Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,4,Mod(1,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, 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("1323.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.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: | \(78.0595269376\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 42x^{4} + 369x^{2} - 112 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.560992\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.560992 | 0.198341 | 0.0991703 | − | 0.995070i | \(-0.468381\pi\) | ||||
0.0991703 | + | 0.995070i | \(0.468381\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.68529 | −0.960661 | ||||||||
\(5\) | −12.9561 | −1.15883 | −0.579415 | − | 0.815033i | \(-0.696719\pi\) | ||||
−0.579415 | + | 0.815033i | \(0.696719\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.79932 | −0.388879 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.26827 | −0.229843 | ||||||||
\(11\) | 48.2286 | 1.32195 | 0.660976 | − | 0.750407i | \(-0.270142\pi\) | ||||
0.660976 | + | 0.750407i | \(0.270142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −36.3241 | −0.774962 | −0.387481 | − | 0.921878i | \(-0.626655\pi\) | ||||
−0.387481 | + | 0.921878i | \(0.626655\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 56.5460 | 0.883531 | ||||||||
\(17\) | −83.2713 | −1.18802 | −0.594008 | − | 0.804459i | \(-0.702455\pi\) | ||||
−0.594008 | + | 0.804459i | \(0.702455\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 67.4359 | 0.814255 | 0.407128 | − | 0.913371i | \(-0.366530\pi\) | ||||
0.407128 | + | 0.913371i | \(0.366530\pi\) | |||||||
\(20\) | 99.5714 | 1.11324 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 27.0559 | 0.262197 | ||||||||
\(23\) | −30.6300 | −0.277687 | −0.138843 | − | 0.990314i | \(-0.544338\pi\) | ||||
−0.138843 | + | 0.990314i | \(0.544338\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 42.8607 | 0.342885 | ||||||||
\(26\) | −20.3775 | −0.153706 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 294.244 | 1.88413 | 0.942065 | − | 0.335431i | \(-0.108882\pi\) | ||||
0.942065 | + | 0.335431i | \(0.108882\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 270.844 | 1.56919 | 0.784597 | − | 0.620006i | \(-0.212870\pi\) | ||||
0.784597 | + | 0.620006i | \(0.212870\pi\) | |||||||
\(32\) | 102.116 | 0.564119 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −46.7145 | −0.235632 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −204.315 | −0.907817 | −0.453909 | − | 0.891048i | \(-0.649971\pi\) | ||||
−0.453909 | + | 0.891048i | \(0.649971\pi\) | |||||||
\(38\) | 37.8310 | 0.161500 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 114.005 | 0.450644 | ||||||||
\(41\) | −287.529 | −1.09523 | −0.547615 | − | 0.836730i | \(-0.684464\pi\) | ||||
−0.547615 | + | 0.836730i | \(0.684464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −55.4901 | −0.196794 | −0.0983972 | − | 0.995147i | \(-0.531372\pi\) | ||||
−0.0983972 | + | 0.995147i | \(0.531372\pi\) | |||||||
\(44\) | −370.651 | −1.26995 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17.1832 | −0.0550765 | ||||||||
\(47\) | 191.301 | 0.593706 | 0.296853 | − | 0.954923i | \(-0.404063\pi\) | ||||
0.296853 | + | 0.954923i | \(0.404063\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 24.0445 | 0.0680081 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 279.161 | 0.744475 | ||||||||
\(53\) | 521.107 | 1.35056 | 0.675278 | − | 0.737563i | \(-0.264024\pi\) | ||||
0.675278 | + | 0.737563i | \(0.264024\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −624.855 | −1.53192 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 165.069 | 0.373699 | ||||||||
\(59\) | 381.074 | 0.840874 | 0.420437 | − | 0.907322i | \(-0.361877\pi\) | ||||
0.420437 | + | 0.907322i | \(0.361877\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 155.465 | 0.326315 | 0.163158 | − | 0.986600i | \(-0.447832\pi\) | ||||
0.163158 | + | 0.986600i | \(0.447832\pi\) | |||||||
\(62\) | 151.941 | 0.311235 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −395.081 | −0.771643 | ||||||||
\(65\) | 470.619 | 0.898048 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −65.1959 | −0.118880 | −0.0594399 | − | 0.998232i | \(-0.518931\pi\) | ||||
−0.0594399 | + | 0.998232i | \(0.518931\pi\) | |||||||
\(68\) | 639.964 | 1.14128 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −256.370 | −0.428529 | −0.214265 | − | 0.976776i | \(-0.568735\pi\) | ||||
−0.214265 | + | 0.976776i | \(0.568735\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 318.625 | 0.510852 | 0.255426 | − | 0.966829i | \(-0.417784\pi\) | ||||
0.255426 | + | 0.966829i | \(0.417784\pi\) | |||||||
\(74\) | −114.619 | −0.180057 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −518.264 | −0.782223 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 77.7532 | 0.110733 | 0.0553666 | − | 0.998466i | \(-0.482367\pi\) | ||||
0.0553666 | + | 0.998466i | \(0.482367\pi\) | |||||||
\(80\) | −732.615 | −1.02386 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −161.301 | −0.217229 | ||||||||
\(83\) | −836.549 | −1.10630 | −0.553152 | − | 0.833081i | \(-0.686575\pi\) | ||||
−0.553152 | + | 0.833081i | \(0.686575\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1078.87 | 1.37671 | ||||||||
\(86\) | −31.1295 | −0.0390323 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −424.379 | −0.514079 | ||||||||
\(89\) | −1590.06 | −1.89377 | −0.946887 | − | 0.321565i | \(-0.895791\pi\) | ||||
−0.946887 | + | 0.321565i | \(0.895791\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 235.400 | 0.266763 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 107.319 | 0.117756 | ||||||||
\(95\) | −873.706 | −0.943583 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1189.88 | −1.24550 | −0.622751 | − | 0.782420i | \(-0.713985\pi\) | ||||
−0.622751 | + | 0.782420i | \(0.713985\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −329.397 | −0.329397 | ||||||||
\(101\) | −507.845 | −0.500321 | −0.250161 | − | 0.968204i | \(-0.580483\pi\) | ||||
−0.250161 | + | 0.968204i | \(0.580483\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1852.78 | −1.77242 | −0.886212 | − | 0.463280i | \(-0.846672\pi\) | ||||
−0.886212 | + | 0.463280i | \(0.846672\pi\) | |||||||
\(104\) | 319.628 | 0.301366 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 292.337 | 0.267870 | ||||||||
\(107\) | 614.904 | 0.555561 | 0.277781 | − | 0.960645i | \(-0.410401\pi\) | ||||
0.277781 | + | 0.960645i | \(0.410401\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1017.92 | 0.894487 | 0.447243 | − | 0.894412i | \(-0.352406\pi\) | ||||
0.447243 | + | 0.894412i | \(0.352406\pi\) | |||||||
\(110\) | −350.539 | −0.303841 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1204.42 | −1.00267 | −0.501337 | − | 0.865252i | \(-0.667158\pi\) | ||||
−0.501337 | + | 0.865252i | \(0.667158\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 396.845 | 0.321792 | ||||||||
\(116\) | −2261.35 | −1.81001 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 213.779 | 0.166779 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 995.000 | 0.747559 | ||||||||
\(122\) | 87.2145 | 0.0647215 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2081.52 | −1.50746 | ||||||||
\(125\) | 1064.21 | 0.761484 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2515.55 | −1.75763 | −0.878813 | − | 0.477165i | \(-0.841664\pi\) | ||||
−0.878813 | + | 0.477165i | \(0.841664\pi\) | |||||||
\(128\) | −1038.57 | −0.717167 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 264.014 | 0.178119 | ||||||||
\(131\) | 2165.37 | 1.44419 | 0.722096 | − | 0.691793i | \(-0.243179\pi\) | ||||
0.722096 | + | 0.691793i | \(0.243179\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −36.5743 | −0.0235787 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 732.731 | 0.461994 | ||||||||
\(137\) | 795.668 | 0.496194 | 0.248097 | − | 0.968735i | \(-0.420195\pi\) | ||||
0.248097 | + | 0.968735i | \(0.420195\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2400.60 | −1.46487 | −0.732433 | − | 0.680839i | \(-0.761615\pi\) | ||||
−0.732433 | + | 0.680839i | \(0.761615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −143.822 | −0.0849947 | ||||||||
\(143\) | −1751.86 | −1.02446 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3812.26 | −2.18338 | ||||||||
\(146\) | 178.746 | 0.101323 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1570.22 | 0.872105 | ||||||||
\(149\) | 1404.26 | 0.772091 | 0.386046 | − | 0.922480i | \(-0.373841\pi\) | ||||
0.386046 | + | 0.922480i | \(0.373841\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1761.48 | −0.949322 | −0.474661 | − | 0.880169i | \(-0.657429\pi\) | ||||
−0.474661 | + | 0.880169i | \(0.657429\pi\) | |||||||
\(152\) | −593.390 | −0.316646 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3509.09 | −1.81843 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1082.03 | −0.550034 | −0.275017 | − | 0.961439i | \(-0.588683\pi\) | ||||
−0.275017 | + | 0.961439i | \(0.588683\pi\) | |||||||
\(158\) | 43.6189 | 0.0219629 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1323.03 | −0.653717 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2473.27 | −1.18847 | −0.594237 | − | 0.804290i | \(-0.702546\pi\) | ||||
−0.594237 | + | 0.804290i | \(0.702546\pi\) | |||||||
\(164\) | 2209.74 | 1.05215 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −469.297 | −0.219425 | ||||||||
\(167\) | −2240.74 | −1.03828 | −0.519142 | − | 0.854688i | \(-0.673748\pi\) | ||||
−0.519142 | + | 0.854688i | \(0.673748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −877.557 | −0.399434 | ||||||||
\(170\) | 605.238 | 0.273057 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 426.457 | 0.189053 | ||||||||
\(173\) | 2121.28 | 0.932242 | 0.466121 | − | 0.884721i | \(-0.345651\pi\) | ||||
0.466121 | + | 0.884721i | \(0.345651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2727.13 | 1.16799 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −892.010 | −0.375612 | ||||||||
\(179\) | 1578.84 | 0.659262 | 0.329631 | − | 0.944110i | \(-0.393076\pi\) | ||||
0.329631 | + | 0.944110i | \(0.393076\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4609.64 | −1.89299 | −0.946496 | − | 0.322716i | \(-0.895404\pi\) | ||||
−0.946496 | + | 0.322716i | \(0.895404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 269.523 | 0.107986 | ||||||||
\(185\) | 2647.13 | 1.05201 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4016.06 | −1.57050 | ||||||||
\(188\) | −1470.21 | −0.570350 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −490.142 | −0.187151 | ||||||||
\(191\) | 1291.72 | 0.489350 | 0.244675 | − | 0.969605i | \(-0.421319\pi\) | ||||
0.244675 | + | 0.969605i | \(0.421319\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1176.01 | 0.438605 | 0.219302 | − | 0.975657i | \(-0.429622\pi\) | ||||
0.219302 | + | 0.975657i | \(0.429622\pi\) | |||||||
\(194\) | −667.511 | −0.247033 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4560.71 | 1.64943 | 0.824713 | − | 0.565552i | \(-0.191337\pi\) | ||||
0.824713 | + | 0.565552i | \(0.191337\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 986.014 | 0.351240 | 0.175620 | − | 0.984458i | \(-0.443807\pi\) | ||||
0.175620 | + | 0.984458i | \(0.443807\pi\) | |||||||
\(200\) | −377.145 | −0.133341 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −284.897 | −0.0992340 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3725.25 | 1.26919 | ||||||||
\(206\) | −1039.39 | −0.351543 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2053.98 | −0.684702 | ||||||||
\(209\) | 3252.34 | 1.07641 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5459.28 | 1.78120 | 0.890598 | − | 0.454792i | \(-0.150286\pi\) | ||||
0.890598 | + | 0.454792i | \(0.150286\pi\) | |||||||
\(212\) | −4004.85 | −1.29743 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 344.956 | 0.110190 | ||||||||
\(215\) | 718.936 | 0.228051 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 571.045 | 0.177413 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4802.19 | 1.47165 | ||||||||
\(221\) | 3024.76 | 0.920666 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4626.41 | −1.38927 | −0.694636 | − | 0.719362i | \(-0.744434\pi\) | ||||
−0.694636 | + | 0.719362i | \(0.744434\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −675.669 | −0.198871 | ||||||||
\(227\) | −2437.77 | −0.712776 | −0.356388 | − | 0.934338i | \(-0.615992\pi\) | ||||
−0.356388 | + | 0.934338i | \(0.615992\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2946.50 | −0.850264 | −0.425132 | − | 0.905131i | \(-0.639772\pi\) | ||||
−0.425132 | + | 0.905131i | \(0.639772\pi\) | |||||||
\(230\) | 222.627 | 0.0638243 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2589.15 | −0.732698 | ||||||||
\(233\) | −3441.49 | −0.967638 | −0.483819 | − | 0.875168i | \(-0.660751\pi\) | ||||
−0.483819 | + | 0.875168i | \(0.660751\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2478.52 | −0.688004 | ||||||||
\(236\) | −2928.66 | −0.807795 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 744.021 | 0.201367 | 0.100684 | − | 0.994918i | \(-0.467897\pi\) | ||||
0.100684 | + | 0.994918i | \(0.467897\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4714.37 | 1.26008 | 0.630040 | − | 0.776562i | \(-0.283038\pi\) | ||||
0.630040 | + | 0.776562i | \(0.283038\pi\) | |||||||
\(242\) | 558.187 | 0.148271 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1194.79 | −0.313478 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2449.55 | −0.631017 | ||||||||
\(248\) | −2383.24 | −0.610226 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 597.011 | 0.151033 | ||||||||
\(251\) | 2248.41 | 0.565411 | 0.282706 | − | 0.959207i | \(-0.408768\pi\) | ||||
0.282706 | + | 0.959207i | \(0.408768\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1477.24 | −0.367089 | ||||||||
\(254\) | −1411.20 | −0.348609 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2578.02 | 0.629400 | ||||||||
\(257\) | −6099.67 | −1.48049 | −0.740247 | − | 0.672335i | \(-0.765291\pi\) | ||||
−0.740247 | + | 0.672335i | \(0.765291\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3616.85 | −0.862720 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1214.75 | 0.286442 | ||||||||
\(263\) | 3493.26 | 0.819026 | 0.409513 | − | 0.912304i | \(-0.365699\pi\) | ||||
0.409513 | + | 0.912304i | \(0.365699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6751.51 | −1.56506 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 501.049 | 0.114203 | ||||||||
\(269\) | 6393.14 | 1.44906 | 0.724529 | − | 0.689244i | \(-0.242057\pi\) | ||||
0.724529 | + | 0.689244i | \(0.242057\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4222.81 | 0.946559 | 0.473279 | − | 0.880912i | \(-0.343070\pi\) | ||||
0.473279 | + | 0.880912i | \(0.343070\pi\) | |||||||
\(272\) | −4708.66 | −1.04965 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 446.363 | 0.0984153 | ||||||||
\(275\) | 2067.11 | 0.453278 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5240.37 | −1.13669 | −0.568345 | − | 0.822790i | \(-0.692416\pi\) | ||||
−0.568345 | + | 0.822790i | \(0.692416\pi\) | |||||||
\(278\) | −1346.72 | −0.290542 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5924.79 | 1.25781 | 0.628903 | − | 0.777484i | \(-0.283504\pi\) | ||||
0.628903 | + | 0.777484i | \(0.283504\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1885.61 | 0.396070 | 0.198035 | − | 0.980195i | \(-0.436544\pi\) | ||||
0.198035 | + | 0.980195i | \(0.436544\pi\) | |||||||
\(284\) | 1970.28 | 0.411671 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −982.781 | −0.203192 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2021.11 | 0.411380 | ||||||||
\(290\) | −2138.65 | −0.433054 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2448.72 | −0.490756 | ||||||||
\(293\) | 3173.12 | 0.632680 | 0.316340 | − | 0.948646i | \(-0.397546\pi\) | ||||
0.316340 | + | 0.948646i | \(0.397546\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4937.23 | −0.974430 | ||||||||
\(296\) | 1797.84 | 0.353031 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 787.779 | 0.153137 | ||||||||
\(299\) | 1112.61 | 0.215197 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −988.179 | −0.188289 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3813.23 | 0.719419 | ||||||||
\(305\) | −2014.22 | −0.378144 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6188.30 | −1.15044 | −0.575220 | − | 0.817999i | \(-0.695084\pi\) | ||||
−0.575220 | + | 0.817999i | \(0.695084\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1968.57 | −0.360668 | ||||||||
\(311\) | −3750.93 | −0.683909 | −0.341954 | − | 0.939717i | \(-0.611089\pi\) | ||||
−0.341954 | + | 0.939717i | \(0.611089\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4172.29 | 0.753456 | 0.376728 | − | 0.926324i | \(-0.377049\pi\) | ||||
0.376728 | + | 0.926324i | \(0.377049\pi\) | |||||||
\(314\) | −607.009 | −0.109094 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −597.556 | −0.106377 | ||||||||
\(317\) | 8410.38 | 1.49014 | 0.745069 | − | 0.666987i | \(-0.232416\pi\) | ||||
0.745069 | + | 0.666987i | \(0.232416\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14191.0 | 2.49073 | ||||||||
\(320\) | 5118.71 | 0.894203 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5615.47 | −0.967347 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1556.88 | −0.265723 | ||||||||
\(326\) | −1387.48 | −0.235723 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2530.06 | 0.425912 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1217.72 | −0.202211 | −0.101105 | − | 0.994876i | \(-0.532238\pi\) | ||||
−0.101105 | + | 0.994876i | \(0.532238\pi\) | |||||||
\(332\) | 6429.12 | 1.06278 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1257.03 | −0.205934 | ||||||||
\(335\) | 844.684 | 0.137761 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3880.01 | 0.627175 | 0.313587 | − | 0.949559i | \(-0.398469\pi\) | ||||
0.313587 | + | 0.949559i | \(0.398469\pi\) | |||||||
\(338\) | −492.302 | −0.0792240 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8291.44 | −1.32255 | ||||||||
\(341\) | 13062.4 | 2.07440 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 488.275 | 0.0765291 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1190.02 | 0.184901 | ||||||||
\(347\) | −9672.45 | −1.49638 | −0.748191 | − | 0.663484i | \(-0.769077\pi\) | ||||
−0.748191 | + | 0.663484i | \(0.769077\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3960.64 | −0.607473 | −0.303737 | − | 0.952756i | \(-0.598234\pi\) | ||||
−0.303737 | + | 0.952756i | \(0.598234\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4924.93 | 0.745738 | ||||||||
\(353\) | 7639.67 | 1.15189 | 0.575947 | − | 0.817487i | \(-0.304633\pi\) | ||||
0.575947 | + | 0.817487i | \(0.304633\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3321.56 | 0.496592 | ||||||||
\(356\) | 12220.1 | 1.81928 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 885.715 | 0.130758 | ||||||||
\(359\) | −9411.16 | −1.38357 | −0.691785 | − | 0.722103i | \(-0.743176\pi\) | ||||
−0.691785 | + | 0.722103i | \(0.743176\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2311.40 | −0.336989 | ||||||||
\(362\) | −2585.97 | −0.375457 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4128.14 | −0.591991 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5707.80 | −0.811838 | −0.405919 | − | 0.913909i | \(-0.633048\pi\) | ||||
−0.405919 | + | 0.913909i | \(0.633048\pi\) | |||||||
\(368\) | −1732.00 | −0.245345 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1485.02 | 0.208655 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9579.55 | −1.32979 | −0.664893 | − | 0.746938i | \(-0.731523\pi\) | ||||
−0.664893 | + | 0.746938i | \(0.731523\pi\) | |||||||
\(374\) | −2252.98 | −0.311494 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1683.32 | −0.230880 | ||||||||
\(377\) | −10688.2 | −1.46013 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8730.92 | 1.18332 | 0.591658 | − | 0.806189i | \(-0.298473\pi\) | ||||
0.591658 | + | 0.806189i | \(0.298473\pi\) | |||||||
\(380\) | 6714.68 | 0.906463 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 724.646 | 0.0970579 | ||||||||
\(383\) | −9623.21 | −1.28387 | −0.641936 | − | 0.766758i | \(-0.721869\pi\) | ||||
−0.641936 | + | 0.766758i | \(0.721869\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 659.730 | 0.0869931 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9144.54 | 1.19650 | ||||||||
\(389\) | −11319.7 | −1.47541 | −0.737704 | − | 0.675125i | \(-0.764090\pi\) | ||||
−0.737704 | + | 0.675125i | \(0.764090\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2550.60 | 0.329896 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2558.52 | 0.327148 | ||||||||
\(395\) | −1007.38 | −0.128321 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2855.87 | −0.361038 | −0.180519 | − | 0.983572i | \(-0.557778\pi\) | ||||
−0.180519 | + | 0.983572i | \(0.557778\pi\) | |||||||
\(398\) | 553.146 | 0.0696651 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2423.60 | 0.302950 | ||||||||
\(401\) | −1975.97 | −0.246073 | −0.123036 | − | 0.992402i | \(-0.539263\pi\) | ||||
−0.123036 | + | 0.992402i | \(0.539263\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9838.18 | −1.21607 | ||||||||
\(404\) | 3902.94 | 0.480639 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9853.85 | −1.20009 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8244.62 | −0.996749 | −0.498375 | − | 0.866962i | \(-0.666070\pi\) | ||||
−0.498375 | + | 0.866962i | \(0.666070\pi\) | |||||||
\(410\) | 2089.84 | 0.251731 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14239.1 | 1.70270 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10838.4 | 1.28202 | ||||||||
\(416\) | −3709.29 | −0.437170 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1824.54 | 0.213495 | ||||||||
\(419\) | −12861.0 | −1.49952 | −0.749761 | − | 0.661709i | \(-0.769831\pi\) | ||||
−0.749761 | + | 0.661709i | \(0.769831\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16467.7 | −1.90638 | −0.953188 | − | 0.302377i | \(-0.902220\pi\) | ||||
−0.953188 | + | 0.302377i | \(0.902220\pi\) | |||||||
\(422\) | 3062.61 | 0.353283 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4585.38 | −0.525203 | ||||||||
\(425\) | −3569.06 | −0.407353 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4725.72 | −0.533706 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 403.317 | 0.0452318 | ||||||||
\(431\) | 273.346 | 0.0305490 | 0.0152745 | − | 0.999883i | \(-0.495138\pi\) | ||||
0.0152745 | + | 0.999883i | \(0.495138\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13765.3 | 1.52776 | 0.763878 | − | 0.645361i | \(-0.223293\pi\) | ||||
0.763878 | + | 0.645361i | \(0.223293\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7823.01 | −0.859298 | ||||||||
\(437\) | −2065.56 | −0.226108 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2965.97 | −0.322456 | −0.161228 | − | 0.986917i | \(-0.551545\pi\) | ||||
−0.161228 | + | 0.986917i | \(0.551545\pi\) | |||||||
\(440\) | 5498.30 | 0.595730 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1696.86 | 0.182605 | ||||||||
\(443\) | −14038.4 | −1.50561 | −0.752806 | − | 0.658242i | \(-0.771300\pi\) | ||||
−0.752806 | + | 0.658242i | \(0.771300\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20601.0 | 2.19456 | ||||||||
\(446\) | −2595.38 | −0.275549 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6338.13 | 0.666180 | 0.333090 | − | 0.942895i | \(-0.391909\pi\) | ||||
0.333090 | + | 0.942895i | \(0.391909\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13867.1 | −1.44784 | ||||||||
\(452\) | 9256.30 | 0.963230 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1367.57 | −0.141372 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9120.26 | 0.933540 | 0.466770 | − | 0.884379i | \(-0.345418\pi\) | ||||
0.466770 | + | 0.884379i | \(0.345418\pi\) | |||||||
\(458\) | −1652.97 | −0.168642 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3049.87 | −0.309133 | ||||||||
\(461\) | 15109.6 | 1.52651 | 0.763256 | − | 0.646096i | \(-0.223600\pi\) | ||||
0.763256 | + | 0.646096i | \(0.223600\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6418.72 | 0.644283 | 0.322142 | − | 0.946692i | \(-0.395597\pi\) | ||||
0.322142 | + | 0.946692i | \(0.395597\pi\) | |||||||
\(464\) | 16638.3 | 1.66469 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1930.65 | −0.191922 | ||||||||
\(467\) | −4304.81 | −0.426559 | −0.213279 | − | 0.976991i | \(-0.568414\pi\) | ||||
−0.213279 | + | 0.976991i | \(0.568414\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1390.43 | −0.136459 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3353.19 | −0.326998 | ||||||||
\(473\) | −2676.21 | −0.260153 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2890.35 | 0.279196 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 417.390 | 0.0399393 | ||||||||
\(479\) | −5030.65 | −0.479867 | −0.239934 | − | 0.970789i | \(-0.577126\pi\) | ||||
−0.239934 | + | 0.970789i | \(0.577126\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7421.58 | 0.703524 | ||||||||
\(482\) | 2644.72 | 0.249925 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7646.87 | −0.718150 | ||||||||
\(485\) | 15416.2 | 1.44332 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13300.6 | −1.23759 | −0.618794 | − | 0.785553i | \(-0.712379\pi\) | ||||
−0.618794 | + | 0.785553i | \(0.712379\pi\) | |||||||
\(488\) | −1367.98 | −0.126897 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9246.30 | 0.849857 | 0.424928 | − | 0.905227i | \(-0.360299\pi\) | ||||
0.424928 | + | 0.905227i | \(0.360299\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24502.1 | −2.23837 | ||||||||
\(494\) | −1374.18 | −0.125156 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15315.1 | 1.38643 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16233.3 | −1.45632 | −0.728160 | − | 0.685407i | \(-0.759624\pi\) | ||||
−0.728160 | + | 0.685407i | \(0.759624\pi\) | |||||||
\(500\) | −8178.73 | −0.731528 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1261.34 | 0.112144 | ||||||||
\(503\) | −1664.13 | −0.147515 | −0.0737575 | − | 0.997276i | \(-0.523499\pi\) | ||||
−0.0737575 | + | 0.997276i | \(0.523499\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6579.69 | 0.579787 | ||||||||
\(506\) | −828.721 | −0.0728086 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19332.7 | 1.68848 | ||||||||
\(509\) | −8757.17 | −0.762583 | −0.381291 | − | 0.924455i | \(-0.624521\pi\) | ||||
−0.381291 | + | 0.924455i | \(0.624521\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 9754.80 | 0.842002 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3421.86 | −0.293642 | ||||||||
\(515\) | 24004.8 | 2.05394 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9226.21 | 0.784851 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4141.13 | −0.349232 | ||||||||
\(521\) | 1641.01 | 0.137993 | 0.0689963 | − | 0.997617i | \(-0.478020\pi\) | ||||
0.0689963 | + | 0.997617i | \(0.478020\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16530.6 | 1.38209 | 0.691043 | − | 0.722813i | \(-0.257151\pi\) | ||||
0.691043 | + | 0.722813i | \(0.257151\pi\) | |||||||
\(524\) | −16641.5 | −1.38738 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1959.69 | 0.162446 | ||||||||
\(527\) | −22553.5 | −1.86423 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11228.8 | −0.922890 | ||||||||
\(530\) | −3787.54 | −0.310416 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10444.2 | 0.848762 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7966.77 | −0.643801 | ||||||||
\(536\) | 573.679 | 0.0462298 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3586.50 | 0.287407 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3418.03 | −0.271631 | −0.135816 | − | 0.990734i | \(-0.543365\pi\) | ||||
−0.135816 | + | 0.990734i | \(0.543365\pi\) | |||||||
\(542\) | 2368.96 | 0.187741 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8503.36 | −0.670181 | ||||||||
\(545\) | −13188.3 | −1.03656 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15983.1 | −1.24934 | −0.624668 | − | 0.780890i | \(-0.714766\pi\) | ||||
−0.624668 | + | 0.780890i | \(0.714766\pi\) | |||||||
\(548\) | −6114.94 | −0.476674 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1159.63 | 0.0899034 | ||||||||
\(551\) | 19842.6 | 1.53416 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2939.80 | −0.225452 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18449.3 | 1.40724 | ||||||||
\(557\) | −8736.81 | −0.664615 | −0.332307 | − | 0.943171i | \(-0.607827\pi\) | ||||
−0.332307 | + | 0.943171i | \(0.607827\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2015.63 | 0.152508 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3323.76 | 0.249474 | ||||||||
\(563\) | 24107.2 | 1.80461 | 0.902306 | − | 0.431095i | \(-0.141873\pi\) | ||||
0.902306 | + | 0.431095i | \(0.141873\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15604.6 | 1.16193 | ||||||||
\(566\) | 1057.81 | 0.0785567 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2255.89 | 0.166646 | ||||||||
\(569\) | −13291.7 | −0.979292 | −0.489646 | − | 0.871921i | \(-0.662874\pi\) | ||||
−0.489646 | + | 0.871921i | \(0.662874\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15208.2 | 1.11461 | 0.557305 | − | 0.830308i | \(-0.311836\pi\) | ||||
0.557305 | + | 0.830308i | \(0.311836\pi\) | |||||||
\(572\) | 13463.6 | 0.984161 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1312.82 | −0.0952147 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10809.5 | −0.779904 | −0.389952 | − | 0.920835i | \(-0.627508\pi\) | ||||
−0.389952 | + | 0.920835i | \(0.627508\pi\) | |||||||
\(578\) | 1133.83 | 0.0815933 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 29298.3 | 2.09749 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25132.3 | 1.78537 | ||||||||
\(584\) | −2803.68 | −0.198660 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1780.09 | 0.125486 | ||||||||
\(587\) | −3843.26 | −0.270236 | −0.135118 | − | 0.990830i | \(-0.543141\pi\) | ||||
−0.135118 | + | 0.990830i | \(0.543141\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18264.6 | 1.27773 | ||||||||
\(590\) | −2769.75 | −0.193269 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11553.2 | −0.802084 | ||||||||
\(593\) | 1402.87 | 0.0971484 | 0.0485742 | − | 0.998820i | \(-0.484532\pi\) | ||||
0.0485742 | + | 0.998820i | \(0.484532\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10792.2 | −0.741718 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 624.164 | 0.0426822 | ||||||||
\(599\) | 12738.8 | 0.868937 | 0.434469 | − | 0.900687i | \(-0.356936\pi\) | ||||
0.434469 | + | 0.900687i | \(0.356936\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17292.7 | 1.17368 | 0.586841 | − | 0.809702i | \(-0.300371\pi\) | ||||
0.586841 | + | 0.809702i | \(0.300371\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13537.5 | 0.911977 | ||||||||
\(605\) | −12891.3 | −0.866293 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27165.6 | 1.81650 | 0.908251 | − | 0.418426i | \(-0.137418\pi\) | ||||
0.908251 | + | 0.418426i | \(0.137418\pi\) | |||||||
\(608\) | 6886.31 | 0.459336 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1129.96 | −0.0750012 | ||||||||
\(611\) | −6948.86 | −0.460100 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10405.5 | −0.685599 | −0.342800 | − | 0.939409i | \(-0.611375\pi\) | ||||
−0.342800 | + | 0.939409i | \(0.611375\pi\) | |||||||
\(614\) | −3471.59 | −0.228179 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18326.4 | 1.19578 | 0.597889 | − | 0.801579i | \(-0.296006\pi\) | ||||
0.597889 | + | 0.801579i | \(0.296006\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3575.13 | −0.232143 | −0.116072 | − | 0.993241i | \(-0.537030\pi\) | ||||
−0.116072 | + | 0.993241i | \(0.537030\pi\) | |||||||
\(620\) | 26968.3 | 1.74689 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2104.24 | −0.135647 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19145.5 | −1.22531 | ||||||||
\(626\) | 2340.62 | 0.149441 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8315.70 | 0.528396 | ||||||||
\(629\) | 17013.6 | 1.07850 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11722.1 | −0.739538 | −0.369769 | − | 0.929124i | \(-0.620563\pi\) | ||||
−0.369769 | + | 0.929124i | \(0.620563\pi\) | |||||||
\(632\) | −684.175 | −0.0430617 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4718.15 | 0.295555 | ||||||||
\(635\) | 32591.7 | 2.03679 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7961.03 | 0.494013 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 13455.8 | 0.831074 | ||||||||
\(641\) | −24327.5 | −1.49903 | −0.749514 | − | 0.661988i | \(-0.769713\pi\) | ||||
−0.749514 | + | 0.661988i | \(0.769713\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10684.8 | 0.655316 | 0.327658 | − | 0.944796i | \(-0.393741\pi\) | ||||
0.327658 | + | 0.944796i | \(0.393741\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3150.23 | −0.191864 | ||||||||
\(647\) | −21203.0 | −1.28837 | −0.644184 | − | 0.764870i | \(-0.722803\pi\) | ||||
−0.644184 | + | 0.764870i | \(0.722803\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18378.7 | 1.11160 | ||||||||
\(650\) | −873.395 | −0.0527037 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19007.8 | 1.14172 | ||||||||
\(653\) | 27562.2 | 1.65175 | 0.825874 | − | 0.563854i | \(-0.190682\pi\) | ||||
0.825874 | + | 0.563854i | \(0.190682\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28054.7 | −1.67357 | ||||||||
\(656\) | −16258.6 | −0.967670 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1389.06 | 0.0821091 | 0.0410546 | − | 0.999157i | \(-0.486928\pi\) | ||||
0.0410546 | + | 0.999157i | \(0.486928\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12490.6 | −0.734989 | −0.367494 | − | 0.930026i | \(-0.619784\pi\) | ||||
−0.367494 | + | 0.930026i | \(0.619784\pi\) | |||||||
\(662\) | −683.130 | −0.0401066 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7361.06 | 0.430218 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9012.70 | −0.523198 | ||||||||
\(668\) | 17220.7 | 0.997438 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 473.861 | 0.0273237 | ||||||||
\(671\) | 7497.85 | 0.431373 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13234.5 | −0.758027 | −0.379014 | − | 0.925391i | \(-0.623737\pi\) | ||||
−0.379014 | + | 0.925391i | \(0.623737\pi\) | |||||||
\(674\) | 2176.66 | 0.124394 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6744.28 | 0.383721 | ||||||||
\(677\) | −4788.89 | −0.271864 | −0.135932 | − | 0.990718i | \(-0.543403\pi\) | ||||
−0.135932 | + | 0.990718i | \(0.543403\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9493.34 | −0.535372 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7327.92 | 0.411438 | ||||||||
\(683\) | −7543.01 | −0.422584 | −0.211292 | − | 0.977423i | \(-0.567767\pi\) | ||||
−0.211292 | + | 0.977423i | \(0.567767\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10308.8 | −0.575004 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3137.74 | −0.173874 | ||||||||
\(689\) | −18928.7 | −1.04663 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27685.3 | 1.52416 | 0.762082 | − | 0.647481i | \(-0.224177\pi\) | ||||
0.762082 | + | 0.647481i | \(0.224177\pi\) | |||||||
\(692\) | −16302.6 | −0.895568 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5426.16 | −0.296793 | ||||||||
\(695\) | 31102.4 | 1.69753 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23942.9 | 1.30115 | ||||||||
\(698\) | −2221.89 | −0.120487 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19866.5 | −1.07040 | −0.535198 | − | 0.844726i | \(-0.679763\pi\) | ||||
−0.535198 | + | 0.844726i | \(0.679763\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13778.2 | −0.739195 | ||||||||
\(704\) | −19054.2 | −1.02008 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4285.79 | 0.228467 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3572.12 | −0.189216 | −0.0946078 | − | 0.995515i | \(-0.530160\pi\) | ||||
−0.0946078 | + | 0.995515i | \(0.530160\pi\) | |||||||
\(710\) | 1863.37 | 0.0984944 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13991.4 | 0.736448 | ||||||||
\(713\) | −8295.95 | −0.435745 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22697.3 | 1.18718 | ||||||||
\(716\) | −12133.8 | −0.633327 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5279.58 | −0.274418 | ||||||||
\(719\) | −32955.5 | −1.70936 | −0.854681 | − | 0.519154i | \(-0.826247\pi\) | ||||
−0.854681 | + | 0.519154i | \(0.826247\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1296.68 | −0.0668385 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 35426.4 | 1.81852 | ||||||||
\(725\) | 12611.5 | 0.646041 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6347.31 | −0.323808 | −0.161904 | − | 0.986806i | \(-0.551764\pi\) | ||||
−0.161904 | + | 0.986806i | \(0.551764\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2315.85 | −0.117416 | ||||||||
\(731\) | 4620.73 | 0.233795 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22488.7 | 1.13321 | 0.566603 | − | 0.823991i | \(-0.308257\pi\) | ||||
0.566603 | + | 0.823991i | \(0.308257\pi\) | |||||||
\(734\) | −3202.03 | −0.161020 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3127.82 | −0.156648 | ||||||||
\(737\) | −3144.31 | −0.157153 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19859.5 | 0.988559 | 0.494279 | − | 0.869303i | \(-0.335432\pi\) | ||||
0.494279 | + | 0.869303i | \(0.335432\pi\) | |||||||
\(740\) | −20344.0 | −1.01062 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16900.0 | −0.834455 | −0.417228 | − | 0.908802i | \(-0.636998\pi\) | ||||
−0.417228 | + | 0.908802i | \(0.636998\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18193.8 | −0.894722 | ||||||||
\(746\) | −5374.05 | −0.263751 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 30864.6 | 1.50872 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19441.1 | 0.944627 | 0.472314 | − | 0.881431i | \(-0.343419\pi\) | ||||
0.472314 | + | 0.881431i | \(0.343419\pi\) | |||||||
\(752\) | 10817.3 | 0.524558 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5995.97 | −0.289603 | ||||||||
\(755\) | 22822.0 | 1.10010 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17481.7 | −0.839343 | −0.419671 | − | 0.907676i | \(-0.637855\pi\) | ||||
−0.419671 | + | 0.907676i | \(0.637855\pi\) | |||||||
\(758\) | 4897.97 | 0.234700 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7688.02 | 0.366939 | ||||||||
\(761\) | 4160.98 | 0.198207 | 0.0991035 | − | 0.995077i | \(-0.468403\pi\) | ||||
0.0991035 | + | 0.995077i | \(0.468403\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −9927.26 | −0.470099 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5398.54 | −0.254644 | ||||||||
\(767\) | −13842.2 | −0.651645 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33004.0 | −1.54766 | −0.773832 | − | 0.633391i | \(-0.781662\pi\) | ||||
−0.773832 | + | 0.633391i | \(0.781662\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9037.94 | −0.421351 | ||||||||
\(773\) | −29291.1 | −1.36291 | −0.681455 | − | 0.731860i | \(-0.738652\pi\) | ||||
−0.681455 | + | 0.731860i | \(0.738652\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11608.6 | 0.538054 | ||||||||
\(776\) | 10470.1 | 0.484349 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6350.28 | −0.292633 | ||||||||
\(779\) | −19389.8 | −0.891797 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12364.4 | −0.566495 | ||||||||
\(782\) | 1430.87 | 0.0654318 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14018.9 | 0.637395 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7935.32 | −0.359420 | −0.179710 | − | 0.983720i | \(-0.557516\pi\) | ||||
−0.179710 | + | 0.983720i | \(0.557516\pi\) | |||||||
\(788\) | −35050.3 | −1.58454 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −565.131 | −0.0254512 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5647.12 | −0.252882 | ||||||||
\(794\) | −1602.12 | −0.0716084 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7577.80 | −0.337422 | ||||||||
\(797\) | −20316.5 | −0.902947 | −0.451473 | − | 0.892285i | \(-0.649101\pi\) | ||||
−0.451473 | + | 0.892285i | \(0.649101\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15929.9 | −0.705332 | ||||||||
\(800\) | 4376.78 | 0.193428 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1108.50 | −0.0488062 | ||||||||
\(803\) | 15366.8 | 0.675323 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5519.14 | −0.241195 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4468.69 | 0.194564 | ||||||||
\(809\) | −12447.0 | −0.540931 | −0.270465 | − | 0.962730i | \(-0.587178\pi\) | ||||
−0.270465 | + | 0.962730i | \(0.587178\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9478.03 | 0.410380 | 0.205190 | − | 0.978722i | \(-0.434219\pi\) | ||||
0.205190 | + | 0.978722i | \(0.434219\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5527.93 | −0.238027 | ||||||||
\(815\) | 32043.9 | 1.37724 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3742.02 | −0.160241 | ||||||||
\(818\) | −4625.17 | −0.197696 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −28629.7 | −1.21926 | ||||||||
\(821\) | −3763.09 | −0.159967 | −0.0799835 | − | 0.996796i | \(-0.525487\pi\) | ||||
−0.0799835 | + | 0.996796i | \(0.525487\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21474.8 | 0.909554 | 0.454777 | − | 0.890605i | \(-0.349719\pi\) | ||||
0.454777 | + | 0.890605i | \(0.349719\pi\) | |||||||
\(824\) | 16303.2 | 0.689258 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45304.9 | −1.90496 | −0.952481 | − | 0.304597i | \(-0.901478\pi\) | ||||
−0.952481 | + | 0.304597i | \(0.901478\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4614.78 | 0.193339 | 0.0966694 | − | 0.995317i | \(-0.469181\pi\) | ||||
0.0966694 | + | 0.995317i | \(0.469181\pi\) | |||||||
\(830\) | 6080.26 | 0.254276 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 14351.0 | 0.597994 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29031.2 | 1.20319 | ||||||||
\(836\) | −24995.2 | −1.03406 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7214.90 | −0.297416 | ||||||||
\(839\) | 18308.4 | 0.753368 | 0.376684 | − | 0.926342i | \(-0.377064\pi\) | ||||
0.376684 | + | 0.926342i | \(0.377064\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62190.6 | 2.54995 | ||||||||
\(842\) | −9238.22 | −0.378112 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −41956.1 | −1.71112 | ||||||||
\(845\) | 11369.7 | 0.462876 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 29466.5 | 1.19326 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2002.22 | −0.0807946 | ||||||||
\(851\) | 6258.18 | 0.252089 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13373.0 | 0.536790 | 0.268395 | − | 0.963309i | \(-0.413507\pi\) | ||||
0.268395 | + | 0.963309i | \(0.413507\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5410.74 | −0.216046 | ||||||||
\(857\) | 17658.0 | 0.703835 | 0.351917 | − | 0.936031i | \(-0.385530\pi\) | ||||
0.351917 | + | 0.936031i | \(0.385530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12413.0 | −0.493044 | −0.246522 | − | 0.969137i | \(-0.579288\pi\) | ||||
−0.246522 | + | 0.969137i | \(0.579288\pi\) | |||||||
\(860\) | −5525.23 | −0.219080 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 153.345 | 0.00605910 | ||||||||
\(863\) | 10219.2 | 0.403087 | 0.201544 | − | 0.979480i | \(-0.435404\pi\) | ||||
0.201544 | + | 0.979480i | \(0.435404\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27483.5 | −1.08031 | ||||||||
\(866\) | 7722.22 | 0.303016 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3749.93 | 0.146384 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2368.18 | 0.0921272 | ||||||||
\(872\) | −8957.00 | −0.347847 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1158.76 | −0.0448464 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 952.207 | 0.0366633 | 0.0183317 | − | 0.999832i | \(-0.494165\pi\) | ||||
0.0183317 | + | 0.999832i | \(0.494165\pi\) | |||||||
\(878\) | −1663.89 | −0.0639561 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −35333.0 | −1.35350 | ||||||||
\(881\) | −25182.5 | −0.963021 | −0.481510 | − | 0.876440i | \(-0.659912\pi\) | ||||
−0.481510 | + | 0.876440i | \(0.659912\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3941.95 | −0.150234 | −0.0751172 | − | 0.997175i | \(-0.523933\pi\) | ||||
−0.0751172 | + | 0.997175i | \(0.523933\pi\) | |||||||
\(884\) | −23246.1 | −0.884448 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7875.45 | −0.298624 | ||||||||
\(887\) | −41630.5 | −1.57589 | −0.787946 | − | 0.615744i | \(-0.788856\pi\) | ||||
−0.787946 | + | 0.615744i | \(0.788856\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 11557.0 | 0.435271 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 35555.3 | 1.33462 | ||||||||
\(893\) | 12900.6 | 0.483428 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20455.6 | −0.763972 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3555.64 | 0.132130 | ||||||||
\(899\) | 79694.3 | 2.95657 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43393.2 | −1.60448 | ||||||||
\(902\) | −7779.34 | −0.287166 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10598.1 | 0.389918 | ||||||||
\(905\) | 59722.9 | 2.19365 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34713.1 | 1.27081 | 0.635407 | − | 0.772177i | \(-0.280832\pi\) | ||||
0.635407 | + | 0.772177i | \(0.280832\pi\) | |||||||
\(908\) | 18734.9 | 0.684737 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22126.6 | −0.804705 | −0.402352 | − | 0.915485i | \(-0.631807\pi\) | ||||
−0.402352 | + | 0.915485i | \(0.631807\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40345.6 | −1.46248 | ||||||||
\(914\) | 5116.39 | 0.185159 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22644.7 | 0.816816 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38198.8 | −1.37112 | −0.685561 | − | 0.728015i | \(-0.740443\pi\) | ||||
−0.685561 | + | 0.728015i | \(0.740443\pi\) | |||||||
\(920\) | −3491.97 | −0.125138 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8476.33 | 0.302769 | ||||||||
\(923\) | 9312.43 | 0.332094 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8757.09 | −0.311277 | ||||||||
\(926\) | 3600.85 | 0.127787 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 30047.1 | 1.06287 | ||||||||
\(929\) | 13387.9 | 0.472813 | 0.236407 | − | 0.971654i | \(-0.424030\pi\) | ||||
0.236407 | + | 0.971654i | \(0.424030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 26448.8 | 0.929572 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2414.96 | −0.0846039 | ||||||||
\(935\) | 52032.5 | 1.81994 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34574.1 | −1.20543 | −0.602715 | − | 0.797957i | \(-0.705914\pi\) | ||||
−0.602715 | + | 0.797957i | \(0.705914\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 19048.2 | 0.660939 | ||||||||
\(941\) | 2922.81 | 0.101255 | 0.0506274 | − | 0.998718i | \(-0.483878\pi\) | ||||
0.0506274 | + | 0.998718i | \(0.483878\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8807.01 | 0.304131 | ||||||||
\(944\) | 21548.2 | 0.742938 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1501.33 | −0.0515989 | ||||||||
\(947\) | −9913.84 | −0.340186 | −0.170093 | − | 0.985428i | \(-0.554407\pi\) | ||||
−0.170093 | + | 0.985428i | \(0.554407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11573.8 | −0.395891 | ||||||||
\(950\) | 1621.46 | 0.0553759 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51173.4 | 1.73942 | 0.869710 | − | 0.493562i | \(-0.164306\pi\) | ||||
0.869710 | + | 0.493562i | \(0.164306\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16735.7 | −0.567073 | ||||||||
\(956\) | −5718.02 | −0.193446 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2822.16 | −0.0951772 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43565.5 | 1.46237 | ||||||||
\(962\) | 4163.45 | 0.139537 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −36231.3 | −1.21051 | ||||||||
\(965\) | −15236.5 | −0.508268 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8758.72 | 0.291273 | 0.145637 | − | 0.989338i | \(-0.453477\pi\) | ||||
0.145637 | + | 0.989338i | \(0.453477\pi\) | |||||||
\(968\) | −8755.33 | −0.290710 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8648.34 | 0.286270 | ||||||||
\(971\) | −8293.18 | −0.274089 | −0.137045 | − | 0.990565i | \(-0.543760\pi\) | ||||
−0.137045 | + | 0.990565i | \(0.543760\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7461.50 | −0.245464 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8790.91 | 0.288309 | ||||||||
\(977\) | 18969.7 | 0.621181 | 0.310590 | − | 0.950544i | \(-0.399473\pi\) | ||||
0.310590 | + | 0.950544i | \(0.399473\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −76686.4 | −2.50348 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5187.10 | 0.168561 | ||||||||
\(983\) | −56313.2 | −1.82718 | −0.913588 | − | 0.406642i | \(-0.866700\pi\) | ||||
−0.913588 | + | 0.406642i | \(0.866700\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −59089.0 | −1.91140 | ||||||||
\(986\) | −13745.5 | −0.443960 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18825.5 | 0.606193 | ||||||||
\(989\) | 1699.66 | 0.0546472 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8558.30 | −0.274332 | −0.137166 | − | 0.990548i | \(-0.543799\pi\) | ||||
−0.137166 | + | 0.990548i | \(0.543799\pi\) | |||||||
\(992\) | 27657.6 | 0.885212 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12774.9 | −0.407027 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36163.8 | −1.14876 | −0.574382 | − | 0.818587i | \(-0.694758\pi\) | ||||
−0.574382 | + | 0.818587i | \(0.694758\pi\) | |||||||
\(998\) | −9106.77 | −0.288847 | ||||||||
\(999\) | 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 | 1323.4.a.bf.1.4 | yes | 6 | |
3.2 | odd | 2 | inner | 1323.4.a.bf.1.3 | ✓ | 6 | |
7.6 | odd | 2 | 1323.4.a.bg.1.4 | yes | 6 | ||
21.20 | even | 2 | 1323.4.a.bg.1.3 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1323.4.a.bf.1.3 | ✓ | 6 | 3.2 | odd | 2 | inner | |
1323.4.a.bf.1.4 | yes | 6 | 1.1 | even | 1 | trivial | |
1323.4.a.bg.1.3 | yes | 6 | 21.20 | even | 2 | ||
1323.4.a.bg.1.4 | yes | 6 | 7.6 | odd | 2 |