Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 217 x^{10} + 520 x^{9} + 16022 x^{8} - 37368 x^{7} - 509640 x^{6} + 989168 x^{5} + \cdots + 14751072 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{17} \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.676012\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | 0 | ||||||||
\(3\) | −0.323988 | −0.0623515 | −0.0311757 | − | 0.999514i | \(-0.509925\pi\) | ||||
−0.0311757 | + | 0.999514i | \(0.509925\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.78413 | 0.517348 | 0.258674 | − | 0.965965i | \(-0.416714\pi\) | ||||
0.258674 | + | 0.965965i | \(0.416714\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −34.7780 | −1.87783 | −0.938917 | − | 0.344143i | \(-0.888169\pi\) | ||||
−0.938917 | + | 0.344143i | \(0.888169\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.8950 | −0.996112 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.6550 | −0.511336 | −0.255668 | − | 0.966765i | \(-0.582295\pi\) | ||||
−0.255668 | + | 0.966765i | \(0.582295\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −38.6717 | −0.825046 | −0.412523 | − | 0.910947i | \(-0.635352\pi\) | ||||
−0.412523 | + | 0.910947i | \(0.635352\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.87399 | −0.0322574 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −101.230 | −1.44422 | −0.722112 | − | 0.691776i | \(-0.756828\pi\) | ||||
−0.722112 | + | 0.691776i | \(0.756828\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.73516 | −0.0209512 | −0.0104756 | − | 0.999945i | \(-0.503335\pi\) | ||||
−0.0104756 | + | 0.999945i | \(0.503335\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.2676 | 0.117086 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.4055 | −0.221257 | −0.110628 | − | 0.993862i | \(-0.535286\pi\) | ||||
−0.110628 | + | 0.993862i | \(0.535286\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −91.5438 | −0.732351 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.4613 | 0.124461 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −186.050 | −1.07792 | −0.538962 | − | 0.842330i | \(-0.681183\pi\) | ||||
−0.538962 | + | 0.842330i | \(0.681183\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.04400 | 0.0318826 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −201.160 | −0.971495 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 339.618 | 1.50900 | 0.754498 | − | 0.656303i | \(-0.227881\pi\) | ||||
0.754498 | + | 0.656303i | \(0.227881\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.5292 | 0.0514429 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 34.8517 | 0.132754 | 0.0663770 | − | 0.997795i | \(-0.478856\pi\) | ||||
0.0663770 | + | 0.997795i | \(0.478856\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −483.340 | −1.71416 | −0.857078 | − | 0.515187i | \(-0.827723\pi\) | ||||
−0.857078 | + | 0.515187i | \(0.827723\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −155.564 | −0.515337 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −266.551 | −0.827244 | −0.413622 | − | 0.910449i | \(-0.635736\pi\) | ||||
−0.413622 | + | 0.910449i | \(0.635736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 866.508 | 2.52626 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 32.7972 | 0.0900495 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −148.821 | −0.385701 | −0.192850 | − | 0.981228i | \(-0.561773\pi\) | ||||
−0.192850 | + | 0.981228i | \(0.561773\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −107.903 | −0.264539 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.562169 | 0.00130634 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.98434 | −0.0154116 | −0.00770579 | − | 0.999970i | \(-0.502453\pi\) | ||||
−0.00770579 | + | 0.999970i | \(0.502453\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −38.0806 | −0.0799298 | −0.0399649 | − | 0.999201i | \(-0.512725\pi\) | ||||
−0.0399649 | + | 0.999201i | \(0.512725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 935.355 | 1.87053 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −223.682 | −0.426836 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −544.060 | −0.992053 | −0.496026 | − | 0.868307i | \(-0.665208\pi\) | ||||
−0.496026 | + | 0.868307i | \(0.665208\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.90710 | 0.0137957 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1064.67 | 1.77962 | 0.889812 | − | 0.456327i | \(-0.150835\pi\) | ||||
0.889812 | + | 0.456327i | \(0.150835\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 688.581 | 1.10400 | 0.552002 | − | 0.833843i | \(-0.313864\pi\) | ||||
0.552002 | + | 0.833843i | \(0.313864\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 29.6591 | 0.0456632 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 648.784 | 0.960205 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −424.529 | −0.604597 | −0.302299 | − | 0.953213i | \(-0.597754\pi\) | ||||
−0.302299 | + | 0.953213i | \(0.597754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 720.509 | 0.988352 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1247.54 | −1.64983 | −0.824913 | − | 0.565260i | \(-0.808776\pi\) | ||||
−0.824913 | + | 0.565260i | \(0.808776\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −585.526 | −0.747167 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.39565 | 0.0115784 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −174.320 | −0.207616 | −0.103808 | − | 0.994597i | \(-0.533103\pi\) | ||||
−0.103808 | + | 0.994597i | \(0.533103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1344.92 | 1.54930 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 60.2781 | 0.0672102 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.0364 | −0.0108390 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 33.7772 | 0.0353563 | 0.0176781 | − | 0.999844i | \(-0.494373\pi\) | ||||
0.0176781 | + | 0.999844i | \(0.494373\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 501.727 | 0.509348 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1665.04 | 1.64037 | 0.820184 | − | 0.572099i | \(-0.193871\pi\) | ||||
0.820184 | + | 0.572099i | \(0.193871\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1040.43 | 0.995309 | 0.497655 | − | 0.867375i | \(-0.334195\pi\) | ||||
0.497655 | + | 0.867375i | \(0.334195\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 65.1735 | 0.0605741 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −377.579 | −0.341139 | −0.170570 | − | 0.985346i | \(-0.554561\pi\) | ||||
−0.170570 | + | 0.985346i | \(0.554561\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 859.283 | 0.755086 | 0.377543 | − | 0.925992i | \(-0.376769\pi\) | ||||
0.377543 | + | 0.925992i | \(0.376769\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −110.032 | −0.0940881 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1386.98 | −1.15465 | −0.577326 | − | 0.816514i | \(-0.695904\pi\) | ||||
−0.577326 | + | 0.816514i | \(0.695904\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −141.165 | −0.114467 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1040.08 | 0.821839 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3520.56 | 2.71201 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −982.991 | −0.738535 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.2915 | −0.00827742 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1252.52 | −0.896229 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −981.731 | −0.685941 | −0.342970 | − | 0.939346i | \(-0.611433\pi\) | ||||
−0.342970 | + | 0.939346i | \(0.611433\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 156.596 | 0.106880 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −668.964 | −0.446166 | −0.223083 | − | 0.974800i | \(-0.571612\pi\) | ||||
−0.223083 | + | 0.974800i | \(0.571612\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 60.3452 | 0.0393428 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 100.999 | 0.0643895 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 138.077 | 0.0861072 | 0.0430536 | − | 0.999073i | \(-0.486291\pi\) | ||||
0.0430536 | + | 0.999073i | \(0.486291\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1004.97 | −0.613241 | −0.306621 | − | 0.951832i | \(-0.599198\pi\) | ||||
−0.306621 | + | 0.951832i | \(0.599198\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 86.3593 | 0.0515799 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 721.421 | 0.421876 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −167.740 | −0.0960692 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −280.738 | −0.157516 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3548.03 | 1.95078 | 0.975388 | − | 0.220495i | \(-0.0707673\pi\) | ||||
0.975388 | + | 0.220495i | \(0.0707673\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1569.44 | 0.845823 | 0.422912 | − | 0.906171i | \(-0.361008\pi\) | ||||
0.422912 | + | 0.906171i | \(0.361008\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2722.58 | 1.43861 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1076.14 | −0.557662 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2180.42 | −1.10839 | −0.554194 | − | 0.832388i | \(-0.686973\pi\) | ||||
−0.554194 | + | 0.832388i | \(0.686973\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 48.2162 | 0.0240490 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 848.775 | 0.415484 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1450.58 | −0.697045 | −0.348523 | − | 0.937300i | \(-0.613317\pi\) | ||||
−0.348523 | + | 0.937300i | \(0.613317\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 34.9593 | 0.0164944 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1600.50 | 0.741618 | 0.370809 | − | 0.928709i | \(-0.379081\pi\) | ||||
0.370809 | + | 0.928709i | \(0.379081\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −701.499 | −0.319299 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 46.6671 | 0.0208697 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1909.39 | −0.839124 | −0.419562 | − | 0.907727i | \(-0.637816\pi\) | ||||
−0.419562 | + | 0.907727i | \(0.637816\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3183.71 | 1.37523 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.26284 | 0.000960936 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2562.06 | −1.06982 | −0.534908 | − | 0.844910i | \(-0.679654\pi\) | ||||
−0.534908 | + | 0.844910i | \(0.679654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1803.16 | −0.740485 | −0.370242 | − | 0.928935i | \(-0.620725\pi\) | ||||
−0.370242 | + | 0.928935i | \(0.620725\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.3376 | 0.00498374 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1964.39 | 0.780676 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1888.44 | 0.738484 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −607.270 | −0.233716 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4097.08 | −1.55212 | −0.776059 | − | 0.630661i | \(-0.782784\pi\) | ||||
−0.776059 | + | 0.630661i | \(0.782784\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2395.56 | 0.893452 | 0.446726 | − | 0.894671i | \(-0.352590\pi\) | ||||
0.446726 | + | 0.894671i | \(0.352590\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 72.4703 | 0.0266139 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2927.37 | 1.05871 | 0.529357 | − | 0.848399i | \(-0.322433\pi\) | ||||
0.529357 | + | 0.848399i | \(0.322433\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2894.37 | −1.03104 | −0.515519 | − | 0.856878i | \(-0.672401\pi\) | ||||
−0.515519 | + | 0.856878i | \(0.672401\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 176.269 | 0.0618560 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1008.56 | 0.348705 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 201.587 | 0.0686801 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 656.388 | 0.220397 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 32.3693 | 0.0107131 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2576.49 | −0.840630 | −0.420315 | − | 0.907378i | \(-0.638080\pi\) | ||||
−0.420315 | + | 0.907378i | \(0.638080\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −344.941 | −0.110962 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2795.70 | −0.886816 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6470.46 | 2.02416 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −223.092 | −0.0688363 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3914.73 | 1.19155 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3521.80 | −1.05756 | −0.528782 | − | 0.848758i | \(-0.677351\pi\) | ||||
−0.528782 | + | 0.848758i | \(0.677351\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2462.07 | 0.729503 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2334.62 | 0.682617 | 0.341308 | − | 0.939951i | \(-0.389130\pi\) | ||||
0.341308 | + | 0.939951i | \(0.389130\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2095.27 | −0.604626 | −0.302313 | − | 0.953209i | \(-0.597759\pi\) | ||||
−0.302313 | + | 0.953209i | \(0.597759\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −210.198 | −0.0598702 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4185.52 | −1.17683 | −0.588417 | − | 0.808557i | \(-0.700249\pi\) | ||||
−0.588417 | + | 0.808557i | \(0.700249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1541.77 | −0.427973 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 137.542 | 0.0376975 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4505.51 | 1.21940 | 0.609702 | − | 0.792631i | \(-0.291289\pi\) | ||||
0.609702 | + | 0.792631i | \(0.291289\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2957.99 | −0.790627 | −0.395313 | − | 0.918546i | \(-0.629364\pi\) | ||||
−0.395313 | + | 0.918546i | \(0.629364\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −704.892 | −0.186086 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5011.99 | 1.30696 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 67.1014 | 0.0172857 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 404.189 | 0.102869 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2524.50 | 0.634842 | 0.317421 | − | 0.948285i | \(-0.397183\pi\) | ||||
0.317421 | + | 0.948285i | \(0.397183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 455.286 | 0.113137 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 189.703 | 0.0465870 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2763.13 | −0.670658 | −0.335329 | − | 0.942101i | \(-0.608847\pi\) | ||||
−0.335329 | + | 0.942101i | \(0.608847\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11811.2 | −2.83364 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 779.956 | 0.184973 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1969.77 | 0.461829 | 0.230914 | − | 0.972974i | \(-0.425828\pi\) | ||||
0.230914 | + | 0.972974i | \(0.425828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −860.800 | −0.199542 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 56.4775 | 0.0129452 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 843.547 | 0.191197 | 0.0955984 | − | 0.995420i | \(-0.469524\pi\) | ||||
0.0955984 | + | 0.995420i | \(0.469524\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2221.93 | −0.498053 | −0.249027 | − | 0.968497i | \(-0.580111\pi\) | ||||
−0.249027 | + | 0.968497i | \(0.580111\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −435.739 | −0.0966012 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1707.75 | 0.374477 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2165.46 | 0.469710 | 0.234855 | − | 0.972030i | \(-0.424538\pi\) | ||||
0.234855 | + | 0.972030i | \(0.424538\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5003.83 | 1.07373 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2378.13 | 0.504867 | 0.252434 | − | 0.967614i | \(-0.418769\pi\) | ||||
0.252434 | + | 0.967614i | \(0.418769\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4690.25 | −0.985181 | −0.492591 | − | 0.870261i | \(-0.663950\pi\) | ||||
−0.492591 | + | 0.870261i | \(0.663950\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.25166 | 0.000675831 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1212.07 | −0.249290 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5334.45 | 1.08578 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.9434 | −0.00220452 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6610.75 | 1.31810 | 0.659051 | − | 0.752098i | \(-0.270958\pi\) | ||||
0.659051 | + | 0.752098i | \(0.270958\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −40.3983 | −0.00797316 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −325.741 | −0.0636412 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 943.804 | 0.182547 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16809.6 | 3.21890 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −539.451 | −0.102279 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −220.263 | −0.0413516 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8217.54 | 1.52769 | 0.763843 | − | 0.645402i | \(-0.223310\pi\) | ||||
0.763843 | + | 0.645402i | \(0.223310\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −337.088 | −0.0620590 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3610.62 | 0.658325 | 0.329163 | − | 0.944273i | \(-0.393234\pi\) | ||||
0.329163 | + | 0.944273i | \(0.393234\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10201.5 | 1.84224 | 0.921119 | − | 0.389280i | \(-0.127276\pi\) | ||||
0.921119 | + | 0.389280i | \(0.127276\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5410.22 | 0.967718 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6875.78 | −1.21824 | −0.609120 | − | 0.793078i | \(-0.708477\pi\) | ||||
−0.609120 | + | 0.793078i | \(0.708477\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 540.995 | 0.0949527 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 122.331 | 0.0212705 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 175.649 | 0.0302582 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3540.16 | 0.604223 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −278.397 | −0.0470807 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9270.10 | 1.55343 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9037.73 | 1.50078 | 0.750391 | − | 0.660995i | \(-0.229865\pi\) | ||||
0.750391 | + | 0.660995i | \(0.229865\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9134.03 | −1.50313 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3146.92 | −0.513237 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −884.371 | −0.142952 | −0.0714759 | − | 0.997442i | \(-0.522771\pi\) | ||||
−0.0714759 | + | 0.997442i | \(0.522771\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 449.363 | 0.0719943 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3470.77 | 0.551181 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18206.5 | −2.86607 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 45.7357 | 0.00713718 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6455.66 | −0.998726 | −0.499363 | − | 0.866393i | \(-0.666433\pi\) | ||||
−0.499363 | + | 0.866393i | \(0.666433\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9893.81 | 1.51749 | 0.758744 | − | 0.651389i | \(-0.225813\pi\) | ||||
0.758744 | + | 0.651389i | \(0.225813\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −675.260 | −0.102686 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11997.3 | 1.80893 | 0.904463 | − | 0.426551i | \(-0.140272\pi\) | ||||
0.904463 | + | 0.426551i | \(0.140272\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6158.20 | 0.920686 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1140.62 | −0.169098 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3692.23 | −0.542810 | −0.271405 | − | 0.962465i | \(-0.587488\pi\) | ||||
−0.271405 | + | 0.962465i | \(0.587488\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6855.99 | −0.999561 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 318.477 | 0.0460488 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3982.84 | 0.571155 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3510.51 | 0.499310 | 0.249655 | − | 0.968335i | \(-0.419683\pi\) | ||||
0.249655 | + | 0.968335i | \(0.419683\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −937.337 | −0.132238 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5175.69 | 0.724282 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6581.99 | −0.913680 | −0.456840 | − | 0.889549i | \(-0.651019\pi\) | ||||
−0.456840 | + | 0.889549i | \(0.651019\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 405.801 | 0.0558812 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1121.48 | 0.153207 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2946.59 | 0.399356 | 0.199678 | − | 0.979862i | \(-0.436010\pi\) | ||||
0.199678 | + | 0.979862i | \(0.436010\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 318.069 | 0.0427694 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5187.37 | 0.692068 | 0.346034 | − | 0.938222i | \(-0.387528\pi\) | ||||
0.346034 | + | 0.938222i | \(0.387528\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3752.65 | 0.496760 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12999.5 | 1.70749 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6926.04 | −0.902736 | −0.451368 | − | 0.892338i | \(-0.649064\pi\) | ||||
−0.451368 | + | 0.892338i | \(0.649064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2470.56 | 0.319544 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 216.736 | 0.0278191 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2455.53 | −0.312787 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4750.53 | −0.600559 | −0.300280 | − | 0.953851i | \(-0.597080\pi\) | ||||
−0.300280 | + | 0.953851i | \(0.597080\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.5511 | −0.00245308 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2766.90 | 0.344569 | 0.172285 | − | 0.985047i | \(-0.444885\pi\) | ||||
0.172285 | + | 0.985047i | \(0.444885\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7194.89 | 0.889337 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4167.52 | 0.511322 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6335.58 | −0.771604 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11381.2 | −1.37595 | −0.687975 | − | 0.725734i | \(-0.741500\pi\) | ||||
−0.687975 | + | 0.725734i | \(0.741500\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −44.7352 | −0.00536891 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 242.901 | 0.0289404 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7215.95 | −0.853535 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 325.599 | 0.0382365 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8513.34 | 0.992611 | 0.496306 | − | 0.868148i | \(-0.334690\pi\) | ||||
0.496306 | + | 0.868148i | \(0.334690\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10096.2 | −1.16878 | −0.584391 | − | 0.811472i | \(-0.698667\pi\) | ||||
−0.584391 | + | 0.811472i | \(0.698667\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7168.90 | 0.824027 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9266.95 | 1.05768 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1324.37 | 0.150095 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −233.732 | −0.0263046 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8704.01 | 0.972755 | 0.486377 | − | 0.873749i | \(-0.338318\pi\) | ||||
0.486377 | + | 0.873749i | \(0.338318\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14332.2 | 1.59067 | 0.795337 | − | 0.606168i | \(-0.207294\pi\) | ||||
0.795337 | + | 0.606168i | \(0.207294\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 54.3457 | 0.00599006 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 42.3474 | 0.00463558 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17693.7 | −1.92363 | −0.961813 | − | 0.273707i | \(-0.911750\pi\) | ||||
−0.961813 | + | 0.273707i | \(0.911750\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −23304.8 | −2.51644 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11328.3 | 1.21495 | 0.607474 | − | 0.794339i | \(-0.292183\pi\) | ||||
0.607474 | + | 0.794339i | \(0.292183\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1008.29 | −0.107410 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1149.52 | −0.121634 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14065.7 | 1.47840 | 0.739198 | − | 0.673488i | \(-0.235205\pi\) | ||||
0.739198 | + | 0.673488i | \(0.235205\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −650.158 | −0.0678820 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −508.480 | −0.0527384 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7779.22 | 0.801528 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13414.1 | −1.37305 | −0.686524 | − | 0.727107i | \(-0.740864\pi\) | ||||
−0.686524 | + | 0.727107i | \(0.740864\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1767.61 | −0.179749 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4676.87 | 0.472502 | 0.236251 | − | 0.971692i | \(-0.424081\pi\) | ||||
0.236251 | + | 0.971692i | \(0.424081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1297.23 | 0.130211 | 0.0651054 | − | 0.997878i | \(-0.479262\pi\) | ||||
0.0651054 | + | 0.997878i | \(0.479262\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 348.656 | 0.0347711 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9912.42 | −0.982210 | −0.491105 | − | 0.871100i | \(-0.663407\pi\) | ||||
−0.491105 | + | 0.871100i | \(0.663407\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18921.3 | 1.86291 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 706.431 | 0.0691096 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9016.72 | 0.876510 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 158.843 | 0.0153436 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4002.55 | 0.384201 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1373.12 | 0.130980 | 0.0654900 | − | 0.997853i | \(-0.479139\pi\) | ||||
0.0654900 | + | 0.997853i | \(0.479139\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13133.6 | −1.24499 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −274.993 | −0.0259060 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 195.372 | 0.0182915 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13565.0 | −1.26220 | −0.631099 | − | 0.775703i | \(-0.717396\pi\) | ||||
−0.631099 | + | 0.775703i | \(0.717396\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 469.971 | 0.0434618 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5322.07 | 0.489168 | 0.244584 | − | 0.969628i | \(-0.421349\pi\) | ||||
0.244584 | + | 0.969628i | \(0.421349\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2935.66 | 0.268186 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2902.06 | 0.263511 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37027.1 | −3.34184 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1151.61 | 0.103313 | 0.0516566 | − | 0.998665i | \(-0.483550\pi\) | ||||
0.0516566 | + | 0.998665i | \(0.483550\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −518.541 | −0.0462410 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15046.7 | −1.33380 | −0.666900 | − | 0.745147i | \(-0.732379\pi\) | ||||
−0.666900 | + | 0.745147i | \(0.732379\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9630.78 | 0.848642 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 227.277 | 0.0199087 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17124.7 | −1.49124 | −0.745619 | − | 0.666373i | \(-0.767846\pi\) | ||||
−0.745619 | + | 0.666373i | \(0.767846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23947.5 | −2.07314 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −30.2981 | −0.00260759 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6018.00 | 0.514922 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4972.51 | 0.423000 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 618.620 | 0.0523206 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15336.5 | 1.28964 | 0.644821 | − | 0.764334i | \(-0.276932\pi\) | ||||
0.644821 | + | 0.764334i | \(0.276932\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16190.8 | −1.35368 | −0.676839 | − | 0.736131i | \(-0.736651\pi\) | ||||
−0.676839 | + | 0.736131i | \(0.736651\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1031.48 | −0.0857478 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18833.8 | 1.55676 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11571.4 | −0.951045 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 187.844 | 0.0153517 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1347.77 | −0.109528 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2183.96 | −0.176488 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 830.075 | 0.0667046 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16164.7 | −1.29177 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13157.9 | −1.04566 | −0.522831 | − | 0.852436i | \(-0.675124\pi\) | ||||
−0.522831 | + | 0.852436i | \(0.675124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 584.202 | 0.0461703 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4970.20 | 0.390643 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19078.0 | −1.49126 | −0.745628 | − | 0.666363i | \(-0.767850\pi\) | ||||
−0.745628 | + | 0.666363i | \(0.767850\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1024.18 | 0.0796191 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 50.3195 | 0.00389053 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14764.2 | 1.13533 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −636.440 | −0.0486763 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 708.764 | 0.0539161 | 0.0269581 | − | 0.999637i | \(-0.491418\pi\) | ||||
0.0269581 | + | 0.999637i | \(0.491418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18691.6 | 1.41426 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −611.832 | −0.0460456 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14875.1 | 1.11352 | 0.556759 | − | 0.830674i | \(-0.312045\pi\) | ||||
0.556759 | + | 0.830674i | \(0.312045\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8022.45 | −0.597357 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −25057.8 | −1.85596 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10910.6 | −0.803863 | −0.401932 | − | 0.915670i | \(-0.631661\pi\) | ||||
−0.401932 | + | 0.915670i | \(0.631661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6711.77 | −0.491907 | −0.245953 | − | 0.969282i | \(-0.579101\pi\) | ||||
−0.245953 | + | 0.969282i | \(0.579101\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1327.40 | 0.0967768 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2234.18 | 0.162038 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18292.6 | −1.31981 | −0.659906 | − | 0.751348i | \(-0.729404\pi\) | ||||
−0.659906 | + | 0.751348i | \(0.729404\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −776.133 | −0.0557081 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 43387.0 | 3.09810 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2776.26 | 0.197223 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6015.94 | 0.425177 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23230.2 | −1.63341 | −0.816705 | − | 0.577056i | \(-0.804201\pi\) | ||||
−0.816705 | + | 0.577056i | \(0.804201\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 322.826 | 0.0225837 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −948.433 | −0.0660124 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10789.9 | −0.747200 | −0.373600 | − | 0.927590i | \(-0.621877\pi\) | ||||
−0.373600 | + | 0.927590i | \(0.621877\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20363.4 | 1.40306 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 937.742 | 0.0642868 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8421.66 | 0.574457 | 0.287228 | − | 0.957862i | \(-0.407266\pi\) | ||||
0.287228 | + | 0.957862i | \(0.407266\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17485.5 | 1.18677 | 0.593385 | − | 0.804919i | \(-0.297791\pi\) | ||||
0.593385 | + | 0.804919i | \(0.297791\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14632.5 | 0.988196 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5685.75 | −0.382080 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17492.2 | −1.16966 | −0.584831 | − | 0.811155i | \(-0.698839\pi\) | ||||
−0.584831 | + | 0.811155i | \(0.698839\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −326.762 | −0.0217423 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10308.0 | 0.682514 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5443.64 | 0.358673 | 0.179337 | − | 0.983788i | \(-0.442605\pi\) | ||||
0.179337 | + | 0.983788i | \(0.442605\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −65.3116 | −0.00428231 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26323.3 | 1.71756 | 0.858781 | − | 0.512343i | \(-0.171222\pi\) | ||||
0.858781 | + | 0.512343i | \(0.171222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15401.0 | −1.00003 | −0.500013 | − | 0.866018i | \(-0.666672\pi\) | ||||
−0.500013 | + | 0.866018i | \(0.666672\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −426.153 | −0.0275377 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6062.49 | 0.389869 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4198.25 | 0.268688 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.4873 | −0.000667977 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34379.4 | −2.17933 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20419.0 | 1.28822 | 0.644110 | − | 0.764933i | \(-0.277228\pi\) | ||||
0.644110 | + | 0.764933i | \(0.277228\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 834.752 | 0.0524145 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5678.46 | −0.354870 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33509.3 | −2.08428 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28634.4 | −1.77271 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11936.3 | −0.735497 | −0.367749 | − | 0.929925i | \(-0.619871\pi\) | ||||
−0.367749 | + | 0.929925i | \(0.619871\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19181.0 | 1.17640 | 0.588199 | − | 0.808716i | \(-0.299837\pi\) | ||||
0.588199 | + | 0.808716i | \(0.299837\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 905.774 | 0.0552943 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4250.18 | 0.258256 | 0.129128 | − | 0.991628i | \(-0.458782\pi\) | ||||
0.129128 | + | 0.991628i | \(0.458782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 130.293 | 0.00788050 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2096.35 | −0.126210 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28165.6 | −1.68791 | −0.843956 | − | 0.536413i | \(-0.819779\pi\) | ||||
−0.843956 | + | 0.536413i | \(0.819779\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3869.38 | −0.230823 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18519.4 | −1.09971 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32600.6 | −1.92707 | −0.963536 | − | 0.267579i | \(-0.913776\pi\) | ||||
−0.963536 | + | 0.267579i | \(0.913776\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10591.5 | 0.623242 | 0.311621 | − | 0.950207i | \(-0.399128\pi\) | ||||
0.311621 | + | 0.950207i | \(0.399128\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1268.32 | −0.0742950 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 349.044 | 0.0203539 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 707.761 | 0.0410864 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1141.02 | 0.0659407 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 710.394 | 0.0408710 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5065.78 | −0.290151 | −0.145075 | − | 0.989421i | \(-0.546342\pi\) | ||||
−0.145075 | + | 0.989421i | \(0.546342\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1598.48 | −0.0911488 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4021.25 | −0.228286 | −0.114143 | − | 0.993464i | \(-0.536412\pi\) | ||||
−0.114143 | + | 0.993464i | \(0.536412\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1174.70 | −0.0663932 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −756.388 | −0.0425622 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4846.20 | −0.271500 | −0.135750 | − | 0.990743i | \(-0.543344\pi\) | ||||
−0.135750 | + | 0.990743i | \(0.543344\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 798.654 | 0.0445474 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 678.842 | 0.0376993 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5755.16 | 0.318221 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13400.8 | 0.737758 | 0.368879 | − | 0.929477i | \(-0.379742\pi\) | ||||
0.368879 | + | 0.929477i | \(0.379742\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −17449.1 | −0.956472 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5812.89 | −0.317259 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3528.02 | −0.191727 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1356.06 | 0.0733774 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22862.4 | −1.23182 | −0.615908 | − | 0.787818i | \(-0.711211\pi\) | ||||
−0.615908 | + | 0.787818i | \(0.711211\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −589.290 | −0.0316152 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 499.513 | 0.0266848 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −57906.6 | −3.08034 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13106.1 | 0.694229 | 0.347115 | − | 0.937823i | \(-0.387161\pi\) | ||||
0.347115 | + | 0.937823i | \(0.387161\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11417.7 | 0.602247 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4540.66 | 0.238498 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4172.80 | 0.218257 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1459.73 | −0.0760316 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7109.97 | 0.368786 | 0.184393 | − | 0.982853i | \(-0.440968\pi\) | ||||
0.184393 | + | 0.982853i | \(0.440968\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36184.1 | −1.86903 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 958.354 | 0.0492968 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2654.77 | 0.135994 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32017.5 | 1.63338 | 0.816689 | − | 0.577079i | \(-0.195807\pi\) | ||||
0.816689 | + | 0.577079i | \(0.195807\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19225.4 | −0.976749 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48928.4 | 2.47563 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1715.94 | −0.0864662 | −0.0432331 | − | 0.999065i | \(-0.513766\pi\) | ||||
−0.0432331 | + | 0.999065i | \(0.513766\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1623.83 | −0.0814908 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10149.5 | 0.507273 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14545.0 | 0.724016 | 0.362008 | − | 0.932175i | \(-0.382091\pi\) | ||||
0.362008 | + | 0.932175i | \(0.382091\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.7400 | −0.00107779 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15502.4 | 0.765447 | 0.382723 | − | 0.923863i | \(-0.374986\pi\) | ||||
0.382723 | + | 0.923863i | \(0.374986\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20522.3 | 1.00923 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 33552.7 | 1.64341 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13131.4 | 0.640603 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32985.0 | 1.60271 | 0.801357 | − | 0.598186i | \(-0.204112\pi\) | ||||
0.801357 | + | 0.598186i | \(0.204112\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −817.909 | −0.0395833 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9077.86 | 0.437585 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38303.7 | 1.83906 | 0.919532 | − | 0.393015i | \(-0.128568\pi\) | ||||
0.919532 | + | 0.393015i | \(0.128568\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −147.507 | −0.00705424 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15993.5 | 0.761843 | 0.380921 | − | 0.924607i | \(-0.375607\pi\) | ||||
0.380921 | + | 0.924607i | \(0.375607\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29884.1 | −1.41793 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15747.7 | 0.744262 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 270.096 | 0.0127153 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5628.40 | −0.263934 | −0.131967 | − | 0.991254i | \(-0.542129\pi\) | ||||
−0.131967 | + | 0.991254i | \(0.542129\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 895.220 | 0.0418165 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4477.85 | −0.208353 | −0.104177 | − | 0.994559i | \(-0.533221\pi\) | ||||
−0.104177 | + | 0.994559i | \(0.533221\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17031.8 | 0.789418 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3826.69 | 0.176682 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −60.4731 | −0.00278135 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19861.5 | −0.909986 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −506.379 | −0.0231118 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12611.9 | −0.573422 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26974.8 | −1.22179 | −0.610894 | − | 0.791712i | \(-0.709190\pi\) | ||||
−0.610894 | + | 0.791712i | \(0.709190\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −638.180 | −0.0287957 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48236.2 | 2.16824 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1472.64 | 0.0659458 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 278.889 | 0.0124417 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14755.0 | −0.655772 | −0.327886 | − | 0.944717i | \(-0.606336\pi\) | ||||
−0.327886 | + | 0.944717i | \(0.606336\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26982.9 | 1.19472 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4688.33 | 0.206809 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12845.5 | −0.564517 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4909.43 | 0.214950 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −273.299 | −0.0119214 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24539.2 | −1.06644 | −0.533222 | − | 0.845975i | \(-0.679019\pi\) | ||||
−0.533222 | + | 0.845975i | \(0.679019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14700.6 | −0.636506 | −0.318253 | − | 0.948006i | \(-0.603096\pi\) | ||||
−0.318253 | + | 0.948006i | \(0.603096\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 719.878 | 0.0310544 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8390.36 | −0.360615 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 838.670 | 0.0359135 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −36171.8 | −1.54328 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20938.7 | −0.890092 | −0.445046 | − | 0.895508i | \(-0.646813\pi\) | ||||
−0.445046 | + | 0.895508i | \(0.646813\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17131.1 | −0.725582 | −0.362791 | − | 0.931870i | \(-0.618176\pi\) | ||||
−0.362791 | + | 0.931870i | \(0.618176\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −553.291 | −0.0233492 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1793.47 | 0.0754111 | 0.0377055 | − | 0.999289i | \(-0.487995\pi\) | ||||
0.0377055 | + | 0.999289i | \(0.487995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41036.5 | 1.71925 | 0.859624 | − | 0.510928i | \(-0.170698\pi\) | ||||
0.859624 | + | 0.510928i | \(0.170698\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −701.582 | −0.0292872 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −87716.3 | −3.64849 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9257.48 | 0.383675 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3248.69 | −0.134159 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13507.8 | −0.555830 | −0.277915 | − | 0.960606i | \(-0.589643\pi\) | ||||
−0.277915 | + | 0.960606i | \(0.589643\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −770.487 | −0.0314792 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4057.56 | −0.165189 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34186.4 | 1.38685 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1519.58 | 0.0614275 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8288.56 | −0.333875 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45261.9 | −1.81681 | −0.908405 | − | 0.418092i | \(-0.862699\pi\) | ||||
−0.908405 | + | 0.418092i | \(0.862699\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 269.928 | 0.0107969 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19373.8 | −0.772224 | −0.386112 | − | 0.922452i | \(-0.626182\pi\) | ||||
−0.386112 | + | 0.922452i | \(0.626182\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16119.9 | 0.640285 | 0.320142 | − | 0.947369i | \(-0.396269\pi\) | ||||
0.320142 | + | 0.947369i | \(0.396269\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 392.696 | 0.0155436 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17377.3 | −0.685434 | −0.342717 | − | 0.939439i | \(-0.611347\pi\) | ||||
−0.342717 | + | 0.939439i | \(0.611347\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11044.2 | −0.434119 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1728.30 | −0.0677002 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7919.58 | 0.309152 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21039.7 | 0.818490 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −908.439 | −0.0352188 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 43560.0 | 1.68297 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19608.7 | −0.755005 | −0.377503 | − | 0.926009i | \(-0.623217\pi\) | ||||
−0.377503 | + | 0.926009i | \(0.623217\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2141.80 | −0.0821856 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40317.9 | −1.54182 | −0.770911 | − | 0.636943i | \(-0.780199\pi\) | ||||
−0.770911 | + | 0.636943i | \(0.780199\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17384.9 | 0.662567 | 0.331284 | − | 0.943531i | \(-0.392518\pi\) | ||||
0.331284 | + | 0.943531i | \(0.392518\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.0886 | 0.000497139 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32214.4 | 1.21945 | 0.609726 | − | 0.792612i | \(-0.291279\pi\) | ||||
0.609726 | + | 0.792612i | \(0.291279\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34142.6 | 1.28808 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13441.1 | −0.505380 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 462.507 | 0.0173317 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14819.3 | −0.553467 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −305.781 | −0.0113821 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5395.46 | 0.200165 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15065.1 | 0.557038 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5446.11 | −0.200703 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10429.7 | −0.383089 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13733.5 | −0.502771 | −0.251385 | − | 0.967887i | \(-0.580886\pi\) | ||||
−0.251385 | + | 0.967887i | \(0.580886\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −44781.2 | −1.63399 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46583.7 | 1.69417 | 0.847085 | − | 0.531458i | \(-0.178356\pi\) | ||||
0.847085 | + | 0.531458i | \(0.178356\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23272.9 | 0.843616 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 71.3626 | 0.00257833 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23265.2 | 0.837825 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50389.1 | −1.80869 | −0.904343 | − | 0.426807i | \(-0.859638\pi\) | ||||
−0.904343 | + | 0.426807i | \(0.859638\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2662.38 | −0.0952535 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −41172.7 | −1.46827 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31089.9 | −1.10511 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −27982.5 | −0.991440 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16132.1 | 0.569728 | 0.284864 | − | 0.958568i | \(-0.408052\pi\) | ||||
0.284864 | + | 0.958568i | \(0.408052\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1503.53 | −0.0529281 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1169.80 | −0.0410476 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10923.0 | 0.382054 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14997.5 | −0.522888 | −0.261444 | − | 0.965219i | \(-0.584199\pi\) | ||||
−0.261444 | + | 0.965219i | \(0.584199\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3305.15 | −0.114866 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47704.3 | −1.65262 | −0.826310 | − | 0.563216i | \(-0.809564\pi\) | ||||
−0.826310 | + | 0.563216i | \(0.809564\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −850.574 | −0.0293727 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3512.53 | −0.120913 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −55295.6 | −1.89743 | −0.948715 | − | 0.316133i | \(-0.897615\pi\) | ||||
−0.948715 | + | 0.316133i | \(0.897615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26628.6 | −0.910855 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2227.67 | 0.0759591 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25225.6 | 0.857438 | 0.428719 | − | 0.903438i | \(-0.358965\pi\) | ||||
0.428719 | + | 0.903438i | \(0.358965\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23698.1 | −0.802985 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −175.276 | −0.00592045 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4802.03 | −0.161695 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4823.75 | 0.161920 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10155.0 | 0.339813 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13856.2 | 0.462226 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8870.00 | −0.294974 | −0.147487 | − | 0.989064i | \(-0.547118\pi\) | ||||
−0.147487 | + | 0.989064i | \(0.547118\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −56.9082 | −0.00188664 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4362.02 | −0.144165 | −0.0720824 | − | 0.997399i | \(-0.522964\pi\) | ||||
−0.0720824 | + | 0.997399i | \(0.522964\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34950.9 | 1.15157 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1146.97 | −0.0376742 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2432.32 | −0.0796486 | −0.0398243 | − | 0.999207i | \(-0.512680\pi\) | ||||
−0.0398243 | + | 0.999207i | \(0.512680\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3251.94 | 0.106162 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23110.4 | −0.752150 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5907.53 | −0.191680 | −0.0958398 | − | 0.995397i | \(-0.530554\pi\) | ||||
−0.0958398 | + | 0.995397i | \(0.530554\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16932.3 | 0.547724 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3003.40 | −0.0968585 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11796.2 | 0.379269 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −485.384 | −0.0155588 | −0.00777938 | − | 0.999970i | \(-0.502476\pi\) | ||||
−0.00777938 | + | 0.999970i | \(0.502476\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2928.11 | −0.0935760 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16741.4 | −0.533406 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32345.7 | −1.02748 | −0.513741 | − | 0.857945i | \(-0.671741\pi\) | ||||
−0.513741 | + | 0.857945i | \(0.671741\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5930.18 | 0.187810 |
(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 | 1856.4.a.bj.1.7 | 12 | ||
4.3 | odd | 2 | 1856.4.a.bl.1.6 | 12 | |||
8.3 | odd | 2 | 928.4.a.h.1.7 | ✓ | 12 | ||
8.5 | even | 2 | 928.4.a.j.1.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.4.a.h.1.7 | ✓ | 12 | 8.3 | odd | 2 | ||
928.4.a.j.1.6 | yes | 12 | 8.5 | even | 2 | ||
1856.4.a.bj.1.7 | 12 | 1.1 | even | 1 | trivial | ||
1856.4.a.bl.1.6 | 12 | 4.3 | odd | 2 |