Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,4,Mod(1,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, 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("490.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.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: | \(28.9109359028\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{46}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 46 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(6.78233\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 7.78233 | 1.49771 | 0.748855 | − | 0.662734i | \(-0.230604\pi\) | ||||
0.748855 | + | 0.662734i | \(0.230604\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −15.5647 | −1.05904 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 33.5647 | 1.24314 | ||||||||
\(10\) | 10.0000 | 0.316228 | ||||||||
\(11\) | −47.5647 | −1.30375 | −0.651877 | − | 0.758325i | \(-0.726018\pi\) | ||||
−0.651877 | + | 0.758325i | \(0.726018\pi\) | |||||||
\(12\) | 31.1293 | 0.748855 | ||||||||
\(13\) | −1.12932 | −0.0240936 | −0.0120468 | − | 0.999927i | \(-0.503835\pi\) | ||||
−0.0120468 | + | 0.999927i | \(0.503835\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −38.9116 | −0.669796 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −136.259 | −1.94397 | −0.971987 | − | 0.235033i | \(-0.924480\pi\) | ||||
−0.971987 | + | 0.235033i | \(0.924480\pi\) | |||||||
\(18\) | −67.1293 | −0.879030 | ||||||||
\(19\) | 88.8707 | 1.07307 | 0.536535 | − | 0.843878i | \(-0.319733\pi\) | ||||
0.536535 | + | 0.843878i | \(0.319733\pi\) | |||||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 95.1293 | 0.921893 | ||||||||
\(23\) | 2.73495 | 0.0247946 | 0.0123973 | − | 0.999923i | \(-0.496054\pi\) | ||||
0.0123973 | + | 0.999923i | \(0.496054\pi\) | |||||||
\(24\) | −62.2586 | −0.529520 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 2.25864 | 0.0170368 | ||||||||
\(27\) | 51.0884 | 0.364147 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −131.082 | −0.839355 | −0.419678 | − | 0.907673i | \(-0.637857\pi\) | ||||
−0.419678 | + | 0.907673i | \(0.637857\pi\) | |||||||
\(30\) | 77.8233 | 0.473618 | ||||||||
\(31\) | −301.470 | −1.74663 | −0.873316 | − | 0.487154i | \(-0.838035\pi\) | ||||
−0.873316 | + | 0.487154i | \(0.838035\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −370.164 | −1.95264 | ||||||||
\(34\) | 272.517 | 1.37460 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 134.259 | 0.621568 | ||||||||
\(37\) | 161.388 | 0.717082 | 0.358541 | − | 0.933514i | \(-0.383274\pi\) | ||||
0.358541 | + | 0.933514i | \(0.383274\pi\) | |||||||
\(38\) | −177.741 | −0.758775 | ||||||||
\(39\) | −8.78874 | −0.0360853 | ||||||||
\(40\) | 40.0000 | 0.158114 | ||||||||
\(41\) | −288.729 | −1.09980 | −0.549900 | − | 0.835230i | \(-0.685334\pi\) | ||||
−0.549900 | + | 0.835230i | \(0.685334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −70.5582 | −0.250233 | −0.125117 | − | 0.992142i | \(-0.539931\pi\) | ||||
−0.125117 | + | 0.992142i | \(0.539931\pi\) | |||||||
\(44\) | −190.259 | −0.651877 | ||||||||
\(45\) | −167.823 | −0.555947 | ||||||||
\(46\) | −5.46990 | −0.0175324 | ||||||||
\(47\) | −136.259 | −0.422880 | −0.211440 | − | 0.977391i | \(-0.567815\pi\) | ||||
−0.211440 | + | 0.977391i | \(0.567815\pi\) | |||||||
\(48\) | 124.517 | 0.374428 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | −1060.41 | −2.91151 | ||||||||
\(52\) | −4.51728 | −0.0120468 | ||||||||
\(53\) | −34.2586 | −0.0887884 | −0.0443942 | − | 0.999014i | \(-0.514136\pi\) | ||||
−0.0443942 | + | 0.999014i | \(0.514136\pi\) | |||||||
\(54\) | −102.177 | −0.257491 | ||||||||
\(55\) | 237.823 | 0.583056 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 691.621 | 1.60715 | ||||||||
\(58\) | 262.164 | 0.593514 | ||||||||
\(59\) | 745.362 | 1.64471 | 0.822355 | − | 0.568975i | \(-0.192660\pi\) | ||||
0.822355 | + | 0.568975i | \(0.192660\pi\) | |||||||
\(60\) | −155.647 | −0.334898 | ||||||||
\(61\) | 683.845 | 1.43537 | 0.717683 | − | 0.696369i | \(-0.245202\pi\) | ||||
0.717683 | + | 0.696369i | \(0.245202\pi\) | |||||||
\(62\) | 602.940 | 1.23506 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 5.64660 | 0.0107750 | ||||||||
\(66\) | 740.328 | 1.38073 | ||||||||
\(67\) | −72.5839 | −0.132351 | −0.0661756 | − | 0.997808i | \(-0.521080\pi\) | ||||
−0.0661756 | + | 0.997808i | \(0.521080\pi\) | |||||||
\(68\) | −545.035 | −0.971987 | ||||||||
\(69\) | 21.2843 | 0.0371352 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −687.293 | −1.14883 | −0.574413 | − | 0.818565i | \(-0.694770\pi\) | ||||
−0.574413 | + | 0.818565i | \(0.694770\pi\) | |||||||
\(72\) | −268.517 | −0.439515 | ||||||||
\(73\) | −84.4482 | −0.135396 | −0.0676980 | − | 0.997706i | \(-0.521565\pi\) | ||||
−0.0676980 | + | 0.997706i | \(0.521565\pi\) | |||||||
\(74\) | −322.776 | −0.507053 | ||||||||
\(75\) | 194.558 | 0.299542 | ||||||||
\(76\) | 355.483 | 0.536535 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 17.5775 | 0.0255161 | ||||||||
\(79\) | −722.069 | −1.02834 | −0.514172 | − | 0.857687i | \(-0.671901\pi\) | ||||
−0.514172 | + | 0.857687i | \(0.671901\pi\) | |||||||
\(80\) | −80.0000 | −0.111803 | ||||||||
\(81\) | −508.659 | −0.697750 | ||||||||
\(82\) | 577.457 | 0.777676 | ||||||||
\(83\) | 1010.36 | 1.33616 | 0.668078 | − | 0.744091i | \(-0.267117\pi\) | ||||
0.668078 | + | 0.744091i | \(0.267117\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 681.293 | 0.869372 | ||||||||
\(86\) | 141.116 | 0.176942 | ||||||||
\(87\) | −1020.12 | −1.25711 | ||||||||
\(88\) | 380.517 | 0.460946 | ||||||||
\(89\) | −424.457 | −0.505532 | −0.252766 | − | 0.967527i | \(-0.581340\pi\) | ||||
−0.252766 | + | 0.967527i | \(0.581340\pi\) | |||||||
\(90\) | 335.647 | 0.393114 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.9398 | 0.0123973 | ||||||||
\(93\) | −2346.14 | −2.61595 | ||||||||
\(94\) | 272.517 | 0.299021 | ||||||||
\(95\) | −444.353 | −0.479892 | ||||||||
\(96\) | −249.035 | −0.264760 | ||||||||
\(97\) | −120.448 | −0.126079 | −0.0630395 | − | 0.998011i | \(-0.520079\pi\) | ||||
−0.0630395 | + | 0.998011i | \(0.520079\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1596.49 | −1.62074 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 244.590 | 0.240967 | 0.120483 | − | 0.992715i | \(-0.461556\pi\) | ||||
0.120483 | + | 0.992715i | \(0.461556\pi\) | |||||||
\(102\) | 2120.82 | 2.05875 | ||||||||
\(103\) | −829.688 | −0.793704 | −0.396852 | − | 0.917883i | \(-0.629897\pi\) | ||||
−0.396852 | + | 0.917883i | \(0.629897\pi\) | |||||||
\(104\) | 9.03456 | 0.00851838 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 68.5173 | 0.0627829 | ||||||||
\(107\) | 786.330 | 0.710443 | 0.355222 | − | 0.934782i | \(-0.384405\pi\) | ||||
0.355222 | + | 0.934782i | \(0.384405\pi\) | |||||||
\(108\) | 204.353 | 0.182073 | ||||||||
\(109\) | −1312.97 | −1.15376 | −0.576881 | − | 0.816828i | \(-0.695731\pi\) | ||||
−0.576881 | + | 0.816828i | \(0.695731\pi\) | |||||||
\(110\) | −475.647 | −0.412283 | ||||||||
\(111\) | 1255.97 | 1.07398 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1970.23 | −1.64021 | −0.820106 | − | 0.572212i | \(-0.806086\pi\) | ||||
−0.820106 | + | 0.572212i | \(0.806086\pi\) | |||||||
\(114\) | −1383.24 | −1.13643 | ||||||||
\(115\) | −13.6747 | −0.0110885 | ||||||||
\(116\) | −524.328 | −0.419678 | ||||||||
\(117\) | −37.9052 | −0.0299516 | ||||||||
\(118\) | −1490.72 | −1.16299 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 311.293 | 0.236809 | ||||||||
\(121\) | 931.397 | 0.699772 | ||||||||
\(122\) | −1367.69 | −1.01496 | ||||||||
\(123\) | −2246.98 | −1.64718 | ||||||||
\(124\) | −1205.88 | −0.873316 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 222.466 | 0.155438 | 0.0777192 | − | 0.996975i | \(-0.475236\pi\) | ||||
0.0777192 | + | 0.996975i | \(0.475236\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −549.108 | −0.374777 | ||||||||
\(130\) | −11.2932 | −0.00761907 | ||||||||
\(131\) | 1466.80 | 0.978283 | 0.489141 | − | 0.872204i | \(-0.337310\pi\) | ||||
0.489141 | + | 0.872204i | \(0.337310\pi\) | |||||||
\(132\) | −1480.66 | −0.976322 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 145.168 | 0.0935865 | ||||||||
\(135\) | −255.442 | −0.162851 | ||||||||
\(136\) | 1090.07 | 0.687299 | ||||||||
\(137\) | −2818.86 | −1.75790 | −0.878948 | − | 0.476918i | \(-0.841754\pi\) | ||||
−0.878948 | + | 0.476918i | \(0.841754\pi\) | |||||||
\(138\) | −42.5686 | −0.0262585 | ||||||||
\(139\) | −2026.67 | −1.23669 | −0.618344 | − | 0.785907i | \(-0.712196\pi\) | ||||
−0.618344 | + | 0.785907i | \(0.712196\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1060.41 | −0.633352 | ||||||||
\(142\) | 1374.59 | 0.812343 | ||||||||
\(143\) | 53.7157 | 0.0314121 | ||||||||
\(144\) | 537.035 | 0.310784 | ||||||||
\(145\) | 655.410 | 0.375371 | ||||||||
\(146\) | 168.896 | 0.0957394 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 645.552 | 0.358541 | ||||||||
\(149\) | 2917.86 | 1.60430 | 0.802150 | − | 0.597123i | \(-0.203690\pi\) | ||||
0.802150 | + | 0.597123i | \(0.203690\pi\) | |||||||
\(150\) | −389.116 | −0.211808 | ||||||||
\(151\) | 2910.69 | 1.56867 | 0.784334 | − | 0.620339i | \(-0.213005\pi\) | ||||
0.784334 | + | 0.620339i | \(0.213005\pi\) | |||||||
\(152\) | −710.965 | −0.379388 | ||||||||
\(153\) | −4573.47 | −2.41662 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1507.35 | 0.781118 | ||||||||
\(156\) | −35.1550 | −0.0180426 | ||||||||
\(157\) | −2075.12 | −1.05486 | −0.527429 | − | 0.849599i | \(-0.676844\pi\) | ||||
−0.527429 | + | 0.849599i | \(0.676844\pi\) | |||||||
\(158\) | 1444.14 | 0.727149 | ||||||||
\(159\) | −266.612 | −0.132979 | ||||||||
\(160\) | 160.000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1017.32 | 0.493383 | ||||||||
\(163\) | −108.535 | −0.0521541 | −0.0260771 | − | 0.999660i | \(-0.508302\pi\) | ||||
−0.0260771 | + | 0.999660i | \(0.508302\pi\) | |||||||
\(164\) | −1154.91 | −0.549900 | ||||||||
\(165\) | 1850.82 | 0.873249 | ||||||||
\(166\) | −2020.71 | −0.944805 | ||||||||
\(167\) | 2904.58 | 1.34589 | 0.672943 | − | 0.739695i | \(-0.265030\pi\) | ||||
0.672943 | + | 0.739695i | \(0.265030\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2195.72 | −0.999419 | ||||||||
\(170\) | −1362.59 | −0.614739 | ||||||||
\(171\) | 2982.91 | 1.33397 | ||||||||
\(172\) | −282.233 | −0.125117 | ||||||||
\(173\) | 1110.89 | 0.488204 | 0.244102 | − | 0.969750i | \(-0.421507\pi\) | ||||
0.244102 | + | 0.969750i | \(0.421507\pi\) | |||||||
\(174\) | 2040.25 | 0.888912 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −761.035 | −0.325938 | ||||||||
\(177\) | 5800.66 | 2.46330 | ||||||||
\(178\) | 848.914 | 0.357465 | ||||||||
\(179\) | −627.426 | −0.261989 | −0.130995 | − | 0.991383i | \(-0.541817\pi\) | ||||
−0.130995 | + | 0.991383i | \(0.541817\pi\) | |||||||
\(180\) | −671.293 | −0.277974 | ||||||||
\(181\) | 1961.52 | 0.805518 | 0.402759 | − | 0.915306i | \(-0.368051\pi\) | ||||
0.402759 | + | 0.915306i | \(0.368051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5321.91 | 2.14976 | ||||||||
\(184\) | −21.8796 | −0.00876622 | ||||||||
\(185\) | −806.940 | −0.320689 | ||||||||
\(186\) | 4692.28 | 1.84975 | ||||||||
\(187\) | 6481.10 | 2.53446 | ||||||||
\(188\) | −545.035 | −0.211440 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 888.707 | 0.339335 | ||||||||
\(191\) | −3100.90 | −1.17473 | −0.587365 | − | 0.809322i | \(-0.699835\pi\) | ||||
−0.587365 | + | 0.809322i | \(0.699835\pi\) | |||||||
\(192\) | 498.069 | 0.187214 | ||||||||
\(193\) | −784.207 | −0.292479 | −0.146240 | − | 0.989249i | \(-0.546717\pi\) | ||||
−0.146240 | + | 0.989249i | \(0.546717\pi\) | |||||||
\(194\) | 240.896 | 0.0891513 | ||||||||
\(195\) | 43.9437 | 0.0161378 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2315.34 | −0.837365 | −0.418683 | − | 0.908133i | \(-0.637508\pi\) | ||||
−0.418683 | + | 0.908133i | \(0.637508\pi\) | |||||||
\(198\) | 3192.98 | 1.14604 | ||||||||
\(199\) | 2776.41 | 0.989019 | 0.494510 | − | 0.869172i | \(-0.335348\pi\) | ||||
0.494510 | + | 0.869172i | \(0.335348\pi\) | |||||||
\(200\) | −200.000 | −0.0707107 | ||||||||
\(201\) | −564.872 | −0.198224 | ||||||||
\(202\) | −489.181 | −0.170389 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4241.64 | −1.45576 | ||||||||
\(205\) | 1443.64 | 0.491846 | ||||||||
\(206\) | 1659.38 | 0.561234 | ||||||||
\(207\) | 91.7977 | 0.0308231 | ||||||||
\(208\) | −18.0691 | −0.00602340 | ||||||||
\(209\) | −4227.10 | −1.39902 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 745.035 | 0.243082 | 0.121541 | − | 0.992586i | \(-0.461216\pi\) | ||||
0.121541 | + | 0.992586i | \(0.461216\pi\) | |||||||
\(212\) | −137.035 | −0.0443942 | ||||||||
\(213\) | −5348.74 | −1.72061 | ||||||||
\(214\) | −1572.66 | −0.502359 | ||||||||
\(215\) | 352.791 | 0.111908 | ||||||||
\(216\) | −408.707 | −0.128745 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2625.95 | 0.815833 | ||||||||
\(219\) | −657.203 | −0.202784 | ||||||||
\(220\) | 951.293 | 0.291528 | ||||||||
\(221\) | 153.880 | 0.0468374 | ||||||||
\(222\) | −2511.95 | −0.759419 | ||||||||
\(223\) | 4379.59 | 1.31515 | 0.657576 | − | 0.753388i | \(-0.271582\pi\) | ||||
0.657576 | + | 0.753388i | \(0.271582\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 839.116 | 0.248627 | ||||||||
\(226\) | 3940.47 | 1.15980 | ||||||||
\(227\) | −882.456 | −0.258021 | −0.129010 | − | 0.991643i | \(-0.541180\pi\) | ||||
−0.129010 | + | 0.991643i | \(0.541180\pi\) | |||||||
\(228\) | 2766.48 | 0.803574 | ||||||||
\(229\) | 3917.95 | 1.13059 | 0.565295 | − | 0.824888i | \(-0.308762\pi\) | ||||
0.565295 | + | 0.824888i | \(0.308762\pi\) | |||||||
\(230\) | 27.3495 | 0.00784075 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1048.66 | 0.296757 | ||||||||
\(233\) | −1367.64 | −0.384536 | −0.192268 | − | 0.981342i | \(-0.561584\pi\) | ||||
−0.192268 | + | 0.981342i | \(0.561584\pi\) | |||||||
\(234\) | 75.8105 | 0.0211790 | ||||||||
\(235\) | 681.293 | 0.189118 | ||||||||
\(236\) | 2981.45 | 0.822355 | ||||||||
\(237\) | −5619.38 | −1.54016 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5080.94 | 1.37514 | 0.687570 | − | 0.726118i | \(-0.258677\pi\) | ||||
0.687570 | + | 0.726118i | \(0.258677\pi\) | |||||||
\(240\) | −622.586 | −0.167449 | ||||||||
\(241\) | 6491.74 | 1.73514 | 0.867572 | − | 0.497311i | \(-0.165679\pi\) | ||||
0.867572 | + | 0.497311i | \(0.165679\pi\) | |||||||
\(242\) | −1862.79 | −0.494814 | ||||||||
\(243\) | −5337.94 | −1.40917 | ||||||||
\(244\) | 2735.38 | 0.717683 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4493.96 | 1.16473 | ||||||||
\(247\) | −100.363 | −0.0258541 | ||||||||
\(248\) | 2411.76 | 0.617528 | ||||||||
\(249\) | 7862.92 | 2.00117 | ||||||||
\(250\) | 250.000 | 0.0632456 | ||||||||
\(251\) | 2112.81 | 0.531313 | 0.265657 | − | 0.964068i | \(-0.414411\pi\) | ||||
0.265657 | + | 0.964068i | \(0.414411\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −130.087 | −0.0323261 | ||||||||
\(254\) | −444.932 | −0.109911 | ||||||||
\(255\) | 5302.05 | 1.30207 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 804.758 | 0.195329 | 0.0976643 | − | 0.995219i | \(-0.468863\pi\) | ||||
0.0976643 | + | 0.995219i | \(0.468863\pi\) | |||||||
\(258\) | 1098.22 | 0.265007 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 22.5864 | 0.00538750 | ||||||||
\(261\) | −4399.72 | −1.04343 | ||||||||
\(262\) | −2933.60 | −0.691750 | ||||||||
\(263\) | −3975.62 | −0.932120 | −0.466060 | − | 0.884753i | \(-0.654327\pi\) | ||||
−0.466060 | + | 0.884753i | \(0.654327\pi\) | |||||||
\(264\) | 2961.31 | 0.690364 | ||||||||
\(265\) | 171.293 | 0.0397074 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3303.27 | −0.757141 | ||||||||
\(268\) | −290.336 | −0.0661756 | ||||||||
\(269\) | −948.880 | −0.215071 | −0.107536 | − | 0.994201i | \(-0.534296\pi\) | ||||
−0.107536 | + | 0.994201i | \(0.534296\pi\) | |||||||
\(270\) | 510.884 | 0.115153 | ||||||||
\(271\) | −128.190 | −0.0287342 | −0.0143671 | − | 0.999897i | \(-0.504573\pi\) | ||||
−0.0143671 | + | 0.999897i | \(0.504573\pi\) | |||||||
\(272\) | −2180.14 | −0.485994 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5637.73 | 1.24302 | ||||||||
\(275\) | −1189.12 | −0.260751 | ||||||||
\(276\) | 85.1371 | 0.0185676 | ||||||||
\(277\) | 3754.86 | 0.814467 | 0.407234 | − | 0.913324i | \(-0.366494\pi\) | ||||
0.407234 | + | 0.913324i | \(0.366494\pi\) | |||||||
\(278\) | 4053.34 | 0.874471 | ||||||||
\(279\) | −10118.7 | −2.17130 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6172.10 | 1.31031 | 0.655155 | − | 0.755495i | \(-0.272603\pi\) | ||||
0.655155 | + | 0.755495i | \(0.272603\pi\) | |||||||
\(282\) | 2120.82 | 0.447847 | ||||||||
\(283\) | −3351.06 | −0.703886 | −0.351943 | − | 0.936021i | \(-0.614479\pi\) | ||||
−0.351943 | + | 0.936021i | \(0.614479\pi\) | |||||||
\(284\) | −2749.17 | −0.574413 | ||||||||
\(285\) | −3458.10 | −0.718738 | ||||||||
\(286\) | −107.431 | −0.0222117 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1074.07 | −0.219757 | ||||||||
\(289\) | 13653.4 | 2.77904 | ||||||||
\(290\) | −1310.82 | −0.265427 | ||||||||
\(291\) | −937.367 | −0.188830 | ||||||||
\(292\) | −337.793 | −0.0676980 | ||||||||
\(293\) | −681.163 | −0.135816 | −0.0679078 | − | 0.997692i | \(-0.521632\pi\) | ||||
−0.0679078 | + | 0.997692i | \(0.521632\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3726.81 | −0.735537 | ||||||||
\(296\) | −1291.10 | −0.253527 | ||||||||
\(297\) | −2430.00 | −0.474757 | ||||||||
\(298\) | −5835.73 | −1.13441 | ||||||||
\(299\) | −3.08863 | −0.000597392 0 | ||||||||
\(300\) | 778.233 | 0.149771 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5821.39 | −1.10922 | ||||||||
\(303\) | 1903.48 | 0.360898 | ||||||||
\(304\) | 1421.93 | 0.268268 | ||||||||
\(305\) | −3419.23 | −0.641916 | ||||||||
\(306\) | 9146.95 | 1.70881 | ||||||||
\(307\) | −6246.87 | −1.16133 | −0.580664 | − | 0.814143i | \(-0.697207\pi\) | ||||
−0.580664 | + | 0.814143i | \(0.697207\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6456.90 | −1.18874 | ||||||||
\(310\) | −3014.70 | −0.552334 | ||||||||
\(311\) | 6065.15 | 1.10586 | 0.552931 | − | 0.833227i | \(-0.313509\pi\) | ||||
0.552931 | + | 0.833227i | \(0.313509\pi\) | |||||||
\(312\) | 70.3099 | 0.0127581 | ||||||||
\(313\) | −8285.23 | −1.49620 | −0.748098 | − | 0.663589i | \(-0.769033\pi\) | ||||
−0.748098 | + | 0.663589i | \(0.769033\pi\) | |||||||
\(314\) | 4150.24 | 0.745897 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2888.28 | −0.514172 | ||||||||
\(317\) | −1191.04 | −0.211028 | −0.105514 | − | 0.994418i | \(-0.533649\pi\) | ||||
−0.105514 | + | 0.994418i | \(0.533649\pi\) | |||||||
\(318\) | 533.224 | 0.0940306 | ||||||||
\(319\) | 6234.87 | 1.09431 | ||||||||
\(320\) | −320.000 | −0.0559017 | ||||||||
\(321\) | 6119.48 | 1.06404 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12109.4 | −2.08602 | ||||||||
\(324\) | −2034.64 | −0.348875 | ||||||||
\(325\) | −28.2330 | −0.00481872 | ||||||||
\(326\) | 217.070 | 0.0368786 | ||||||||
\(327\) | −10218.0 | −1.72800 | ||||||||
\(328\) | 2309.83 | 0.388838 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3701.64 | −0.617480 | ||||||||
\(331\) | −4789.90 | −0.795398 | −0.397699 | − | 0.917516i | \(-0.630191\pi\) | ||||
−0.397699 | + | 0.917516i | \(0.630191\pi\) | |||||||
\(332\) | 4041.42 | 0.668078 | ||||||||
\(333\) | 5416.93 | 0.891430 | ||||||||
\(334\) | −5809.15 | −0.951685 | ||||||||
\(335\) | 362.919 | 0.0591893 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −948.778 | −0.153363 | −0.0766814 | − | 0.997056i | \(-0.524432\pi\) | ||||
−0.0766814 | + | 0.997056i | \(0.524432\pi\) | |||||||
\(338\) | 4391.45 | 0.706696 | ||||||||
\(339\) | −15333.0 | −2.45656 | ||||||||
\(340\) | 2725.17 | 0.434686 | ||||||||
\(341\) | 14339.3 | 2.27718 | ||||||||
\(342\) | −5965.83 | −0.943260 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 564.466 | 0.0884708 | ||||||||
\(345\) | −106.421 | −0.0166074 | ||||||||
\(346\) | −2221.78 | −0.345212 | ||||||||
\(347\) | −5663.76 | −0.876216 | −0.438108 | − | 0.898922i | \(-0.644351\pi\) | ||||
−0.438108 | + | 0.898922i | \(0.644351\pi\) | |||||||
\(348\) | −4080.49 | −0.628555 | ||||||||
\(349\) | 2369.73 | 0.363463 | 0.181732 | − | 0.983348i | \(-0.441830\pi\) | ||||
0.181732 | + | 0.983348i | \(0.441830\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −57.6951 | −0.00877361 | ||||||||
\(352\) | 1522.07 | 0.230473 | ||||||||
\(353\) | 1416.15 | 0.213525 | 0.106762 | − | 0.994285i | \(-0.465952\pi\) | ||||
0.106762 | + | 0.994285i | \(0.465952\pi\) | |||||||
\(354\) | −11601.3 | −1.74182 | ||||||||
\(355\) | 3436.47 | 0.513771 | ||||||||
\(356\) | −1697.83 | −0.252766 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1254.85 | 0.185254 | ||||||||
\(359\) | −7772.84 | −1.14272 | −0.571358 | − | 0.820701i | \(-0.693583\pi\) | ||||
−0.571358 | + | 0.820701i | \(0.693583\pi\) | |||||||
\(360\) | 1342.59 | 0.196557 | ||||||||
\(361\) | 1039.00 | 0.151479 | ||||||||
\(362\) | −3923.04 | −0.569587 | ||||||||
\(363\) | 7248.44 | 1.04806 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 422.241 | 0.0605509 | ||||||||
\(366\) | −10643.8 | −1.52011 | ||||||||
\(367\) | 432.717 | 0.0615467 | 0.0307734 | − | 0.999526i | \(-0.490203\pi\) | ||||
0.0307734 | + | 0.999526i | \(0.490203\pi\) | |||||||
\(368\) | 43.7592 | 0.00619866 | ||||||||
\(369\) | −9691.08 | −1.36720 | ||||||||
\(370\) | 1613.88 | 0.226761 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9384.55 | −1.30797 | ||||||||
\(373\) | 6157.79 | 0.854795 | 0.427397 | − | 0.904064i | \(-0.359431\pi\) | ||||
0.427397 | + | 0.904064i | \(0.359431\pi\) | |||||||
\(374\) | −12962.2 | −1.79214 | ||||||||
\(375\) | −972.791 | −0.133959 | ||||||||
\(376\) | 1090.07 | 0.149511 | ||||||||
\(377\) | 148.033 | 0.0202231 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10109.6 | 1.37017 | 0.685087 | − | 0.728462i | \(-0.259764\pi\) | ||||
0.685087 | + | 0.728462i | \(0.259764\pi\) | |||||||
\(380\) | −1777.41 | −0.239946 | ||||||||
\(381\) | 1731.30 | 0.232802 | ||||||||
\(382\) | 6201.80 | 0.830659 | ||||||||
\(383\) | 8208.37 | 1.09511 | 0.547556 | − | 0.836769i | \(-0.315558\pi\) | ||||
0.547556 | + | 0.836769i | \(0.315558\pi\) | |||||||
\(384\) | −996.138 | −0.132380 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1568.41 | 0.206814 | ||||||||
\(387\) | −2368.26 | −0.311074 | ||||||||
\(388\) | −481.793 | −0.0630395 | ||||||||
\(389\) | 4918.31 | 0.641050 | 0.320525 | − | 0.947240i | \(-0.396141\pi\) | ||||
0.320525 | + | 0.947240i | \(0.396141\pi\) | |||||||
\(390\) | −87.8874 | −0.0114112 | ||||||||
\(391\) | −372.661 | −0.0482001 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11415.1 | 1.46518 | ||||||||
\(394\) | 4630.67 | 0.592106 | ||||||||
\(395\) | 3610.35 | 0.459889 | ||||||||
\(396\) | −6385.97 | −0.810371 | ||||||||
\(397\) | −8138.95 | −1.02892 | −0.514461 | − | 0.857514i | \(-0.672008\pi\) | ||||
−0.514461 | + | 0.857514i | \(0.672008\pi\) | |||||||
\(398\) | −5552.83 | −0.699342 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | −345.948 | −0.0430818 | −0.0215409 | − | 0.999768i | \(-0.506857\pi\) | ||||
−0.0215409 | + | 0.999768i | \(0.506857\pi\) | |||||||
\(402\) | 1129.74 | 0.140165 | ||||||||
\(403\) | 340.456 | 0.0420827 | ||||||||
\(404\) | 978.361 | 0.120483 | ||||||||
\(405\) | 2543.30 | 0.312043 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7676.36 | −0.934897 | ||||||||
\(408\) | 8483.28 | 1.02937 | ||||||||
\(409\) | 366.127 | 0.0442635 | 0.0221318 | − | 0.999755i | \(-0.492955\pi\) | ||||
0.0221318 | + | 0.999755i | \(0.492955\pi\) | |||||||
\(410\) | −2887.29 | −0.347787 | ||||||||
\(411\) | −21937.3 | −2.63282 | ||||||||
\(412\) | −3318.75 | −0.396852 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −183.595 | −0.0217952 | ||||||||
\(415\) | −5051.78 | −0.597547 | ||||||||
\(416\) | 36.1382 | 0.00425919 | ||||||||
\(417\) | −15772.2 | −1.85220 | ||||||||
\(418\) | 8454.21 | 0.989255 | ||||||||
\(419\) | 6915.52 | 0.806313 | 0.403157 | − | 0.915131i | \(-0.367913\pi\) | ||||
0.403157 | + | 0.915131i | \(0.367913\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6467.62 | 0.748724 | 0.374362 | − | 0.927283i | \(-0.377862\pi\) | ||||
0.374362 | + | 0.927283i | \(0.377862\pi\) | |||||||
\(422\) | −1490.07 | −0.171885 | ||||||||
\(423\) | −4573.47 | −0.525697 | ||||||||
\(424\) | 274.069 | 0.0313914 | ||||||||
\(425\) | −3406.47 | −0.388795 | ||||||||
\(426\) | 10697.5 | 1.21665 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3145.32 | 0.355222 | ||||||||
\(429\) | 418.033 | 0.0470463 | ||||||||
\(430\) | −705.582 | −0.0791307 | ||||||||
\(431\) | −9470.21 | −1.05839 | −0.529193 | − | 0.848502i | \(-0.677505\pi\) | ||||
−0.529193 | + | 0.848502i | \(0.677505\pi\) | |||||||
\(432\) | 817.414 | 0.0910366 | ||||||||
\(433\) | −5097.47 | −0.565748 | −0.282874 | − | 0.959157i | \(-0.591288\pi\) | ||||
−0.282874 | + | 0.959157i | \(0.591288\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5100.61 | 0.562197 | ||||||||
\(436\) | −5251.90 | −0.576881 | ||||||||
\(437\) | 243.057 | 0.0266064 | ||||||||
\(438\) | 1314.41 | 0.143390 | ||||||||
\(439\) | 113.511 | 0.0123407 | 0.00617035 | − | 0.999981i | \(-0.498036\pi\) | ||||
0.00617035 | + | 0.999981i | \(0.498036\pi\) | |||||||
\(440\) | −1902.59 | −0.206141 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −307.759 | −0.0331190 | ||||||||
\(443\) | −17199.1 | −1.84459 | −0.922294 | − | 0.386488i | \(-0.873688\pi\) | ||||
−0.922294 | + | 0.386488i | \(0.873688\pi\) | |||||||
\(444\) | 5023.90 | 0.536990 | ||||||||
\(445\) | 2122.29 | 0.226081 | ||||||||
\(446\) | −8759.18 | −0.929953 | ||||||||
\(447\) | 22707.8 | 2.40278 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2452.08 | 0.257730 | 0.128865 | − | 0.991662i | \(-0.458867\pi\) | ||||
0.128865 | + | 0.991662i | \(0.458867\pi\) | |||||||
\(450\) | −1678.23 | −0.175806 | ||||||||
\(451\) | 13733.3 | 1.43387 | ||||||||
\(452\) | −7880.93 | −0.820106 | ||||||||
\(453\) | 22652.0 | 2.34941 | ||||||||
\(454\) | 1764.91 | 0.182448 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5532.97 | −0.568213 | ||||||||
\(457\) | −13424.5 | −1.37411 | −0.687057 | − | 0.726604i | \(-0.741098\pi\) | ||||
−0.687057 | + | 0.726604i | \(0.741098\pi\) | |||||||
\(458\) | −7835.90 | −0.799449 | ||||||||
\(459\) | −6961.23 | −0.707892 | ||||||||
\(460\) | −54.6990 | −0.00554425 | ||||||||
\(461\) | 3681.74 | 0.371965 | 0.185983 | − | 0.982553i | \(-0.440453\pi\) | ||||
0.185983 | + | 0.982553i | \(0.440453\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1700.08 | 0.170647 | 0.0853236 | − | 0.996353i | \(-0.472808\pi\) | ||||
0.0853236 | + | 0.996353i | \(0.472808\pi\) | |||||||
\(464\) | −2097.31 | −0.209839 | ||||||||
\(465\) | 11730.7 | 1.16989 | ||||||||
\(466\) | 2735.28 | 0.271908 | ||||||||
\(467\) | 7951.90 | 0.787945 | 0.393972 | − | 0.919122i | \(-0.371101\pi\) | ||||
0.393972 | + | 0.919122i | \(0.371101\pi\) | |||||||
\(468\) | −151.621 | −0.0149758 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1362.59 | −0.133726 | ||||||||
\(471\) | −16149.3 | −1.57987 | ||||||||
\(472\) | −5962.90 | −0.581493 | ||||||||
\(473\) | 3356.08 | 0.326242 | ||||||||
\(474\) | 11238.8 | 1.08906 | ||||||||
\(475\) | 2221.77 | 0.214614 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1149.88 | −0.110376 | ||||||||
\(478\) | −10161.9 | −0.972371 | ||||||||
\(479\) | −12820.3 | −1.22291 | −0.611453 | − | 0.791280i | \(-0.709415\pi\) | ||||
−0.611453 | + | 0.791280i | \(0.709415\pi\) | |||||||
\(480\) | 1245.17 | 0.118404 | ||||||||
\(481\) | −182.259 | −0.0172771 | ||||||||
\(482\) | −12983.5 | −1.22693 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3725.59 | 0.349886 | ||||||||
\(485\) | 602.241 | 0.0563842 | ||||||||
\(486\) | 10675.9 | 0.996436 | ||||||||
\(487\) | 5543.73 | 0.515832 | 0.257916 | − | 0.966167i | \(-0.416964\pi\) | ||||
0.257916 | + | 0.966167i | \(0.416964\pi\) | |||||||
\(488\) | −5470.76 | −0.507479 | ||||||||
\(489\) | −844.656 | −0.0781118 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16382.1 | −1.50573 | −0.752865 | − | 0.658175i | \(-0.771329\pi\) | ||||
−0.752865 | + | 0.658175i | \(0.771329\pi\) | |||||||
\(492\) | −8987.92 | −0.823591 | ||||||||
\(493\) | 17861.0 | 1.63169 | ||||||||
\(494\) | 200.727 | 0.0182816 | ||||||||
\(495\) | 7982.46 | 0.724818 | ||||||||
\(496\) | −4823.52 | −0.436658 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −15725.8 | −1.41504 | ||||||||
\(499\) | 11537.6 | 1.03506 | 0.517529 | − | 0.855666i | \(-0.326852\pi\) | ||||
0.517529 | + | 0.855666i | \(0.326852\pi\) | |||||||
\(500\) | −500.000 | −0.0447214 | ||||||||
\(501\) | 22604.4 | 2.01575 | ||||||||
\(502\) | −4225.63 | −0.375695 | ||||||||
\(503\) | 13364.5 | 1.18468 | 0.592338 | − | 0.805690i | \(-0.298205\pi\) | ||||
0.592338 | + | 0.805690i | \(0.298205\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1222.95 | −0.107764 | ||||||||
\(506\) | 260.174 | 0.0228580 | ||||||||
\(507\) | −17087.9 | −1.49684 | ||||||||
\(508\) | 889.864 | 0.0777192 | ||||||||
\(509\) | 6874.82 | 0.598666 | 0.299333 | − | 0.954149i | \(-0.403236\pi\) | ||||
0.299333 | + | 0.954149i | \(0.403236\pi\) | |||||||
\(510\) | −10604.1 | −0.920701 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 4540.26 | 0.390755 | ||||||||
\(514\) | −1609.52 | −0.138118 | ||||||||
\(515\) | 4148.44 | 0.354955 | ||||||||
\(516\) | −2196.43 | −0.187388 | ||||||||
\(517\) | 6481.10 | 0.551331 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8645.30 | 0.731188 | ||||||||
\(520\) | −45.1728 | −0.00380954 | ||||||||
\(521\) | −15396.4 | −1.29468 | −0.647342 | − | 0.762200i | \(-0.724119\pi\) | ||||
−0.647342 | + | 0.762200i | \(0.724119\pi\) | |||||||
\(522\) | 8799.44 | 0.737818 | ||||||||
\(523\) | −21761.3 | −1.81941 | −0.909707 | − | 0.415252i | \(-0.863694\pi\) | ||||
−0.909707 | + | 0.415252i | \(0.863694\pi\) | |||||||
\(524\) | 5867.21 | 0.489141 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7951.25 | 0.659108 | ||||||||
\(527\) | 41077.9 | 3.39541 | ||||||||
\(528\) | −5922.62 | −0.488161 | ||||||||
\(529\) | −12159.5 | −0.999385 | ||||||||
\(530\) | −342.586 | −0.0280774 | ||||||||
\(531\) | 25017.8 | 2.04460 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 326.067 | 0.0264982 | ||||||||
\(534\) | 6606.53 | 0.535379 | ||||||||
\(535\) | −3931.65 | −0.317720 | ||||||||
\(536\) | 580.671 | 0.0467932 | ||||||||
\(537\) | −4882.84 | −0.392384 | ||||||||
\(538\) | 1897.76 | 0.152078 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1021.77 | −0.0814256 | ||||||||
\(541\) | 7050.81 | 0.560329 | 0.280165 | − | 0.959952i | \(-0.409611\pi\) | ||||
0.280165 | + | 0.959952i | \(0.409611\pi\) | |||||||
\(542\) | 256.379 | 0.0203181 | ||||||||
\(543\) | 15265.2 | 1.20643 | ||||||||
\(544\) | 4360.28 | 0.343649 | ||||||||
\(545\) | 6564.87 | 0.515978 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7083.09 | 0.553658 | 0.276829 | − | 0.960919i | \(-0.410716\pi\) | ||||
0.276829 | + | 0.960919i | \(0.410716\pi\) | |||||||
\(548\) | −11275.5 | −0.878948 | ||||||||
\(549\) | 22953.0 | 1.78436 | ||||||||
\(550\) | 2378.23 | 0.184379 | ||||||||
\(551\) | −11649.3 | −0.900687 | ||||||||
\(552\) | −170.274 | −0.0131293 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −7509.71 | −0.575915 | ||||||||
\(555\) | −6279.87 | −0.480299 | ||||||||
\(556\) | −8106.67 | −0.618344 | ||||||||
\(557\) | −11654.7 | −0.886581 | −0.443291 | − | 0.896378i | \(-0.646189\pi\) | ||||
−0.443291 | + | 0.896378i | \(0.646189\pi\) | |||||||
\(558\) | 20237.5 | 1.53534 | ||||||||
\(559\) | 79.6828 | 0.00602902 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 50438.0 | 3.79589 | ||||||||
\(562\) | −12344.2 | −0.926529 | ||||||||
\(563\) | −5910.23 | −0.442427 | −0.221214 | − | 0.975225i | \(-0.571002\pi\) | ||||
−0.221214 | + | 0.975225i | \(0.571002\pi\) | |||||||
\(564\) | −4241.64 | −0.316676 | ||||||||
\(565\) | 9851.16 | 0.733525 | ||||||||
\(566\) | 6702.12 | 0.497723 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5498.35 | 0.406172 | ||||||||
\(569\) | −3632.95 | −0.267665 | −0.133832 | − | 0.991004i | \(-0.542728\pi\) | ||||
−0.133832 | + | 0.991004i | \(0.542728\pi\) | |||||||
\(570\) | 6916.21 | 0.508225 | ||||||||
\(571\) | 9704.22 | 0.711224 | 0.355612 | − | 0.934634i | \(-0.384272\pi\) | ||||
0.355612 | + | 0.934634i | \(0.384272\pi\) | |||||||
\(572\) | 214.863 | 0.0157061 | ||||||||
\(573\) | −24132.2 | −1.75940 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 68.3737 | 0.00495893 | ||||||||
\(576\) | 2148.14 | 0.155392 | ||||||||
\(577\) | 5559.91 | 0.401147 | 0.200574 | − | 0.979679i | \(-0.435719\pi\) | ||||
0.200574 | + | 0.979679i | \(0.435719\pi\) | |||||||
\(578\) | −27306.8 | −1.96508 | ||||||||
\(579\) | −6102.96 | −0.438049 | ||||||||
\(580\) | 2621.64 | 0.187686 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1874.73 | 0.133523 | ||||||||
\(583\) | 1629.50 | 0.115758 | ||||||||
\(584\) | 675.585 | 0.0478697 | ||||||||
\(585\) | 189.526 | 0.0133948 | ||||||||
\(586\) | 1362.33 | 0.0960361 | ||||||||
\(587\) | −22559.1 | −1.58622 | −0.793111 | − | 0.609077i | \(-0.791540\pi\) | ||||
−0.793111 | + | 0.609077i | \(0.791540\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26791.8 | −1.87426 | ||||||||
\(590\) | 7453.62 | 0.520103 | ||||||||
\(591\) | −18018.7 | −1.25413 | ||||||||
\(592\) | 2582.21 | 0.179270 | ||||||||
\(593\) | −1487.62 | −0.103017 | −0.0515085 | − | 0.998673i | \(-0.516403\pi\) | ||||
−0.0515085 | + | 0.998673i | \(0.516403\pi\) | |||||||
\(594\) | 4860.00 | 0.335704 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11671.5 | 0.802150 | ||||||||
\(597\) | 21607.0 | 1.48126 | ||||||||
\(598\) | 6.17727 | 0.000422420 0 | ||||||||
\(599\) | −3908.33 | −0.266594 | −0.133297 | − | 0.991076i | \(-0.542556\pi\) | ||||
−0.133297 | + | 0.991076i | \(0.542556\pi\) | |||||||
\(600\) | −1556.47 | −0.105904 | ||||||||
\(601\) | −14849.4 | −1.00785 | −0.503927 | − | 0.863747i | \(-0.668112\pi\) | ||||
−0.503927 | + | 0.863747i | \(0.668112\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2436.25 | −0.164531 | ||||||||
\(604\) | 11642.8 | 0.784334 | ||||||||
\(605\) | −4656.98 | −0.312948 | ||||||||
\(606\) | −3806.96 | −0.255194 | ||||||||
\(607\) | 1923.28 | 0.128606 | 0.0643028 | − | 0.997930i | \(-0.479518\pi\) | ||||
0.0643028 | + | 0.997930i | \(0.479518\pi\) | |||||||
\(608\) | −2843.86 | −0.189694 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6838.45 | 0.453903 | ||||||||
\(611\) | 153.880 | 0.0101887 | ||||||||
\(612\) | −18293.9 | −1.20831 | ||||||||
\(613\) | 6887.96 | 0.453837 | 0.226919 | − | 0.973914i | \(-0.427135\pi\) | ||||
0.226919 | + | 0.973914i | \(0.427135\pi\) | |||||||
\(614\) | 12493.7 | 0.821183 | ||||||||
\(615\) | 11234.9 | 0.736642 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4032.07 | 0.263088 | 0.131544 | − | 0.991310i | \(-0.458007\pi\) | ||||
0.131544 | + | 0.991310i | \(0.458007\pi\) | |||||||
\(618\) | 12913.8 | 0.840565 | ||||||||
\(619\) | −12643.8 | −0.820996 | −0.410498 | − | 0.911861i | \(-0.634645\pi\) | ||||
−0.410498 | + | 0.911861i | \(0.634645\pi\) | |||||||
\(620\) | 6029.40 | 0.390559 | ||||||||
\(621\) | 139.724 | 0.00902888 | ||||||||
\(622\) | −12130.3 | −0.781962 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −140.620 | −0.00902131 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 16570.5 | 1.05797 | ||||||||
\(627\) | −32896.7 | −2.09532 | ||||||||
\(628\) | −8300.49 | −0.527429 | ||||||||
\(629\) | −21990.5 | −1.39399 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19282.6 | −1.21652 | −0.608262 | − | 0.793736i | \(-0.708133\pi\) | ||||
−0.608262 | + | 0.793736i | \(0.708133\pi\) | |||||||
\(632\) | 5776.55 | 0.363574 | ||||||||
\(633\) | 5798.10 | 0.364066 | ||||||||
\(634\) | 2382.09 | 0.149219 | ||||||||
\(635\) | −1112.33 | −0.0695141 | ||||||||
\(636\) | −1066.45 | −0.0664897 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −12469.7 | −0.773796 | ||||||||
\(639\) | −23068.8 | −1.42815 | ||||||||
\(640\) | 640.000 | 0.0395285 | ||||||||
\(641\) | 4821.65 | 0.297104 | 0.148552 | − | 0.988905i | \(-0.452539\pi\) | ||||
0.148552 | + | 0.988905i | \(0.452539\pi\) | |||||||
\(642\) | −12239.0 | −0.752388 | ||||||||
\(643\) | −31195.9 | −1.91329 | −0.956645 | − | 0.291255i | \(-0.905927\pi\) | ||||
−0.956645 | + | 0.291255i | \(0.905927\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2745.54 | 0.167605 | ||||||||
\(646\) | 24218.8 | 1.47504 | ||||||||
\(647\) | −20524.7 | −1.24715 | −0.623577 | − | 0.781762i | \(-0.714321\pi\) | ||||
−0.623577 | + | 0.781762i | \(0.714321\pi\) | |||||||
\(648\) | 4069.28 | 0.246692 | ||||||||
\(649\) | −35452.9 | −2.14430 | ||||||||
\(650\) | 56.4660 | 0.00340735 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −434.140 | −0.0260771 | ||||||||
\(653\) | 1562.03 | 0.0936095 | 0.0468048 | − | 0.998904i | \(-0.485096\pi\) | ||||
0.0468048 | + | 0.998904i | \(0.485096\pi\) | |||||||
\(654\) | 20436.0 | 1.22188 | ||||||||
\(655\) | −7334.01 | −0.437501 | ||||||||
\(656\) | −4619.66 | −0.274950 | ||||||||
\(657\) | −2834.47 | −0.168316 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18041.4 | −1.06646 | −0.533228 | − | 0.845971i | \(-0.679021\pi\) | ||||
−0.533228 | + | 0.845971i | \(0.679021\pi\) | |||||||
\(660\) | 7403.28 | 0.436625 | ||||||||
\(661\) | 25703.4 | 1.51247 | 0.756236 | − | 0.654298i | \(-0.227036\pi\) | ||||
0.756236 | + | 0.654298i | \(0.227036\pi\) | |||||||
\(662\) | 9579.80 | 0.562431 | ||||||||
\(663\) | 1197.54 | 0.0701488 | ||||||||
\(664\) | −8082.85 | −0.472403 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10833.9 | −0.630336 | ||||||||
\(667\) | −358.503 | −0.0208115 | ||||||||
\(668\) | 11618.3 | 0.672943 | ||||||||
\(669\) | 34083.4 | 1.96972 | ||||||||
\(670\) | −725.839 | −0.0418531 | ||||||||
\(671\) | −32526.9 | −1.87136 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21106.5 | −1.20891 | −0.604454 | − | 0.796640i | \(-0.706609\pi\) | ||||
−0.604454 | + | 0.796640i | \(0.706609\pi\) | |||||||
\(674\) | 1897.56 | 0.108444 | ||||||||
\(675\) | 1277.21 | 0.0728293 | ||||||||
\(676\) | −8782.90 | −0.499710 | ||||||||
\(677\) | 26770.9 | 1.51978 | 0.759889 | − | 0.650053i | \(-0.225253\pi\) | ||||
0.759889 | + | 0.650053i | \(0.225253\pi\) | |||||||
\(678\) | 30666.0 | 1.73705 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5450.35 | −0.307369 | ||||||||
\(681\) | −6867.56 | −0.386440 | ||||||||
\(682\) | −28678.6 | −1.61021 | ||||||||
\(683\) | 4157.06 | 0.232892 | 0.116446 | − | 0.993197i | \(-0.462850\pi\) | ||||
0.116446 | + | 0.993197i | \(0.462850\pi\) | |||||||
\(684\) | 11931.7 | 0.666986 | ||||||||
\(685\) | 14094.3 | 0.786155 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30490.8 | 1.69330 | ||||||||
\(688\) | −1128.93 | −0.0625583 | ||||||||
\(689\) | 38.6890 | 0.00213923 | ||||||||
\(690\) | 212.843 | 0.0117432 | ||||||||
\(691\) | 8598.82 | 0.473393 | 0.236696 | − | 0.971584i | \(-0.423935\pi\) | ||||
0.236696 | + | 0.971584i | \(0.423935\pi\) | |||||||
\(692\) | 4443.55 | 0.244102 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11327.5 | 0.619578 | ||||||||
\(695\) | 10133.3 | 0.553064 | ||||||||
\(696\) | 8160.98 | 0.444456 | ||||||||
\(697\) | 39341.8 | 2.13798 | ||||||||
\(698\) | −4739.46 | −0.257007 | ||||||||
\(699\) | −10643.4 | −0.575924 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8786.01 | −0.473385 | −0.236693 | − | 0.971585i | \(-0.576063\pi\) | ||||
−0.236693 | + | 0.971585i | \(0.576063\pi\) | |||||||
\(702\) | 115.390 | 0.00620388 | ||||||||
\(703\) | 14342.7 | 0.769479 | ||||||||
\(704\) | −3044.14 | −0.162969 | ||||||||
\(705\) | 5302.05 | 0.283244 | ||||||||
\(706\) | −2832.31 | −0.150985 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 23202.6 | 1.23165 | ||||||||
\(709\) | −22322.6 | −1.18243 | −0.591214 | − | 0.806514i | \(-0.701351\pi\) | ||||
−0.591214 | + | 0.806514i | \(0.701351\pi\) | |||||||
\(710\) | −6872.93 | −0.363291 | ||||||||
\(711\) | −24236.0 | −1.27837 | ||||||||
\(712\) | 3395.66 | 0.178733 | ||||||||
\(713\) | −824.505 | −0.0433071 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −268.579 | −0.0140479 | ||||||||
\(716\) | −2509.71 | −0.130995 | ||||||||
\(717\) | 39541.5 | 2.05956 | ||||||||
\(718\) | 15545.7 | 0.808022 | ||||||||
\(719\) | 7668.32 | 0.397747 | 0.198874 | − | 0.980025i | \(-0.436272\pi\) | ||||
0.198874 | + | 0.980025i | \(0.436272\pi\) | |||||||
\(720\) | −2685.17 | −0.138987 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2078.00 | −0.107112 | ||||||||
\(723\) | 50520.9 | 2.59874 | ||||||||
\(724\) | 7846.09 | 0.402759 | ||||||||
\(725\) | −3277.05 | −0.167871 | ||||||||
\(726\) | −14496.9 | −0.741087 | ||||||||
\(727\) | 15189.8 | 0.774907 | 0.387453 | − | 0.921889i | \(-0.373355\pi\) | ||||
0.387453 | + | 0.921889i | \(0.373355\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27807.8 | −1.41278 | ||||||||
\(730\) | −844.482 | −0.0428160 | ||||||||
\(731\) | 9614.17 | 0.486447 | ||||||||
\(732\) | 21287.6 | 1.07488 | ||||||||
\(733\) | 10061.0 | 0.506976 | 0.253488 | − | 0.967339i | \(-0.418422\pi\) | ||||
0.253488 | + | 0.967339i | \(0.418422\pi\) | |||||||
\(734\) | −865.434 | −0.0435201 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −87.5184 | −0.00438311 | ||||||||
\(737\) | 3452.43 | 0.172553 | ||||||||
\(738\) | 19382.2 | 0.966757 | ||||||||
\(739\) | −5137.10 | −0.255712 | −0.127856 | − | 0.991793i | \(-0.540810\pi\) | ||||
−0.127856 | + | 0.991793i | \(0.540810\pi\) | |||||||
\(740\) | −3227.76 | −0.160344 | ||||||||
\(741\) | −781.061 | −0.0387220 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32710.9 | −1.61514 | −0.807569 | − | 0.589773i | \(-0.799217\pi\) | ||||
−0.807569 | + | 0.589773i | \(0.799217\pi\) | |||||||
\(744\) | 18769.1 | 0.924877 | ||||||||
\(745\) | −14589.3 | −0.717465 | ||||||||
\(746\) | −12315.6 | −0.604431 | ||||||||
\(747\) | 33912.3 | 1.66102 | ||||||||
\(748\) | 25924.4 | 1.26723 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1945.58 | 0.0947235 | ||||||||
\(751\) | −19293.9 | −0.937474 | −0.468737 | − | 0.883338i | \(-0.655291\pi\) | ||||
−0.468737 | + | 0.883338i | \(0.655291\pi\) | |||||||
\(752\) | −2180.14 | −0.105720 | ||||||||
\(753\) | 16442.6 | 0.795753 | ||||||||
\(754\) | −296.067 | −0.0142999 | ||||||||
\(755\) | −14553.5 | −0.701530 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2631.70 | 0.126355 | 0.0631775 | − | 0.998002i | \(-0.479877\pi\) | ||||
0.0631775 | + | 0.998002i | \(0.479877\pi\) | |||||||
\(758\) | −20219.2 | −0.968859 | ||||||||
\(759\) | −1012.38 | −0.0484151 | ||||||||
\(760\) | 3554.83 | 0.169667 | ||||||||
\(761\) | 12339.7 | 0.587796 | 0.293898 | − | 0.955837i | \(-0.405047\pi\) | ||||
0.293898 | + | 0.955837i | \(0.405047\pi\) | |||||||
\(762\) | −3462.61 | −0.164616 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12403.6 | −0.587365 | ||||||||
\(765\) | 22867.4 | 1.08075 | ||||||||
\(766\) | −16416.7 | −0.774361 | ||||||||
\(767\) | −841.753 | −0.0396270 | ||||||||
\(768\) | 1992.28 | 0.0936069 | ||||||||
\(769\) | −1477.03 | −0.0692627 | −0.0346313 | − | 0.999400i | \(-0.511026\pi\) | ||||
−0.0346313 | + | 0.999400i | \(0.511026\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6262.89 | 0.292546 | ||||||||
\(772\) | −3136.83 | −0.146240 | ||||||||
\(773\) | −10308.3 | −0.479641 | −0.239820 | − | 0.970817i | \(-0.577089\pi\) | ||||
−0.239820 | + | 0.970817i | \(0.577089\pi\) | |||||||
\(774\) | 4736.53 | 0.219962 | ||||||||
\(775\) | −7536.75 | −0.349326 | ||||||||
\(776\) | 963.585 | 0.0445756 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9836.62 | −0.453291 | ||||||||
\(779\) | −25659.5 | −1.18016 | ||||||||
\(780\) | 175.775 | 0.00806891 | ||||||||
\(781\) | 32690.9 | 1.49779 | ||||||||
\(782\) | 745.321 | 0.0340826 | ||||||||
\(783\) | −6696.76 | −0.305648 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10375.6 | 0.471747 | ||||||||
\(786\) | −22830.3 | −1.03604 | ||||||||
\(787\) | −10430.1 | −0.472418 | −0.236209 | − | 0.971702i | \(-0.575905\pi\) | ||||
−0.236209 | + | 0.971702i | \(0.575905\pi\) | |||||||
\(788\) | −9261.35 | −0.418683 | ||||||||
\(789\) | −30939.6 | −1.39604 | ||||||||
\(790\) | −7220.69 | −0.325191 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 12771.9 | 0.573019 | ||||||||
\(793\) | −772.280 | −0.0345832 | ||||||||
\(794\) | 16277.9 | 0.727558 | ||||||||
\(795\) | 1333.06 | 0.0594702 | ||||||||
\(796\) | 11105.7 | 0.494510 | ||||||||
\(797\) | −10521.2 | −0.467602 | −0.233801 | − | 0.972285i | \(-0.575116\pi\) | ||||
−0.233801 | + | 0.972285i | \(0.575116\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18566.4 | 0.822068 | ||||||||
\(800\) | −800.000 | −0.0353553 | ||||||||
\(801\) | −14246.8 | −0.628445 | ||||||||
\(802\) | 691.895 | 0.0304634 | ||||||||
\(803\) | 4016.75 | 0.176523 | ||||||||
\(804\) | −2259.49 | −0.0991119 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −680.912 | −0.0297569 | ||||||||
\(807\) | −7384.49 | −0.322115 | ||||||||
\(808\) | −1956.72 | −0.0851946 | ||||||||
\(809\) | −25637.6 | −1.11418 | −0.557088 | − | 0.830453i | \(-0.688081\pi\) | ||||
−0.557088 | + | 0.830453i | \(0.688081\pi\) | |||||||
\(810\) | −5086.59 | −0.220648 | ||||||||
\(811\) | −21946.1 | −0.950225 | −0.475112 | − | 0.879925i | \(-0.657593\pi\) | ||||
−0.475112 | + | 0.879925i | \(0.657593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −997.613 | −0.0430354 | ||||||||
\(814\) | 15352.7 | 0.661072 | ||||||||
\(815\) | 542.676 | 0.0233240 | ||||||||
\(816\) | −16966.6 | −0.727878 | ||||||||
\(817\) | −6270.56 | −0.268518 | ||||||||
\(818\) | −732.253 | −0.0312991 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5774.57 | 0.245923 | ||||||||
\(821\) | 24586.1 | 1.04514 | 0.522572 | − | 0.852595i | \(-0.324973\pi\) | ||||
0.522572 | + | 0.852595i | \(0.324973\pi\) | |||||||
\(822\) | 43874.6 | 1.86168 | ||||||||
\(823\) | −22966.4 | −0.972731 | −0.486366 | − | 0.873755i | \(-0.661678\pi\) | ||||
−0.486366 | + | 0.873755i | \(0.661678\pi\) | |||||||
\(824\) | 6637.50 | 0.280617 | ||||||||
\(825\) | −9254.10 | −0.390529 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38028.0 | 1.59899 | 0.799494 | − | 0.600674i | \(-0.205101\pi\) | ||||
0.799494 | + | 0.600674i | \(0.205101\pi\) | |||||||
\(828\) | 367.191 | 0.0154115 | ||||||||
\(829\) | 27697.2 | 1.16039 | 0.580194 | − | 0.814478i | \(-0.302977\pi\) | ||||
0.580194 | + | 0.814478i | \(0.302977\pi\) | |||||||
\(830\) | 10103.6 | 0.422530 | ||||||||
\(831\) | 29221.5 | 1.21984 | ||||||||
\(832\) | −72.2765 | −0.00301170 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 31544.4 | 1.30970 | ||||||||
\(835\) | −14522.9 | −0.601898 | ||||||||
\(836\) | −16908.4 | −0.699509 | ||||||||
\(837\) | −15401.6 | −0.636030 | ||||||||
\(838\) | −13831.0 | −0.570149 | ||||||||
\(839\) | −5304.21 | −0.218262 | −0.109131 | − | 0.994027i | \(-0.534807\pi\) | ||||
−0.109131 | + | 0.994027i | \(0.534807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7206.53 | −0.295483 | ||||||||
\(842\) | −12935.2 | −0.529427 | ||||||||
\(843\) | 48033.4 | 1.96246 | ||||||||
\(844\) | 2980.14 | 0.121541 | ||||||||
\(845\) | 10978.6 | 0.446954 | ||||||||
\(846\) | 9146.95 | 0.371724 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −548.138 | −0.0221971 | ||||||||
\(849\) | −26079.1 | −1.05422 | ||||||||
\(850\) | 6812.93 | 0.274920 | ||||||||
\(851\) | 441.388 | 0.0177798 | ||||||||
\(852\) | −21395.0 | −0.860305 | ||||||||
\(853\) | 14972.1 | 0.600980 | 0.300490 | − | 0.953785i | \(-0.402850\pi\) | ||||
0.300490 | + | 0.953785i | \(0.402850\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14914.6 | −0.596570 | ||||||||
\(856\) | −6290.64 | −0.251180 | ||||||||
\(857\) | 8884.53 | 0.354130 | 0.177065 | − | 0.984199i | \(-0.443340\pi\) | ||||
0.177065 | + | 0.984199i | \(0.443340\pi\) | |||||||
\(858\) | −836.067 | −0.0332667 | ||||||||
\(859\) | −16654.0 | −0.661499 | −0.330749 | − | 0.943719i | \(-0.607301\pi\) | ||||
−0.330749 | + | 0.943719i | \(0.607301\pi\) | |||||||
\(860\) | 1411.16 | 0.0559539 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18940.4 | 0.748391 | ||||||||
\(863\) | −24985.4 | −0.985531 | −0.492766 | − | 0.870162i | \(-0.664014\pi\) | ||||
−0.492766 | + | 0.870162i | \(0.664014\pi\) | |||||||
\(864\) | −1634.83 | −0.0643726 | ||||||||
\(865\) | −5554.44 | −0.218331 | ||||||||
\(866\) | 10194.9 | 0.400044 | ||||||||
\(867\) | 106255. | 4.16219 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34345.0 | 1.34071 | ||||||||
\(870\) | −10201.2 | −0.397533 | ||||||||
\(871\) | 81.9704 | 0.00318882 | ||||||||
\(872\) | 10503.8 | 0.407917 | ||||||||
\(873\) | −4042.80 | −0.156733 | ||||||||
\(874\) | −486.114 | −0.0188135 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2628.81 | −0.101392 | ||||||||
\(877\) | 17465.3 | 0.672474 | 0.336237 | − | 0.941777i | \(-0.390846\pi\) | ||||
0.336237 | + | 0.941777i | \(0.390846\pi\) | |||||||
\(878\) | −227.021 | −0.00872619 | ||||||||
\(879\) | −5301.03 | −0.203412 | ||||||||
\(880\) | 3805.17 | 0.145764 | ||||||||
\(881\) | −15147.3 | −0.579259 | −0.289629 | − | 0.957139i | \(-0.593532\pi\) | ||||
−0.289629 | + | 0.957139i | \(0.593532\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9446.54 | −0.360024 | −0.180012 | − | 0.983664i | \(-0.557614\pi\) | ||||
−0.180012 | + | 0.983664i | \(0.557614\pi\) | |||||||
\(884\) | 615.518 | 0.0234187 | ||||||||
\(885\) | −29003.3 | −1.10162 | ||||||||
\(886\) | 34398.2 | 1.30432 | ||||||||
\(887\) | −16388.8 | −0.620384 | −0.310192 | − | 0.950674i | \(-0.600393\pi\) | ||||
−0.310192 | + | 0.950674i | \(0.600393\pi\) | |||||||
\(888\) | −10047.8 | −0.379709 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4244.57 | −0.159863 | ||||||||
\(891\) | 24194.2 | 0.909693 | ||||||||
\(892\) | 17518.4 | 0.657576 | ||||||||
\(893\) | −12109.4 | −0.453780 | ||||||||
\(894\) | −45415.5 | −1.69902 | ||||||||
\(895\) | 3137.13 | 0.117165 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.0368 | −0.000894720 0 | ||||||||
\(898\) | −4904.15 | −0.182242 | ||||||||
\(899\) | 39517.3 | 1.46604 | ||||||||
\(900\) | 3356.47 | 0.124314 | ||||||||
\(901\) | 4668.04 | 0.172602 | ||||||||
\(902\) | −27466.5 | −1.01390 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15761.9 | 0.579902 | ||||||||
\(905\) | −9807.61 | −0.360239 | ||||||||
\(906\) | −45304.0 | −1.66128 | ||||||||
\(907\) | −18465.3 | −0.675997 | −0.337998 | − | 0.941147i | \(-0.609750\pi\) | ||||
−0.337998 | + | 0.941147i | \(0.609750\pi\) | |||||||
\(908\) | −3529.82 | −0.129010 | ||||||||
\(909\) | 8209.59 | 0.299554 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29356.9 | −1.06766 | −0.533830 | − | 0.845592i | \(-0.679248\pi\) | ||||
−0.533830 | + | 0.845592i | \(0.679248\pi\) | |||||||
\(912\) | 11065.9 | 0.401787 | ||||||||
\(913\) | −48057.2 | −1.74202 | ||||||||
\(914\) | 26848.9 | 0.971645 | ||||||||
\(915\) | −26609.5 | −0.961404 | ||||||||
\(916\) | 15671.8 | 0.565295 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13922.5 | 0.500555 | ||||||||
\(919\) | 911.579 | 0.0327206 | 0.0163603 | − | 0.999866i | \(-0.494792\pi\) | ||||
0.0163603 | + | 0.999866i | \(0.494792\pi\) | |||||||
\(920\) | 109.398 | 0.00392037 | ||||||||
\(921\) | −48615.2 | −1.73933 | ||||||||
\(922\) | −7363.49 | −0.263019 | ||||||||
\(923\) | 776.174 | 0.0276794 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4034.70 | 0.143416 | ||||||||
\(926\) | −3400.17 | −0.120666 | ||||||||
\(927\) | −27848.2 | −0.986682 | ||||||||
\(928\) | 4194.62 | 0.148378 | ||||||||
\(929\) | 47788.8 | 1.68773 | 0.843864 | − | 0.536557i | \(-0.180275\pi\) | ||||
0.843864 | + | 0.536557i | \(0.180275\pi\) | |||||||
\(930\) | −23461.4 | −0.827236 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5470.56 | −0.192268 | ||||||||
\(933\) | 47201.0 | 1.65626 | ||||||||
\(934\) | −15903.8 | −0.557161 | ||||||||
\(935\) | −32405.5 | −1.13345 | ||||||||
\(936\) | 303.242 | 0.0105895 | ||||||||
\(937\) | 41650.7 | 1.45216 | 0.726078 | − | 0.687612i | \(-0.241341\pi\) | ||||
0.726078 | + | 0.687612i | \(0.241341\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −64478.4 | −2.24087 | ||||||||
\(940\) | 2725.17 | 0.0945589 | ||||||||
\(941\) | −51606.4 | −1.78780 | −0.893901 | − | 0.448264i | \(-0.852042\pi\) | ||||
−0.893901 | + | 0.448264i | \(0.852042\pi\) | |||||||
\(942\) | 32298.6 | 1.11714 | ||||||||
\(943\) | −789.658 | −0.0272691 | ||||||||
\(944\) | 11925.8 | 0.411178 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6712.16 | −0.230688 | ||||||||
\(947\) | −28910.3 | −0.992038 | −0.496019 | − | 0.868312i | \(-0.665205\pi\) | ||||
−0.496019 | + | 0.868312i | \(0.665205\pi\) | |||||||
\(948\) | −22477.5 | −0.770080 | ||||||||
\(949\) | 95.3690 | 0.00326218 | ||||||||
\(950\) | −4443.53 | −0.151755 | ||||||||
\(951\) | −9269.10 | −0.316058 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37077.6 | 1.26029 | 0.630147 | − | 0.776476i | \(-0.282995\pi\) | ||||
0.630147 | + | 0.776476i | \(0.282995\pi\) | |||||||
\(954\) | 2299.76 | 0.0780476 | ||||||||
\(955\) | 15504.5 | 0.525355 | ||||||||
\(956\) | 20323.7 | 0.687570 | ||||||||
\(957\) | 48521.8 | 1.63896 | ||||||||
\(958\) | 25640.5 | 0.864726 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2490.35 | −0.0837245 | ||||||||
\(961\) | 61093.1 | 2.05072 | ||||||||
\(962\) | 364.517 | 0.0122167 | ||||||||
\(963\) | 26392.9 | 0.883177 | ||||||||
\(964\) | 25967.0 | 0.867572 | ||||||||
\(965\) | 3921.04 | 0.130801 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36422.8 | 1.21125 | 0.605625 | − | 0.795750i | \(-0.292923\pi\) | ||||
0.605625 | + | 0.795750i | \(0.292923\pi\) | |||||||
\(968\) | −7451.18 | −0.247407 | ||||||||
\(969\) | −94239.3 | −3.12426 | ||||||||
\(970\) | −1204.48 | −0.0398697 | ||||||||
\(971\) | −13119.2 | −0.433590 | −0.216795 | − | 0.976217i | \(-0.569560\pi\) | ||||
−0.216795 | + | 0.976217i | \(0.569560\pi\) | |||||||
\(972\) | −21351.8 | −0.704587 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11087.5 | −0.364748 | ||||||||
\(975\) | −219.719 | −0.00721705 | ||||||||
\(976\) | 10941.5 | 0.358842 | ||||||||
\(977\) | 11606.2 | 0.380057 | 0.190028 | − | 0.981779i | \(-0.439142\pi\) | ||||
0.190028 | + | 0.981779i | \(0.439142\pi\) | |||||||
\(978\) | 1689.31 | 0.0552334 | ||||||||
\(979\) | 20189.2 | 0.659089 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44069.5 | −1.43428 | ||||||||
\(982\) | 32764.2 | 1.06471 | ||||||||
\(983\) | −30458.7 | −0.988283 | −0.494142 | − | 0.869381i | \(-0.664518\pi\) | ||||
−0.494142 | + | 0.869381i | \(0.664518\pi\) | |||||||
\(984\) | 17975.8 | 0.582367 | ||||||||
\(985\) | 11576.7 | 0.374481 | ||||||||
\(986\) | −35722.1 | −1.15378 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −401.454 | −0.0129271 | ||||||||
\(989\) | −192.973 | −0.00620444 | ||||||||
\(990\) | −15964.9 | −0.512524 | ||||||||
\(991\) | −39763.4 | −1.27460 | −0.637299 | − | 0.770617i | \(-0.719948\pi\) | ||||
−0.637299 | + | 0.770617i | \(0.719948\pi\) | |||||||
\(992\) | 9647.04 | 0.308764 | ||||||||
\(993\) | −37276.6 | −1.19128 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13882.1 | −0.442303 | ||||||||
\(996\) | 31451.7 | 1.00059 | ||||||||
\(997\) | 40668.8 | 1.29187 | 0.645935 | − | 0.763393i | \(-0.276468\pi\) | ||||
0.645935 | + | 0.763393i | \(0.276468\pi\) | |||||||
\(998\) | −23075.2 | −0.731896 | ||||||||
\(999\) | 8245.04 | 0.261123 |
(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 | 490.4.a.t.1.2 | 2 | ||
5.4 | even | 2 | 2450.4.a.bv.1.1 | 2 | |||
7.2 | even | 3 | 490.4.e.u.361.1 | 4 | |||
7.3 | odd | 6 | 70.4.e.d.51.2 | yes | 4 | ||
7.4 | even | 3 | 490.4.e.u.471.1 | 4 | |||
7.5 | odd | 6 | 70.4.e.d.11.2 | ✓ | 4 | ||
7.6 | odd | 2 | 490.4.a.r.1.1 | 2 | |||
21.5 | even | 6 | 630.4.k.l.361.2 | 4 | |||
21.17 | even | 6 | 630.4.k.l.541.2 | 4 | |||
28.3 | even | 6 | 560.4.q.j.401.1 | 4 | |||
28.19 | even | 6 | 560.4.q.j.81.1 | 4 | |||
35.3 | even | 12 | 350.4.j.g.149.1 | 8 | |||
35.12 | even | 12 | 350.4.j.g.249.1 | 8 | |||
35.17 | even | 12 | 350.4.j.g.149.4 | 8 | |||
35.19 | odd | 6 | 350.4.e.h.151.1 | 4 | |||
35.24 | odd | 6 | 350.4.e.h.51.1 | 4 | |||
35.33 | even | 12 | 350.4.j.g.249.4 | 8 | |||
35.34 | odd | 2 | 2450.4.a.bz.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.4.e.d.11.2 | ✓ | 4 | 7.5 | odd | 6 | ||
70.4.e.d.51.2 | yes | 4 | 7.3 | odd | 6 | ||
350.4.e.h.51.1 | 4 | 35.24 | odd | 6 | |||
350.4.e.h.151.1 | 4 | 35.19 | odd | 6 | |||
350.4.j.g.149.1 | 8 | 35.3 | even | 12 | |||
350.4.j.g.149.4 | 8 | 35.17 | even | 12 | |||
350.4.j.g.249.1 | 8 | 35.12 | even | 12 | |||
350.4.j.g.249.4 | 8 | 35.33 | even | 12 | |||
490.4.a.r.1.1 | 2 | 7.6 | odd | 2 | |||
490.4.a.t.1.2 | 2 | 1.1 | even | 1 | trivial | ||
490.4.e.u.361.1 | 4 | 7.2 | even | 3 | |||
490.4.e.u.471.1 | 4 | 7.4 | even | 3 | |||
560.4.q.j.81.1 | 4 | 28.19 | even | 6 | |||
560.4.q.j.401.1 | 4 | 28.3 | even | 6 | |||
630.4.k.l.361.2 | 4 | 21.5 | even | 6 | |||
630.4.k.l.541.2 | 4 | 21.17 | even | 6 | |||
2450.4.a.bv.1.1 | 2 | 5.4 | even | 2 | |||
2450.4.a.bz.1.2 | 2 | 35.34 | odd | 2 |