Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,4,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2013.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(118.770844842\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.691390 | −0.244443 | −0.122222 | − | 0.992503i | \(-0.539002\pi\) | ||||
−0.122222 | + | 0.992503i | \(0.539002\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −7.52198 | −0.940247 | ||||||||
\(5\) | −5.77110 | −0.516183 | −0.258091 | − | 0.966121i | \(-0.583094\pi\) | ||||
−0.258091 | + | 0.966121i | \(0.583094\pi\) | |||||||
\(6\) | 2.07417 | 0.141129 | ||||||||
\(7\) | 9.57605 | 0.517058 | 0.258529 | − | 0.966003i | \(-0.416762\pi\) | ||||
0.258529 | + | 0.966003i | \(0.416762\pi\) | |||||||
\(8\) | 10.7317 | 0.474281 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 3.99008 | 0.126177 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 22.5659 | 0.542852 | ||||||||
\(13\) | 4.33531 | 0.0924922 | 0.0462461 | − | 0.998930i | \(-0.485274\pi\) | ||||
0.0462461 | + | 0.998930i | \(0.485274\pi\) | |||||||
\(14\) | −6.62079 | −0.126391 | ||||||||
\(15\) | 17.3133 | 0.298018 | ||||||||
\(16\) | 52.7560 | 0.824313 | ||||||||
\(17\) | −93.4391 | −1.33308 | −0.666539 | − | 0.745470i | \(-0.732225\pi\) | ||||
−0.666539 | + | 0.745470i | \(0.732225\pi\) | |||||||
\(18\) | −6.22251 | −0.0814811 | ||||||||
\(19\) | −19.5165 | −0.235652 | −0.117826 | − | 0.993034i | \(-0.537593\pi\) | ||||
−0.117826 | + | 0.993034i | \(0.537593\pi\) | |||||||
\(20\) | 43.4101 | 0.485339 | ||||||||
\(21\) | −28.7282 | −0.298524 | ||||||||
\(22\) | 7.60529 | 0.0737024 | ||||||||
\(23\) | 105.934 | 0.960377 | 0.480188 | − | 0.877165i | \(-0.340568\pi\) | ||||
0.480188 | + | 0.877165i | \(0.340568\pi\) | |||||||
\(24\) | −32.1952 | −0.273826 | ||||||||
\(25\) | −91.6944 | −0.733555 | ||||||||
\(26\) | −2.99739 | −0.0226091 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −72.0309 | −0.486163 | ||||||||
\(29\) | −157.498 | −1.00850 | −0.504252 | − | 0.863557i | \(-0.668232\pi\) | ||||
−0.504252 | + | 0.863557i | \(0.668232\pi\) | |||||||
\(30\) | −11.9702 | −0.0728485 | ||||||||
\(31\) | 208.500 | 1.20799 | 0.603997 | − | 0.796987i | \(-0.293574\pi\) | ||||
0.603997 | + | 0.796987i | \(0.293574\pi\) | |||||||
\(32\) | −122.329 | −0.675778 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | 64.6029 | 0.325862 | ||||||||
\(35\) | −55.2643 | −0.266896 | ||||||||
\(36\) | −67.6978 | −0.313416 | ||||||||
\(37\) | −270.554 | −1.20213 | −0.601064 | − | 0.799201i | \(-0.705256\pi\) | ||||
−0.601064 | + | 0.799201i | \(0.705256\pi\) | |||||||
\(38\) | 13.4935 | 0.0576037 | ||||||||
\(39\) | −13.0059 | −0.0534004 | ||||||||
\(40\) | −61.9339 | −0.244815 | ||||||||
\(41\) | 401.469 | 1.52924 | 0.764620 | − | 0.644481i | \(-0.222927\pi\) | ||||
0.764620 | + | 0.644481i | \(0.222927\pi\) | |||||||
\(42\) | 19.8624 | 0.0729721 | ||||||||
\(43\) | 125.478 | 0.445004 | 0.222502 | − | 0.974932i | \(-0.428578\pi\) | ||||
0.222502 | + | 0.974932i | \(0.428578\pi\) | |||||||
\(44\) | 82.7418 | 0.283495 | ||||||||
\(45\) | −51.9399 | −0.172061 | ||||||||
\(46\) | −73.2414 | −0.234758 | ||||||||
\(47\) | 22.5963 | 0.0701277 | 0.0350639 | − | 0.999385i | \(-0.488837\pi\) | ||||
0.0350639 | + | 0.999385i | \(0.488837\pi\) | |||||||
\(48\) | −158.268 | −0.475917 | ||||||||
\(49\) | −251.299 | −0.732651 | ||||||||
\(50\) | 63.3966 | 0.179313 | ||||||||
\(51\) | 280.317 | 0.769653 | ||||||||
\(52\) | −32.6101 | −0.0869655 | ||||||||
\(53\) | 722.523 | 1.87257 | 0.936284 | − | 0.351244i | \(-0.114241\pi\) | ||||
0.936284 | + | 0.351244i | \(0.114241\pi\) | |||||||
\(54\) | 18.6675 | 0.0470431 | ||||||||
\(55\) | 63.4821 | 0.155635 | ||||||||
\(56\) | 102.768 | 0.245231 | ||||||||
\(57\) | 58.5495 | 0.136054 | ||||||||
\(58\) | 108.892 | 0.246522 | ||||||||
\(59\) | −208.134 | −0.459266 | −0.229633 | − | 0.973277i | \(-0.573753\pi\) | ||||
−0.229633 | + | 0.973277i | \(0.573753\pi\) | |||||||
\(60\) | −130.230 | −0.280211 | ||||||||
\(61\) | 61.0000 | 0.128037 | ||||||||
\(62\) | −144.155 | −0.295286 | ||||||||
\(63\) | 86.1845 | 0.172353 | ||||||||
\(64\) | −337.471 | −0.659123 | ||||||||
\(65\) | −25.0195 | −0.0477429 | ||||||||
\(66\) | −22.8159 | −0.0425521 | ||||||||
\(67\) | 441.709 | 0.805423 | 0.402711 | − | 0.915327i | \(-0.368068\pi\) | ||||
0.402711 | + | 0.915327i | \(0.368068\pi\) | |||||||
\(68\) | 702.847 | 1.25342 | ||||||||
\(69\) | −317.801 | −0.554474 | ||||||||
\(70\) | 38.2092 | 0.0652410 | ||||||||
\(71\) | 1021.30 | 1.70714 | 0.853568 | − | 0.520982i | \(-0.174434\pi\) | ||||
0.853568 | + | 0.520982i | \(0.174434\pi\) | |||||||
\(72\) | 96.5857 | 0.158094 | ||||||||
\(73\) | −950.129 | −1.52335 | −0.761673 | − | 0.647962i | \(-0.775622\pi\) | ||||
−0.761673 | + | 0.647962i | \(0.775622\pi\) | |||||||
\(74\) | 187.058 | 0.293852 | ||||||||
\(75\) | 275.083 | 0.423518 | ||||||||
\(76\) | 146.803 | 0.221572 | ||||||||
\(77\) | −105.337 | −0.155899 | ||||||||
\(78\) | 8.99217 | 0.0130534 | ||||||||
\(79\) | 1068.50 | 1.52172 | 0.760858 | − | 0.648919i | \(-0.224779\pi\) | ||||
0.760858 | + | 0.648919i | \(0.224779\pi\) | |||||||
\(80\) | −304.460 | −0.425496 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −277.571 | −0.373813 | ||||||||
\(83\) | 448.493 | 0.593115 | 0.296558 | − | 0.955015i | \(-0.404161\pi\) | ||||
0.296558 | + | 0.955015i | \(0.404161\pi\) | |||||||
\(84\) | 216.093 | 0.280686 | ||||||||
\(85\) | 539.246 | 0.688111 | ||||||||
\(86\) | −86.7541 | −0.108778 | ||||||||
\(87\) | 472.493 | 0.582260 | ||||||||
\(88\) | −118.049 | −0.143001 | ||||||||
\(89\) | −1018.27 | −1.21276 | −0.606382 | − | 0.795173i | \(-0.707380\pi\) | ||||
−0.606382 | + | 0.795173i | \(0.707380\pi\) | |||||||
\(90\) | 35.9107 | 0.0420591 | ||||||||
\(91\) | 41.5151 | 0.0478238 | ||||||||
\(92\) | −796.830 | −0.902992 | ||||||||
\(93\) | −625.501 | −0.697435 | ||||||||
\(94\) | −15.6228 | −0.0171422 | ||||||||
\(95\) | 112.632 | 0.121640 | ||||||||
\(96\) | 366.987 | 0.390161 | ||||||||
\(97\) | 1383.13 | 1.44779 | 0.723895 | − | 0.689910i | \(-0.242350\pi\) | ||||
0.723895 | + | 0.689910i | \(0.242350\pi\) | |||||||
\(98\) | 173.746 | 0.179092 | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 689.724 | 0.689724 | ||||||||
\(101\) | −1365.97 | −1.34573 | −0.672866 | − | 0.739764i | \(-0.734937\pi\) | ||||
−0.672866 | + | 0.739764i | \(0.734937\pi\) | |||||||
\(102\) | −193.809 | −0.188136 | ||||||||
\(103\) | −34.9333 | −0.0334182 | −0.0167091 | − | 0.999860i | \(-0.505319\pi\) | ||||
−0.0167091 | + | 0.999860i | \(0.505319\pi\) | |||||||
\(104\) | 46.5254 | 0.0438672 | ||||||||
\(105\) | 165.793 | 0.154093 | ||||||||
\(106\) | −499.545 | −0.457737 | ||||||||
\(107\) | 1822.90 | 1.64698 | 0.823490 | − | 0.567331i | \(-0.192024\pi\) | ||||
0.823490 | + | 0.567331i | \(0.192024\pi\) | |||||||
\(108\) | 203.093 | 0.180951 | ||||||||
\(109\) | 589.626 | 0.518128 | 0.259064 | − | 0.965860i | \(-0.416586\pi\) | ||||
0.259064 | + | 0.965860i | \(0.416586\pi\) | |||||||
\(110\) | −43.8909 | −0.0380439 | ||||||||
\(111\) | 811.661 | 0.694049 | ||||||||
\(112\) | 505.194 | 0.426218 | ||||||||
\(113\) | −782.039 | −0.651045 | −0.325522 | − | 0.945534i | \(-0.605540\pi\) | ||||
−0.325522 | + | 0.945534i | \(0.605540\pi\) | |||||||
\(114\) | −40.4806 | −0.0332575 | ||||||||
\(115\) | −611.353 | −0.495730 | ||||||||
\(116\) | 1184.69 | 0.948243 | ||||||||
\(117\) | 39.0178 | 0.0308307 | ||||||||
\(118\) | 143.902 | 0.112265 | ||||||||
\(119\) | −894.778 | −0.689278 | ||||||||
\(120\) | 185.802 | 0.141344 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −42.1748 | −0.0312978 | ||||||||
\(123\) | −1204.41 | −0.882907 | ||||||||
\(124\) | −1568.34 | −1.13581 | ||||||||
\(125\) | 1250.56 | 0.894831 | ||||||||
\(126\) | −59.5871 | −0.0421305 | ||||||||
\(127\) | 56.0503 | 0.0391627 | 0.0195813 | − | 0.999808i | \(-0.493767\pi\) | ||||
0.0195813 | + | 0.999808i | \(0.493767\pi\) | |||||||
\(128\) | 1211.96 | 0.836897 | ||||||||
\(129\) | −376.433 | −0.256923 | ||||||||
\(130\) | 17.2982 | 0.0116704 | ||||||||
\(131\) | 1040.66 | 0.694065 | 0.347032 | − | 0.937853i | \(-0.387189\pi\) | ||||
0.347032 | + | 0.937853i | \(0.387189\pi\) | |||||||
\(132\) | −248.225 | −0.163676 | ||||||||
\(133\) | −186.891 | −0.121846 | ||||||||
\(134\) | −305.393 | −0.196880 | ||||||||
\(135\) | 155.820 | 0.0993394 | ||||||||
\(136\) | −1002.76 | −0.632253 | ||||||||
\(137\) | −617.195 | −0.384894 | −0.192447 | − | 0.981307i | \(-0.561642\pi\) | ||||
−0.192447 | + | 0.981307i | \(0.561642\pi\) | |||||||
\(138\) | 219.724 | 0.135537 | ||||||||
\(139\) | 735.445 | 0.448774 | 0.224387 | − | 0.974500i | \(-0.427962\pi\) | ||||
0.224387 | + | 0.974500i | \(0.427962\pi\) | |||||||
\(140\) | 415.697 | 0.250949 | ||||||||
\(141\) | −67.7888 | −0.0404883 | ||||||||
\(142\) | −706.120 | −0.417298 | ||||||||
\(143\) | −47.6884 | −0.0278874 | ||||||||
\(144\) | 474.804 | 0.274771 | ||||||||
\(145\) | 908.935 | 0.520572 | ||||||||
\(146\) | 656.910 | 0.372372 | ||||||||
\(147\) | 753.898 | 0.422996 | ||||||||
\(148\) | 2035.10 | 1.13030 | ||||||||
\(149\) | 1817.50 | 0.999297 | 0.499649 | − | 0.866228i | \(-0.333462\pi\) | ||||
0.499649 | + | 0.866228i | \(0.333462\pi\) | |||||||
\(150\) | −190.190 | −0.103526 | ||||||||
\(151\) | 42.7845 | 0.0230579 | 0.0115290 | − | 0.999934i | \(-0.496330\pi\) | ||||
0.0115290 | + | 0.999934i | \(0.496330\pi\) | |||||||
\(152\) | −209.446 | −0.111765 | ||||||||
\(153\) | −840.952 | −0.444359 | ||||||||
\(154\) | 72.8286 | 0.0381084 | ||||||||
\(155\) | −1203.28 | −0.623545 | ||||||||
\(156\) | 97.8303 | 0.0502096 | ||||||||
\(157\) | −3035.49 | −1.54305 | −0.771525 | − | 0.636199i | \(-0.780506\pi\) | ||||
−0.771525 | + | 0.636199i | \(0.780506\pi\) | |||||||
\(158\) | −738.749 | −0.371973 | ||||||||
\(159\) | −2167.57 | −1.08113 | ||||||||
\(160\) | 705.972 | 0.348825 | ||||||||
\(161\) | 1014.42 | 0.496571 | ||||||||
\(162\) | −56.0026 | −0.0271604 | ||||||||
\(163\) | −1475.93 | −0.709225 | −0.354613 | − | 0.935013i | \(-0.615387\pi\) | ||||
−0.354613 | + | 0.935013i | \(0.615387\pi\) | |||||||
\(164\) | −3019.84 | −1.43786 | ||||||||
\(165\) | −190.446 | −0.0898559 | ||||||||
\(166\) | −310.084 | −0.144983 | ||||||||
\(167\) | −1020.18 | −0.472717 | −0.236359 | − | 0.971666i | \(-0.575954\pi\) | ||||
−0.236359 | + | 0.971666i | \(0.575954\pi\) | |||||||
\(168\) | −308.303 | −0.141584 | ||||||||
\(169\) | −2178.21 | −0.991445 | ||||||||
\(170\) | −372.829 | −0.168204 | ||||||||
\(171\) | −175.649 | −0.0785508 | ||||||||
\(172\) | −943.841 | −0.418414 | ||||||||
\(173\) | −3434.79 | −1.50949 | −0.754747 | − | 0.656016i | \(-0.772240\pi\) | ||||
−0.754747 | + | 0.656016i | \(0.772240\pi\) | |||||||
\(174\) | −326.677 | −0.142329 | ||||||||
\(175\) | −878.071 | −0.379291 | ||||||||
\(176\) | −580.316 | −0.248540 | ||||||||
\(177\) | 624.401 | 0.265157 | ||||||||
\(178\) | 704.019 | 0.296452 | ||||||||
\(179\) | −17.3569 | −0.00724758 | −0.00362379 | − | 0.999993i | \(-0.501153\pi\) | ||||
−0.00362379 | + | 0.999993i | \(0.501153\pi\) | |||||||
\(180\) | 390.691 | 0.161780 | ||||||||
\(181\) | 3102.71 | 1.27416 | 0.637078 | − | 0.770799i | \(-0.280143\pi\) | ||||
0.637078 | + | 0.770799i | \(0.280143\pi\) | |||||||
\(182\) | −28.7032 | −0.0116902 | ||||||||
\(183\) | −183.000 | −0.0739221 | ||||||||
\(184\) | 1136.85 | 0.455488 | ||||||||
\(185\) | 1561.39 | 0.620518 | ||||||||
\(186\) | 432.465 | 0.170483 | ||||||||
\(187\) | 1027.83 | 0.401938 | ||||||||
\(188\) | −169.969 | −0.0659374 | ||||||||
\(189\) | −258.553 | −0.0995079 | ||||||||
\(190\) | −77.8724 | −0.0297340 | ||||||||
\(191\) | 49.1965 | 0.0186373 | 0.00931867 | − | 0.999957i | \(-0.497034\pi\) | ||||
0.00931867 | + | 0.999957i | \(0.497034\pi\) | |||||||
\(192\) | 1012.41 | 0.380545 | ||||||||
\(193\) | −835.282 | −0.311528 | −0.155764 | − | 0.987794i | \(-0.549784\pi\) | ||||
−0.155764 | + | 0.987794i | \(0.549784\pi\) | |||||||
\(194\) | −956.283 | −0.353903 | ||||||||
\(195\) | 75.0585 | 0.0275644 | ||||||||
\(196\) | 1890.27 | 0.688873 | ||||||||
\(197\) | 1664.85 | 0.602111 | 0.301056 | − | 0.953607i | \(-0.402661\pi\) | ||||
0.301056 | + | 0.953607i | \(0.402661\pi\) | |||||||
\(198\) | 68.4476 | 0.0245675 | ||||||||
\(199\) | −4475.48 | −1.59426 | −0.797131 | − | 0.603807i | \(-0.793650\pi\) | ||||
−0.797131 | + | 0.603807i | \(0.793650\pi\) | |||||||
\(200\) | −984.041 | −0.347911 | ||||||||
\(201\) | −1325.13 | −0.465011 | ||||||||
\(202\) | 944.417 | 0.328955 | ||||||||
\(203\) | −1508.21 | −0.521455 | ||||||||
\(204\) | −2108.54 | −0.723664 | ||||||||
\(205\) | −2316.91 | −0.789367 | ||||||||
\(206\) | 24.1525 | 0.00816887 | ||||||||
\(207\) | 953.402 | 0.320126 | ||||||||
\(208\) | 228.714 | 0.0762425 | ||||||||
\(209\) | 214.682 | 0.0710519 | ||||||||
\(210\) | −114.628 | −0.0376669 | ||||||||
\(211\) | −235.867 | −0.0769562 | −0.0384781 | − | 0.999259i | \(-0.512251\pi\) | ||||
−0.0384781 | + | 0.999259i | \(0.512251\pi\) | |||||||
\(212\) | −5434.80 | −1.76068 | ||||||||
\(213\) | −3063.91 | −0.985615 | ||||||||
\(214\) | −1260.34 | −0.402593 | ||||||||
\(215\) | −724.144 | −0.229703 | ||||||||
\(216\) | −289.757 | −0.0912753 | ||||||||
\(217\) | 1996.61 | 0.624603 | ||||||||
\(218\) | −407.661 | −0.126653 | ||||||||
\(219\) | 2850.39 | 0.879504 | ||||||||
\(220\) | −477.511 | −0.146335 | ||||||||
\(221\) | −405.087 | −0.123299 | ||||||||
\(222\) | −561.175 | −0.169656 | ||||||||
\(223\) | −3441.70 | −1.03351 | −0.516756 | − | 0.856133i | \(-0.672860\pi\) | ||||
−0.516756 | + | 0.856133i | \(0.672860\pi\) | |||||||
\(224\) | −1171.43 | −0.349417 | ||||||||
\(225\) | −825.250 | −0.244518 | ||||||||
\(226\) | 540.694 | 0.159144 | ||||||||
\(227\) | −2413.10 | −0.705563 | −0.352782 | − | 0.935706i | \(-0.614764\pi\) | ||||
−0.352782 | + | 0.935706i | \(0.614764\pi\) | |||||||
\(228\) | −440.409 | −0.127924 | ||||||||
\(229\) | −4545.17 | −1.31159 | −0.655793 | − | 0.754941i | \(-0.727665\pi\) | ||||
−0.655793 | + | 0.754941i | \(0.727665\pi\) | |||||||
\(230\) | 422.683 | 0.121178 | ||||||||
\(231\) | 316.010 | 0.0900083 | ||||||||
\(232\) | −1690.23 | −0.478313 | ||||||||
\(233\) | −3810.75 | −1.07146 | −0.535731 | − | 0.844389i | \(-0.679964\pi\) | ||||
−0.535731 | + | 0.844389i | \(0.679964\pi\) | |||||||
\(234\) | −26.9765 | −0.00753637 | ||||||||
\(235\) | −130.405 | −0.0361987 | ||||||||
\(236\) | 1565.58 | 0.431824 | ||||||||
\(237\) | −3205.50 | −0.878563 | ||||||||
\(238\) | 618.640 | 0.168489 | ||||||||
\(239\) | −18.7088 | −0.00506347 | −0.00253173 | − | 0.999997i | \(-0.500806\pi\) | ||||
−0.00253173 | + | 0.999997i | \(0.500806\pi\) | |||||||
\(240\) | 913.380 | 0.245660 | ||||||||
\(241\) | 3310.23 | 0.884775 | 0.442388 | − | 0.896824i | \(-0.354132\pi\) | ||||
0.442388 | + | 0.896824i | \(0.354132\pi\) | |||||||
\(242\) | −83.6582 | −0.0222221 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −458.841 | −0.120386 | ||||||||
\(245\) | 1450.27 | 0.378182 | ||||||||
\(246\) | 832.714 | 0.215821 | ||||||||
\(247\) | −84.6101 | −0.0217960 | ||||||||
\(248\) | 2237.57 | 0.572928 | ||||||||
\(249\) | −1345.48 | −0.342435 | ||||||||
\(250\) | −864.628 | −0.218736 | ||||||||
\(251\) | 3873.30 | 0.974025 | 0.487012 | − | 0.873395i | \(-0.338087\pi\) | ||||
0.487012 | + | 0.873395i | \(0.338087\pi\) | |||||||
\(252\) | −648.278 | −0.162054 | ||||||||
\(253\) | −1165.27 | −0.289565 | ||||||||
\(254\) | −38.7526 | −0.00957306 | ||||||||
\(255\) | −1617.74 | −0.397281 | ||||||||
\(256\) | 1861.84 | 0.454550 | ||||||||
\(257\) | −1747.26 | −0.424089 | −0.212044 | − | 0.977260i | \(-0.568012\pi\) | ||||
−0.212044 | + | 0.977260i | \(0.568012\pi\) | |||||||
\(258\) | 260.262 | 0.0628032 | ||||||||
\(259\) | −2590.84 | −0.621570 | ||||||||
\(260\) | 188.196 | 0.0448901 | ||||||||
\(261\) | −1417.48 | −0.336168 | ||||||||
\(262\) | −719.499 | −0.169660 | ||||||||
\(263\) | 1521.15 | 0.356648 | 0.178324 | − | 0.983972i | \(-0.442932\pi\) | ||||
0.178324 | + | 0.983972i | \(0.442932\pi\) | |||||||
\(264\) | 354.148 | 0.0825616 | ||||||||
\(265\) | −4169.75 | −0.966587 | ||||||||
\(266\) | 129.215 | 0.0297844 | ||||||||
\(267\) | 3054.80 | 0.700190 | ||||||||
\(268\) | −3322.52 | −0.757297 | ||||||||
\(269\) | −4991.11 | −1.13128 | −0.565638 | − | 0.824653i | \(-0.691370\pi\) | ||||
−0.565638 | + | 0.824653i | \(0.691370\pi\) | |||||||
\(270\) | −107.732 | −0.0242828 | ||||||||
\(271\) | 1377.97 | 0.308877 | 0.154438 | − | 0.988002i | \(-0.450643\pi\) | ||||
0.154438 | + | 0.988002i | \(0.450643\pi\) | |||||||
\(272\) | −4929.48 | −1.09887 | ||||||||
\(273\) | −124.545 | −0.0276111 | ||||||||
\(274\) | 426.723 | 0.0940849 | ||||||||
\(275\) | 1008.64 | 0.221175 | ||||||||
\(276\) | 2390.49 | 0.521343 | ||||||||
\(277\) | 1232.77 | 0.267400 | 0.133700 | − | 0.991022i | \(-0.457314\pi\) | ||||
0.133700 | + | 0.991022i | \(0.457314\pi\) | |||||||
\(278\) | −508.480 | −0.109700 | ||||||||
\(279\) | 1876.50 | 0.402664 | ||||||||
\(280\) | −593.082 | −0.126584 | ||||||||
\(281\) | −2368.83 | −0.502892 | −0.251446 | − | 0.967871i | \(-0.580906\pi\) | ||||
−0.251446 | + | 0.967871i | \(0.580906\pi\) | |||||||
\(282\) | 46.8685 | 0.00989708 | ||||||||
\(283\) | −983.445 | −0.206572 | −0.103286 | − | 0.994652i | \(-0.532936\pi\) | ||||
−0.103286 | + | 0.994652i | \(0.532936\pi\) | |||||||
\(284\) | −7682.23 | −1.60513 | ||||||||
\(285\) | −337.895 | −0.0702287 | ||||||||
\(286\) | 32.9713 | 0.00681690 | ||||||||
\(287\) | 3844.48 | 0.790706 | ||||||||
\(288\) | −1100.96 | −0.225259 | ||||||||
\(289\) | 3817.87 | 0.777095 | ||||||||
\(290\) | −628.429 | −0.127250 | ||||||||
\(291\) | −4149.39 | −0.835882 | ||||||||
\(292\) | 7146.85 | 1.43232 | ||||||||
\(293\) | −6326.87 | −1.26150 | −0.630750 | − | 0.775986i | \(-0.717253\pi\) | ||||
−0.630750 | + | 0.775986i | \(0.717253\pi\) | |||||||
\(294\) | −521.237 | −0.103399 | ||||||||
\(295\) | 1201.16 | 0.237065 | ||||||||
\(296\) | −2903.51 | −0.570146 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | −1256.60 | −0.244272 | ||||||||
\(299\) | 459.255 | 0.0888274 | ||||||||
\(300\) | −2069.17 | −0.398212 | ||||||||
\(301\) | 1201.58 | 0.230093 | ||||||||
\(302\) | −29.5807 | −0.00563636 | ||||||||
\(303\) | 4097.90 | 0.776959 | ||||||||
\(304\) | −1029.61 | −0.194251 | ||||||||
\(305\) | −352.037 | −0.0660904 | ||||||||
\(306\) | 581.426 | 0.108621 | ||||||||
\(307\) | −167.480 | −0.0311354 | −0.0155677 | − | 0.999879i | \(-0.504956\pi\) | ||||
−0.0155677 | + | 0.999879i | \(0.504956\pi\) | |||||||
\(308\) | 792.339 | 0.146584 | ||||||||
\(309\) | 104.800 | 0.0192940 | ||||||||
\(310\) | 831.933 | 0.152421 | ||||||||
\(311\) | 4838.40 | 0.882189 | 0.441094 | − | 0.897461i | \(-0.354590\pi\) | ||||
0.441094 | + | 0.897461i | \(0.354590\pi\) | |||||||
\(312\) | −139.576 | −0.0253268 | ||||||||
\(313\) | −7205.76 | −1.30126 | −0.650629 | − | 0.759396i | \(-0.725495\pi\) | ||||
−0.650629 | + | 0.759396i | \(0.725495\pi\) | |||||||
\(314\) | 2098.71 | 0.377188 | ||||||||
\(315\) | −497.379 | −0.0889655 | ||||||||
\(316\) | −8037.23 | −1.43079 | ||||||||
\(317\) | −6064.61 | −1.07452 | −0.537259 | − | 0.843417i | \(-0.680540\pi\) | ||||
−0.537259 | + | 0.843417i | \(0.680540\pi\) | |||||||
\(318\) | 1498.63 | 0.264274 | ||||||||
\(319\) | 1732.48 | 0.304075 | ||||||||
\(320\) | 1947.58 | 0.340228 | ||||||||
\(321\) | −5468.71 | −0.950884 | ||||||||
\(322\) | −701.363 | −0.121383 | ||||||||
\(323\) | 1823.61 | 0.314143 | ||||||||
\(324\) | −609.280 | −0.104472 | ||||||||
\(325\) | −397.524 | −0.0678482 | ||||||||
\(326\) | 1020.44 | 0.173365 | ||||||||
\(327\) | −1768.88 | −0.299141 | ||||||||
\(328\) | 4308.46 | 0.725289 | ||||||||
\(329\) | 216.383 | 0.0362601 | ||||||||
\(330\) | 131.673 | 0.0219647 | ||||||||
\(331\) | −9237.23 | −1.53391 | −0.766955 | − | 0.641701i | \(-0.778229\pi\) | ||||
−0.766955 | + | 0.641701i | \(0.778229\pi\) | |||||||
\(332\) | −3373.56 | −0.557675 | ||||||||
\(333\) | −2434.98 | −0.400710 | ||||||||
\(334\) | 705.341 | 0.115553 | ||||||||
\(335\) | −2549.14 | −0.415745 | ||||||||
\(336\) | −1515.58 | −0.246077 | ||||||||
\(337\) | 5647.02 | 0.912798 | 0.456399 | − | 0.889775i | \(-0.349139\pi\) | ||||
0.456399 | + | 0.889775i | \(0.349139\pi\) | |||||||
\(338\) | 1505.99 | 0.242352 | ||||||||
\(339\) | 2346.12 | 0.375881 | ||||||||
\(340\) | −4056.20 | −0.646995 | ||||||||
\(341\) | −2293.51 | −0.364224 | ||||||||
\(342\) | 121.442 | 0.0192012 | ||||||||
\(343\) | −5691.04 | −0.895881 | ||||||||
\(344\) | 1346.60 | 0.211057 | ||||||||
\(345\) | 1834.06 | 0.286210 | ||||||||
\(346\) | 2374.78 | 0.368986 | ||||||||
\(347\) | −2697.74 | −0.417356 | −0.208678 | − | 0.977984i | \(-0.566916\pi\) | ||||
−0.208678 | + | 0.977984i | \(0.566916\pi\) | |||||||
\(348\) | −3554.08 | −0.547468 | ||||||||
\(349\) | −1031.77 | −0.158251 | −0.0791254 | − | 0.996865i | \(-0.525213\pi\) | ||||
−0.0791254 | + | 0.996865i | \(0.525213\pi\) | |||||||
\(350\) | 607.089 | 0.0927151 | ||||||||
\(351\) | −117.053 | −0.0178001 | ||||||||
\(352\) | 1345.62 | 0.203755 | ||||||||
\(353\) | 10049.0 | 1.51516 | 0.757580 | − | 0.652742i | \(-0.226381\pi\) | ||||
0.757580 | + | 0.652742i | \(0.226381\pi\) | |||||||
\(354\) | −431.705 | −0.0648160 | ||||||||
\(355\) | −5894.05 | −0.881193 | ||||||||
\(356\) | 7659.38 | 1.14030 | ||||||||
\(357\) | 2684.33 | 0.397955 | ||||||||
\(358\) | 12.0004 | 0.00177162 | ||||||||
\(359\) | −7448.59 | −1.09505 | −0.547523 | − | 0.836791i | \(-0.684429\pi\) | ||||
−0.547523 | + | 0.836791i | \(0.684429\pi\) | |||||||
\(360\) | −557.405 | −0.0816051 | ||||||||
\(361\) | −6478.11 | −0.944468 | ||||||||
\(362\) | −2145.18 | −0.311459 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | −312.276 | −0.0449662 | ||||||||
\(365\) | 5483.29 | 0.786325 | ||||||||
\(366\) | 126.524 | 0.0180698 | ||||||||
\(367\) | 6837.94 | 0.972582 | 0.486291 | − | 0.873797i | \(-0.338350\pi\) | ||||
0.486291 | + | 0.873797i | \(0.338350\pi\) | |||||||
\(368\) | 5588.63 | 0.791651 | ||||||||
\(369\) | 3613.22 | 0.509747 | ||||||||
\(370\) | −1079.53 | −0.151681 | ||||||||
\(371\) | 6918.91 | 0.968227 | ||||||||
\(372\) | 4705.01 | 0.655762 | ||||||||
\(373\) | −6477.65 | −0.899195 | −0.449598 | − | 0.893231i | \(-0.648433\pi\) | ||||
−0.449598 | + | 0.893231i | \(0.648433\pi\) | |||||||
\(374\) | −710.632 | −0.0982510 | ||||||||
\(375\) | −3751.69 | −0.516631 | ||||||||
\(376\) | 242.497 | 0.0332602 | ||||||||
\(377\) | −682.801 | −0.0932787 | ||||||||
\(378\) | 178.761 | 0.0243240 | ||||||||
\(379\) | 6982.26 | 0.946318 | 0.473159 | − | 0.880977i | \(-0.343114\pi\) | ||||
0.473159 | + | 0.880977i | \(0.343114\pi\) | |||||||
\(380\) | −847.213 | −0.114371 | ||||||||
\(381\) | −168.151 | −0.0226106 | ||||||||
\(382\) | −34.0140 | −0.00455577 | ||||||||
\(383\) | 8827.37 | 1.17770 | 0.588848 | − | 0.808244i | \(-0.299582\pi\) | ||||
0.588848 | + | 0.808244i | \(0.299582\pi\) | |||||||
\(384\) | −3635.87 | −0.483182 | ||||||||
\(385\) | 607.907 | 0.0804723 | ||||||||
\(386\) | 577.506 | 0.0761510 | ||||||||
\(387\) | 1129.30 | 0.148335 | ||||||||
\(388\) | −10403.9 | −1.36128 | ||||||||
\(389\) | −7531.99 | −0.981714 | −0.490857 | − | 0.871240i | \(-0.663316\pi\) | ||||
−0.490857 | + | 0.871240i | \(0.663316\pi\) | |||||||
\(390\) | −51.8947 | −0.00673792 | ||||||||
\(391\) | −9898.34 | −1.28026 | ||||||||
\(392\) | −2696.88 | −0.347482 | ||||||||
\(393\) | −3121.97 | −0.400719 | ||||||||
\(394\) | −1151.06 | −0.147182 | ||||||||
\(395\) | −6166.41 | −0.785483 | ||||||||
\(396\) | 744.676 | 0.0944984 | ||||||||
\(397\) | −2514.47 | −0.317879 | −0.158939 | − | 0.987288i | \(-0.550807\pi\) | ||||
−0.158939 | + | 0.987288i | \(0.550807\pi\) | |||||||
\(398\) | 3094.30 | 0.389707 | ||||||||
\(399\) | 560.673 | 0.0703478 | ||||||||
\(400\) | −4837.43 | −0.604679 | ||||||||
\(401\) | 13254.8 | 1.65066 | 0.825330 | − | 0.564651i | \(-0.190989\pi\) | ||||
0.825330 | + | 0.564651i | \(0.190989\pi\) | |||||||
\(402\) | 916.179 | 0.113669 | ||||||||
\(403\) | 903.914 | 0.111730 | ||||||||
\(404\) | 10274.8 | 1.26532 | ||||||||
\(405\) | −467.459 | −0.0573536 | ||||||||
\(406\) | 1042.76 | 0.127466 | ||||||||
\(407\) | 2976.09 | 0.362455 | ||||||||
\(408\) | 3008.29 | 0.365031 | ||||||||
\(409\) | −3996.59 | −0.483176 | −0.241588 | − | 0.970379i | \(-0.577668\pi\) | ||||
−0.241588 | + | 0.970379i | \(0.577668\pi\) | |||||||
\(410\) | 1601.89 | 0.192956 | ||||||||
\(411\) | 1851.59 | 0.222219 | ||||||||
\(412\) | 262.767 | 0.0314214 | ||||||||
\(413\) | −1993.10 | −0.237467 | ||||||||
\(414\) | −659.173 | −0.0782526 | ||||||||
\(415\) | −2588.30 | −0.306156 | ||||||||
\(416\) | −530.334 | −0.0625042 | ||||||||
\(417\) | −2206.34 | −0.259100 | ||||||||
\(418\) | −148.429 | −0.0173682 | ||||||||
\(419\) | 16323.6 | 1.90324 | 0.951621 | − | 0.307273i | \(-0.0994165\pi\) | ||||
0.951621 | + | 0.307273i | \(0.0994165\pi\) | |||||||
\(420\) | −1247.09 | −0.144885 | ||||||||
\(421\) | −6285.98 | −0.727696 | −0.363848 | − | 0.931458i | \(-0.618537\pi\) | ||||
−0.363848 | + | 0.931458i | \(0.618537\pi\) | |||||||
\(422\) | 163.076 | 0.0188114 | ||||||||
\(423\) | 203.366 | 0.0233759 | ||||||||
\(424\) | 7753.93 | 0.888123 | ||||||||
\(425\) | 8567.85 | 0.977886 | ||||||||
\(426\) | 2118.36 | 0.240927 | ||||||||
\(427\) | 584.139 | 0.0662025 | ||||||||
\(428\) | −13711.8 | −1.54857 | ||||||||
\(429\) | 143.065 | 0.0161008 | ||||||||
\(430\) | 500.666 | 0.0561495 | ||||||||
\(431\) | 12368.1 | 1.38225 | 0.691124 | − | 0.722736i | \(-0.257116\pi\) | ||||
0.691124 | + | 0.722736i | \(0.257116\pi\) | |||||||
\(432\) | −1424.41 | −0.158639 | ||||||||
\(433\) | 12508.6 | 1.38828 | 0.694139 | − | 0.719841i | \(-0.255785\pi\) | ||||
0.694139 | + | 0.719841i | \(0.255785\pi\) | |||||||
\(434\) | −1380.44 | −0.152680 | ||||||||
\(435\) | −2726.80 | −0.300552 | ||||||||
\(436\) | −4435.15 | −0.487168 | ||||||||
\(437\) | −2067.45 | −0.226315 | ||||||||
\(438\) | −1970.73 | −0.214989 | ||||||||
\(439\) | −9708.25 | −1.05547 | −0.527733 | − | 0.849410i | \(-0.676958\pi\) | ||||
−0.527733 | + | 0.849410i | \(0.676958\pi\) | |||||||
\(440\) | 681.273 | 0.0738146 | ||||||||
\(441\) | −2261.69 | −0.244217 | ||||||||
\(442\) | 280.073 | 0.0301397 | ||||||||
\(443\) | 12399.9 | 1.32988 | 0.664941 | − | 0.746896i | \(-0.268457\pi\) | ||||
0.664941 | + | 0.746896i | \(0.268457\pi\) | |||||||
\(444\) | −6105.30 | −0.652578 | ||||||||
\(445\) | 5876.51 | 0.626008 | ||||||||
\(446\) | 2379.56 | 0.252635 | ||||||||
\(447\) | −5452.50 | −0.576945 | ||||||||
\(448\) | −3231.64 | −0.340805 | ||||||||
\(449\) | −6452.34 | −0.678185 | −0.339092 | − | 0.940753i | \(-0.610120\pi\) | ||||
−0.339092 | + | 0.940753i | \(0.610120\pi\) | |||||||
\(450\) | 570.570 | 0.0597709 | ||||||||
\(451\) | −4416.15 | −0.461083 | ||||||||
\(452\) | 5882.49 | 0.612143 | ||||||||
\(453\) | −128.353 | −0.0133125 | ||||||||
\(454\) | 1668.39 | 0.172470 | ||||||||
\(455\) | −239.588 | −0.0246858 | ||||||||
\(456\) | 628.339 | 0.0645277 | ||||||||
\(457\) | 753.511 | 0.0771286 | 0.0385643 | − | 0.999256i | \(-0.487722\pi\) | ||||
0.0385643 | + | 0.999256i | \(0.487722\pi\) | |||||||
\(458\) | 3142.48 | 0.320608 | ||||||||
\(459\) | 2522.86 | 0.256551 | ||||||||
\(460\) | 4598.58 | 0.466109 | ||||||||
\(461\) | −16347.1 | −1.65154 | −0.825771 | − | 0.564006i | \(-0.809260\pi\) | ||||
−0.825771 | + | 0.564006i | \(0.809260\pi\) | |||||||
\(462\) | −218.486 | −0.0220019 | ||||||||
\(463\) | 4770.36 | 0.478828 | 0.239414 | − | 0.970918i | \(-0.423045\pi\) | ||||
0.239414 | + | 0.970918i | \(0.423045\pi\) | |||||||
\(464\) | −8308.95 | −0.831322 | ||||||||
\(465\) | 3609.83 | 0.360004 | ||||||||
\(466\) | 2634.71 | 0.261912 | ||||||||
\(467\) | −11452.5 | −1.13481 | −0.567406 | − | 0.823438i | \(-0.692053\pi\) | ||||
−0.567406 | + | 0.823438i | \(0.692053\pi\) | |||||||
\(468\) | −293.491 | −0.0289885 | ||||||||
\(469\) | 4229.83 | 0.416450 | ||||||||
\(470\) | 90.1608 | 0.00884853 | ||||||||
\(471\) | 9106.48 | 0.890880 | ||||||||
\(472\) | −2233.64 | −0.217821 | ||||||||
\(473\) | −1380.26 | −0.134174 | ||||||||
\(474\) | 2216.25 | 0.214759 | ||||||||
\(475\) | 1789.56 | 0.172864 | ||||||||
\(476\) | 6730.50 | 0.648092 | ||||||||
\(477\) | 6502.70 | 0.624189 | ||||||||
\(478\) | 12.9350 | 0.00123773 | ||||||||
\(479\) | 2864.72 | 0.273261 | 0.136631 | − | 0.990622i | \(-0.456373\pi\) | ||||
0.136631 | + | 0.990622i | \(0.456373\pi\) | |||||||
\(480\) | −2117.92 | −0.201394 | ||||||||
\(481\) | −1172.93 | −0.111188 | ||||||||
\(482\) | −2288.66 | −0.216277 | ||||||||
\(483\) | −3043.27 | −0.286695 | ||||||||
\(484\) | −910.160 | −0.0854770 | ||||||||
\(485\) | −7982.18 | −0.747324 | ||||||||
\(486\) | 168.008 | 0.0156810 | ||||||||
\(487\) | −11482.6 | −1.06843 | −0.534215 | − | 0.845348i | \(-0.679393\pi\) | ||||
−0.534215 | + | 0.845348i | \(0.679393\pi\) | |||||||
\(488\) | 654.636 | 0.0607254 | ||||||||
\(489\) | 4427.79 | 0.409471 | ||||||||
\(490\) | −1002.70 | −0.0924440 | ||||||||
\(491\) | −16656.7 | −1.53097 | −0.765485 | − | 0.643454i | \(-0.777501\pi\) | ||||
−0.765485 | + | 0.643454i | \(0.777501\pi\) | |||||||
\(492\) | 9059.51 | 0.830151 | ||||||||
\(493\) | 14716.5 | 1.34441 | ||||||||
\(494\) | 58.4986 | 0.00532789 | ||||||||
\(495\) | 571.339 | 0.0518783 | ||||||||
\(496\) | 10999.7 | 0.995764 | ||||||||
\(497\) | 9780.07 | 0.882688 | ||||||||
\(498\) | 930.252 | 0.0837060 | ||||||||
\(499\) | 133.927 | 0.0120148 | 0.00600740 | − | 0.999982i | \(-0.498088\pi\) | ||||
0.00600740 | + | 0.999982i | \(0.498088\pi\) | |||||||
\(500\) | −9406.72 | −0.841363 | ||||||||
\(501\) | 3060.53 | 0.272923 | ||||||||
\(502\) | −2677.96 | −0.238094 | ||||||||
\(503\) | 13578.4 | 1.20364 | 0.601818 | − | 0.798633i | \(-0.294443\pi\) | ||||
0.601818 | + | 0.798633i | \(0.294443\pi\) | |||||||
\(504\) | 924.909 | 0.0817435 | ||||||||
\(505\) | 7883.14 | 0.694643 | ||||||||
\(506\) | 805.655 | 0.0707821 | ||||||||
\(507\) | 6534.62 | 0.572411 | ||||||||
\(508\) | −421.609 | −0.0368226 | ||||||||
\(509\) | 5715.38 | 0.497701 | 0.248851 | − | 0.968542i | \(-0.419947\pi\) | ||||
0.248851 | + | 0.968542i | \(0.419947\pi\) | |||||||
\(510\) | 1118.49 | 0.0971127 | ||||||||
\(511\) | −9098.49 | −0.787658 | ||||||||
\(512\) | −10982.9 | −0.948008 | ||||||||
\(513\) | 526.946 | 0.0453513 | ||||||||
\(514\) | 1208.04 | 0.103666 | ||||||||
\(515\) | 201.603 | 0.0172499 | ||||||||
\(516\) | 2831.52 | 0.241571 | ||||||||
\(517\) | −248.559 | −0.0211443 | ||||||||
\(518\) | 1791.28 | 0.151939 | ||||||||
\(519\) | 10304.4 | 0.871507 | ||||||||
\(520\) | −268.503 | −0.0226435 | ||||||||
\(521\) | −4008.33 | −0.337060 | −0.168530 | − | 0.985697i | \(-0.553902\pi\) | ||||
−0.168530 | + | 0.985697i | \(0.553902\pi\) | |||||||
\(522\) | 980.031 | 0.0821740 | ||||||||
\(523\) | −9654.48 | −0.807191 | −0.403596 | − | 0.914938i | \(-0.632240\pi\) | ||||
−0.403596 | + | 0.914938i | \(0.632240\pi\) | |||||||
\(524\) | −7827.79 | −0.652593 | ||||||||
\(525\) | 2634.21 | 0.218984 | ||||||||
\(526\) | −1051.71 | −0.0871802 | ||||||||
\(527\) | −19482.1 | −1.61035 | ||||||||
\(528\) | 1740.95 | 0.143494 | ||||||||
\(529\) | −945.086 | −0.0776761 | ||||||||
\(530\) | 2882.92 | 0.236276 | ||||||||
\(531\) | −1873.20 | −0.153089 | ||||||||
\(532\) | 1405.79 | 0.114565 | ||||||||
\(533\) | 1740.49 | 0.141443 | ||||||||
\(534\) | −2112.06 | −0.171157 | ||||||||
\(535\) | −10520.2 | −0.850142 | ||||||||
\(536\) | 4740.31 | 0.381996 | ||||||||
\(537\) | 52.0708 | 0.00418439 | ||||||||
\(538\) | 3450.80 | 0.276533 | ||||||||
\(539\) | 2764.29 | 0.220903 | ||||||||
\(540\) | −1172.07 | −0.0934036 | ||||||||
\(541\) | −9846.84 | −0.782530 | −0.391265 | − | 0.920278i | \(-0.627962\pi\) | ||||
−0.391265 | + | 0.920278i | \(0.627962\pi\) | |||||||
\(542\) | −952.714 | −0.0755029 | ||||||||
\(543\) | −9308.12 | −0.735635 | ||||||||
\(544\) | 11430.3 | 0.900865 | ||||||||
\(545\) | −3402.79 | −0.267449 | ||||||||
\(546\) | 86.1095 | 0.00674935 | ||||||||
\(547\) | −4488.13 | −0.350820 | −0.175410 | − | 0.984495i | \(-0.556125\pi\) | ||||
−0.175410 | + | 0.984495i | \(0.556125\pi\) | |||||||
\(548\) | 4642.53 | 0.361896 | ||||||||
\(549\) | 549.000 | 0.0426790 | ||||||||
\(550\) | −697.363 | −0.0540648 | ||||||||
\(551\) | 3073.81 | 0.237656 | ||||||||
\(552\) | −3410.55 | −0.262976 | ||||||||
\(553\) | 10232.0 | 0.786815 | ||||||||
\(554\) | −852.322 | −0.0653641 | ||||||||
\(555\) | −4684.18 | −0.358256 | ||||||||
\(556\) | −5532.00 | −0.421959 | ||||||||
\(557\) | 2353.34 | 0.179020 | 0.0895101 | − | 0.995986i | \(-0.471470\pi\) | ||||
0.0895101 | + | 0.995986i | \(0.471470\pi\) | |||||||
\(558\) | −1297.40 | −0.0984286 | ||||||||
\(559\) | 543.985 | 0.0411594 | ||||||||
\(560\) | −2915.53 | −0.220006 | ||||||||
\(561\) | −3083.49 | −0.232059 | ||||||||
\(562\) | 1637.79 | 0.122929 | ||||||||
\(563\) | −20402.6 | −1.52729 | −0.763646 | − | 0.645635i | \(-0.776593\pi\) | ||||
−0.763646 | + | 0.645635i | \(0.776593\pi\) | |||||||
\(564\) | 509.906 | 0.0380690 | ||||||||
\(565\) | 4513.23 | 0.336058 | ||||||||
\(566\) | 679.944 | 0.0504950 | ||||||||
\(567\) | 775.660 | 0.0574509 | ||||||||
\(568\) | 10960.4 | 0.809661 | ||||||||
\(569\) | −15098.8 | −1.11243 | −0.556215 | − | 0.831038i | \(-0.687747\pi\) | ||||
−0.556215 | + | 0.831038i | \(0.687747\pi\) | |||||||
\(570\) | 233.617 | 0.0171669 | ||||||||
\(571\) | −24889.9 | −1.82418 | −0.912091 | − | 0.409987i | \(-0.865533\pi\) | ||||
−0.912091 | + | 0.409987i | \(0.865533\pi\) | |||||||
\(572\) | 358.711 | 0.0262211 | ||||||||
\(573\) | −147.589 | −0.0107603 | ||||||||
\(574\) | −2658.04 | −0.193283 | ||||||||
\(575\) | −9713.52 | −0.704490 | ||||||||
\(576\) | −3037.24 | −0.219708 | ||||||||
\(577\) | −2787.82 | −0.201142 | −0.100571 | − | 0.994930i | \(-0.532067\pi\) | ||||
−0.100571 | + | 0.994930i | \(0.532067\pi\) | |||||||
\(578\) | −2639.64 | −0.189956 | ||||||||
\(579\) | 2505.85 | 0.179861 | ||||||||
\(580\) | −6836.99 | −0.489466 | ||||||||
\(581\) | 4294.80 | 0.306675 | ||||||||
\(582\) | 2868.85 | 0.204326 | ||||||||
\(583\) | −7947.75 | −0.564601 | ||||||||
\(584\) | −10196.5 | −0.722493 | ||||||||
\(585\) | −225.175 | −0.0159143 | ||||||||
\(586\) | 4374.33 | 0.308365 | ||||||||
\(587\) | −7595.35 | −0.534061 | −0.267030 | − | 0.963688i | \(-0.586042\pi\) | ||||
−0.267030 | + | 0.963688i | \(0.586042\pi\) | |||||||
\(588\) | −5670.80 | −0.397721 | ||||||||
\(589\) | −4069.20 | −0.284666 | ||||||||
\(590\) | −830.470 | −0.0579490 | ||||||||
\(591\) | −4994.56 | −0.347629 | ||||||||
\(592\) | −14273.3 | −0.990930 | ||||||||
\(593\) | 4203.35 | 0.291081 | 0.145540 | − | 0.989352i | \(-0.453508\pi\) | ||||
0.145540 | + | 0.989352i | \(0.453508\pi\) | |||||||
\(594\) | −205.343 | −0.0141840 | ||||||||
\(595\) | 5163.85 | 0.355794 | ||||||||
\(596\) | −13671.2 | −0.939587 | ||||||||
\(597\) | 13426.4 | 0.920447 | ||||||||
\(598\) | −317.524 | −0.0217133 | ||||||||
\(599\) | −9560.25 | −0.652122 | −0.326061 | − | 0.945349i | \(-0.605722\pi\) | ||||
−0.326061 | + | 0.945349i | \(0.605722\pi\) | |||||||
\(600\) | 2952.12 | 0.200867 | ||||||||
\(601\) | −4567.57 | −0.310008 | −0.155004 | − | 0.987914i | \(-0.549539\pi\) | ||||
−0.155004 | + | 0.987914i | \(0.549539\pi\) | |||||||
\(602\) | −830.761 | −0.0562447 | ||||||||
\(603\) | 3975.38 | 0.268474 | ||||||||
\(604\) | −321.824 | −0.0216802 | ||||||||
\(605\) | −698.303 | −0.0469257 | ||||||||
\(606\) | −2833.25 | −0.189922 | ||||||||
\(607\) | 7570.91 | 0.506250 | 0.253125 | − | 0.967434i | \(-0.418542\pi\) | ||||
0.253125 | + | 0.967434i | \(0.418542\pi\) | |||||||
\(608\) | 2387.43 | 0.159249 | ||||||||
\(609\) | 4524.62 | 0.301062 | ||||||||
\(610\) | 243.395 | 0.0161554 | ||||||||
\(611\) | 97.9618 | 0.00648627 | ||||||||
\(612\) | 6325.62 | 0.417808 | ||||||||
\(613\) | −6472.22 | −0.426445 | −0.213222 | − | 0.977004i | \(-0.568396\pi\) | ||||
−0.213222 | + | 0.977004i | \(0.568396\pi\) | |||||||
\(614\) | 115.794 | 0.00761083 | ||||||||
\(615\) | 6950.74 | 0.455741 | ||||||||
\(616\) | −1130.44 | −0.0739398 | ||||||||
\(617\) | 17863.6 | 1.16558 | 0.582788 | − | 0.812624i | \(-0.301962\pi\) | ||||
0.582788 | + | 0.812624i | \(0.301962\pi\) | |||||||
\(618\) | −72.4576 | −0.00471630 | ||||||||
\(619\) | −24730.9 | −1.60585 | −0.802924 | − | 0.596081i | \(-0.796724\pi\) | ||||
−0.802924 | + | 0.596081i | \(0.796724\pi\) | |||||||
\(620\) | 9051.02 | 0.586287 | ||||||||
\(621\) | −2860.21 | −0.184825 | ||||||||
\(622\) | −3345.22 | −0.215645 | ||||||||
\(623\) | −9750.97 | −0.627070 | ||||||||
\(624\) | −686.141 | −0.0440186 | ||||||||
\(625\) | 4244.67 | 0.271659 | ||||||||
\(626\) | 4981.99 | 0.318084 | ||||||||
\(627\) | −644.045 | −0.0410218 | ||||||||
\(628\) | 22832.9 | 1.45085 | ||||||||
\(629\) | 25280.3 | 1.60253 | ||||||||
\(630\) | 343.883 | 0.0217470 | ||||||||
\(631\) | 1133.99 | 0.0715425 | 0.0357713 | − | 0.999360i | \(-0.488611\pi\) | ||||
0.0357713 | + | 0.999360i | \(0.488611\pi\) | |||||||
\(632\) | 11466.9 | 0.721720 | ||||||||
\(633\) | 707.601 | 0.0444307 | ||||||||
\(634\) | 4193.01 | 0.262659 | ||||||||
\(635\) | −323.472 | −0.0202151 | ||||||||
\(636\) | 16304.4 | 1.01653 | ||||||||
\(637\) | −1089.46 | −0.0677645 | ||||||||
\(638\) | −1197.82 | −0.0743291 | ||||||||
\(639\) | 9191.74 | 0.569045 | ||||||||
\(640\) | −6994.31 | −0.431991 | ||||||||
\(641\) | 8252.20 | 0.508490 | 0.254245 | − | 0.967140i | \(-0.418173\pi\) | ||||
0.254245 | + | 0.967140i | \(0.418173\pi\) | |||||||
\(642\) | 3781.01 | 0.232437 | ||||||||
\(643\) | −10318.2 | −0.632831 | −0.316416 | − | 0.948621i | \(-0.602479\pi\) | ||||
−0.316416 | + | 0.948621i | \(0.602479\pi\) | |||||||
\(644\) | −7630.48 | −0.466899 | ||||||||
\(645\) | 2172.43 | 0.132619 | ||||||||
\(646\) | −1260.82 | −0.0767901 | ||||||||
\(647\) | 22922.7 | 1.39286 | 0.696432 | − | 0.717623i | \(-0.254770\pi\) | ||||
0.696432 | + | 0.717623i | \(0.254770\pi\) | |||||||
\(648\) | 869.271 | 0.0526978 | ||||||||
\(649\) | 2289.47 | 0.138474 | ||||||||
\(650\) | 274.844 | 0.0165850 | ||||||||
\(651\) | −5989.83 | −0.360615 | ||||||||
\(652\) | 11101.9 | 0.666847 | ||||||||
\(653\) | 3186.91 | 0.190985 | 0.0954927 | − | 0.995430i | \(-0.469557\pi\) | ||||
0.0954927 | + | 0.995430i | \(0.469557\pi\) | |||||||
\(654\) | 1222.98 | 0.0731231 | ||||||||
\(655\) | −6005.73 | −0.358264 | ||||||||
\(656\) | 21179.9 | 1.26057 | ||||||||
\(657\) | −8551.17 | −0.507782 | ||||||||
\(658\) | −149.605 | −0.00886354 | ||||||||
\(659\) | 7696.64 | 0.454960 | 0.227480 | − | 0.973783i | \(-0.426951\pi\) | ||||
0.227480 | + | 0.973783i | \(0.426951\pi\) | |||||||
\(660\) | 1432.53 | 0.0844867 | ||||||||
\(661\) | −17859.0 | −1.05088 | −0.525441 | − | 0.850830i | \(-0.676100\pi\) | ||||
−0.525441 | + | 0.850830i | \(0.676100\pi\) | |||||||
\(662\) | 6386.53 | 0.374954 | ||||||||
\(663\) | 1215.26 | 0.0711868 | ||||||||
\(664\) | 4813.12 | 0.281303 | ||||||||
\(665\) | 1078.57 | 0.0628948 | ||||||||
\(666\) | 1683.52 | 0.0979508 | ||||||||
\(667\) | −16684.3 | −0.968543 | ||||||||
\(668\) | 7673.76 | 0.444471 | ||||||||
\(669\) | 10325.1 | 0.596698 | ||||||||
\(670\) | 1762.45 | 0.101626 | ||||||||
\(671\) | −671.000 | −0.0386046 | ||||||||
\(672\) | 3514.28 | 0.201736 | ||||||||
\(673\) | 2562.62 | 0.146778 | 0.0733890 | − | 0.997303i | \(-0.476619\pi\) | ||||
0.0733890 | + | 0.997303i | \(0.476619\pi\) | |||||||
\(674\) | −3904.29 | −0.223127 | ||||||||
\(675\) | 2475.75 | 0.141173 | ||||||||
\(676\) | 16384.4 | 0.932204 | ||||||||
\(677\) | 2836.43 | 0.161024 | 0.0805118 | − | 0.996754i | \(-0.474345\pi\) | ||||
0.0805118 | + | 0.996754i | \(0.474345\pi\) | |||||||
\(678\) | −1622.08 | −0.0918816 | ||||||||
\(679\) | 13244.9 | 0.748591 | ||||||||
\(680\) | 5787.05 | 0.326358 | ||||||||
\(681\) | 7239.29 | 0.407357 | ||||||||
\(682\) | 1585.71 | 0.0890320 | ||||||||
\(683\) | 7120.78 | 0.398930 | 0.199465 | − | 0.979905i | \(-0.436080\pi\) | ||||
0.199465 | + | 0.979905i | \(0.436080\pi\) | |||||||
\(684\) | 1321.23 | 0.0738572 | ||||||||
\(685\) | 3561.89 | 0.198676 | ||||||||
\(686\) | 3934.73 | 0.218992 | ||||||||
\(687\) | 13635.5 | 0.757244 | ||||||||
\(688\) | 6619.71 | 0.366823 | ||||||||
\(689\) | 3132.36 | 0.173198 | ||||||||
\(690\) | −1268.05 | −0.0699621 | ||||||||
\(691\) | 20058.2 | 1.10427 | 0.552136 | − | 0.833754i | \(-0.313813\pi\) | ||||
0.552136 | + | 0.833754i | \(0.313813\pi\) | |||||||
\(692\) | 25836.4 | 1.41930 | ||||||||
\(693\) | −948.029 | −0.0519663 | ||||||||
\(694\) | 1865.19 | 0.102020 | ||||||||
\(695\) | −4244.33 | −0.231650 | ||||||||
\(696\) | 5070.68 | 0.276154 | ||||||||
\(697\) | −37512.9 | −2.03860 | ||||||||
\(698\) | 713.357 | 0.0386833 | ||||||||
\(699\) | 11432.2 | 0.618608 | ||||||||
\(700\) | 6604.83 | 0.356627 | ||||||||
\(701\) | 1876.96 | 0.101130 | 0.0505649 | − | 0.998721i | \(-0.483898\pi\) | ||||
0.0505649 | + | 0.998721i | \(0.483898\pi\) | |||||||
\(702\) | 80.9295 | 0.00435112 | ||||||||
\(703\) | 5280.27 | 0.283285 | ||||||||
\(704\) | 3712.18 | 0.198733 | ||||||||
\(705\) | 391.216 | 0.0208993 | ||||||||
\(706\) | −6947.75 | −0.370371 | ||||||||
\(707\) | −13080.6 | −0.695822 | ||||||||
\(708\) | −4696.73 | −0.249314 | ||||||||
\(709\) | −18659.3 | −0.988384 | −0.494192 | − | 0.869353i | \(-0.664536\pi\) | ||||
−0.494192 | + | 0.869353i | \(0.664536\pi\) | |||||||
\(710\) | 4075.09 | 0.215402 | ||||||||
\(711\) | 9616.49 | 0.507238 | ||||||||
\(712\) | −10927.8 | −0.575190 | ||||||||
\(713\) | 22087.2 | 1.16013 | ||||||||
\(714\) | −1855.92 | −0.0972775 | ||||||||
\(715\) | 275.214 | 0.0143950 | ||||||||
\(716\) | 130.558 | 0.00681452 | ||||||||
\(717\) | 56.1263 | 0.00292339 | ||||||||
\(718\) | 5149.88 | 0.267677 | ||||||||
\(719\) | −26207.5 | −1.35935 | −0.679676 | − | 0.733512i | \(-0.737880\pi\) | ||||
−0.679676 | + | 0.733512i | \(0.737880\pi\) | |||||||
\(720\) | −2740.14 | −0.141832 | ||||||||
\(721\) | −334.523 | −0.0172792 | ||||||||
\(722\) | 4478.90 | 0.230869 | ||||||||
\(723\) | −9930.70 | −0.510825 | ||||||||
\(724\) | −23338.5 | −1.19802 | ||||||||
\(725\) | 14441.7 | 0.739793 | ||||||||
\(726\) | 250.975 | 0.0128299 | ||||||||
\(727\) | 2640.28 | 0.134694 | 0.0673469 | − | 0.997730i | \(-0.478547\pi\) | ||||
0.0673469 | + | 0.997730i | \(0.478547\pi\) | |||||||
\(728\) | 445.530 | 0.0226819 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −3791.09 | −0.192212 | ||||||||
\(731\) | −11724.5 | −0.593225 | ||||||||
\(732\) | 1376.52 | 0.0695051 | ||||||||
\(733\) | 11603.6 | 0.584706 | 0.292353 | − | 0.956310i | \(-0.405562\pi\) | ||||
0.292353 | + | 0.956310i | \(0.405562\pi\) | |||||||
\(734\) | −4727.68 | −0.237741 | ||||||||
\(735\) | −4350.82 | −0.218343 | ||||||||
\(736\) | −12958.7 | −0.649002 | ||||||||
\(737\) | −4858.80 | −0.242844 | ||||||||
\(738\) | −2498.14 | −0.124604 | ||||||||
\(739\) | 1984.17 | 0.0987669 | 0.0493835 | − | 0.998780i | \(-0.484274\pi\) | ||||
0.0493835 | + | 0.998780i | \(0.484274\pi\) | |||||||
\(740\) | −11744.8 | −0.583441 | ||||||||
\(741\) | 253.830 | 0.0125839 | ||||||||
\(742\) | −4783.67 | −0.236676 | ||||||||
\(743\) | −2107.31 | −0.104051 | −0.0520253 | − | 0.998646i | \(-0.516568\pi\) | ||||
−0.0520253 | + | 0.998646i | \(0.516568\pi\) | |||||||
\(744\) | −6712.72 | −0.330780 | ||||||||
\(745\) | −10489.0 | −0.515820 | ||||||||
\(746\) | 4478.58 | 0.219802 | ||||||||
\(747\) | 4036.44 | 0.197705 | ||||||||
\(748\) | −7731.32 | −0.377921 | ||||||||
\(749\) | 17456.2 | 0.851584 | ||||||||
\(750\) | 2593.88 | 0.126287 | ||||||||
\(751\) | −31313.5 | −1.52150 | −0.760750 | − | 0.649044i | \(-0.775169\pi\) | ||||
−0.760750 | + | 0.649044i | \(0.775169\pi\) | |||||||
\(752\) | 1192.09 | 0.0578072 | ||||||||
\(753\) | −11619.9 | −0.562353 | ||||||||
\(754\) | 472.082 | 0.0228014 | ||||||||
\(755\) | −246.913 | −0.0119021 | ||||||||
\(756\) | 1944.83 | 0.0935620 | ||||||||
\(757\) | −29093.4 | −1.39686 | −0.698428 | − | 0.715681i | \(-0.746117\pi\) | ||||
−0.698428 | + | 0.715681i | \(0.746117\pi\) | |||||||
\(758\) | −4827.46 | −0.231321 | ||||||||
\(759\) | 3495.81 | 0.167180 | ||||||||
\(760\) | 1208.73 | 0.0576913 | ||||||||
\(761\) | 12126.2 | 0.577627 | 0.288814 | − | 0.957385i | \(-0.406739\pi\) | ||||
0.288814 | + | 0.957385i | \(0.406739\pi\) | |||||||
\(762\) | 116.258 | 0.00552701 | ||||||||
\(763\) | 5646.29 | 0.267902 | ||||||||
\(764\) | −370.055 | −0.0175237 | ||||||||
\(765\) | 4853.22 | 0.229370 | ||||||||
\(766\) | −6103.15 | −0.287880 | ||||||||
\(767\) | −902.324 | −0.0424785 | ||||||||
\(768\) | −5585.51 | −0.262434 | ||||||||
\(769\) | −33071.4 | −1.55083 | −0.775414 | − | 0.631454i | \(-0.782459\pi\) | ||||
−0.775414 | + | 0.631454i | \(0.782459\pi\) | |||||||
\(770\) | −420.301 | −0.0196709 | ||||||||
\(771\) | 5241.77 | 0.244848 | ||||||||
\(772\) | 6282.98 | 0.292914 | ||||||||
\(773\) | −8450.24 | −0.393188 | −0.196594 | − | 0.980485i | \(-0.562988\pi\) | ||||
−0.196594 | + | 0.980485i | \(0.562988\pi\) | |||||||
\(774\) | −780.787 | −0.0362594 | ||||||||
\(775\) | −19118.3 | −0.886130 | ||||||||
\(776\) | 14843.4 | 0.686658 | ||||||||
\(777\) | 7772.51 | 0.358864 | ||||||||
\(778\) | 5207.54 | 0.239973 | ||||||||
\(779\) | −7835.27 | −0.360369 | ||||||||
\(780\) | −564.588 | −0.0259173 | ||||||||
\(781\) | −11234.4 | −0.514721 | ||||||||
\(782\) | 6843.61 | 0.312950 | ||||||||
\(783\) | 4252.44 | 0.194087 | ||||||||
\(784\) | −13257.5 | −0.603934 | ||||||||
\(785\) | 17518.1 | 0.796495 | ||||||||
\(786\) | 2158.50 | 0.0979530 | ||||||||
\(787\) | 16384.4 | 0.742109 | 0.371054 | − | 0.928611i | \(-0.378996\pi\) | ||||
0.371054 | + | 0.928611i | \(0.378996\pi\) | |||||||
\(788\) | −12523.0 | −0.566134 | ||||||||
\(789\) | −4563.46 | −0.205911 | ||||||||
\(790\) | 4263.39 | 0.192006 | ||||||||
\(791\) | −7488.85 | −0.336628 | ||||||||
\(792\) | −1062.44 | −0.0476670 | ||||||||
\(793\) | 264.454 | 0.0118424 | ||||||||
\(794\) | 1738.48 | 0.0777033 | ||||||||
\(795\) | 12509.2 | 0.558059 | ||||||||
\(796\) | 33664.4 | 1.49900 | ||||||||
\(797\) | 17380.6 | 0.772463 | 0.386232 | − | 0.922402i | \(-0.373776\pi\) | ||||
0.386232 | + | 0.922402i | \(0.373776\pi\) | |||||||
\(798\) | −387.644 | −0.0171961 | ||||||||
\(799\) | −2111.37 | −0.0934857 | ||||||||
\(800\) | 11216.9 | 0.495721 | ||||||||
\(801\) | −9164.40 | −0.404255 | ||||||||
\(802\) | −9164.26 | −0.403493 | ||||||||
\(803\) | 10451.4 | 0.459306 | ||||||||
\(804\) | 9967.57 | 0.437225 | ||||||||
\(805\) | −5854.34 | −0.256321 | ||||||||
\(806\) | −624.957 | −0.0273116 | ||||||||
\(807\) | 14973.3 | 0.653143 | ||||||||
\(808\) | −14659.2 | −0.638254 | ||||||||
\(809\) | 29376.8 | 1.27668 | 0.638339 | − | 0.769755i | \(-0.279622\pi\) | ||||
0.638339 | + | 0.769755i | \(0.279622\pi\) | |||||||
\(810\) | 323.196 | 0.0140197 | ||||||||
\(811\) | 21916.4 | 0.948936 | 0.474468 | − | 0.880273i | \(-0.342640\pi\) | ||||
0.474468 | + | 0.880273i | \(0.342640\pi\) | |||||||
\(812\) | 11344.7 | 0.490297 | ||||||||
\(813\) | −4133.91 | −0.178330 | ||||||||
\(814\) | −2057.64 | −0.0885998 | ||||||||
\(815\) | 8517.73 | 0.366090 | ||||||||
\(816\) | 14788.4 | 0.634434 | ||||||||
\(817\) | −2448.89 | −0.104866 | ||||||||
\(818\) | 2763.20 | 0.118109 | ||||||||
\(819\) | 373.636 | 0.0159413 | ||||||||
\(820\) | 17427.8 | 0.742201 | ||||||||
\(821\) | 26037.6 | 1.10685 | 0.553423 | − | 0.832901i | \(-0.313321\pi\) | ||||
0.553423 | + | 0.832901i | \(0.313321\pi\) | |||||||
\(822\) | −1280.17 | −0.0543199 | ||||||||
\(823\) | 18719.8 | 0.792869 | 0.396435 | − | 0.918063i | \(-0.370247\pi\) | ||||
0.396435 | + | 0.918063i | \(0.370247\pi\) | |||||||
\(824\) | −374.895 | −0.0158496 | ||||||||
\(825\) | −3025.92 | −0.127696 | ||||||||
\(826\) | 1378.01 | 0.0580473 | ||||||||
\(827\) | 3873.31 | 0.162864 | 0.0814319 | − | 0.996679i | \(-0.474051\pi\) | ||||
0.0814319 | + | 0.996679i | \(0.474051\pi\) | |||||||
\(828\) | −7171.47 | −0.300997 | ||||||||
\(829\) | −29488.0 | −1.23542 | −0.617708 | − | 0.786407i | \(-0.711939\pi\) | ||||
−0.617708 | + | 0.786407i | \(0.711939\pi\) | |||||||
\(830\) | 1789.52 | 0.0748377 | ||||||||
\(831\) | −3698.30 | −0.154383 | ||||||||
\(832\) | −1463.04 | −0.0609638 | ||||||||
\(833\) | 23481.2 | 0.976680 | ||||||||
\(834\) | 1525.44 | 0.0633353 | ||||||||
\(835\) | 5887.55 | 0.244008 | ||||||||
\(836\) | −1614.83 | −0.0668063 | ||||||||
\(837\) | −5629.51 | −0.232478 | ||||||||
\(838\) | −11286.0 | −0.465235 | ||||||||
\(839\) | 18869.6 | 0.776460 | 0.388230 | − | 0.921562i | \(-0.373087\pi\) | ||||
0.388230 | + | 0.921562i | \(0.373087\pi\) | |||||||
\(840\) | 1779.25 | 0.0730832 | ||||||||
\(841\) | 416.542 | 0.0170791 | ||||||||
\(842\) | 4346.07 | 0.177880 | ||||||||
\(843\) | 7106.50 | 0.290345 | ||||||||
\(844\) | 1774.19 | 0.0723579 | ||||||||
\(845\) | 12570.6 | 0.511767 | ||||||||
\(846\) | −140.605 | −0.00571408 | ||||||||
\(847\) | 1158.70 | 0.0470053 | ||||||||
\(848\) | 38117.4 | 1.54358 | ||||||||
\(849\) | 2950.34 | 0.119264 | ||||||||
\(850\) | −5923.72 | −0.239038 | ||||||||
\(851\) | −28660.7 | −1.15450 | ||||||||
\(852\) | 23046.7 | 0.926722 | ||||||||
\(853\) | −27104.8 | −1.08799 | −0.543993 | − | 0.839090i | \(-0.683088\pi\) | ||||
−0.543993 | + | 0.839090i | \(0.683088\pi\) | |||||||
\(854\) | −403.868 | −0.0161828 | ||||||||
\(855\) | 1013.69 | 0.0405466 | ||||||||
\(856\) | 19562.9 | 0.781130 | ||||||||
\(857\) | 4563.91 | 0.181914 | 0.0909569 | − | 0.995855i | \(-0.471007\pi\) | ||||
0.0909569 | + | 0.995855i | \(0.471007\pi\) | |||||||
\(858\) | −98.9139 | −0.00393574 | ||||||||
\(859\) | −6440.88 | −0.255833 | −0.127916 | − | 0.991785i | \(-0.540829\pi\) | ||||
−0.127916 | + | 0.991785i | \(0.540829\pi\) | |||||||
\(860\) | 5447.00 | 0.215978 | ||||||||
\(861\) | −11533.4 | −0.456514 | ||||||||
\(862\) | −8551.16 | −0.337881 | ||||||||
\(863\) | 8935.24 | 0.352444 | 0.176222 | − | 0.984350i | \(-0.443612\pi\) | ||||
0.176222 | + | 0.984350i | \(0.443612\pi\) | |||||||
\(864\) | 3302.88 | 0.130054 | ||||||||
\(865\) | 19822.5 | 0.779175 | ||||||||
\(866\) | −8648.32 | −0.339355 | ||||||||
\(867\) | −11453.6 | −0.448656 | ||||||||
\(868\) | −15018.5 | −0.587281 | ||||||||
\(869\) | −11753.5 | −0.458814 | ||||||||
\(870\) | 1885.29 | 0.0734680 | ||||||||
\(871\) | 1914.94 | 0.0744953 | ||||||||
\(872\) | 6327.71 | 0.245738 | ||||||||
\(873\) | 12448.2 | 0.482597 | ||||||||
\(874\) | 1429.42 | 0.0553212 | ||||||||
\(875\) | 11975.5 | 0.462680 | ||||||||
\(876\) | −21440.6 | −0.826952 | ||||||||
\(877\) | −22372.5 | −0.861419 | −0.430710 | − | 0.902491i | \(-0.641737\pi\) | ||||
−0.430710 | + | 0.902491i | \(0.641737\pi\) | |||||||
\(878\) | 6712.19 | 0.258002 | ||||||||
\(879\) | 18980.6 | 0.728327 | ||||||||
\(880\) | 3349.06 | 0.128292 | ||||||||
\(881\) | 30759.5 | 1.17629 | 0.588147 | − | 0.808754i | \(-0.299858\pi\) | ||||
0.588147 | + | 0.808754i | \(0.299858\pi\) | |||||||
\(882\) | 1563.71 | 0.0596972 | ||||||||
\(883\) | −15736.3 | −0.599740 | −0.299870 | − | 0.953980i | \(-0.596943\pi\) | ||||
−0.299870 | + | 0.953980i | \(0.596943\pi\) | |||||||
\(884\) | 3047.06 | 0.115932 | ||||||||
\(885\) | −3603.48 | −0.136870 | ||||||||
\(886\) | −8573.17 | −0.325081 | ||||||||
\(887\) | −24637.2 | −0.932621 | −0.466310 | − | 0.884621i | \(-0.654417\pi\) | ||||
−0.466310 | + | 0.884621i | \(0.654417\pi\) | |||||||
\(888\) | 8710.54 | 0.329174 | ||||||||
\(889\) | 536.741 | 0.0202494 | ||||||||
\(890\) | −4062.96 | −0.153023 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | 25888.4 | 0.971757 | ||||||||
\(893\) | −441.000 | −0.0165258 | ||||||||
\(894\) | 3769.80 | 0.141030 | ||||||||
\(895\) | 100.168 | 0.00374108 | ||||||||
\(896\) | 11605.7 | 0.432724 | ||||||||
\(897\) | −1377.76 | −0.0512845 | ||||||||
\(898\) | 4461.09 | 0.165778 | ||||||||
\(899\) | −32838.4 | −1.21827 | ||||||||
\(900\) | 6207.51 | 0.229908 | ||||||||
\(901\) | −67511.9 | −2.49628 | ||||||||
\(902\) | 3053.28 | 0.112709 | ||||||||
\(903\) | −3604.74 | −0.132844 | ||||||||
\(904\) | −8392.65 | −0.308778 | ||||||||
\(905\) | −17906.0 | −0.657698 | ||||||||
\(906\) | 88.7422 | 0.00325415 | ||||||||
\(907\) | −1540.61 | −0.0564003 | −0.0282001 | − | 0.999602i | \(-0.508978\pi\) | ||||
−0.0282001 | + | 0.999602i | \(0.508978\pi\) | |||||||
\(908\) | 18151.3 | 0.663404 | ||||||||
\(909\) | −12293.7 | −0.448577 | ||||||||
\(910\) | 165.649 | 0.00603429 | ||||||||
\(911\) | 14440.4 | 0.525174 | 0.262587 | − | 0.964908i | \(-0.415424\pi\) | ||||
0.262587 | + | 0.964908i | \(0.415424\pi\) | |||||||
\(912\) | 3088.84 | 0.112151 | ||||||||
\(913\) | −4933.43 | −0.178831 | ||||||||
\(914\) | −520.970 | −0.0188536 | ||||||||
\(915\) | 1056.11 | 0.0381573 | ||||||||
\(916\) | 34188.6 | 1.23321 | ||||||||
\(917\) | 9965.37 | 0.358872 | ||||||||
\(918\) | −1744.28 | −0.0627121 | ||||||||
\(919\) | 51492.4 | 1.84829 | 0.924145 | − | 0.382041i | \(-0.124779\pi\) | ||||
0.924145 | + | 0.382041i | \(0.124779\pi\) | |||||||
\(920\) | −6560.88 | −0.235115 | ||||||||
\(921\) | 502.439 | 0.0179760 | ||||||||
\(922\) | 11302.2 | 0.403708 | ||||||||
\(923\) | 4427.67 | 0.157897 | ||||||||
\(924\) | −2377.02 | −0.0846300 | ||||||||
\(925\) | 24808.3 | 0.881828 | ||||||||
\(926\) | −3298.18 | −0.117046 | ||||||||
\(927\) | −314.400 | −0.0111394 | ||||||||
\(928\) | 19266.5 | 0.681525 | ||||||||
\(929\) | 14890.5 | 0.525878 | 0.262939 | − | 0.964813i | \(-0.415308\pi\) | ||||
0.262939 | + | 0.964813i | \(0.415308\pi\) | |||||||
\(930\) | −2495.80 | −0.0880006 | ||||||||
\(931\) | 4904.49 | 0.172651 | ||||||||
\(932\) | 28664.4 | 1.00744 | ||||||||
\(933\) | −14515.2 | −0.509332 | ||||||||
\(934\) | 7918.13 | 0.277397 | ||||||||
\(935\) | −5931.71 | −0.207473 | ||||||||
\(936\) | 418.729 | 0.0146224 | ||||||||
\(937\) | 14349.8 | 0.500305 | 0.250153 | − | 0.968206i | \(-0.419519\pi\) | ||||
0.250153 | + | 0.968206i | \(0.419519\pi\) | |||||||
\(938\) | −2924.46 | −0.101798 | ||||||||
\(939\) | 21617.3 | 0.751282 | ||||||||
\(940\) | 980.905 | 0.0340357 | ||||||||
\(941\) | −47139.8 | −1.63307 | −0.816533 | − | 0.577299i | \(-0.804107\pi\) | ||||
−0.816533 | + | 0.577299i | \(0.804107\pi\) | |||||||
\(942\) | −6296.13 | −0.217770 | ||||||||
\(943\) | 42529.0 | 1.46865 | ||||||||
\(944\) | −10980.3 | −0.378579 | ||||||||
\(945\) | 1492.14 | 0.0513642 | ||||||||
\(946\) | 954.295 | 0.0327979 | ||||||||
\(947\) | 10424.6 | 0.357714 | 0.178857 | − | 0.983875i | \(-0.442760\pi\) | ||||
0.178857 | + | 0.983875i | \(0.442760\pi\) | |||||||
\(948\) | 24111.7 | 0.826066 | ||||||||
\(949\) | −4119.11 | −0.140898 | ||||||||
\(950\) | −1237.28 | −0.0422555 | ||||||||
\(951\) | 18193.8 | 0.620374 | ||||||||
\(952\) | −9602.52 | −0.326911 | ||||||||
\(953\) | −18189.2 | −0.618264 | −0.309132 | − | 0.951019i | \(-0.600038\pi\) | ||||
−0.309132 | + | 0.951019i | \(0.600038\pi\) | |||||||
\(954\) | −4495.90 | −0.152579 | ||||||||
\(955\) | −283.918 | −0.00962027 | ||||||||
\(956\) | 140.727 | 0.00476091 | ||||||||
\(957\) | −5197.43 | −0.175558 | ||||||||
\(958\) | −1980.64 | −0.0667969 | ||||||||
\(959\) | −5910.29 | −0.199013 | ||||||||
\(960\) | −5842.74 | −0.196431 | ||||||||
\(961\) | 13681.4 | 0.459248 | ||||||||
\(962\) | 810.955 | 0.0271790 | ||||||||
\(963\) | 16406.1 | 0.548993 | ||||||||
\(964\) | −24899.5 | −0.831908 | ||||||||
\(965\) | 4820.50 | 0.160805 | ||||||||
\(966\) | 2104.09 | 0.0700807 | ||||||||
\(967\) | −8458.98 | −0.281305 | −0.140653 | − | 0.990059i | \(-0.544920\pi\) | ||||
−0.140653 | + | 0.990059i | \(0.544920\pi\) | |||||||
\(968\) | 1298.54 | 0.0431164 | ||||||||
\(969\) | −5470.82 | −0.181370 | ||||||||
\(970\) | 5518.80 | 0.182678 | ||||||||
\(971\) | −11544.2 | −0.381535 | −0.190767 | − | 0.981635i | \(-0.561098\pi\) | ||||
−0.190767 | + | 0.981635i | \(0.561098\pi\) | |||||||
\(972\) | 1827.84 | 0.0603169 | ||||||||
\(973\) | 7042.66 | 0.232042 | ||||||||
\(974\) | 7938.95 | 0.261171 | ||||||||
\(975\) | 1192.57 | 0.0391721 | ||||||||
\(976\) | 3218.12 | 0.105542 | ||||||||
\(977\) | −30832.8 | −1.00965 | −0.504825 | − | 0.863222i | \(-0.668443\pi\) | ||||
−0.504825 | + | 0.863222i | \(0.668443\pi\) | |||||||
\(978\) | −3061.33 | −0.100093 | ||||||||
\(979\) | 11200.9 | 0.365662 | ||||||||
\(980\) | −10908.9 | −0.355584 | ||||||||
\(981\) | 5306.63 | 0.172709 | ||||||||
\(982\) | 11516.3 | 0.374235 | ||||||||
\(983\) | −17920.8 | −0.581471 | −0.290736 | − | 0.956803i | \(-0.593900\pi\) | ||||
−0.290736 | + | 0.956803i | \(0.593900\pi\) | |||||||
\(984\) | −12925.4 | −0.418746 | ||||||||
\(985\) | −9608.03 | −0.310799 | ||||||||
\(986\) | −10174.8 | −0.328633 | ||||||||
\(987\) | −649.149 | −0.0209348 | ||||||||
\(988\) | 636.436 | 0.0204936 | ||||||||
\(989\) | 13292.3 | 0.427372 | ||||||||
\(990\) | −395.018 | −0.0126813 | ||||||||
\(991\) | −58693.2 | −1.88138 | −0.940691 | − | 0.339265i | \(-0.889822\pi\) | ||||
−0.940691 | + | 0.339265i | \(0.889822\pi\) | |||||||
\(992\) | −25505.6 | −0.816336 | ||||||||
\(993\) | 27711.7 | 0.885603 | ||||||||
\(994\) | −6761.84 | −0.215767 | ||||||||
\(995\) | 25828.4 | 0.822930 | ||||||||
\(996\) | 10120.7 | 0.321974 | ||||||||
\(997\) | 1278.85 | 0.0406236 | 0.0203118 | − | 0.999794i | \(-0.493534\pi\) | ||||
0.0203118 | + | 0.999794i | \(0.493534\pi\) | |||||||
\(998\) | −92.5956 | −0.00293694 | ||||||||
\(999\) | 7304.95 | 0.231350 |
(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 | 2013.4.a.b.1.16 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.4.a.b.1.16 | ✓ | 36 | 1.1 | even | 1 | trivial |