917332 | −0.458666 | − | 0.888609i | \(-0.651673\pi\) | ||||
−0.458666 | + | 0.888609i | \(0.651673\pi\) | |||||||
\(368\) | −2869.60 | −0.406490 | ||||||||
\(369\) | 2818.39 | 0.397614 | ||||||||
\(370\) | 12971.9 | 1.82264 | ||||||||
\(371\) | −1660.71 | −0.232398 | ||||||||
\(372\) | 2125.31 | 0.296215 | ||||||||
\(373\) | 7648.89 | 1.06178 | 0.530891 | − | 0.847440i | \(-0.321857\pi\) | ||||
0.530891 | + | 0.847440i | \(0.321857\pi\) | |||||||
\(374\) | 3212.49 | 0.444154 | ||||||||
\(375\) | −594.487 | −0.0818645 | ||||||||
\(376\) | 7798.08 | 1.06956 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −642.112 | −0.0873722 | ||||||||
\(379\) | −10297.8 | −1.39567 | −0.697837 | − | 0.716256i | \(-0.745854\pi\) | ||||
−0.697837 | + | 0.716256i | \(0.745854\pi\) | |||||||
\(380\) | −4396.28 | −0.593486 | ||||||||
\(381\) | −5855.06 | −0.787307 | ||||||||
\(382\) | 10479.9 | 1.40366 | ||||||||
\(383\) | 10258.0 | 1.36856 | 0.684282 | − | 0.729217i | \(-0.260116\pi\) | ||||
0.684282 | + | 0.729217i | \(0.260116\pi\) | |||||||
\(384\) | 1326.22 | 0.176245 | ||||||||
\(385\) | −2350.73 | −0.311180 | ||||||||
\(386\) | −7745.63 | −1.02135 | ||||||||
\(387\) | −2670.31 | −0.350749 | ||||||||
\(388\) | 1378.03 | 0.180307 | ||||||||
\(389\) | −4771.57 | −0.621924 | −0.310962 | − | 0.950422i | \(-0.600651\pi\) | ||||
−0.310962 | + | 0.950422i | \(0.600651\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6882.00 | 0.890122 | ||||||||
\(392\) | 5918.24 | 0.762541 | ||||||||
\(393\) | −4426.84 | −0.568205 | ||||||||
\(394\) | 6979.82 | 0.892483 | ||||||||
\(395\) | −7647.50 | −0.974145 | ||||||||
\(396\) | −337.693 | −0.0428528 | ||||||||
\(397\) | 2291.22 | 0.289655 | 0.144827 | − | 0.989457i | \(-0.453737\pi\) | ||||
0.144827 | + | 0.989457i | \(0.453737\pi\) | |||||||
\(398\) | −12747.6 | −1.60548 | ||||||||
\(399\) | −3484.50 | −0.437201 | ||||||||
\(400\) | −4247.07 | −0.530883 | ||||||||
\(401\) | 7534.63 | 0.938308 | 0.469154 | − | 0.883116i | \(-0.344559\pi\) | ||||
0.469154 | + | 0.883116i | \(0.344559\pi\) | |||||||
\(402\) | −1693.51 | −0.210111 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1902.48 | 0.234287 | ||||||||
\(405\) | 1247.33 | 0.153037 | ||||||||
\(406\) | −5108.76 | −0.624491 | ||||||||
\(407\) | 5407.18 | 0.658535 | ||||||||
\(408\) | −6710.08 | −0.814211 | ||||||||
\(409\) | −1517.97 | −0.183517 | −0.0917587 | − | 0.995781i | \(-0.529249\pi\) | ||||
−0.0917587 | + | 0.995781i | \(0.529249\pi\) | |||||||
\(410\) | 11319.2 | 1.36345 | ||||||||
\(411\) | −5702.14 | −0.684345 | ||||||||
\(412\) | −454.528 | −0.0543519 | ||||||||
\(413\) | −2574.97 | −0.306794 | ||||||||
\(414\) | 1600.54 | 0.190005 | ||||||||
\(415\) | 6044.56 | 0.714978 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6980.28 | −0.819726 | ||||||||
\(418\) | 4054.36 | 0.474415 | ||||||||
\(419\) | 8080.97 | 0.942199 | 0.471100 | − | 0.882080i | \(-0.343857\pi\) | ||||
0.471100 | + | 0.882080i | \(0.343857\pi\) | |||||||
\(420\) | 1165.61 | 0.135419 | ||||||||
\(421\) | 8073.13 | 0.934585 | 0.467293 | − | 0.884103i | \(-0.345229\pi\) | ||||
0.467293 | + | 0.884103i | \(0.345229\pi\) | |||||||
\(422\) | 2883.05 | 0.332570 | ||||||||
\(423\) | −2850.22 | −0.327618 | ||||||||
\(424\) | −4036.09 | −0.462287 | ||||||||
\(425\) | 10185.5 | 1.16252 | ||||||||
\(426\) | 6671.80 | 0.758803 | ||||||||
\(427\) | 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 | \(0.460027\pi\) | |||||||
\(432\) | −1022.65 | −0.113894 | ||||||||
\(433\) | 10237.9 | 1.13626 | 0.568130 | − | 0.822939i | \(-0.307667\pi\) | ||||
0.568130 | + | 0.822939i | \(0.307667\pi\) | |||||||
\(434\) | 6765.39 | 0.748270 | ||||||||
\(435\) | 9923.94 | 1.09383 | ||||||||
\(436\) | −4418.88 | −0.485380 | ||||||||
\(437\) | 8685.52 | 0.950766 | ||||||||
\(438\) | −3033.00 | −0.330872 | ||||||||
\(439\) | −5416.69 | −0.588894 | −0.294447 | − | 0.955668i | \(-0.595135\pi\) | ||||
−0.294447 | + | 0.955668i | \(0.595135\pi\) | |||||||
\(440\) | −5713.08 | −0.619001 | ||||||||
\(441\) | −2163.13 | −0.233574 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2537.44 | −0.272138 | −0.136069 | − | 0.990699i | \(-0.543447\pi\) | ||||
−0.136069 | + | 0.990699i | \(0.543447\pi\) | |||||||
\(444\) | −2681.16 | −0.286582 | ||||||||
\(445\) | 15089.5 | 1.60744 | ||||||||
\(446\) | −1608.48 | −0.170771 | ||||||||
\(447\) | −4112.77 | −0.435184 | ||||||||
\(448\) | −5640.43 | −0.594833 | ||||||||
\(449\) | 7790.61 | 0.818846 | 0.409423 | − | 0.912345i | \(-0.365730\pi\) | ||||
0.409423 | + | 0.912345i | \(0.365730\pi\) | |||||||
\(450\) | 2368.83 | 0.248150 | ||||||||
\(451\) | 4718.26 | 0.492626 | ||||||||
\(452\) | −1039.18 | −0.108139 | ||||||||
\(453\) | 3532.70 | 0.366403 | ||||||||
\(454\) | 673.825 | 0.0696568 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8468.55 | −0.869685 | ||||||||
\(457\) | 6599.71 | 0.675539 | 0.337770 | − | 0.941229i | \(-0.390328\pi\) | ||||
0.337770 | + | 0.941229i | \(0.390328\pi\) | |||||||
\(458\) | −5403.95 | −0.551332 | ||||||||
\(459\) | 2452.55 | 0.249401 | ||||||||
\(460\) | −2905.43 | −0.294492 | ||||||||
\(461\) | 4482.57 | 0.452872 | 0.226436 | − | 0.974026i | \(-0.427293\pi\) | ||||
0.226436 | + | 0.974026i | \(0.427293\pi\) | |||||||
\(462\) | −1074.96 | −0.108250 | ||||||||
\(463\) | −3805.86 | −0.382016 | −0.191008 | − | 0.981589i | \(-0.561176\pi\) | ||||
−0.191008 | + | 0.981589i | \(0.561176\pi\) | |||||||
\(464\) | −8136.35 | −0.814053 | ||||||||
\(465\) | −13142.0 | −1.31064 | ||||||||
\(466\) | −2278.31 | −0.226482 | ||||||||
\(467\) | 14778.8 | 1.46441 | 0.732207 | − | 0.681082i | \(-0.238490\pi\) | ||||
0.732207 | + | 0.681082i | \(0.238490\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2436.62 | 0.239899 | ||||||||
\(470\) | −11447.0 | −1.12343 | ||||||||
\(471\) | 4864.71 | 0.475911 | ||||||||
\(472\) | −6258.06 | −0.610277 | ||||||||
\(473\) | −4470.37 | −0.434562 | ||||||||
\(474\) | −3497.11 | −0.338877 | ||||||||
\(475\) | 12854.8 | 1.24172 | ||||||||
\(476\) | 2291.89 | 0.220690 | ||||||||
\(477\) | 1475.20 | 0.141603 | ||||||||
\(478\) | −11753.7 | −1.12469 | ||||||||
\(479\) | 11171.2 | 1.06560 | 0.532801 | − | 0.846240i | \(-0.321139\pi\) | ||||
0.532801 | + | 0.846240i | \(0.321139\pi\) | |||||||
\(480\) | 4993.20 | 0.474807 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1267.74 | −0.119801 | ||||||||
\(483\) | −2302.85 | −0.216942 | ||||||||
\(484\) | 2749.29 | 0.258197 | ||||||||
\(485\) | −8521.18 | −0.797787 | ||||||||
\(486\) | 570.387 | 0.0532372 | ||||||||
\(487\) | 6046.57 | 0.562621 | 0.281310 | − | 0.959617i | \(-0.409231\pi\) | ||||
0.281310 | + | 0.959617i | \(0.409231\pi\) | |||||||
\(488\) | 23029.2 | 2.13623 | ||||||||
\(489\) | −399.390 | −0.0369347 | ||||||||
\(490\) | −8687.57 | −0.800948 | ||||||||
\(491\) | −1035.04 | −0.0951338 | −0.0475669 | − | 0.998868i | \(-0.515147\pi\) | ||||
−0.0475669 | + | 0.998868i | \(0.515147\pi\) | |||||||
\(492\) | −2339.56 | −0.214381 | ||||||||
\(493\) | 19512.9 | 1.78259 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2088.15 | 0.189606 | ||||||||
\(496\) | 10774.7 | 0.975404 | ||||||||
\(497\) | −9599.37 | −0.866379 | ||||||||
\(498\) | 2764.10 | 0.248720 | ||||||||
\(499\) | −11698.3 | −1.04947 | −0.524736 | − | 0.851265i | \(-0.675836\pi\) | ||||
−0.524736 | + | 0.851265i | \(0.675836\pi\) | |||||||
\(500\) | 493.488 | 0.0441389 | ||||||||
\(501\) | −1472.17 | −0.131281 | ||||||||
\(502\) | −14289.7 | −1.27048 | ||||||||
\(503\) | −13552.0 | −1.20130 | −0.600651 | − | 0.799511i | \(-0.705092\pi\) | ||||
−0.600651 | + | 0.799511i | \(0.705092\pi\) | |||||||
\(504\) | 2245.32 | 0.198441 | ||||||||
\(505\) | −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 | \(0.429058\pi\) | |||||||
\(510\) | 9849.94 | 0.855221 | ||||||||
\(511\) | 4363.86 | 0.377781 | ||||||||
\(512\) | −11554.9 | −0.997380 | ||||||||
\(513\) | 3095.28 | 0.266393 | ||||||||
\(514\) | −11962.5 | −1.02654 | ||||||||
\(515\) | 2810.60 | 0.240486 | ||||||||
\(516\) | 2216.65 | 0.189113 | ||||||||
\(517\) | −4771.55 | −0.405904 | ||||||||
\(518\) | −8534.81 | −0.723934 | ||||||||
\(519\) | 6024.40 | 0.509522 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8493.73 | −0.714236 | −0.357118 | − | 0.934059i | \(-0.616241\pi\) | ||||
−0.357118 | + | 0.934059i | \(0.616241\pi\) | |||||||
\(522\) | 4538.10 | 0.380512 | ||||||||
\(523\) | −1384.53 | −0.115758 | −0.0578789 | − | 0.998324i | \(-0.518434\pi\) | ||||
−0.0578789 | + | 0.998324i | \(0.518434\pi\) | |||||||
\(524\) | 3674.75 | 0.306359 | ||||||||
\(525\) | −3408.26 | −0.283331 | ||||||||
\(526\) | 7993.64 | 0.662622 | ||||||||
\(527\) | −25840.4 | −2.13592 | ||||||||
\(528\) | −1712.01 | −0.141109 | ||||||||
\(529\) | −6426.89 | −0.528223 | ||||||||
\(530\) | 5924.71 | 0.485571 | ||||||||
\(531\) | 2287.34 | 0.186934 | ||||||||
\(532\) | 2892.51 | 0.235726 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6900.24 | 0.559181 | ||||||||
\(535\) | 2828.80 | 0.228598 | ||||||||
\(536\) | 5921.82 | 0.477208 | ||||||||
\(537\) | −6457.80 | −0.518947 | ||||||||
\(538\) | −6385.62 | −0.511717 | ||||||||
\(539\) | −3621.30 | −0.289388 | ||||||||
\(540\) | −1035.41 | −0.0825131 | ||||||||
\(541\) | 5026.83 | 0.399483 | 0.199742 | − | 0.979849i | \(-0.435990\pi\) | ||||
0.199742 | + | 0.979849i | \(0.435990\pi\) | |||||||
\(542\) | 16323.6 | 1.29365 | ||||||||
\(543\) | 2504.07 | 0.197900 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | −8417.23 | −0.654351 | ||||||||
\(550\) | 3965.65 | 0.307447 | ||||||||
\(551\) | 24626.6 | 1.90404 | ||||||||
\(552\) | −5596.72 | −0.431544 | ||||||||
\(553\) | 5031.63 | 0.386920 | ||||||||
\(554\) | −15407.4 | −1.18158 | ||||||||
\(555\) | 16579.2 | 1.26801 | ||||||||
\(556\) | 5794.38 | 0.441972 | ||||||||
\(557\) | −8550.51 | −0.650443 | −0.325221 | − | 0.945638i | \(-0.605439\pi\) | ||||
−0.325221 | + | 0.945638i | \(0.605439\pi\) | |||||||
\(558\) | −6009.68 | −0.455932 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 5909.35 | 0.445921 | ||||||||
\(561\) | 4105.81 | 0.308998 | ||||||||
\(562\) | −1532.30 | −0.115011 | ||||||||
\(563\) | −6569.35 | −0.491768 | −0.245884 | − | 0.969299i | \(-0.579078\pi\) | ||||
−0.245884 | + | 0.969299i | \(0.579078\pi\) | |||||||
\(564\) | 2365.99 | 0.176642 | ||||||||
\(565\) | 6425.85 | 0.478473 | ||||||||
\(566\) | 14108.5 | 1.04775 | ||||||||
\(567\) | −820.671 | −0.0607847 | ||||||||
\(568\) | −23329.8 | −1.72341 | ||||||||
\(569\) | 23766.1 | 1.75102 | 0.875508 | − | 0.483204i | \(-0.160527\pi\) | ||||
0.875508 | + | 0.483204i | \(0.160527\pi\) | |||||||
\(570\) | 12431.3 | 0.913488 | ||||||||
\(571\) | −24971.7 | −1.83018 | −0.915091 | − | 0.403248i | \(-0.867881\pi\) | ||||
−0.915091 | + | 0.403248i | \(0.867881\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13394.1 | 0.976524 | ||||||||
\(574\) | −7447.41 | −0.541549 | ||||||||
\(575\) | 8495.48 | 0.616150 | ||||||||
\(576\) | 5010.38 | 0.362441 | ||||||||
\(577\) | −16643.4 | −1.20082 | −0.600409 | − | 0.799693i | \(-0.704996\pi\) | ||||
−0.600409 | + | 0.799693i | \(0.704996\pi\) | |||||||
\(578\) | 7835.28 | 0.563849 | ||||||||
\(579\) | −9899.53 | −0.710553 | ||||||||
\(580\) | −8237.93 | −0.589761 | ||||||||
\(581\) | −3976.98 | −0.283981 | ||||||||
\(582\) | −3896.63 | −0.277527 | ||||||||
\(583\) | 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 | \(0.575928\pi\) | |||||||
\(588\) | 1795.63 | 0.125936 | ||||||||
\(589\) | −32612.3 | −2.28144 | ||||||||
\(590\) | 9186.41 | 0.641014 | ||||||||
\(591\) | 8920.77 | 0.620899 | ||||||||
\(592\) | −13592.8 | −0.943681 | ||||||||
\(593\) | 26349.8 | 1.82471 | 0.912357 | − | 0.409395i | \(-0.134260\pi\) | ||||
0.912357 | + | 0.409395i | \(0.134260\pi\) | |||||||
\(594\) | 954.884 | 0.0659586 | ||||||||
\(595\) | −14172.1 | −0.976466 | ||||||||
\(596\) | 3414.04 | 0.234638 | ||||||||
\(597\) | −16292.4 | −1.11693 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6136.81 | −0.418603 | −0.209302 | − | 0.977851i | \(-0.567119\pi\) | ||||
−0.209302 | + | 0.977851i | \(0.567119\pi\) | |||||||
\(600\) | −8283.25 | −0.563604 | ||||||||
\(601\) | 12493.7 | 0.847966 | 0.423983 | − | 0.905670i | \(-0.360632\pi\) | ||||
0.423983 | + | 0.905670i | \(0.360632\pi\) | |||||||
\(602\) | 7056.14 | 0.477719 | ||||||||
\(603\) | −2164.44 | −0.146174 | ||||||||
\(604\) | −2932.51 | −0.197553 | ||||||||
\(605\) | −17000.4 | −1.14242 | ||||||||
\(606\) | −5379.60 | −0.360613 | ||||||||
\(607\) | 18696.6 | 1.25020 | 0.625099 | − | 0.780545i | \(-0.285059\pi\) | ||||
0.625099 | + | 0.780545i | \(0.285059\pi\) | |||||||
\(608\) | 12390.8 | 0.826501 | ||||||||
\(609\) | −6529.40 | −0.434458 | ||||||||
\(610\) | −33805.3 | −2.24383 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2035.88 | −0.134470 | ||||||||
\(613\) | 1238.64 | 0.0816123 | 0.0408062 | − | 0.999167i | \(-0.487007\pi\) | ||||
0.0408062 | + | 0.999167i | \(0.487007\pi\) | |||||||
\(614\) | −4654.81 | −0.305949 | ||||||||
\(615\) | 14466.9 | 0.948553 | ||||||||
\(616\) | 3758.89 | 0.245860 | ||||||||
\(617\) | 16549.5 | 1.07983 | 0.539917 | − | 0.841718i | \(-0.318456\pi\) | ||||
0.539917 | + | 0.841718i | \(0.318456\pi\) | |||||||
\(618\) | 1285.26 | 0.0836579 | ||||||||
\(619\) | 13945.4 | 0.905513 | 0.452756 | − | 0.891634i | \(-0.350441\pi\) | ||||
0.452756 | + | 0.891634i | \(0.350441\pi\) | |||||||
\(620\) | 10909.3 | 0.706656 | ||||||||
\(621\) | 2045.62 | 0.132186 | ||||||||
\(622\) | 4445.17 | 0.286552 | ||||||||
\(623\) | −9928.03 | −0.638456 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17068.0 | −1.09235 | ||||||||
\(626\) | 10736.9 | 0.685513 | ||||||||
\(627\) | 5181.80 | 0.330050 | ||||||||
\(628\) | −4038.23 | −0.256597 | ||||||||
\(629\) | 32598.8 | 2.06645 | ||||||||
\(630\) | −3295.98 | −0.208436 | ||||||||
\(631\) | 15343.1 | 0.967987 | 0.483994 | − | 0.875072i | \(-0.339186\pi\) | ||||
0.483994 | + | 0.875072i | \(0.339186\pi\) | |||||||
\(632\) | 12228.6 | 0.769663 | ||||||||
\(633\) | 3684.76 | 0.231368 | ||||||||
\(634\) | 17826.4 | 1.11668 | ||||||||
\(635\) | −30054.2 | −1.87821 | ||||||||
\(636\) | −1224.58 | −0.0763484 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7597.23 | 0.471438 | ||||||||
\(639\) | 8527.10 | 0.527898 | ||||||||
\(640\) | 6807.51 | 0.420454 | ||||||||
\(641\) | 11067.7 | 0.681979 | 0.340989 | − | 0.940067i | \(-0.389238\pi\) | ||||
0.340989 | + | 0.940067i | \(0.389238\pi\) | |||||||
\(642\) | 1293.58 | 0.0795224 | ||||||||
\(643\) | −25118.7 | −1.54057 | −0.770284 | − | 0.637701i | \(-0.779885\pi\) | ||||
−0.770284 | + | 0.637701i | \(0.779885\pi\) | |||||||
\(644\) | 1911.61 | 0.116969 | ||||||||
\(645\) | −13706.8 | −0.836751 | ||||||||
\(646\) | 24442.9 | 1.48869 | ||||||||
\(647\) | −4447.03 | −0.270217 | −0.135109 | − | 0.990831i | \(-0.543138\pi\) | ||||
−0.135109 | + | 0.990831i | \(0.543138\pi\) | |||||||
\(648\) | −1994.51 | −0.120913 | ||||||||
\(649\) | 3829.23 | 0.231603 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8646.71 | 0.520570 | ||||||||
\(652\) | 331.537 | 0.0199141 | ||||||||
\(653\) | −19426.2 | −1.16418 | −0.582088 | − | 0.813126i | \(-0.697764\pi\) | ||||
−0.582088 | + | 0.813126i | \(0.697764\pi\) | |||||||
\(654\) | 12495.1 | 0.747093 | ||||||||
\(655\) | −22723.1 | −1.35552 | ||||||||
\(656\) | −11861.0 | −0.705934 | ||||||||
\(657\) | −3876.41 | −0.230187 | ||||||||
\(658\) | 7531.52 | 0.446215 | ||||||||
\(659\) | −14099.4 | −0.833438 | −0.416719 | − | 0.909035i | \(-0.636820\pi\) | ||||
−0.416719 | + | 0.909035i | \(0.636820\pi\) | |||||||
\(660\) | −1733.38 | −0.102230 | ||||||||
\(661\) | 2754.25 | 0.162070 | 0.0810348 | − | 0.996711i | \(-0.474177\pi\) | ||||
0.0810348 | + | 0.996711i | \(0.474177\pi\) | |||||||
\(662\) | −4080.93 | −0.239592 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9665.44 | −0.564898 | ||||||||
\(665\) | −17886.0 | −1.04299 | ||||||||
\(666\) | 7581.45 | 0.441104 | ||||||||
\(667\) | 16275.3 | 0.944800 | ||||||||
\(668\) | 1222.06 | 0.0707828 | ||||||||
\(669\) | −2055.77 | −0.118805 | ||||||||
\(670\) | −8692.83 | −0.501244 | ||||||||
\(671\) | −14091.3 | −0.810712 | ||||||||
\(672\) | −3285.25 | −0.188588 | ||||||||
\(673\) | 11936.8 | 0.683700 | 0.341850 | − | 0.939754i | \(-0.388946\pi\) | ||||
0.341850 | + | 0.939754i | \(0.388946\pi\) | |||||||
\(674\) | −6362.53 | −0.363613 | ||||||||
\(675\) | 3027.55 | 0.172638 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10255.2 | −0.582186 | −0.291093 | − | 0.956695i | \(-0.594019\pi\) | ||||
−0.291093 | + | 0.956695i | \(0.594019\pi\) | |||||||
\(678\) | 2938.46 | 0.166447 | ||||||||
\(679\) | 5606.46 | 0.316872 | ||||||||
\(680\) | −34443.0 | −1.94239 | ||||||||
\(681\) | 861.202 | 0.0484601 | ||||||||
\(682\) | −10060.8 | −0.564880 | ||||||||
\(683\) | 10605.7 | 0.594169 | 0.297085 | − | 0.954851i | \(-0.403986\pi\) | ||||
0.297085 | + | 0.954851i | \(0.403986\pi\) | |||||||
\(684\) | −2569.41 | −0.143631 | ||||||||
\(685\) | −29269.2 | −1.63258 | ||||||||
\(686\) | 13873.1 | 0.772127 | ||||||||
\(687\) | −6906.69 | −0.383561 | ||||||||
\(688\) | 11237.8 | 0.622728 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 8215.60 | 0.453279 | ||||||||
\(691\) | 4660.14 | 0.256556 | 0.128278 | − | 0.991738i | \(-0.459055\pi\) | ||||
0.128278 | + | 0.991738i | \(0.459055\pi\) | |||||||
\(692\) | −5000.90 | −0.274719 | ||||||||
\(693\) | −1373.88 | −0.0753096 | ||||||||
\(694\) | −5884.15 | −0.321844 | ||||||||
\(695\) | −35829.9 | −1.95555 | ||||||||
\(696\) | −15868.7 | −0.864227 | ||||||||
\(697\) | 28445.4 | 1.54584 | ||||||||
\(698\) | 17690.2 | 0.959287 | ||||||||
\(699\) | −2911.86 | −0.157563 | ||||||||
\(700\) | 2829.22 | 0.152764 | ||||||||
\(701\) | −24016.9 | −1.29402 | −0.647008 | − | 0.762483i | \(-0.723980\pi\) | ||||
−0.647008 | + | 0.762483i | \(0.723980\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41141.7 | 2.20724 | ||||||||
\(704\) | 8387.88 | 0.449048 | ||||||||
\(705\) | −14630.2 | −0.781570 | ||||||||
\(706\) | −21108.7 | −1.12527 | ||||||||
\(707\) | 7740.15 | 0.411737 | ||||||||
\(708\) | −1898.74 | −0.100789 | ||||||||
\(709\) | −7252.56 | −0.384169 | −0.192084 | − | 0.981378i | \(-0.561525\pi\) | ||||
−0.192084 | + | 0.981378i | \(0.561525\pi\) | |||||||
\(710\) | 34246.5 | 1.81021 | ||||||||
\(711\) | −4469.58 | −0.235756 | ||||||||
\(712\) | −24128.6 | −1.27002 | ||||||||
\(713\) | −21552.9 | −1.13207 | ||||||||
\(714\) | −6480.71 | −0.339684 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5360.66 | 0.279801 | ||||||||
\(717\) | −15022.2 | −0.782447 | ||||||||
\(718\) | −10719.1 | −0.557151 | ||||||||
\(719\) | 10951.7 | 0.568050 | 0.284025 | − | 0.958817i | \(-0.408330\pi\) | ||||
0.284025 | + | 0.958817i | \(0.408330\pi\) | |||||||
\(720\) | −5249.26 | −0.271706 | ||||||||
\(721\) | −1849.22 | −0.0955182 | ||||||||
\(722\) | 14748.6 | 0.760231 | ||||||||
\(723\) | −1620.28 | −0.0833454 | ||||||||
\(724\) | −2078.65 | −0.106702 | ||||||||
\(725\) | 24087.7 | 1.23393 | ||||||||
\(726\) | −7774.08 | −0.397415 | ||||||||
\(727\) | −27856.0 | −1.42108 | −0.710538 | − | 0.703658i | \(-0.751549\pi\) | ||||
−0.710538 | + | 0.703658i | \(0.751549\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −15568.4 | −0.789334 | ||||||||
\(731\) | −26951.0 | −1.36364 | ||||||||
\(732\) | 6987.20 | 0.352806 | ||||||||
\(733\) | −31213.8 | −1.57286 | −0.786431 | − | 0.617678i | \(-0.788073\pi\) | ||||
−0.786431 | + | 0.617678i | \(0.788073\pi\) | |||||||
\(734\) | −15138.7 | −0.761281 | ||||||||
\(735\) | −11103.4 | −0.557218 | ||||||||
\(736\) | 8188.85 | 0.410116 | ||||||||
\(737\) | −3623.49 | −0.181103 | ||||||||
\(738\) | 6615.52 | 0.329974 | ||||||||
\(739\) | 14423.1 | 0.717946 | 0.358973 | − | 0.933348i | \(-0.383127\pi\) | ||||
0.358973 | + | 0.933348i | \(0.383127\pi\) | |||||||
\(740\) | −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 | \(0.392095\pi\) | |||||||
\(744\) | 21014.5 | 1.03552 | ||||||||
\(745\) | −21111.0 | −1.03818 | ||||||||
\(746\) | 17954.0 | 0.881158 | ||||||||
\(747\) | 3532.75 | 0.173034 | ||||||||
\(748\) | −3408.26 | −0.166602 | ||||||||
\(749\) | −1861.19 | −0.0907965 | ||||||||
\(750\) | −1395.42 | −0.0679381 | ||||||||
\(751\) | −32033.6 | −1.55649 | −0.778245 | − | 0.627961i | \(-0.783890\pi\) | ||||
−0.778245 | + | 0.627961i | \(0.783890\pi\) | |||||||
\(752\) | 11994.9 | 0.581661 | ||||||||
\(753\) | −18263.4 | −0.883871 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18133.4 | 0.874096 | ||||||||
\(756\) | 681.244 | 0.0327733 | ||||||||
\(757\) | −26097.2 | −1.25300 | −0.626498 | − | 0.779423i | \(-0.715512\pi\) | ||||
−0.626498 | + | 0.779423i | \(0.715512\pi\) | |||||||
\(758\) | −24171.6 | −1.15825 | ||||||||
\(759\) | 3424.56 | 0.163773 | ||||||||
\(760\) | −43469.3 | −2.07473 | ||||||||
\(761\) | 18238.2 | 0.868772 | 0.434386 | − | 0.900727i | \(-0.356965\pi\) | ||||
0.434386 | + | 0.900727i | \(0.356965\pi\) | |||||||
\(762\) | −13743.4 | −0.653375 | ||||||||
\(763\) | −17978.0 | −0.853009 | ||||||||
\(764\) | −11118.6 | −0.526513 | ||||||||
\(765\) | 12589.0 | 0.594976 | ||||||||
\(766\) | 24078.4 | 1.13575 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −10248.0 | −0.481502 | ||||||||
\(769\) | −18817.0 | −0.882390 | −0.441195 | − | 0.897411i | \(-0.645445\pi\) | ||||
−0.441195 | + | 0.897411i | \(0.645445\pi\) | |||||||
\(770\) | −5517.79 | −0.258243 | ||||||||
\(771\) | −15289.0 | −0.714164 | ||||||||
\(772\) | 8217.67 | 0.383109 | ||||||||
\(773\) | −13795.6 | −0.641904 | −0.320952 | − | 0.947095i | \(-0.604003\pi\) | ||||
−0.320952 | + | 0.947095i | \(0.604003\pi\) | |||||||
\(774\) | −6267.95 | −0.291081 | ||||||||
\(775\) | −31898.7 | −1.47850 | ||||||||
\(776\) | 13625.6 | 0.630325 | ||||||||
\(777\) | −10908.2 | −0.503640 | ||||||||
\(778\) | −11200.2 | −0.516126 | ||||||||
\(779\) | 35900.0 | 1.65116 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14275.2 | 0.654043 | ||||||||
\(782\) | 16153.9 | 0.738699 | ||||||||
\(783\) | 5800.05 | 0.264722 | ||||||||
\(784\) | 9103.36 | 0.414694 | ||||||||
\(785\) | 24970.7 | 1.13534 | ||||||||
\(786\) | −10391.0 | −0.471545 | ||||||||
\(787\) | −40545.4 | −1.83645 | −0.918227 | − | 0.396055i | \(-0.870379\pi\) | ||||
−0.918227 | + | 0.396055i | \(0.870379\pi\) | |||||||
\(788\) | −7405.19 | −0.334770 | ||||||||
\(789\) | 10216.5 | 0.460985 | ||||||||
\(790\) | −17950.7 | −0.808429 | ||||||||
\(791\) | −4227.85 | −0.190044 | ||||||||
\(792\) | −3339.01 | −0.149806 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 5378.11 | 0.240380 | ||||||||
\(795\) | 7572.25 | 0.337811 | ||||||||
\(796\) | 13524.5 | 0.602214 | ||||||||
\(797\) | −31576.4 | −1.40338 | −0.701690 | − | 0.712482i | \(-0.747571\pi\) | ||||
−0.701690 | + | 0.712482i | \(0.747571\pi\) | |||||||
\(798\) | −8179.07 | −0.362827 | ||||||||
\(799\) | −28766.7 | −1.27371 | ||||||||
\(800\) | 12119.7 | 0.535619 | ||||||||
\(801\) | 8819.05 | 0.389021 | ||||||||
\(802\) | 17685.8 | 0.778688 | ||||||||
\(803\) | −6489.50 | −0.285192 | ||||||||
\(804\) | 1796.72 | 0.0788126 | ||||||||
\(805\) | −11820.6 | −0.517541 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8161.33 | −0.356001 | ||||||||
\(808\) | 18811.2 | 0.819031 | ||||||||
\(809\) | 31130.1 | 1.35287 | 0.676437 | − | 0.736501i | \(-0.263523\pi\) | ||||
0.676437 | + | 0.736501i | \(0.263523\pi\) | |||||||
\(810\) | 2927.81 | 0.127003 | ||||||||
\(811\) | −8733.71 | −0.378153 | −0.189076 | − | 0.981962i | \(-0.560549\pi\) | ||||
−0.189076 | + | 0.981962i | \(0.560549\pi\) | |||||||
\(812\) | 5420.10 | 0.234247 | ||||||||
\(813\) | 20862.8 | 0.899988 | ||||||||
\(814\) | 12692.1 | 0.546509 | ||||||||
\(815\) | −2050.08 | −0.0881119 | ||||||||
\(816\) | −10321.4 | −0.442794 | ||||||||
\(817\) | −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 | \(0.787633\pi\) | |||||||
\(822\) | −13384.5 | −0.567928 | ||||||||
\(823\) | 20509.7 | 0.868679 | 0.434340 | − | 0.900749i | \(-0.356982\pi\) | ||||
0.434340 | + | 0.900749i | \(0.356982\pi\) | |||||||
\(824\) | −4494.25 | −0.190006 | ||||||||
\(825\) | 5068.42 | 0.213891 | ||||||||
\(826\) | −6044.15 | −0.254604 | ||||||||
\(827\) | −11533.4 | −0.484952 | −0.242476 | − | 0.970157i | \(-0.577960\pi\) | ||||
−0.242476 | + | 0.970157i | \(0.577960\pi\) | |||||||
\(828\) | −1698.08 | −0.0712709 | ||||||||
\(829\) | 34096.4 | 1.42849 | 0.714244 | − | 0.699897i | \(-0.246771\pi\) | ||||
0.714244 | + | 0.699897i | \(0.246771\pi\) | |||||||
\(830\) | 14188.2 | 0.593350 | ||||||||
\(831\) | −19691.9 | −0.822026 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21832.1 | −0.908087 | ||||||||
\(834\) | −16384.6 | −0.680279 | ||||||||
\(835\) | −7556.69 | −0.313186 | ||||||||
\(836\) | −4301.45 | −0.177953 | ||||||||
\(837\) | −7680.85 | −0.317191 | ||||||||
\(838\) | 18968.2 | 0.781917 | ||||||||
\(839\) | −1855.42 | −0.0763484 | −0.0381742 | − | 0.999271i | \(-0.512154\pi\) | ||||
−0.0381742 | + | 0.999271i | \(0.512154\pi\) | |||||||
\(840\) | 11525.3 | 0.473405 | ||||||||
\(841\) | 21757.3 | 0.892094 | ||||||||
\(842\) | 18949.8 | 0.775599 | ||||||||
\(843\) | −1958.40 | −0.0800129 | ||||||||
\(844\) | −3058.75 | −0.124747 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6690.24 | −0.271885 | ||||||||
\(847\) | 11185.3 | 0.453757 | ||||||||
\(848\) | −6208.26 | −0.251406 | ||||||||
\(849\) | 18031.9 | 0.728918 | ||||||||
\(850\) | 23908.1 | 0.964755 | ||||||||
\(851\) | 27189.9 | 1.09525 | ||||||||
\(852\) | −7078.40 | −0.284627 | ||||||||
\(853\) | −28668.7 | −1.15076 | −0.575380 | − | 0.817886i | \(-0.695146\pi\) | ||||
−0.575380 | + | 0.817886i | \(0.695146\pi\) | |||||||
\(854\) | 22242.0 | 0.891224 | ||||||||
\(855\) | 15888.1 | 0.635512 | ||||||||
\(856\) | −4523.35 | −0.180613 | ||||||||
\(857\) | 449.310 | 0.0179091 | 0.00895457 | − | 0.999960i | \(-0.497150\pi\) | ||||
0.00895457 | + | 0.999960i | \(0.497150\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | −9518.39 | −0.376755 | ||||||||
\(862\) | 5261.14 | 0.207883 | ||||||||
\(863\) | −25097.5 | −0.989953 | −0.494976 | − | 0.868906i | \(-0.664823\pi\) | ||||
−0.494976 | + | 0.868906i | \(0.664823\pi\) | |||||||
\(864\) | 2918.28 | 0.114910 | ||||||||
\(865\) | 30923.4 | 1.21552 | ||||||||
\(866\) | 24031.0 | 0.942965 | ||||||||
\(867\) | 10014.1 | 0.392269 | ||||||||
\(868\) | −7177.69 | −0.280676 | ||||||||
\(869\) | −7482.53 | −0.292091 | ||||||||
\(870\) | 23294.2 | 0.907755 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −43692.7 | −1.69681 | ||||||||
\(873\) | −4980.21 | −0.193075 | ||||||||
\(874\) | 20387.3 | 0.789027 | ||||||||
\(875\) | 2007.73 | 0.0775698 | ||||||||
\(876\) | 3217.83 | 0.124110 | ||||||||
\(877\) | 27015.2 | 1.04018 | 0.520090 | − | 0.854112i | \(-0.325899\pi\) | ||||
0.520090 | + | 0.854112i | \(0.325899\pi\) | |||||||
\(878\) | −12714.4 | −0.488715 | ||||||||
\(879\) | −5738.15 | −0.220185 | ||||||||
\(880\) | −8787.79 | −0.336632 | ||||||||
\(881\) | 48638.7 | 1.86002 | 0.930010 | − | 0.367534i | \(-0.119798\pi\) | ||||
0.930010 | + | 0.367534i | \(0.119798\pi\) | |||||||
\(882\) | −5077.46 | −0.193840 | ||||||||
\(883\) | −25479.0 | −0.971048 | −0.485524 | − | 0.874223i | \(-0.661371\pi\) | ||||
−0.485524 | + | 0.874223i | \(0.661371\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11741.0 | 0.445953 | ||||||||
\(886\) | −5956.05 | −0.225843 | ||||||||
\(887\) | 42359.7 | 1.60350 | 0.801748 | − | 0.597663i | \(-0.203904\pi\) | ||||
0.801748 | + | 0.597663i | \(0.203904\pi\) | |||||||
\(888\) | −26510.6 | −1.00184 | ||||||||
\(889\) | 19774.0 | 0.746005 | ||||||||
\(890\) | 35419.1 | 1.33399 | ||||||||
\(891\) | 1220.42 | 0.0458873 | ||||||||
\(892\) | 1706.51 | 0.0640561 | ||||||||
\(893\) | −36305.4 | −1.36049 | ||||||||
\(894\) | −9653.78 | −0.361153 | ||||||||
\(895\) | −33148.1 | −1.23801 | ||||||||
\(896\) | −4478.96 | −0.167000 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18286.7 | 0.679548 | ||||||||
\(899\) | −61110.3 | −2.26712 | ||||||||
\(900\) | −2513.19 | −0.0930811 | ||||||||
\(901\) | 14888.9 | 0.550524 | ||||||||
\(902\) | 11075.0 | 0.408823 | ||||||||
\(903\) | 9018.31 | 0.332348 | ||||||||
\(904\) | −10275.1 | −0.378038 | ||||||||
\(905\) | 12853.5 | 0.472114 | ||||||||
\(906\) | 8292.19 | 0.304072 | ||||||||
\(907\) | −5314.91 | −0.194574 | −0.0972871 | − | 0.995256i | \(-0.531016\pi\) | ||||
−0.0972871 | + | 0.995256i | \(0.531016\pi\) | |||||||
\(908\) | −714.890 | −0.0261283 | ||||||||
\(909\) | −6875.56 | −0.250878 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2471.71 | 0.0898919 | 0.0449459 | − | 0.998989i | \(-0.485688\pi\) | ||||
0.0449459 | + | 0.998989i | \(0.485688\pi\) | |||||||
\(912\) | −13026.2 | −0.472962 | ||||||||
\(913\) | 5914.17 | 0.214382 | ||||||||
\(914\) | 15491.3 | 0.560620 | ||||||||
\(915\) | −43205.8 | −1.56103 | ||||||||
\(916\) | 5733.29 | 0.206805 | ||||||||
\(917\) | 14950.5 | 0.538396 | ||||||||
\(918\) | 5756.80 | 0.206975 | ||||||||
\(919\) | −9636.13 | −0.345883 | −0.172942 | − | 0.984932i | \(-0.555327\pi\) | ||||
−0.172942 | + | 0.984932i | \(0.555327\pi\) | |||||||
\(920\) | −28728.1 | −1.02950 | ||||||||
\(921\) | −5949.22 | −0.212849 | ||||||||
\(922\) | 10521.8 | 0.375832 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1140.47 | 0.0406047 | ||||||||
\(925\) | 40241.5 | 1.43041 | ||||||||
\(926\) | −8933.38 | −0.317029 | ||||||||
\(927\) | 1642.66 | 0.0582007 | ||||||||
\(928\) | 23218.3 | 0.821314 | ||||||||
\(929\) | −53249.1 | −1.88057 | −0.940283 | − | 0.340394i | \(-0.889439\pi\) | ||||
−0.940283 | + | 0.340394i | \(0.889439\pi\) | |||||||
\(930\) | −30847.8 | −1.08768 | ||||||||
\(931\) | −27553.5 | −0.969955 | ||||||||
\(932\) | 2417.16 | 0.0849534 | ||||||||
\(933\) | 5681.28 | 0.199354 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 13722.6 | 0.476911 | ||||||||
\(940\) | 12144.7 | 0.421399 | ||||||||
\(941\) | −8005.71 | −0.277342 | −0.138671 | − | 0.990339i | \(-0.544283\pi\) | ||||
−0.138671 | + | 0.990339i | \(0.544283\pi\) | |||||||
\(942\) | 11418.8 | 0.394952 | ||||||||
\(943\) | 23725.7 | 0.819315 | ||||||||
\(944\) | −9626.07 | −0.331888 | ||||||||
\(945\) | −4212.52 | −0.145009 | ||||||||
\(946\) | −10493.2 | −0.360637 | ||||||||
\(947\) | −17468.6 | −0.599424 | −0.299712 | − | 0.954030i | \(-0.596891\pi\) | ||||
−0.299712 | + | 0.954030i | \(0.596891\pi\) | |||||||
\(948\) | 3710.23 | 0.127113 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 30173.6 | 1.03048 | ||||||||
\(951\) | 22783.6 | 0.776875 | ||||||||
\(952\) | 22661.6 | 0.771498 | ||||||||
\(953\) | 30681.4 | 1.04288 | 0.521442 | − | 0.853287i | \(-0.325394\pi\) | ||||
0.521442 | + | 0.853287i | \(0.325394\pi\) | |||||||
\(954\) | 3462.70 | 0.117515 | ||||||||
\(955\) | 68752.5 | 2.32961 | ||||||||
\(956\) | 12470.0 | 0.421872 | ||||||||
\(957\) | 9709.87 | 0.327979 | ||||||||
\(958\) | 26221.8 | 0.884328 | ||||||||
\(959\) | 19257.5 | 0.648444 | ||||||||
\(960\) | 25718.4 | 0.864644 | ||||||||
\(961\) | 51135.6 | 1.71648 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1653.29 | 0.0553237 | ||||||||
\(964\) | 1345.00 | 0.0449373 | ||||||||
\(965\) | −50814.5 | −1.69511 | ||||||||
\(966\) | −5405.41 | −0.180037 | ||||||||
\(967\) | 15616.0 | 0.519313 | 0.259656 | − | 0.965701i | \(-0.416391\pi\) | ||||
0.259656 | + | 0.965701i | \(0.416391\pi\) | |||||||
\(968\) | 27184.2 | 0.902617 | ||||||||
\(969\) | 31240.0 | 1.03568 | ||||||||
\(970\) | −20001.5 | −0.662072 | ||||||||
\(971\) | 7185.98 | 0.237496 | 0.118748 | − | 0.992924i | \(-0.462112\pi\) | ||||
0.118748 | + | 0.992924i | \(0.462112\pi\) | |||||||
\(972\) | −605.148 | −0.0199693 | ||||||||
\(973\) | 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 | \(0.317283\pi\) | |||||||
\(978\) | −937.477 | −0.0306516 | ||||||||
\(979\) | 14764.0 | 0.481980 | ||||||||
\(980\) | 9217.01 | 0.300435 | ||||||||
\(981\) | 15969.8 | 0.519752 | ||||||||
\(982\) | −2429.52 | −0.0789502 | ||||||||
\(983\) | −11658.7 | −0.378287 | −0.189143 | − | 0.981949i | \(-0.560571\pi\) | ||||
−0.189143 | + | 0.981949i | \(0.560571\pi\) | |||||||
\(984\) | −23133.0 | −0.749444 | ||||||||
\(985\) | 45790.5 | 1.48123 | ||||||||
\(986\) | 45802.1 | 1.47935 | ||||||||
\(987\) | 9625.89 | 0.310431 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22479.2 | −0.722746 | ||||||||
\(990\) | 4901.45 | 0.157352 | ||||||||
\(991\) | −1957.32 | −0.0627409 | −0.0313704 | − | 0.999508i | \(-0.509987\pi\) | ||||
−0.0313704 | + | 0.999508i | \(0.509987\pi\) | |||||||
\(992\) | −30747.4 | −0.984104 | ||||||||
\(993\) | −5215.75 | −0.166684 | ||||||||
\(994\) | −22532.3 | −0.718996 | ||||||||
\(995\) | −83629.5 | −2.66456 | ||||||||
\(996\) | −2932.56 | −0.0932948 | ||||||||
\(997\) | −11434.8 | −0.363233 | −0.181617 | − | 0.983369i | \(-0.558133\pi\) | ||||
−0.181617 | + | 0.983369i | \(0.558133\pi\) | |||||||
\(998\) | −27459.0 | −0.870942 | ||||||||
\(999\) | 9689.70 | 0.306876 |
(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 | 507.4.a.p.1.6 | yes | 9 | |
3.2 | odd | 2 | 1521.4.a.bf.1.4 | 9 | |||
13.5 | odd | 4 | 507.4.b.k.337.7 | 18 | |||
13.8 | odd | 4 | 507.4.b.k.337.12 | 18 | |||
13.12 | even | 2 | 507.4.a.o.1.4 | ✓ | 9 | ||
39.38 | odd | 2 | 1521.4.a.bi.1.6 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.4 | ✓ | 9 | 13.12 | even | 2 | ||
507.4.a.p.1.6 | yes | 9 | 1.1 | even | 1 | trivial | |
507.4.b.k.337.7 | 18 | 13.5 | odd | 4 | |||
507.4.b.k.337.12 | 18 | 13.8 | odd | 4 | |||
1521.4.a.bf.1.4 | 9 | 3.2 | odd | 2 | |||
1521.4.a.bi.1.6 | 9 | 39.38 | odd | 2 |