Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.33237 | −1.88528 | −0.942639 | − | 0.333814i | \(-0.891664\pi\) | ||||
−0.942639 | + | 0.333814i | \(0.891664\pi\) | |||||||
\(3\) | 5.38049 | 1.03548 | 0.517738 | − | 0.855539i | \(-0.326774\pi\) | ||||
0.517738 | + | 0.855539i | \(0.326774\pi\) | |||||||
\(4\) | 20.4342 | 2.55427 | ||||||||
\(5\) | 1.13957 | 0.101926 | 0.0509629 | − | 0.998701i | \(-0.483771\pi\) | ||||
0.0509629 | + | 0.998701i | \(0.483771\pi\) | |||||||
\(6\) | −28.6907 | −1.95216 | ||||||||
\(7\) | 19.4433 | 1.04984 | 0.524920 | − | 0.851152i | \(-0.324095\pi\) | ||||
0.524920 | + | 0.851152i | \(0.324095\pi\) | |||||||
\(8\) | −66.3036 | −2.93023 | ||||||||
\(9\) | 1.94964 | 0.0722088 | ||||||||
\(10\) | −6.07658 | −0.192158 | ||||||||
\(11\) | 11.2409 | 0.308113 | 0.154057 | − | 0.988062i | \(-0.450766\pi\) | ||||
0.154057 | + | 0.988062i | \(0.450766\pi\) | |||||||
\(12\) | 109.946 | 2.64488 | ||||||||
\(13\) | 82.3500 | 1.75691 | 0.878453 | − | 0.477829i | \(-0.158576\pi\) | ||||
0.878453 | + | 0.477829i | \(0.158576\pi\) | |||||||
\(14\) | −103.679 | −1.97924 | ||||||||
\(15\) | 6.13142 | 0.105542 | ||||||||
\(16\) | 190.082 | 2.97003 | ||||||||
\(17\) | −132.630 | −1.89221 | −0.946106 | − | 0.323856i | \(-0.895021\pi\) | ||||
−0.946106 | + | 0.323856i | \(0.895021\pi\) | |||||||
\(18\) | −10.3962 | −0.136134 | ||||||||
\(19\) | 41.5526 | 0.501727 | 0.250864 | − | 0.968022i | \(-0.419285\pi\) | ||||
0.250864 | + | 0.968022i | \(0.419285\pi\) | |||||||
\(20\) | 23.2861 | 0.260346 | ||||||||
\(21\) | 104.614 | 1.08708 | ||||||||
\(22\) | −59.9405 | −0.580879 | ||||||||
\(23\) | 97.0017 | 0.879402 | 0.439701 | − | 0.898144i | \(-0.355084\pi\) | ||||
0.439701 | + | 0.898144i | \(0.355084\pi\) | |||||||
\(24\) | −356.746 | −3.03418 | ||||||||
\(25\) | −123.701 | −0.989611 | ||||||||
\(26\) | −439.121 | −3.31225 | ||||||||
\(27\) | −134.783 | −0.960705 | ||||||||
\(28\) | 397.308 | 2.68157 | ||||||||
\(29\) | −94.9288 | −0.607856 | −0.303928 | − | 0.952695i | \(-0.598298\pi\) | ||||
−0.303928 | + | 0.952695i | \(0.598298\pi\) | |||||||
\(30\) | −32.6950 | −0.198975 | ||||||||
\(31\) | −265.836 | −1.54018 | −0.770091 | − | 0.637935i | \(-0.779789\pi\) | ||||
−0.770091 | + | 0.637935i | \(0.779789\pi\) | |||||||
\(32\) | −483.159 | −2.66910 | ||||||||
\(33\) | 60.4813 | 0.319044 | ||||||||
\(34\) | 707.235 | 3.56735 | ||||||||
\(35\) | 22.1569 | 0.107006 | ||||||||
\(36\) | 39.8392 | 0.184441 | ||||||||
\(37\) | −70.0555 | −0.311272 | −0.155636 | − | 0.987814i | \(-0.549743\pi\) | ||||
−0.155636 | + | 0.987814i | \(0.549743\pi\) | |||||||
\(38\) | −221.574 | −0.945896 | ||||||||
\(39\) | 443.083 | 1.81923 | ||||||||
\(40\) | −75.5573 | −0.298666 | ||||||||
\(41\) | 30.4482 | 0.115981 | 0.0579903 | − | 0.998317i | \(-0.481531\pi\) | ||||
0.0579903 | + | 0.998317i | \(0.481531\pi\) | |||||||
\(42\) | −557.843 | −2.04945 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 229.698 | 0.787006 | ||||||||
\(45\) | 2.22174 | 0.00735994 | ||||||||
\(46\) | −517.249 | −1.65792 | ||||||||
\(47\) | −418.189 | −1.29785 | −0.648927 | − | 0.760850i | \(-0.724782\pi\) | ||||
−0.648927 | + | 0.760850i | \(0.724782\pi\) | |||||||
\(48\) | 1022.73 | 3.07539 | ||||||||
\(49\) | 35.0417 | 0.102162 | ||||||||
\(50\) | 659.622 | 1.86569 | ||||||||
\(51\) | −713.617 | −1.95934 | ||||||||
\(52\) | 1682.75 | 4.48761 | ||||||||
\(53\) | −399.944 | −1.03654 | −0.518269 | − | 0.855218i | \(-0.673423\pi\) | ||||
−0.518269 | + | 0.855218i | \(0.673423\pi\) | |||||||
\(54\) | 718.714 | 1.81120 | ||||||||
\(55\) | 12.8097 | 0.0314047 | ||||||||
\(56\) | −1289.16 | −3.07627 | ||||||||
\(57\) | 223.573 | 0.519526 | ||||||||
\(58\) | 506.195 | 1.14598 | ||||||||
\(59\) | −57.1424 | −0.126090 | −0.0630450 | − | 0.998011i | \(-0.520081\pi\) | ||||
−0.0630450 | + | 0.998011i | \(0.520081\pi\) | |||||||
\(60\) | 125.290 | 0.269582 | ||||||||
\(61\) | 331.172 | 0.695118 | 0.347559 | − | 0.937658i | \(-0.387011\pi\) | ||||
0.347559 | + | 0.937658i | \(0.387011\pi\) | |||||||
\(62\) | 1417.54 | 2.90367 | ||||||||
\(63\) | 37.9074 | 0.0758077 | ||||||||
\(64\) | 1055.73 | 2.06196 | ||||||||
\(65\) | 93.8432 | 0.179074 | ||||||||
\(66\) | −322.509 | −0.601486 | ||||||||
\(67\) | 156.263 | 0.284934 | 0.142467 | − | 0.989800i | \(-0.454496\pi\) | ||||
0.142467 | + | 0.989800i | \(0.454496\pi\) | |||||||
\(68\) | −2710.19 | −4.83322 | ||||||||
\(69\) | 521.916 | 0.910599 | ||||||||
\(70\) | −118.149 | −0.201735 | ||||||||
\(71\) | −564.356 | −0.943335 | −0.471667 | − | 0.881777i | \(-0.656348\pi\) | ||||
−0.471667 | + | 0.881777i | \(0.656348\pi\) | |||||||
\(72\) | −129.268 | −0.211589 | ||||||||
\(73\) | 69.0808 | 0.110758 | 0.0553788 | − | 0.998465i | \(-0.482363\pi\) | ||||
0.0553788 | + | 0.998465i | \(0.482363\pi\) | |||||||
\(74\) | 373.562 | 0.586834 | ||||||||
\(75\) | −665.574 | −1.02472 | ||||||||
\(76\) | 849.093 | 1.28155 | ||||||||
\(77\) | 218.559 | 0.323470 | ||||||||
\(78\) | −2362.68 | −3.42976 | ||||||||
\(79\) | −569.629 | −0.811244 | −0.405622 | − | 0.914041i | \(-0.632945\pi\) | ||||
−0.405622 | + | 0.914041i | \(0.632945\pi\) | |||||||
\(80\) | 216.611 | 0.302723 | ||||||||
\(81\) | −777.839 | −1.06699 | ||||||||
\(82\) | −162.361 | −0.218656 | ||||||||
\(83\) | −785.399 | −1.03866 | −0.519330 | − | 0.854574i | \(-0.673818\pi\) | ||||
−0.519330 | + | 0.854574i | \(0.673818\pi\) | |||||||
\(84\) | 2137.71 | 2.77670 | ||||||||
\(85\) | −151.141 | −0.192865 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −510.763 | −0.629420 | ||||||||
\(88\) | −745.310 | −0.902844 | ||||||||
\(89\) | −429.427 | −0.511451 | −0.255726 | − | 0.966749i | \(-0.582314\pi\) | ||||
−0.255726 | + | 0.966749i | \(0.582314\pi\) | |||||||
\(90\) | −11.8471 | −0.0138755 | ||||||||
\(91\) | 1601.15 | 1.84447 | ||||||||
\(92\) | 1982.15 | 2.24623 | ||||||||
\(93\) | −1430.33 | −1.59482 | ||||||||
\(94\) | 2229.94 | 2.44682 | ||||||||
\(95\) | 47.3519 | 0.0511390 | ||||||||
\(96\) | −2599.63 | −2.76379 | ||||||||
\(97\) | −1161.42 | −1.21572 | −0.607858 | − | 0.794046i | \(-0.707971\pi\) | ||||
−0.607858 | + | 0.794046i | \(0.707971\pi\) | |||||||
\(98\) | −186.855 | −0.192604 | ||||||||
\(99\) | 21.9156 | 0.0222485 | ||||||||
\(100\) | −2527.74 | −2.52774 | ||||||||
\(101\) | 190.011 | 0.187196 | 0.0935978 | − | 0.995610i | \(-0.470163\pi\) | ||||
0.0935978 | + | 0.995610i | \(0.470163\pi\) | |||||||
\(102\) | 3805.27 | 3.69390 | ||||||||
\(103\) | −552.932 | −0.528952 | −0.264476 | − | 0.964392i | \(-0.585199\pi\) | ||||
−0.264476 | + | 0.964392i | \(0.585199\pi\) | |||||||
\(104\) | −5460.10 | −5.14814 | ||||||||
\(105\) | 119.215 | 0.110802 | ||||||||
\(106\) | 2132.65 | 1.95416 | ||||||||
\(107\) | −1660.97 | −1.50067 | −0.750336 | − | 0.661057i | \(-0.770108\pi\) | ||||
−0.750336 | + | 0.661057i | \(0.770108\pi\) | |||||||
\(108\) | −2754.18 | −2.45390 | ||||||||
\(109\) | −851.383 | −0.748144 | −0.374072 | − | 0.927400i | \(-0.622039\pi\) | ||||
−0.374072 | + | 0.927400i | \(0.622039\pi\) | |||||||
\(110\) | −68.3061 | −0.0592066 | ||||||||
\(111\) | −376.933 | −0.322314 | ||||||||
\(112\) | 3695.82 | 3.11806 | ||||||||
\(113\) | 336.677 | 0.280282 | 0.140141 | − | 0.990132i | \(-0.455244\pi\) | ||||
0.140141 | + | 0.990132i | \(0.455244\pi\) | |||||||
\(114\) | −1192.18 | −0.979451 | ||||||||
\(115\) | 110.540 | 0.0896337 | ||||||||
\(116\) | −1939.79 | −1.55263 | ||||||||
\(117\) | 160.553 | 0.126864 | ||||||||
\(118\) | 304.705 | 0.237715 | ||||||||
\(119\) | −2578.77 | −1.98652 | ||||||||
\(120\) | −406.535 | −0.309262 | ||||||||
\(121\) | −1204.64 | −0.905066 | ||||||||
\(122\) | −1765.93 | −1.31049 | ||||||||
\(123\) | 163.826 | 0.120095 | ||||||||
\(124\) | −5432.15 | −3.93404 | ||||||||
\(125\) | −283.411 | −0.202793 | ||||||||
\(126\) | −202.136 | −0.142918 | ||||||||
\(127\) | 1906.99 | 1.33242 | 0.666212 | − | 0.745762i | \(-0.267914\pi\) | ||||
0.666212 | + | 0.745762i | \(0.267914\pi\) | |||||||
\(128\) | −1764.25 | −1.21827 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −500.407 | −0.337604 | ||||||||
\(131\) | 1298.17 | 0.865815 | 0.432908 | − | 0.901438i | \(-0.357488\pi\) | ||||
0.432908 | + | 0.901438i | \(0.357488\pi\) | |||||||
\(132\) | 1235.89 | 0.814925 | ||||||||
\(133\) | 807.920 | 0.526733 | ||||||||
\(134\) | −833.253 | −0.537180 | ||||||||
\(135\) | −153.594 | −0.0979206 | ||||||||
\(136\) | 8793.88 | 5.54462 | ||||||||
\(137\) | −259.404 | −0.161769 | −0.0808847 | − | 0.996723i | \(-0.525775\pi\) | ||||
−0.0808847 | + | 0.996723i | \(0.525775\pi\) | |||||||
\(138\) | −2783.05 | −1.71673 | ||||||||
\(139\) | −52.2455 | −0.0318806 | −0.0159403 | − | 0.999873i | \(-0.505074\pi\) | ||||
−0.0159403 | + | 0.999873i | \(0.505074\pi\) | |||||||
\(140\) | 452.758 | 0.273322 | ||||||||
\(141\) | −2250.06 | −1.34390 | ||||||||
\(142\) | 3009.36 | 1.77845 | ||||||||
\(143\) | 925.685 | 0.541326 | ||||||||
\(144\) | 370.591 | 0.214462 | ||||||||
\(145\) | −108.178 | −0.0619562 | ||||||||
\(146\) | −368.365 | −0.208809 | ||||||||
\(147\) | 188.541 | 0.105787 | ||||||||
\(148\) | −1431.53 | −0.795073 | ||||||||
\(149\) | −3239.65 | −1.78123 | −0.890613 | − | 0.454762i | \(-0.849724\pi\) | ||||
−0.890613 | + | 0.454762i | \(0.849724\pi\) | |||||||
\(150\) | 3549.09 | 1.93188 | ||||||||
\(151\) | 2294.66 | 1.23667 | 0.618334 | − | 0.785915i | \(-0.287808\pi\) | ||||
0.618334 | + | 0.785915i | \(0.287808\pi\) | |||||||
\(152\) | −2755.09 | −1.47018 | ||||||||
\(153\) | −258.581 | −0.136634 | ||||||||
\(154\) | −1165.44 | −0.609830 | ||||||||
\(155\) | −302.938 | −0.156984 | ||||||||
\(156\) | 9054.03 | 4.64681 | ||||||||
\(157\) | 3333.45 | 1.69451 | 0.847257 | − | 0.531184i | \(-0.178253\pi\) | ||||
0.847257 | + | 0.531184i | \(0.178253\pi\) | |||||||
\(158\) | 3037.47 | 1.52942 | ||||||||
\(159\) | −2151.89 | −1.07331 | ||||||||
\(160\) | −550.591 | −0.272050 | ||||||||
\(161\) | 1886.03 | 0.923231 | ||||||||
\(162\) | 4147.73 | 2.01158 | ||||||||
\(163\) | −1886.07 | −0.906310 | −0.453155 | − | 0.891432i | \(-0.649702\pi\) | ||||
−0.453155 | + | 0.891432i | \(0.649702\pi\) | |||||||
\(164\) | 622.183 | 0.296246 | ||||||||
\(165\) | 68.9224 | 0.0325188 | ||||||||
\(166\) | 4188.04 | 1.95816 | ||||||||
\(167\) | −628.615 | −0.291280 | −0.145640 | − | 0.989338i | \(-0.546524\pi\) | ||||
−0.145640 | + | 0.989338i | \(0.546524\pi\) | |||||||
\(168\) | −6936.31 | −3.18541 | ||||||||
\(169\) | 4584.52 | 2.08672 | ||||||||
\(170\) | 805.940 | 0.363605 | ||||||||
\(171\) | 81.0126 | 0.0362292 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2010.27 | 0.883456 | 0.441728 | − | 0.897149i | \(-0.354366\pi\) | ||||
0.441728 | + | 0.897149i | \(0.354366\pi\) | |||||||
\(174\) | 2723.58 | 1.18663 | ||||||||
\(175\) | −2405.16 | −1.03893 | ||||||||
\(176\) | 2136.69 | 0.915107 | ||||||||
\(177\) | −307.454 | −0.130563 | ||||||||
\(178\) | 2289.86 | 0.964228 | ||||||||
\(179\) | 1442.47 | 0.602320 | 0.301160 | − | 0.953574i | \(-0.402626\pi\) | ||||
0.301160 | + | 0.953574i | \(0.402626\pi\) | |||||||
\(180\) | 45.3994 | 0.0187993 | ||||||||
\(181\) | −1243.78 | −0.510770 | −0.255385 | − | 0.966839i | \(-0.582202\pi\) | ||||
−0.255385 | + | 0.966839i | \(0.582202\pi\) | |||||||
\(182\) | −8537.95 | −3.47734 | ||||||||
\(183\) | 1781.86 | 0.719777 | ||||||||
\(184\) | −6431.56 | −2.57685 | ||||||||
\(185\) | −79.8329 | −0.0317266 | ||||||||
\(186\) | 7627.04 | 3.00668 | ||||||||
\(187\) | −1490.88 | −0.583016 | ||||||||
\(188\) | −8545.35 | −3.31507 | ||||||||
\(189\) | −2620.63 | −1.00859 | ||||||||
\(190\) | −252.498 | −0.0964112 | ||||||||
\(191\) | 3169.52 | 1.20072 | 0.600362 | − | 0.799728i | \(-0.295023\pi\) | ||||
0.600362 | + | 0.799728i | \(0.295023\pi\) | |||||||
\(192\) | 5680.32 | 2.13511 | ||||||||
\(193\) | −2034.25 | −0.758698 | −0.379349 | − | 0.925254i | \(-0.623852\pi\) | ||||
−0.379349 | + | 0.925254i | \(0.623852\pi\) | |||||||
\(194\) | 6193.13 | 2.29196 | ||||||||
\(195\) | 504.922 | 0.185427 | ||||||||
\(196\) | 716.048 | 0.260950 | ||||||||
\(197\) | 3188.91 | 1.15330 | 0.576650 | − | 0.816991i | \(-0.304360\pi\) | ||||
0.576650 | + | 0.816991i | \(0.304360\pi\) | |||||||
\(198\) | −116.862 | −0.0419446 | ||||||||
\(199\) | −1546.27 | −0.550814 | −0.275407 | − | 0.961328i | \(-0.588813\pi\) | ||||
−0.275407 | + | 0.961328i | \(0.588813\pi\) | |||||||
\(200\) | 8201.85 | 2.89979 | ||||||||
\(201\) | 840.772 | 0.295042 | ||||||||
\(202\) | −1013.21 | −0.352916 | ||||||||
\(203\) | −1845.73 | −0.638151 | ||||||||
\(204\) | −14582.2 | −5.00468 | ||||||||
\(205\) | 34.6977 | 0.0118214 | ||||||||
\(206\) | 2948.44 | 0.997221 | ||||||||
\(207\) | 189.118 | 0.0635006 | ||||||||
\(208\) | 15653.3 | 5.21807 | ||||||||
\(209\) | 467.087 | 0.154589 | ||||||||
\(210\) | −635.698 | −0.208892 | ||||||||
\(211\) | 4947.03 | 1.61406 | 0.807032 | − | 0.590508i | \(-0.201072\pi\) | ||||
0.807032 | + | 0.590508i | \(0.201072\pi\) | |||||||
\(212\) | −8172.52 | −2.64760 | ||||||||
\(213\) | −3036.51 | −0.976800 | ||||||||
\(214\) | 8856.90 | 2.82918 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8936.61 | 2.81509 | ||||||||
\(217\) | −5168.73 | −1.61694 | ||||||||
\(218\) | 4539.89 | 1.41046 | ||||||||
\(219\) | 371.688 | 0.114687 | ||||||||
\(220\) | 261.756 | 0.0802162 | ||||||||
\(221\) | −10922.1 | −3.32444 | ||||||||
\(222\) | 2009.95 | 0.607652 | ||||||||
\(223\) | −1020.68 | −0.306501 | −0.153251 | − | 0.988187i | \(-0.548974\pi\) | ||||
−0.153251 | + | 0.988187i | \(0.548974\pi\) | |||||||
\(224\) | −9394.20 | −2.80213 | ||||||||
\(225\) | −241.173 | −0.0714587 | ||||||||
\(226\) | −1795.29 | −0.528410 | ||||||||
\(227\) | 1897.59 | 0.554836 | 0.277418 | − | 0.960749i | \(-0.410521\pi\) | ||||
0.277418 | + | 0.960749i | \(0.410521\pi\) | |||||||
\(228\) | 4568.53 | 1.32701 | ||||||||
\(229\) | 3784.45 | 1.09207 | 0.546034 | − | 0.837763i | \(-0.316137\pi\) | ||||
0.546034 | + | 0.837763i | \(0.316137\pi\) | |||||||
\(230\) | −589.439 | −0.168984 | ||||||||
\(231\) | 1175.96 | 0.334945 | ||||||||
\(232\) | 6294.12 | 1.78116 | ||||||||
\(233\) | −5821.37 | −1.63678 | −0.818391 | − | 0.574661i | \(-0.805134\pi\) | ||||
−0.818391 | + | 0.574661i | \(0.805134\pi\) | |||||||
\(234\) | −856.126 | −0.239174 | ||||||||
\(235\) | −476.554 | −0.132285 | ||||||||
\(236\) | −1167.66 | −0.322068 | ||||||||
\(237\) | −3064.88 | −0.840023 | ||||||||
\(238\) | 13751.0 | 3.74514 | ||||||||
\(239\) | 3277.24 | 0.886975 | 0.443488 | − | 0.896280i | \(-0.353741\pi\) | ||||
0.443488 | + | 0.896280i | \(0.353741\pi\) | |||||||
\(240\) | 1165.47 | 0.313462 | ||||||||
\(241\) | −3524.53 | −0.942054 | −0.471027 | − | 0.882119i | \(-0.656117\pi\) | ||||
−0.471027 | + | 0.882119i | \(0.656117\pi\) | |||||||
\(242\) | 6423.60 | 1.70630 | ||||||||
\(243\) | −546.008 | −0.144142 | ||||||||
\(244\) | 6767.22 | 1.77552 | ||||||||
\(245\) | 39.9323 | 0.0104130 | ||||||||
\(246\) | −873.581 | −0.226413 | ||||||||
\(247\) | 3421.86 | 0.881488 | ||||||||
\(248\) | 17625.9 | 4.51309 | ||||||||
\(249\) | −4225.83 | −1.07551 | ||||||||
\(250\) | 1511.25 | 0.382321 | ||||||||
\(251\) | 658.193 | 0.165517 | 0.0827585 | − | 0.996570i | \(-0.473627\pi\) | ||||
0.0827585 | + | 0.996570i | \(0.473627\pi\) | |||||||
\(252\) | 774.606 | 0.193633 | ||||||||
\(253\) | 1090.38 | 0.270956 | ||||||||
\(254\) | −10168.8 | −2.51199 | ||||||||
\(255\) | −813.213 | −0.199707 | ||||||||
\(256\) | 961.825 | 0.234821 | ||||||||
\(257\) | 4247.86 | 1.03103 | 0.515514 | − | 0.856881i | \(-0.327601\pi\) | ||||
0.515514 | + | 0.856881i | \(0.327601\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1362.11 | −0.326785 | ||||||||
\(260\) | 1917.61 | 0.457404 | ||||||||
\(261\) | −185.077 | −0.0438926 | ||||||||
\(262\) | −6922.33 | −1.63230 | ||||||||
\(263\) | 2058.13 | 0.482547 | 0.241274 | − | 0.970457i | \(-0.422435\pi\) | ||||
0.241274 | + | 0.970457i | \(0.422435\pi\) | |||||||
\(264\) | −4010.13 | −0.934873 | ||||||||
\(265\) | −455.762 | −0.105650 | ||||||||
\(266\) | −4308.13 | −0.993038 | ||||||||
\(267\) | −2310.53 | −0.529595 | ||||||||
\(268\) | 3193.11 | 0.727799 | ||||||||
\(269\) | 4941.92 | 1.12013 | 0.560064 | − | 0.828450i | \(-0.310777\pi\) | ||||
0.560064 | + | 0.828450i | \(0.310777\pi\) | |||||||
\(270\) | 819.021 | 0.184608 | ||||||||
\(271\) | 7166.71 | 1.60644 | 0.803222 | − | 0.595679i | \(-0.203117\pi\) | ||||
0.803222 | + | 0.595679i | \(0.203117\pi\) | |||||||
\(272\) | −25210.7 | −5.61993 | ||||||||
\(273\) | 8614.99 | 1.90990 | ||||||||
\(274\) | 1383.24 | 0.304980 | ||||||||
\(275\) | −1390.51 | −0.304913 | ||||||||
\(276\) | 10664.9 | 2.32592 | ||||||||
\(277\) | −1097.77 | −0.238118 | −0.119059 | − | 0.992887i | \(-0.537988\pi\) | ||||
−0.119059 | + | 0.992887i | \(0.537988\pi\) | |||||||
\(278\) | 278.592 | 0.0601038 | ||||||||
\(279\) | −518.285 | −0.111215 | ||||||||
\(280\) | −1469.08 | −0.313552 | ||||||||
\(281\) | −3052.94 | −0.648125 | −0.324062 | − | 0.946036i | \(-0.605049\pi\) | ||||
−0.324062 | + | 0.946036i | \(0.605049\pi\) | |||||||
\(282\) | 11998.2 | 2.53362 | ||||||||
\(283\) | −3952.97 | −0.830316 | −0.415158 | − | 0.909749i | \(-0.636274\pi\) | ||||
−0.415158 | + | 0.909749i | \(0.636274\pi\) | |||||||
\(284\) | −11532.2 | −2.40953 | ||||||||
\(285\) | 254.776 | 0.0529531 | ||||||||
\(286\) | −4936.10 | −1.02055 | ||||||||
\(287\) | 592.013 | 0.121761 | ||||||||
\(288\) | −941.985 | −0.192733 | ||||||||
\(289\) | 12677.8 | 2.58047 | ||||||||
\(290\) | 576.843 | 0.116805 | ||||||||
\(291\) | −6249.01 | −1.25884 | ||||||||
\(292\) | 1411.61 | 0.282905 | ||||||||
\(293\) | −229.679 | −0.0457953 | −0.0228976 | − | 0.999738i | \(-0.507289\pi\) | ||||
−0.0228976 | + | 0.999738i | \(0.507289\pi\) | |||||||
\(294\) | −1005.37 | −0.199437 | ||||||||
\(295\) | −65.1175 | −0.0128518 | ||||||||
\(296\) | 4644.93 | 0.912099 | ||||||||
\(297\) | −1515.08 | −0.296006 | ||||||||
\(298\) | 17275.0 | 3.35810 | ||||||||
\(299\) | 7988.08 | 1.54503 | ||||||||
\(300\) | −13600.4 | −2.61741 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12236.0 | −2.33146 | ||||||||
\(303\) | 1022.35 | 0.193836 | ||||||||
\(304\) | 7898.40 | 1.49015 | ||||||||
\(305\) | 377.392 | 0.0708504 | ||||||||
\(306\) | 1378.85 | 0.257594 | ||||||||
\(307\) | 3264.44 | 0.606878 | 0.303439 | − | 0.952851i | \(-0.401865\pi\) | ||||
0.303439 | + | 0.952851i | \(0.401865\pi\) | |||||||
\(308\) | 4466.08 | 0.826229 | ||||||||
\(309\) | −2975.05 | −0.547717 | ||||||||
\(310\) | 1615.38 | 0.295959 | ||||||||
\(311\) | 6556.37 | 1.19543 | 0.597713 | − | 0.801710i | \(-0.296076\pi\) | ||||
0.597713 | + | 0.801710i | \(0.296076\pi\) | |||||||
\(312\) | −29378.0 | −5.33077 | ||||||||
\(313\) | −7030.21 | −1.26956 | −0.634778 | − | 0.772694i | \(-0.718909\pi\) | ||||
−0.634778 | + | 0.772694i | \(0.718909\pi\) | |||||||
\(314\) | −17775.2 | −3.19463 | ||||||||
\(315\) | 43.1979 | 0.00772676 | ||||||||
\(316\) | −11639.9 | −2.07214 | ||||||||
\(317\) | 6485.38 | 1.14907 | 0.574535 | − | 0.818480i | \(-0.305183\pi\) | ||||
0.574535 | + | 0.818480i | \(0.305183\pi\) | |||||||
\(318\) | 11474.7 | 2.02349 | ||||||||
\(319\) | −1067.08 | −0.187289 | ||||||||
\(320\) | 1203.07 | 0.210167 | ||||||||
\(321\) | −8936.82 | −1.55391 | ||||||||
\(322\) | −10057.0 | −1.74055 | ||||||||
\(323\) | −5511.14 | −0.949375 | ||||||||
\(324\) | −15894.5 | −2.72539 | ||||||||
\(325\) | −10186.8 | −1.73865 | ||||||||
\(326\) | 10057.2 | 1.70865 | ||||||||
\(327\) | −4580.85 | −0.774684 | ||||||||
\(328\) | −2018.82 | −0.339850 | ||||||||
\(329\) | −8130.98 | −1.36254 | ||||||||
\(330\) | −367.520 | −0.0613070 | ||||||||
\(331\) | −5097.58 | −0.846490 | −0.423245 | − | 0.906015i | \(-0.639109\pi\) | ||||
−0.423245 | + | 0.906015i | \(0.639109\pi\) | |||||||
\(332\) | −16049.0 | −2.65302 | ||||||||
\(333\) | −136.583 | −0.0224766 | ||||||||
\(334\) | 3352.01 | 0.549143 | ||||||||
\(335\) | 178.072 | 0.0290422 | ||||||||
\(336\) | 19885.3 | 3.22867 | ||||||||
\(337\) | −6280.94 | −1.01527 | −0.507633 | − | 0.861574i | \(-0.669479\pi\) | ||||
−0.507633 | + | 0.861574i | \(0.669479\pi\) | |||||||
\(338\) | −24446.4 | −3.93404 | ||||||||
\(339\) | 1811.49 | 0.290225 | ||||||||
\(340\) | −3088.44 | −0.492630 | ||||||||
\(341\) | −2988.23 | −0.474551 | ||||||||
\(342\) | −431.989 | −0.0683020 | ||||||||
\(343\) | −5987.72 | −0.942585 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 594.757 | 0.0928135 | ||||||||
\(346\) | −10719.5 | −1.66556 | ||||||||
\(347\) | −2180.02 | −0.337261 | −0.168631 | − | 0.985679i | \(-0.553935\pi\) | ||||
−0.168631 | + | 0.985679i | \(0.553935\pi\) | |||||||
\(348\) | −10437.0 | −1.60771 | ||||||||
\(349\) | 9644.24 | 1.47921 | 0.739605 | − | 0.673041i | \(-0.235012\pi\) | ||||
0.739605 | + | 0.673041i | \(0.235012\pi\) | |||||||
\(350\) | 12825.2 | 1.95868 | ||||||||
\(351\) | −11099.4 | −1.68787 | ||||||||
\(352\) | −5431.12 | −0.822386 | ||||||||
\(353\) | −5127.42 | −0.773103 | −0.386551 | − | 0.922268i | \(-0.626334\pi\) | ||||
−0.386551 | + | 0.922268i | \(0.626334\pi\) | |||||||
\(354\) | 1639.46 | 0.246148 | ||||||||
\(355\) | −643.121 | −0.0961502 | ||||||||
\(356\) | −8774.98 | −1.30639 | ||||||||
\(357\) | −13875.1 | −2.05699 | ||||||||
\(358\) | −7691.79 | −1.13554 | ||||||||
\(359\) | −5232.56 | −0.769259 | −0.384629 | − | 0.923071i | \(-0.625671\pi\) | ||||
−0.384629 | + | 0.923071i | \(0.625671\pi\) | |||||||
\(360\) | −147.309 | −0.0215664 | ||||||||
\(361\) | −5132.38 | −0.748270 | ||||||||
\(362\) | 6632.30 | 0.962944 | ||||||||
\(363\) | −6481.57 | −0.937173 | ||||||||
\(364\) | 32718.3 | 4.71127 | ||||||||
\(365\) | 78.7221 | 0.0112890 | ||||||||
\(366\) | −9501.56 | −1.35698 | ||||||||
\(367\) | 5608.15 | 0.797666 | 0.398833 | − | 0.917024i | \(-0.369415\pi\) | ||||
0.398833 | + | 0.917024i | \(0.369415\pi\) | |||||||
\(368\) | 18438.3 | 2.61185 | ||||||||
\(369\) | 59.3629 | 0.00837483 | ||||||||
\(370\) | 425.698 | 0.0598135 | ||||||||
\(371\) | −7776.23 | −1.08820 | ||||||||
\(372\) | −29227.6 | −4.07360 | ||||||||
\(373\) | −5236.17 | −0.726860 | −0.363430 | − | 0.931621i | \(-0.618394\pi\) | ||||
−0.363430 | + | 0.931621i | \(0.618394\pi\) | |||||||
\(374\) | 7949.93 | 1.09915 | ||||||||
\(375\) | −1524.89 | −0.209987 | ||||||||
\(376\) | 27727.5 | 3.80302 | ||||||||
\(377\) | −7817.38 | −1.06795 | ||||||||
\(378\) | 13974.2 | 1.90146 | ||||||||
\(379\) | −3323.14 | −0.450392 | −0.225196 | − | 0.974314i | \(-0.572302\pi\) | ||||
−0.225196 | + | 0.974314i | \(0.572302\pi\) | |||||||
\(380\) | 967.597 | 0.130623 | ||||||||
\(381\) | 10260.5 | 1.37969 | ||||||||
\(382\) | −16901.0 | −2.26370 | ||||||||
\(383\) | 7934.47 | 1.05857 | 0.529285 | − | 0.848444i | \(-0.322460\pi\) | ||||
0.529285 | + | 0.848444i | \(0.322460\pi\) | |||||||
\(384\) | −9492.52 | −1.26149 | ||||||||
\(385\) | 249.063 | 0.0329699 | ||||||||
\(386\) | 10847.4 | 1.43036 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −23732.7 | −3.10527 | ||||||||
\(389\) | 2071.19 | 0.269958 | 0.134979 | − | 0.990848i | \(-0.456903\pi\) | ||||
0.134979 | + | 0.990848i | \(0.456903\pi\) | |||||||
\(390\) | −2692.43 | −0.349581 | ||||||||
\(391\) | −12865.4 | −1.66402 | ||||||||
\(392\) | −2323.39 | −0.299360 | ||||||||
\(393\) | 6984.80 | 0.896530 | ||||||||
\(394\) | −17004.4 | −2.17429 | ||||||||
\(395\) | −649.129 | −0.0826867 | ||||||||
\(396\) | 447.828 | 0.0568287 | ||||||||
\(397\) | 7588.62 | 0.959349 | 0.479675 | − | 0.877446i | \(-0.340755\pi\) | ||||
0.479675 | + | 0.877446i | \(0.340755\pi\) | |||||||
\(398\) | 8245.27 | 1.03844 | ||||||||
\(399\) | 4347.00 | 0.545419 | ||||||||
\(400\) | −23513.4 | −2.93918 | ||||||||
\(401\) | −2081.48 | −0.259212 | −0.129606 | − | 0.991566i | \(-0.541371\pi\) | ||||
−0.129606 | + | 0.991566i | \(0.541371\pi\) | |||||||
\(402\) | −4483.31 | −0.556237 | ||||||||
\(403\) | −21891.6 | −2.70595 | ||||||||
\(404\) | 3882.71 | 0.478148 | ||||||||
\(405\) | −886.398 | −0.108754 | ||||||||
\(406\) | 9842.11 | 1.20309 | ||||||||
\(407\) | −787.485 | −0.0959071 | ||||||||
\(408\) | 47315.4 | 5.74132 | ||||||||
\(409\) | −3217.52 | −0.388988 | −0.194494 | − | 0.980904i | \(-0.562306\pi\) | ||||
−0.194494 | + | 0.980904i | \(0.562306\pi\) | |||||||
\(410\) | −185.021 | −0.0222867 | ||||||||
\(411\) | −1395.72 | −0.167508 | ||||||||
\(412\) | −11298.7 | −1.35109 | ||||||||
\(413\) | −1111.04 | −0.132374 | ||||||||
\(414\) | −1008.45 | −0.119716 | ||||||||
\(415\) | −895.013 | −0.105866 | ||||||||
\(416\) | −39788.1 | −4.68936 | ||||||||
\(417\) | −281.106 | −0.0330116 | ||||||||
\(418\) | −2490.68 | −0.291443 | ||||||||
\(419\) | −7694.73 | −0.897165 | −0.448582 | − | 0.893741i | \(-0.648071\pi\) | ||||
−0.448582 | + | 0.893741i | \(0.648071\pi\) | |||||||
\(420\) | 2436.06 | 0.283018 | ||||||||
\(421\) | 1838.05 | 0.212781 | 0.106391 | − | 0.994324i | \(-0.466071\pi\) | ||||
0.106391 | + | 0.994324i | \(0.466071\pi\) | |||||||
\(422\) | −26379.4 | −3.04296 | ||||||||
\(423\) | −815.318 | −0.0937166 | ||||||||
\(424\) | 26517.7 | 3.03730 | ||||||||
\(425\) | 16406.6 | 1.87255 | ||||||||
\(426\) | 16191.8 | 1.84154 | ||||||||
\(427\) | 6439.07 | 0.729762 | ||||||||
\(428\) | −33940.5 | −3.83312 | ||||||||
\(429\) | 4980.64 | 0.560530 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4840.45 | −0.540966 | −0.270483 | − | 0.962725i | \(-0.587183\pi\) | ||||
−0.270483 | + | 0.962725i | \(0.587183\pi\) | |||||||
\(432\) | −25619.9 | −2.85332 | ||||||||
\(433\) | −3091.82 | −0.343148 | −0.171574 | − | 0.985171i | \(-0.554885\pi\) | ||||
−0.171574 | + | 0.985171i | \(0.554885\pi\) | |||||||
\(434\) | 27561.6 | 3.04839 | ||||||||
\(435\) | −582.048 | −0.0641541 | ||||||||
\(436\) | −17397.3 | −1.91096 | ||||||||
\(437\) | 4030.67 | 0.441220 | ||||||||
\(438\) | −1981.98 | −0.216216 | ||||||||
\(439\) | −8495.03 | −0.923566 | −0.461783 | − | 0.886993i | \(-0.652790\pi\) | ||||
−0.461783 | + | 0.886993i | \(0.652790\pi\) | |||||||
\(440\) | −849.329 | −0.0920231 | ||||||||
\(441\) | 68.3186 | 0.00737702 | ||||||||
\(442\) | 58240.8 | 6.26749 | ||||||||
\(443\) | −7752.60 | −0.831461 | −0.415730 | − | 0.909488i | \(-0.636474\pi\) | ||||
−0.415730 | + | 0.909488i | \(0.636474\pi\) | |||||||
\(444\) | −7702.31 | −0.823278 | ||||||||
\(445\) | −489.360 | −0.0521301 | ||||||||
\(446\) | 5442.64 | 0.577840 | ||||||||
\(447\) | −17430.9 | −1.84441 | ||||||||
\(448\) | 20526.8 | 2.16473 | ||||||||
\(449\) | −2654.77 | −0.279034 | −0.139517 | − | 0.990220i | \(-0.544555\pi\) | ||||
−0.139517 | + | 0.990220i | \(0.544555\pi\) | |||||||
\(450\) | 1286.02 | 0.134719 | ||||||||
\(451\) | 342.264 | 0.0357352 | ||||||||
\(452\) | 6879.72 | 0.715917 | ||||||||
\(453\) | 12346.4 | 1.28054 | ||||||||
\(454\) | −10118.7 | −1.04602 | ||||||||
\(455\) | 1824.62 | 0.187999 | ||||||||
\(456\) | −14823.7 | −1.52233 | ||||||||
\(457\) | 1223.05 | 0.125190 | 0.0625952 | − | 0.998039i | \(-0.480062\pi\) | ||||
0.0625952 | + | 0.998039i | \(0.480062\pi\) | |||||||
\(458\) | −20180.1 | −2.05885 | ||||||||
\(459\) | 17876.4 | 1.81786 | ||||||||
\(460\) | 2258.79 | 0.228949 | ||||||||
\(461\) | −15665.7 | −1.58270 | −0.791350 | − | 0.611364i | \(-0.790621\pi\) | ||||
−0.791350 | + | 0.611364i | \(0.790621\pi\) | |||||||
\(462\) | −6270.63 | −0.631464 | ||||||||
\(463\) | −7084.10 | −0.711072 | −0.355536 | − | 0.934663i | \(-0.615702\pi\) | ||||
−0.355536 | + | 0.934663i | \(0.615702\pi\) | |||||||
\(464\) | −18044.3 | −1.80535 | ||||||||
\(465\) | −1629.95 | −0.162553 | ||||||||
\(466\) | 31041.7 | 3.08579 | ||||||||
\(467\) | 9122.22 | 0.903910 | 0.451955 | − | 0.892041i | \(-0.350727\pi\) | ||||
0.451955 | + | 0.892041i | \(0.350727\pi\) | |||||||
\(468\) | 3280.76 | 0.324045 | ||||||||
\(469\) | 3038.27 | 0.299135 | ||||||||
\(470\) | 2541.16 | 0.249394 | ||||||||
\(471\) | 17935.6 | 1.75463 | ||||||||
\(472\) | 3788.75 | 0.369473 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 16343.1 | 1.58368 | ||||||||
\(475\) | −5140.12 | −0.496515 | ||||||||
\(476\) | −52695.1 | −5.07411 | ||||||||
\(477\) | −779.746 | −0.0748472 | ||||||||
\(478\) | −17475.5 | −1.67219 | ||||||||
\(479\) | 5530.27 | 0.527525 | 0.263762 | − | 0.964588i | \(-0.415037\pi\) | ||||
0.263762 | + | 0.964588i | \(0.415037\pi\) | |||||||
\(480\) | −2962.45 | −0.281701 | ||||||||
\(481\) | −5769.07 | −0.546875 | ||||||||
\(482\) | 18794.1 | 1.77603 | ||||||||
\(483\) | 10147.8 | 0.955982 | ||||||||
\(484\) | −24615.9 | −2.31178 | ||||||||
\(485\) | −1323.52 | −0.123913 | ||||||||
\(486\) | 2911.52 | 0.271747 | ||||||||
\(487\) | 8915.86 | 0.829602 | 0.414801 | − | 0.909912i | \(-0.363851\pi\) | ||||
0.414801 | + | 0.909912i | \(0.363851\pi\) | |||||||
\(488\) | −21957.9 | −2.03686 | ||||||||
\(489\) | −10148.0 | −0.938462 | ||||||||
\(490\) | −212.934 | −0.0196314 | ||||||||
\(491\) | −10178.5 | −0.935535 | −0.467767 | − | 0.883852i | \(-0.654942\pi\) | ||||
−0.467767 | + | 0.883852i | \(0.654942\pi\) | |||||||
\(492\) | 3347.65 | 0.306755 | ||||||||
\(493\) | 12590.4 | 1.15019 | ||||||||
\(494\) | −18246.6 | −1.66185 | ||||||||
\(495\) | 24.9743 | 0.00226770 | ||||||||
\(496\) | −50530.7 | −4.57439 | ||||||||
\(497\) | −10972.9 | −0.990350 | ||||||||
\(498\) | 22533.7 | 2.02763 | ||||||||
\(499\) | −2520.11 | −0.226083 | −0.113042 | − | 0.993590i | \(-0.536059\pi\) | ||||
−0.113042 | + | 0.993590i | \(0.536059\pi\) | |||||||
\(500\) | −5791.28 | −0.517988 | ||||||||
\(501\) | −3382.25 | −0.301613 | ||||||||
\(502\) | −3509.73 | −0.312045 | ||||||||
\(503\) | 13769.0 | 1.22053 | 0.610267 | − | 0.792196i | \(-0.291062\pi\) | ||||
0.610267 | + | 0.792196i | \(0.291062\pi\) | |||||||
\(504\) | −2513.40 | −0.222134 | ||||||||
\(505\) | 216.529 | 0.0190801 | ||||||||
\(506\) | −5814.32 | −0.510826 | ||||||||
\(507\) | 24666.9 | 2.16074 | ||||||||
\(508\) | 38967.7 | 3.40337 | ||||||||
\(509\) | −2487.17 | −0.216585 | −0.108292 | − | 0.994119i | \(-0.534538\pi\) | ||||
−0.108292 | + | 0.994119i | \(0.534538\pi\) | |||||||
\(510\) | 4336.35 | 0.376504 | ||||||||
\(511\) | 1343.16 | 0.116278 | ||||||||
\(512\) | 8985.19 | 0.775572 | ||||||||
\(513\) | −5600.59 | −0.482012 | ||||||||
\(514\) | −22651.1 | −1.94377 | ||||||||
\(515\) | −630.103 | −0.0539139 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4700.81 | −0.399887 | ||||||||
\(518\) | 7263.28 | 0.616081 | ||||||||
\(519\) | 10816.2 | 0.914797 | ||||||||
\(520\) | −6222.14 | −0.524729 | ||||||||
\(521\) | 10805.0 | 0.908594 | 0.454297 | − | 0.890850i | \(-0.349891\pi\) | ||||
0.454297 | + | 0.890850i | \(0.349891\pi\) | |||||||
\(522\) | 986.898 | 0.0827497 | ||||||||
\(523\) | 15831.2 | 1.32361 | 0.661805 | − | 0.749676i | \(-0.269791\pi\) | ||||
0.661805 | + | 0.749676i | \(0.269791\pi\) | |||||||
\(524\) | 26527.1 | 2.21153 | ||||||||
\(525\) | −12940.9 | −1.07579 | ||||||||
\(526\) | −10974.7 | −0.909736 | ||||||||
\(527\) | 35258.0 | 2.91435 | ||||||||
\(528\) | 11496.4 | 0.947570 | ||||||||
\(529\) | −2757.68 | −0.226652 | ||||||||
\(530\) | 2430.29 | 0.199180 | ||||||||
\(531\) | −111.407 | −0.00910481 | ||||||||
\(532\) | 16509.2 | 1.34542 | ||||||||
\(533\) | 2507.41 | 0.203767 | ||||||||
\(534\) | 12320.6 | 0.998434 | ||||||||
\(535\) | −1892.78 | −0.152957 | ||||||||
\(536\) | −10360.8 | −0.834924 | ||||||||
\(537\) | 7761.20 | 0.623688 | ||||||||
\(538\) | −26352.2 | −2.11175 | ||||||||
\(539\) | 393.899 | 0.0314776 | ||||||||
\(540\) | −3138.57 | −0.250116 | ||||||||
\(541\) | 6016.44 | 0.478128 | 0.239064 | − | 0.971004i | \(-0.423159\pi\) | ||||
0.239064 | + | 0.971004i | \(0.423159\pi\) | |||||||
\(542\) | −38215.5 | −3.02859 | ||||||||
\(543\) | −6692.14 | −0.528890 | ||||||||
\(544\) | 64081.6 | 5.05051 | ||||||||
\(545\) | −970.206 | −0.0762552 | ||||||||
\(546\) | −45938.3 | −3.60069 | ||||||||
\(547\) | 13119.1 | 1.02547 | 0.512734 | − | 0.858547i | \(-0.328633\pi\) | ||||
0.512734 | + | 0.858547i | \(0.328633\pi\) | |||||||
\(548\) | −5300.71 | −0.413203 | ||||||||
\(549\) | 645.665 | 0.0501936 | ||||||||
\(550\) | 7414.72 | 0.574845 | ||||||||
\(551\) | −3944.54 | −0.304978 | ||||||||
\(552\) | −34604.9 | −2.66827 | ||||||||
\(553\) | −11075.5 | −0.851676 | ||||||||
\(554\) | 5853.73 | 0.448919 | ||||||||
\(555\) | −429.540 | −0.0328521 | ||||||||
\(556\) | −1067.59 | −0.0814317 | ||||||||
\(557\) | −7200.35 | −0.547736 | −0.273868 | − | 0.961767i | \(-0.588303\pi\) | ||||
−0.273868 | + | 0.961767i | \(0.588303\pi\) | |||||||
\(558\) | 2763.69 | 0.209671 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4211.63 | 0.317810 | ||||||||
\(561\) | −8021.67 | −0.603699 | ||||||||
\(562\) | 16279.4 | 1.22189 | ||||||||
\(563\) | −22074.0 | −1.65241 | −0.826205 | − | 0.563369i | \(-0.809505\pi\) | ||||
−0.826205 | + | 0.563369i | \(0.809505\pi\) | |||||||
\(564\) | −45978.2 | −3.43268 | ||||||||
\(565\) | 383.665 | 0.0285680 | ||||||||
\(566\) | 21078.7 | 1.56538 | ||||||||
\(567\) | −15123.8 | −1.12017 | ||||||||
\(568\) | 37418.9 | 2.76419 | ||||||||
\(569\) | 13386.6 | 0.986286 | 0.493143 | − | 0.869948i | \(-0.335848\pi\) | ||||
0.493143 | + | 0.869948i | \(0.335848\pi\) | |||||||
\(570\) | −1358.56 | −0.0998314 | ||||||||
\(571\) | −22610.4 | −1.65712 | −0.828561 | − | 0.559899i | \(-0.810840\pi\) | ||||
−0.828561 | + | 0.559899i | \(0.810840\pi\) | |||||||
\(572\) | 18915.6 | 1.38269 | ||||||||
\(573\) | 17053.6 | 1.24332 | ||||||||
\(574\) | −3156.83 | −0.229553 | ||||||||
\(575\) | −11999.2 | −0.870266 | ||||||||
\(576\) | 2058.28 | 0.148892 | ||||||||
\(577\) | 1067.23 | 0.0770006 | 0.0385003 | − | 0.999259i | \(-0.487742\pi\) | ||||
0.0385003 | + | 0.999259i | \(0.487742\pi\) | |||||||
\(578\) | −67603.0 | −4.86490 | ||||||||
\(579\) | −10945.3 | −0.785613 | ||||||||
\(580\) | −2210.52 | −0.158253 | ||||||||
\(581\) | −15270.7 | −1.09043 | ||||||||
\(582\) | 33322.0 | 2.37327 | ||||||||
\(583\) | −4495.72 | −0.319371 | ||||||||
\(584\) | −4580.31 | −0.324545 | ||||||||
\(585\) | 182.960 | 0.0129307 | ||||||||
\(586\) | 1224.74 | 0.0863368 | ||||||||
\(587\) | 6633.97 | 0.466462 | 0.233231 | − | 0.972421i | \(-0.425070\pi\) | ||||
0.233231 | + | 0.972421i | \(0.425070\pi\) | |||||||
\(588\) | 3852.69 | 0.270208 | ||||||||
\(589\) | −11046.2 | −0.772751 | ||||||||
\(590\) | 347.231 | 0.0242293 | ||||||||
\(591\) | 17157.9 | 1.19421 | ||||||||
\(592\) | −13316.3 | −0.924487 | ||||||||
\(593\) | −20524.6 | −1.42133 | −0.710663 | − | 0.703533i | \(-0.751605\pi\) | ||||
−0.710663 | + | 0.703533i | \(0.751605\pi\) | |||||||
\(594\) | 8078.96 | 0.558054 | ||||||||
\(595\) | −2938.68 | −0.202478 | ||||||||
\(596\) | −66199.6 | −4.54973 | ||||||||
\(597\) | −8319.68 | −0.570355 | ||||||||
\(598\) | −42595.4 | −2.91280 | ||||||||
\(599\) | 4328.83 | 0.295277 | 0.147639 | − | 0.989041i | \(-0.452833\pi\) | ||||
0.147639 | + | 0.989041i | \(0.452833\pi\) | |||||||
\(600\) | 44129.9 | 3.00266 | ||||||||
\(601\) | −22901.3 | −1.55435 | −0.777174 | − | 0.629286i | \(-0.783348\pi\) | ||||
−0.777174 | + | 0.629286i | \(0.783348\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 304.657 | 0.0205748 | ||||||||
\(604\) | 46889.5 | 3.15879 | ||||||||
\(605\) | −1372.77 | −0.0922496 | ||||||||
\(606\) | −5451.54 | −0.365435 | ||||||||
\(607\) | −3876.30 | −0.259199 | −0.129600 | − | 0.991566i | \(-0.541369\pi\) | ||||
−0.129600 | + | 0.991566i | \(0.541369\pi\) | |||||||
\(608\) | −20076.5 | −1.33916 | ||||||||
\(609\) | −9930.92 | −0.660790 | ||||||||
\(610\) | −2012.39 | −0.133573 | ||||||||
\(611\) | −34437.9 | −2.28021 | ||||||||
\(612\) | −5283.90 | −0.349002 | ||||||||
\(613\) | 26240.8 | 1.72897 | 0.864484 | − | 0.502660i | \(-0.167645\pi\) | ||||
0.864484 | + | 0.502660i | \(0.167645\pi\) | |||||||
\(614\) | −17407.2 | −1.14413 | ||||||||
\(615\) | 186.690 | 0.0122408 | ||||||||
\(616\) | −14491.3 | −0.947841 | ||||||||
\(617\) | 29037.2 | 1.89464 | 0.947321 | − | 0.320286i | \(-0.103779\pi\) | ||||
0.947321 | + | 0.320286i | \(0.103779\pi\) | |||||||
\(618\) | 15864.0 | 1.03260 | ||||||||
\(619\) | 951.665 | 0.0617942 | 0.0308971 | − | 0.999523i | \(-0.490164\pi\) | ||||
0.0308971 | + | 0.999523i | \(0.490164\pi\) | |||||||
\(620\) | −6190.28 | −0.400980 | ||||||||
\(621\) | −13074.2 | −0.844846 | ||||||||
\(622\) | −34961.0 | −2.25371 | ||||||||
\(623\) | −8349.47 | −0.536942 | ||||||||
\(624\) | 84222.1 | 5.40318 | ||||||||
\(625\) | 15139.7 | 0.968941 | ||||||||
\(626\) | 37487.7 | 2.39347 | ||||||||
\(627\) | 2513.16 | 0.160073 | ||||||||
\(628\) | 68116.4 | 4.32825 | ||||||||
\(629\) | 9291.50 | 0.588993 | ||||||||
\(630\) | −230.347 | −0.0145671 | ||||||||
\(631\) | 7974.08 | 0.503079 | 0.251540 | − | 0.967847i | \(-0.419063\pi\) | ||||
0.251540 | + | 0.967847i | \(0.419063\pi\) | |||||||
\(632\) | 37768.5 | 2.37713 | ||||||||
\(633\) | 26617.4 | 1.67132 | ||||||||
\(634\) | −34582.5 | −2.16632 | ||||||||
\(635\) | 2173.14 | 0.135808 | ||||||||
\(636\) | −43972.2 | −2.74152 | ||||||||
\(637\) | 2885.68 | 0.179490 | ||||||||
\(638\) | 5690.07 | 0.353091 | ||||||||
\(639\) | −1100.29 | −0.0681171 | ||||||||
\(640\) | −2010.48 | −0.124174 | ||||||||
\(641\) | −25568.9 | −1.57552 | −0.787761 | − | 0.615981i | \(-0.788760\pi\) | ||||
−0.787761 | + | 0.615981i | \(0.788760\pi\) | |||||||
\(642\) | 47654.4 | 2.92955 | ||||||||
\(643\) | −14114.5 | −0.865663 | −0.432832 | − | 0.901475i | \(-0.642486\pi\) | ||||
−0.432832 | + | 0.901475i | \(0.642486\pi\) | |||||||
\(644\) | 38539.5 | 2.35818 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 29387.5 | 1.78984 | ||||||||
\(647\) | 4730.36 | 0.287434 | 0.143717 | − | 0.989619i | \(-0.454095\pi\) | ||||
0.143717 | + | 0.989619i | \(0.454095\pi\) | |||||||
\(648\) | 51573.5 | 3.12654 | ||||||||
\(649\) | −642.330 | −0.0388500 | ||||||||
\(650\) | 54319.8 | 3.27784 | ||||||||
\(651\) | −27810.3 | −1.67430 | ||||||||
\(652\) | −38540.3 | −2.31496 | ||||||||
\(653\) | −1693.66 | −0.101498 | −0.0507490 | − | 0.998711i | \(-0.516161\pi\) | ||||
−0.0507490 | + | 0.998711i | \(0.516161\pi\) | |||||||
\(654\) | 24426.8 | 1.46050 | ||||||||
\(655\) | 1479.35 | 0.0882489 | ||||||||
\(656\) | 5787.65 | 0.344466 | ||||||||
\(657\) | 134.683 | 0.00799767 | ||||||||
\(658\) | 43357.4 | 2.56876 | ||||||||
\(659\) | −8066.13 | −0.476801 | −0.238400 | − | 0.971167i | \(-0.576623\pi\) | ||||
−0.238400 | + | 0.971167i | \(0.576623\pi\) | |||||||
\(660\) | 1408.37 | 0.0830619 | ||||||||
\(661\) | −226.554 | −0.0133312 | −0.00666560 | − | 0.999978i | \(-0.502122\pi\) | ||||
−0.00666560 | + | 0.999978i | \(0.502122\pi\) | |||||||
\(662\) | 27182.2 | 1.59587 | ||||||||
\(663\) | −58766.3 | −3.44237 | ||||||||
\(664\) | 52074.8 | 3.04351 | ||||||||
\(665\) | 920.677 | 0.0536877 | ||||||||
\(666\) | 728.311 | 0.0423746 | ||||||||
\(667\) | −9208.25 | −0.534550 | ||||||||
\(668\) | −12845.2 | −0.744007 | ||||||||
\(669\) | −5491.75 | −0.317374 | ||||||||
\(670\) | −949.547 | −0.0547525 | ||||||||
\(671\) | 3722.65 | 0.214175 | ||||||||
\(672\) | −50545.4 | −2.90153 | ||||||||
\(673\) | −7867.98 | −0.450651 | −0.225326 | − | 0.974284i | \(-0.572345\pi\) | ||||
−0.225326 | + | 0.974284i | \(0.572345\pi\) | |||||||
\(674\) | 33492.3 | 1.91406 | ||||||||
\(675\) | 16672.9 | 0.950724 | ||||||||
\(676\) | 93680.8 | 5.33004 | ||||||||
\(677\) | −20935.2 | −1.18848 | −0.594242 | − | 0.804287i | \(-0.702548\pi\) | ||||
−0.594242 | + | 0.804287i | \(0.702548\pi\) | |||||||
\(678\) | −9659.52 | −0.547156 | ||||||||
\(679\) | −22581.9 | −1.27631 | ||||||||
\(680\) | 10021.2 | 0.565140 | ||||||||
\(681\) | 10210.0 | 0.574519 | ||||||||
\(682\) | 15934.4 | 0.894660 | ||||||||
\(683\) | 13418.1 | 0.751726 | 0.375863 | − | 0.926675i | \(-0.377346\pi\) | ||||
0.375863 | + | 0.926675i | \(0.377346\pi\) | |||||||
\(684\) | 1655.42 | 0.0925391 | ||||||||
\(685\) | −295.608 | −0.0164885 | ||||||||
\(686\) | 31928.8 | 1.77703 | ||||||||
\(687\) | 20362.2 | 1.13081 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32935.4 | −1.82110 | ||||||||
\(690\) | −3171.47 | −0.174979 | ||||||||
\(691\) | 28272.5 | 1.55649 | 0.778246 | − | 0.627960i | \(-0.216110\pi\) | ||||
0.778246 | + | 0.627960i | \(0.216110\pi\) | |||||||
\(692\) | 41078.2 | 2.25659 | ||||||||
\(693\) | 426.112 | 0.0233574 | ||||||||
\(694\) | 11624.7 | 0.635831 | ||||||||
\(695\) | −59.5371 | −0.00324946 | ||||||||
\(696\) | 33865.4 | 1.84435 | ||||||||
\(697\) | −4038.36 | −0.219460 | ||||||||
\(698\) | −51426.6 | −2.78872 | ||||||||
\(699\) | −31321.8 | −1.69485 | ||||||||
\(700\) | −49147.5 | −2.65372 | ||||||||
\(701\) | −8270.14 | −0.445590 | −0.222795 | − | 0.974865i | \(-0.571518\pi\) | ||||
−0.222795 | + | 0.974865i | \(0.571518\pi\) | |||||||
\(702\) | 59186.0 | 3.18210 | ||||||||
\(703\) | −2910.99 | −0.156174 | ||||||||
\(704\) | 11867.3 | 0.635319 | ||||||||
\(705\) | −2564.09 | −0.136978 | ||||||||
\(706\) | 27341.3 | 1.45751 | ||||||||
\(707\) | 3694.43 | 0.196525 | ||||||||
\(708\) | −6282.57 | −0.333493 | ||||||||
\(709\) | −18435.9 | −0.976549 | −0.488274 | − | 0.872690i | \(-0.662373\pi\) | ||||
−0.488274 | + | 0.872690i | \(0.662373\pi\) | |||||||
\(710\) | 3429.36 | 0.181270 | ||||||||
\(711\) | −1110.57 | −0.0585790 | ||||||||
\(712\) | 28472.6 | 1.49867 | ||||||||
\(713\) | −25786.6 | −1.35444 | ||||||||
\(714\) | 73986.9 | 3.87800 | ||||||||
\(715\) | 1054.88 | 0.0551751 | ||||||||
\(716\) | 29475.7 | 1.53849 | ||||||||
\(717\) | 17633.2 | 0.918441 | ||||||||
\(718\) | 27901.9 | 1.45027 | ||||||||
\(719\) | 807.291 | 0.0418733 | 0.0209366 | − | 0.999781i | \(-0.493335\pi\) | ||||
0.0209366 | + | 0.999781i | \(0.493335\pi\) | |||||||
\(720\) | 422.313 | 0.0218593 | ||||||||
\(721\) | −10750.8 | −0.555314 | ||||||||
\(722\) | 27367.8 | 1.41070 | ||||||||
\(723\) | −18963.7 | −0.975474 | ||||||||
\(724\) | −25415.6 | −1.30465 | ||||||||
\(725\) | 11742.8 | 0.601541 | ||||||||
\(726\) | 34562.1 | 1.76683 | ||||||||
\(727\) | 6429.96 | 0.328025 | 0.164012 | − | 0.986458i | \(-0.447556\pi\) | ||||
0.164012 | + | 0.986458i | \(0.447556\pi\) | |||||||
\(728\) | −106162. | −5.40472 | ||||||||
\(729\) | 18063.9 | 0.917739 | ||||||||
\(730\) | −419.775 | −0.0212830 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 36410.9 | 1.83851 | ||||||||
\(733\) | −21819.9 | −1.09951 | −0.549753 | − | 0.835327i | \(-0.685278\pi\) | ||||
−0.549753 | + | 0.835327i | \(0.685278\pi\) | |||||||
\(734\) | −29904.8 | −1.50382 | ||||||||
\(735\) | 214.855 | 0.0107824 | ||||||||
\(736\) | −46867.2 | −2.34721 | ||||||||
\(737\) | 1756.53 | 0.0877921 | ||||||||
\(738\) | −316.545 | −0.0157889 | ||||||||
\(739\) | 19531.5 | 0.972228 | 0.486114 | − | 0.873896i | \(-0.338414\pi\) | ||||
0.486114 | + | 0.873896i | \(0.338414\pi\) | |||||||
\(740\) | −1631.32 | −0.0810384 | ||||||||
\(741\) | 18411.3 | 0.912759 | ||||||||
\(742\) | 41465.7 | 2.05156 | ||||||||
\(743\) | 24083.9 | 1.18917 | 0.594585 | − | 0.804033i | \(-0.297316\pi\) | ||||
0.594585 | + | 0.804033i | \(0.297316\pi\) | |||||||
\(744\) | 94836.0 | 4.67319 | ||||||||
\(745\) | −3691.79 | −0.181553 | ||||||||
\(746\) | 27921.2 | 1.37033 | ||||||||
\(747\) | −1531.24 | −0.0750004 | ||||||||
\(748\) | −30464.9 | −1.48918 | ||||||||
\(749\) | −32294.7 | −1.57546 | ||||||||
\(750\) | 8131.29 | 0.395883 | ||||||||
\(751\) | −12480.5 | −0.606417 | −0.303209 | − | 0.952924i | \(-0.598058\pi\) | ||||
−0.303209 | + | 0.952924i | \(0.598058\pi\) | |||||||
\(752\) | −79490.3 | −3.85467 | ||||||||
\(753\) | 3541.40 | 0.171389 | ||||||||
\(754\) | 41685.2 | 2.01337 | ||||||||
\(755\) | 2614.92 | 0.126048 | ||||||||
\(756\) | −53550.4 | −2.57620 | ||||||||
\(757\) | −37150.9 | −1.78372 | −0.891858 | − | 0.452315i | \(-0.850598\pi\) | ||||
−0.891858 | + | 0.452315i | \(0.850598\pi\) | |||||||
\(758\) | 17720.2 | 0.849113 | ||||||||
\(759\) | 5866.79 | 0.280568 | ||||||||
\(760\) | −3139.60 | −0.149849 | ||||||||
\(761\) | −32130.3 | −1.53052 | −0.765258 | − | 0.643724i | \(-0.777388\pi\) | ||||
−0.765258 | + | 0.643724i | \(0.777388\pi\) | |||||||
\(762\) | −54712.9 | −2.60110 | ||||||||
\(763\) | −16553.7 | −0.785431 | ||||||||
\(764\) | 64766.5 | 3.06698 | ||||||||
\(765\) | −294.670 | −0.0139266 | ||||||||
\(766\) | −42309.5 | −1.99570 | ||||||||
\(767\) | −4705.68 | −0.221528 | ||||||||
\(768\) | 5175.09 | 0.243151 | ||||||||
\(769\) | −19725.3 | −0.924984 | −0.462492 | − | 0.886624i | \(-0.653045\pi\) | ||||
−0.462492 | + | 0.886624i | \(0.653045\pi\) | |||||||
\(770\) | −1328.09 | −0.0621574 | ||||||||
\(771\) | 22855.5 | 1.06760 | ||||||||
\(772\) | −41568.3 | −1.93792 | ||||||||
\(773\) | −4215.71 | −0.196156 | −0.0980780 | − | 0.995179i | \(-0.531269\pi\) | ||||
−0.0980780 | + | 0.995179i | \(0.531269\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32884.3 | 1.52418 | ||||||||
\(776\) | 77006.4 | 3.56233 | ||||||||
\(777\) | −7328.82 | −0.338378 | ||||||||
\(778\) | −11044.4 | −0.508945 | ||||||||
\(779\) | 1265.20 | 0.0581907 | ||||||||
\(780\) | 10317.7 | 0.473630 | ||||||||
\(781\) | −6343.85 | −0.290654 | ||||||||
\(782\) | 68602.9 | 3.13713 | ||||||||
\(783\) | 12794.8 | 0.583970 | ||||||||
\(784\) | 6660.79 | 0.303425 | ||||||||
\(785\) | 3798.69 | 0.172715 | ||||||||
\(786\) | −37245.5 | −1.69021 | ||||||||
\(787\) | −35244.1 | −1.59634 | −0.798169 | − | 0.602434i | \(-0.794198\pi\) | ||||
−0.798169 | + | 0.602434i | \(0.794198\pi\) | |||||||
\(788\) | 65162.6 | 2.94584 | ||||||||
\(789\) | 11073.8 | 0.499666 | ||||||||
\(790\) | 3461.40 | 0.155887 | ||||||||
\(791\) | 6546.11 | 0.294251 | ||||||||
\(792\) | −1453.08 | −0.0651933 | ||||||||
\(793\) | 27272.0 | 1.22126 | ||||||||
\(794\) | −40465.3 | −1.80864 | ||||||||
\(795\) | −2452.22 | −0.109398 | ||||||||
\(796\) | −31596.7 | −1.40693 | ||||||||
\(797\) | 17073.8 | 0.758828 | 0.379414 | − | 0.925227i | \(-0.376126\pi\) | ||||
0.379414 | + | 0.925227i | \(0.376126\pi\) | |||||||
\(798\) | −23179.8 | −1.02827 | ||||||||
\(799\) | 55464.7 | 2.45582 | ||||||||
\(800\) | 59767.4 | 2.64137 | ||||||||
\(801\) | −837.227 | −0.0369313 | ||||||||
\(802\) | 11099.2 | 0.488687 | ||||||||
\(803\) | 776.528 | 0.0341259 | ||||||||
\(804\) | 17180.5 | 0.753618 | ||||||||
\(805\) | 2149.26 | 0.0941010 | ||||||||
\(806\) | 116734. | 5.10147 | ||||||||
\(807\) | 26589.9 | 1.15986 | ||||||||
\(808\) | −12598.4 | −0.548527 | ||||||||
\(809\) | 12016.0 | 0.522202 | 0.261101 | − | 0.965312i | \(-0.415914\pi\) | ||||
0.261101 | + | 0.965312i | \(0.415914\pi\) | |||||||
\(810\) | 4726.60 | 0.205032 | ||||||||
\(811\) | 41834.3 | 1.81135 | 0.905673 | − | 0.423976i | \(-0.139366\pi\) | ||||
0.905673 | + | 0.423976i | \(0.139366\pi\) | |||||||
\(812\) | −37715.9 | −1.63001 | ||||||||
\(813\) | 38560.4 | 1.66343 | ||||||||
\(814\) | 4199.16 | 0.180811 | ||||||||
\(815\) | −2149.30 | −0.0923764 | ||||||||
\(816\) | −135646. | −5.81930 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 17157.0 | 0.733350 | ||||||||
\(819\) | 3121.67 | 0.133187 | ||||||||
\(820\) | 709.018 | 0.0301951 | ||||||||
\(821\) | 26438.7 | 1.12389 | 0.561947 | − | 0.827173i | \(-0.310052\pi\) | ||||
0.561947 | + | 0.827173i | \(0.310052\pi\) | |||||||
\(822\) | 7442.50 | 0.315799 | ||||||||
\(823\) | 16854.2 | 0.713853 | 0.356926 | − | 0.934132i | \(-0.383825\pi\) | ||||
0.356926 | + | 0.934132i | \(0.383825\pi\) | |||||||
\(824\) | 36661.4 | 1.54995 | ||||||||
\(825\) | −7481.62 | −0.315729 | ||||||||
\(826\) | 5924.46 | 0.249562 | ||||||||
\(827\) | −20262.0 | −0.851970 | −0.425985 | − | 0.904730i | \(-0.640072\pi\) | ||||
−0.425985 | + | 0.904730i | \(0.640072\pi\) | |||||||
\(828\) | 3864.47 | 0.162198 | ||||||||
\(829\) | −15273.0 | −0.639869 | −0.319935 | − | 0.947440i | \(-0.603661\pi\) | ||||
−0.319935 | + | 0.947440i | \(0.603661\pi\) | |||||||
\(830\) | 4772.54 | 0.199587 | ||||||||
\(831\) | −5906.55 | −0.246566 | ||||||||
\(832\) | 86939.0 | 3.62268 | ||||||||
\(833\) | −4647.60 | −0.193313 | ||||||||
\(834\) | 1498.96 | 0.0622360 | ||||||||
\(835\) | −716.348 | −0.0296889 | ||||||||
\(836\) | 9544.54 | 0.394862 | ||||||||
\(837\) | 35830.3 | 1.47966 | ||||||||
\(838\) | 41031.1 | 1.69140 | ||||||||
\(839\) | 38209.7 | 1.57228 | 0.786142 | − | 0.618046i | \(-0.212076\pi\) | ||||
0.786142 | + | 0.618046i | \(0.212076\pi\) | |||||||
\(840\) | −7904.38 | −0.324675 | ||||||||
\(841\) | −15377.5 | −0.630511 | ||||||||
\(842\) | −9801.15 | −0.401152 | ||||||||
\(843\) | −16426.3 | −0.671117 | ||||||||
\(844\) | 101088. | 4.12276 | ||||||||
\(845\) | 5224.36 | 0.212690 | ||||||||
\(846\) | 4347.58 | 0.176682 | ||||||||
\(847\) | −23422.2 | −0.950174 | ||||||||
\(848\) | −76022.2 | −3.07855 | ||||||||
\(849\) | −21268.9 | −0.859772 | ||||||||
\(850\) | −87485.9 | −3.53029 | ||||||||
\(851\) | −6795.50 | −0.273733 | ||||||||
\(852\) | −62048.6 | −2.49501 | ||||||||
\(853\) | −37931.9 | −1.52258 | −0.761292 | − | 0.648409i | \(-0.775435\pi\) | ||||
−0.761292 | + | 0.648409i | \(0.775435\pi\) | |||||||
\(854\) | −34335.5 | −1.37580 | ||||||||
\(855\) | 92.3191 | 0.00369269 | ||||||||
\(856\) | 110128. | 4.39732 | ||||||||
\(857\) | 13948.7 | 0.555984 | 0.277992 | − | 0.960583i | \(-0.410331\pi\) | ||||
0.277992 | + | 0.960583i | \(0.410331\pi\) | |||||||
\(858\) | −26558.6 | −1.05675 | ||||||||
\(859\) | 15379.3 | 0.610869 | 0.305434 | − | 0.952213i | \(-0.401198\pi\) | ||||
0.305434 | + | 0.952213i | \(0.401198\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3185.32 | 0.126081 | ||||||||
\(862\) | 25811.1 | 1.01987 | ||||||||
\(863\) | −4157.99 | −0.164009 | −0.0820043 | − | 0.996632i | \(-0.526132\pi\) | ||||
−0.0820043 | + | 0.996632i | \(0.526132\pi\) | |||||||
\(864\) | 65121.7 | 2.56422 | ||||||||
\(865\) | 2290.83 | 0.0900470 | ||||||||
\(866\) | 16486.7 | 0.646930 | ||||||||
\(867\) | 68213.0 | 2.67201 | ||||||||
\(868\) | −105619. | −4.13011 | ||||||||
\(869\) | −6403.12 | −0.249955 | ||||||||
\(870\) | 3103.69 | 0.120948 | ||||||||
\(871\) | 12868.3 | 0.500603 | ||||||||
\(872\) | 56449.8 | 2.19224 | ||||||||
\(873\) | −2264.35 | −0.0877854 | ||||||||
\(874\) | −21493.0 | −0.831822 | ||||||||
\(875\) | −5510.45 | −0.212900 | ||||||||
\(876\) | 7595.15 | 0.292941 | ||||||||
\(877\) | −38274.3 | −1.47370 | −0.736848 | − | 0.676059i | \(-0.763687\pi\) | ||||
−0.736848 | + | 0.676059i | \(0.763687\pi\) | |||||||
\(878\) | 45298.6 | 1.74118 | ||||||||
\(879\) | −1235.79 | −0.0474199 | ||||||||
\(880\) | 2434.89 | 0.0932730 | ||||||||
\(881\) | −16695.5 | −0.638462 | −0.319231 | − | 0.947677i | \(-0.603425\pi\) | ||||
−0.319231 | + | 0.947677i | \(0.603425\pi\) | |||||||
\(882\) | −364.300 | −0.0139077 | ||||||||
\(883\) | −45928.1 | −1.75040 | −0.875200 | − | 0.483762i | \(-0.839270\pi\) | ||||
−0.875200 | + | 0.483762i | \(0.839270\pi\) | |||||||
\(884\) | −223184. | −8.49152 | ||||||||
\(885\) | −350.364 | −0.0133077 | ||||||||
\(886\) | 41339.7 | 1.56753 | ||||||||
\(887\) | −14180.1 | −0.536779 | −0.268389 | − | 0.963311i | \(-0.586491\pi\) | ||||
−0.268389 | + | 0.963311i | \(0.586491\pi\) | |||||||
\(888\) | 24992.0 | 0.944456 | ||||||||
\(889\) | 37078.2 | 1.39883 | ||||||||
\(890\) | 2609.45 | 0.0982797 | ||||||||
\(891\) | −8743.58 | −0.328755 | ||||||||
\(892\) | −20856.7 | −0.782887 | ||||||||
\(893\) | −17376.9 | −0.651170 | ||||||||
\(894\) | 92948.0 | 3.47723 | ||||||||
\(895\) | 1643.79 | 0.0613920 | ||||||||
\(896\) | −34302.8 | −1.27899 | ||||||||
\(897\) | 42979.8 | 1.59984 | ||||||||
\(898\) | 14156.2 | 0.526057 | ||||||||
\(899\) | 25235.5 | 0.936209 | ||||||||
\(900\) | −4928.17 | −0.182525 | ||||||||
\(901\) | 53044.8 | 1.96135 | ||||||||
\(902\) | −1825.08 | −0.0673708 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22322.9 | −0.821293 | ||||||||
\(905\) | −1417.37 | −0.0520607 | ||||||||
\(906\) | −65835.5 | −2.41417 | ||||||||
\(907\) | 23302.1 | 0.853071 | 0.426535 | − | 0.904471i | \(-0.359734\pi\) | ||||
0.426535 | + | 0.904471i | \(0.359734\pi\) | |||||||
\(908\) | 38775.8 | 1.41720 | ||||||||
\(909\) | 370.452 | 0.0135172 | ||||||||
\(910\) | −9729.55 | −0.354430 | ||||||||
\(911\) | −26596.3 | −0.967260 | −0.483630 | − | 0.875273i | \(-0.660682\pi\) | ||||
−0.483630 | + | 0.875273i | \(0.660682\pi\) | |||||||
\(912\) | 42497.3 | 1.54301 | ||||||||
\(913\) | −8828.56 | −0.320025 | ||||||||
\(914\) | −6521.77 | −0.236019 | ||||||||
\(915\) | 2030.55 | 0.0733639 | ||||||||
\(916\) | 77332.2 | 2.78944 | ||||||||
\(917\) | 25240.7 | 0.908967 | ||||||||
\(918\) | −95323.3 | −3.42717 | ||||||||
\(919\) | 40133.3 | 1.44056 | 0.720281 | − | 0.693683i | \(-0.244013\pi\) | ||||
0.720281 | + | 0.693683i | \(0.244013\pi\) | |||||||
\(920\) | −7329.18 | −0.262648 | ||||||||
\(921\) | 17564.3 | 0.628407 | ||||||||
\(922\) | 83535.3 | 2.98383 | ||||||||
\(923\) | −46474.7 | −1.65735 | ||||||||
\(924\) | 24029.7 | 0.855540 | ||||||||
\(925\) | 8665.97 | 0.308038 | ||||||||
\(926\) | 37775.1 | 1.34057 | ||||||||
\(927\) | −1078.02 | −0.0381950 | ||||||||
\(928\) | 45865.7 | 1.62243 | ||||||||
\(929\) | −8697.44 | −0.307162 | −0.153581 | − | 0.988136i | \(-0.549081\pi\) | ||||
−0.153581 | + | 0.988136i | \(0.549081\pi\) | |||||||
\(930\) | 8691.51 | 0.306458 | ||||||||
\(931\) | 1456.07 | 0.0512577 | ||||||||
\(932\) | −118955. | −4.18079 | ||||||||
\(933\) | 35276.5 | 1.23783 | ||||||||
\(934\) | −48643.0 | −1.70412 | ||||||||
\(935\) | −1698.96 | −0.0594244 | ||||||||
\(936\) | −10645.2 | −0.371741 | ||||||||
\(937\) | 33520.7 | 1.16870 | 0.584351 | − | 0.811501i | \(-0.301349\pi\) | ||||
0.584351 | + | 0.811501i | \(0.301349\pi\) | |||||||
\(938\) | −16201.2 | −0.563953 | ||||||||
\(939\) | −37826.0 | −1.31459 | ||||||||
\(940\) | −9737.99 | −0.337892 | ||||||||
\(941\) | −24899.8 | −0.862604 | −0.431302 | − | 0.902208i | \(-0.641946\pi\) | ||||
−0.431302 | + | 0.902208i | \(0.641946\pi\) | |||||||
\(942\) | −95639.3 | −3.30796 | ||||||||
\(943\) | 2953.52 | 0.101994 | ||||||||
\(944\) | −10861.7 | −0.374491 | ||||||||
\(945\) | −2986.38 | −0.102801 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22969.3 | −0.788175 | −0.394087 | − | 0.919073i | \(-0.628939\pi\) | ||||
−0.394087 | + | 0.919073i | \(0.628939\pi\) | |||||||
\(948\) | −62628.3 | −2.14565 | ||||||||
\(949\) | 5688.80 | 0.194591 | ||||||||
\(950\) | 27409.0 | 0.936069 | ||||||||
\(951\) | 34894.5 | 1.18983 | ||||||||
\(952\) | 170982. | 5.82096 | ||||||||
\(953\) | −23618.2 | −0.802799 | −0.401399 | − | 0.915903i | \(-0.631476\pi\) | ||||
−0.401399 | + | 0.915903i | \(0.631476\pi\) | |||||||
\(954\) | 4157.89 | 0.141108 | ||||||||
\(955\) | 3611.87 | 0.122385 | ||||||||
\(956\) | 66967.7 | 2.26558 | ||||||||
\(957\) | −5741.42 | −0.193933 | ||||||||
\(958\) | −29489.4 | −0.994531 | ||||||||
\(959\) | −5043.67 | −0.169832 | ||||||||
\(960\) | 6473.09 | 0.217623 | ||||||||
\(961\) | 40878.0 | 1.37216 | ||||||||
\(962\) | 30762.8 | 1.03101 | ||||||||
\(963\) | −3238.29 | −0.108362 | ||||||||
\(964\) | −72020.9 | −2.40626 | ||||||||
\(965\) | −2318.17 | −0.0773310 | ||||||||
\(966\) | −54111.7 | −1.80229 | ||||||||
\(967\) | 41439.3 | 1.37807 | 0.689036 | − | 0.724727i | \(-0.258034\pi\) | ||||
0.689036 | + | 0.724727i | \(0.258034\pi\) | |||||||
\(968\) | 79872.2 | 2.65205 | ||||||||
\(969\) | −29652.6 | −0.983054 | ||||||||
\(970\) | 7057.47 | 0.233610 | ||||||||
\(971\) | −47537.5 | −1.57111 | −0.785557 | − | 0.618790i | \(-0.787623\pi\) | ||||
−0.785557 | + | 0.618790i | \(0.787623\pi\) | |||||||
\(972\) | −11157.2 | −0.368177 | ||||||||
\(973\) | −1015.82 | −0.0334695 | ||||||||
\(974\) | −47542.7 | −1.56403 | ||||||||
\(975\) | −54810.0 | −1.80033 | ||||||||
\(976\) | 62949.8 | 2.06452 | ||||||||
\(977\) | −46979.4 | −1.53839 | −0.769194 | − | 0.639016i | \(-0.779342\pi\) | ||||
−0.769194 | + | 0.639016i | \(0.779342\pi\) | |||||||
\(978\) | 54112.8 | 1.76926 | ||||||||
\(979\) | −4827.13 | −0.157585 | ||||||||
\(980\) | 815.983 | 0.0265976 | ||||||||
\(981\) | −1659.89 | −0.0540226 | ||||||||
\(982\) | 54275.3 | 1.76374 | ||||||||
\(983\) | −6249.99 | −0.202791 | −0.101396 | − | 0.994846i | \(-0.532331\pi\) | ||||
−0.101396 | + | 0.994846i | \(0.532331\pi\) | |||||||
\(984\) | −10862.3 | −0.351907 | ||||||||
\(985\) | 3633.97 | 0.117551 | ||||||||
\(986\) | −67136.9 | −2.16843 | ||||||||
\(987\) | −43748.6 | −1.41088 | ||||||||
\(988\) | 69922.8 | 2.25156 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −133.172 | −0.00427524 | ||||||||
\(991\) | 9689.00 | 0.310576 | 0.155288 | − | 0.987869i | \(-0.450369\pi\) | ||||
0.155288 | + | 0.987869i | \(0.450369\pi\) | |||||||
\(992\) | 128441. | 4.11090 | ||||||||
\(993\) | −27427.5 | −0.876519 | ||||||||
\(994\) | 58511.8 | 1.86708 | ||||||||
\(995\) | −1762.07 | −0.0561422 | ||||||||
\(996\) | −86351.3 | −2.74713 | ||||||||
\(997\) | −26955.2 | −0.856247 | −0.428124 | − | 0.903720i | \(-0.640825\pi\) | ||||
−0.428124 | + | 0.903720i | \(0.640825\pi\) | |||||||
\(998\) | 13438.1 | 0.426229 | ||||||||
\(999\) | 9442.30 | 0.299040 |
(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 | 1849.4.a.j.1.1 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.50 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.50 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.1 | yes | 50 | 1.1 | even | 1 | trivial |