Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(109.507544971\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 232) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.254102\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.04399 | 1.74052 | 0.870259 | − | 0.492595i | \(-0.163952\pi\) | ||||
0.870259 | + | 0.492595i | \(0.163952\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.15672 | −0.192903 | −0.0964515 | − | 0.995338i | \(-0.530749\pi\) | ||||
−0.0964515 | + | 0.995338i | \(0.530749\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −27.7969 | −1.50089 | −0.750446 | − | 0.660932i | \(-0.770161\pi\) | ||||
−0.750446 | + | 0.660932i | \(0.770161\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 54.7938 | 2.02940 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.351483 | −0.00963419 | −0.00481709 | − | 0.999988i | \(-0.501533\pi\) | ||||
−0.00481709 | + | 0.999988i | \(0.501533\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 65.3652 | 1.39454 | 0.697271 | − | 0.716807i | \(-0.254397\pi\) | ||||
0.697271 | + | 0.716807i | \(0.254397\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −19.5054 | −0.335751 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −68.3296 | −0.974845 | −0.487422 | − | 0.873166i | \(-0.662063\pi\) | ||||
−0.487422 | + | 0.873166i | \(0.662063\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 89.8292 | 1.08464 | 0.542322 | − | 0.840171i | \(-0.317545\pi\) | ||||
0.542322 | + | 0.840171i | \(0.317545\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −251.395 | −2.61233 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −110.709 | −1.00367 | −0.501834 | − | 0.864964i | \(-0.667341\pi\) | ||||
−0.501834 | + | 0.864964i | \(0.667341\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −120.349 | −0.962788 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 251.367 | 1.79169 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 258.256 | 1.49626 | 0.748132 | − | 0.663550i | \(-0.230951\pi\) | ||||
0.748132 | + | 0.663550i | \(0.230951\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.17881 | −0.0167685 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 59.9501 | 0.289526 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 128.225 | 0.569733 | 0.284866 | − | 0.958567i | \(-0.408051\pi\) | ||||
0.284866 | + | 0.958567i | \(0.408051\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 591.163 | 2.42723 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 283.005 | 1.07800 | 0.539000 | − | 0.842306i | \(-0.318802\pi\) | ||||
0.539000 | + | 0.842306i | \(0.318802\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 339.318 | 1.20338 | 0.601692 | − | 0.798728i | \(-0.294493\pi\) | ||||
0.601692 | + | 0.798728i | \(0.294493\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −118.175 | −0.391477 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 147.455 | 0.457628 | 0.228814 | − | 0.973470i | \(-0.426515\pi\) | ||||
0.228814 | + | 0.973470i | \(0.426515\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 429.668 | 1.25268 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −617.972 | −1.69673 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −518.354 | −1.34342 | −0.671712 | − | 0.740813i | \(-0.734441\pi\) | ||||
−0.671712 | + | 0.740813i | \(0.734441\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.758050 | 0.00185846 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 812.414 | 1.88784 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −102.347 | −0.225838 | −0.112919 | − | 0.993604i | \(-0.536020\pi\) | ||||
−0.112919 | + | 0.993604i | \(0.536020\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 791.964 | 1.66230 | 0.831152 | − | 0.556045i | \(-0.187682\pi\) | ||||
0.831152 | + | 0.556045i | \(0.187682\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1523.10 | −3.04591 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −140.975 | −0.269011 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 287.326 | 0.523918 | 0.261959 | − | 0.965079i | \(-0.415632\pi\) | ||||
0.261959 | + | 0.965079i | \(0.415632\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1001.25 | −1.74690 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 546.837 | 0.914050 | 0.457025 | − | 0.889454i | \(-0.348915\pi\) | ||||
0.457025 | + | 0.889454i | \(0.348915\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −260.144 | −0.417089 | −0.208545 | − | 0.978013i | \(-0.566873\pi\) | ||||
−0.208545 | + | 0.978013i | \(0.566873\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1088.43 | −1.67575 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.77013 | 0.0144599 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 204.498 | 0.291238 | 0.145619 | − | 0.989341i | \(-0.453483\pi\) | ||||
0.145619 | + | 0.989341i | \(0.453483\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 793.927 | 1.08906 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −949.003 | −1.25502 | −0.627510 | − | 0.778609i | \(-0.715926\pi\) | ||||
−0.627510 | + | 0.778609i | \(0.715926\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 147.368 | 0.188050 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 262.276 | 0.323206 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1390.02 | 1.65553 | 0.827765 | − | 0.561074i | \(-0.189612\pi\) | ||||
0.827765 | + | 0.561074i | \(0.189612\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1816.95 | −2.09306 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2335.67 | 2.60427 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −193.736 | −0.209231 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1228.30 | 1.28572 | 0.642861 | − | 0.765983i | \(-0.277747\pi\) | ||||
0.642861 | + | 0.765983i | \(0.277747\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −19.2591 | −0.0195516 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1090.25 | −1.07410 | −0.537049 | − | 0.843551i | \(-0.680461\pi\) | ||||
−0.537049 | + | 0.843551i | \(0.680461\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1226.95 | 1.17374 | 0.586869 | − | 0.809682i | \(-0.300360\pi\) | ||||
0.586869 | + | 0.809682i | \(0.300360\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 542.189 | 0.503926 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −365.324 | −0.330067 | −0.165034 | − | 0.986288i | \(-0.552773\pi\) | ||||
−0.165034 | + | 0.986288i | \(0.552773\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1759.55 | 1.54619 | 0.773093 | − | 0.634292i | \(-0.218708\pi\) | ||||
0.773093 | + | 0.634292i | \(0.218708\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1159.67 | 0.991629 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1764.47 | −1.46891 | −0.734457 | − | 0.678655i | \(-0.762563\pi\) | ||||
−0.734457 | + | 0.678655i | \(0.762563\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 238.768 | 0.193610 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3581.61 | 2.83008 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1899.35 | 1.46314 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.88 | −0.999907 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2559.50 | 1.87628 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 529.148 | 0.378628 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1121.29 | 0.783453 | 0.391726 | − | 0.920082i | \(-0.371878\pi\) | ||||
0.391726 | + | 0.920082i | \(0.371878\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3068.79 | 2.09451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1276.32 | 0.851240 | 0.425620 | − | 0.904902i | \(-0.360056\pi\) | ||||
0.425620 | + | 0.904902i | \(0.360056\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2496.97 | −1.62793 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −542.128 | −0.345622 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1564.49 | −0.975644 | −0.487822 | − | 0.872943i | \(-0.662208\pi\) | ||||
−0.487822 | + | 0.872943i | \(0.662208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2231.83 | 1.36188 | 0.680940 | − | 0.732339i | \(-0.261572\pi\) | ||||
0.680940 | + | 0.732339i | \(0.261572\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1333.58 | 0.796509 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.9748 | −0.0134353 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −62.5449 | −0.0358212 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3885.91 | 2.18030 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3474.95 | 1.91060 | 0.955300 | − | 0.295639i | \(-0.0955326\pi\) | ||||
0.955300 | + | 0.295639i | \(0.0955326\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1061.60 | −0.572131 | −0.286066 | − | 0.958210i | \(-0.592348\pi\) | ||||
−0.286066 | + | 0.958210i | \(0.592348\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3744.04 | −1.97835 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −556.986 | −0.288634 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1664.40 | 0.846073 | 0.423036 | − | 0.906113i | \(-0.360964\pi\) | ||||
0.423036 | + | 0.906113i | \(0.360964\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4687.99 | −2.33825 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3077.36 | 1.50640 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −239.164 | −0.114925 | −0.0574624 | − | 0.998348i | \(-0.518301\pi\) | ||||
−0.0574624 | + | 0.998348i | \(0.518301\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.85580 | 0.00323469 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1330.43 | −0.616477 | −0.308238 | − | 0.951309i | \(-0.599739\pi\) | ||||
−0.308238 | + | 0.951309i | \(0.599739\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2075.61 | 0.944749 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4922.08 | 2.20118 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3007.36 | −1.32165 | −0.660824 | − | 0.750541i | \(-0.729793\pi\) | ||||
−0.660824 | + | 0.750541i | \(0.729793\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3345.32 | 1.44504 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −925.627 | −0.393076 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 722.292 | 0.301601 | 0.150801 | − | 0.988564i | \(-0.451815\pi\) | ||||
0.150801 | + | 0.988564i | \(0.451815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2763.91 | −1.13503 | −0.567514 | − | 0.823364i | \(-0.692095\pi\) | ||||
−0.567514 | + | 0.823364i | \(0.692095\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7162.51 | 2.89327 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −276.546 | −0.109903 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.0167 | 0.00939184 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6987.22 | −2.68913 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −719.960 | −0.272746 | −0.136373 | − | 0.990658i | \(-0.543545\pi\) | ||||
−0.136373 | + | 0.990658i | \(0.543545\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1020.08 | 0.380452 | 0.190226 | − | 0.981740i | \(-0.439078\pi\) | ||||
0.190226 | + | 0.981740i | \(0.439078\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1274.97 | −0.468219 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −182.348 | −0.0659482 | −0.0329741 | − | 0.999456i | \(-0.510498\pi\) | ||||
−0.0329741 | + | 0.999456i | \(0.510498\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3150.60 | 1.12231 | 0.561156 | − | 0.827710i | \(-0.310357\pi\) | ||||
0.561156 | + | 0.827710i | \(0.310357\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2598.58 | 0.911888 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −806.110 | −0.278709 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −610.363 | −0.207949 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6066.15 | −2.03684 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −31.5734 | −0.0104497 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2028.36 | 0.661793 | 0.330897 | − | 0.943667i | \(-0.392649\pi\) | ||||
0.330897 | + | 0.943667i | \(0.392649\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4945.59 | 1.59092 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −731.815 | −0.232136 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7178.72 | −2.24573 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2352.74 | −0.725951 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4466.38 | −1.35946 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1942.22 | 0.583232 | 0.291616 | − | 0.956535i | \(-0.405807\pi\) | ||||
0.291616 | + | 0.956535i | \(0.405807\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6594.35 | −1.95388 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3476.41 | 1.01646 | 0.508232 | − | 0.861220i | \(-0.330299\pi\) | ||||
0.508232 | + | 0.861220i | \(0.330299\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3015.30 | −0.870116 | −0.435058 | − | 0.900402i | \(-0.643272\pi\) | ||||
−0.435058 | + | 0.900402i | \(0.643272\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 88.3610 | 0.0251677 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5510.20 | 1.54929 | 0.774646 | − | 0.632395i | \(-0.217928\pi\) | ||||
0.774646 | + | 0.632395i | \(0.217928\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −318.019 | −0.0882778 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1849.48 | 0.506905 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1742.92 | −0.471716 | −0.235858 | − | 0.971787i | \(-0.575790\pi\) | ||||
−0.235858 | + | 0.971787i | \(0.575790\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1188.65 | −0.317707 | −0.158854 | − | 0.987302i | \(-0.550780\pi\) | ||||
−0.158854 | + | 0.987302i | \(0.550780\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 393.366 | 0.103846 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −926.673 | −0.241645 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5871.70 | 1.51258 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8582.78 | −2.18438 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4679.47 | 1.17675 | 0.588377 | − | 0.808587i | \(-0.299767\pi\) | ||||
0.588377 | + | 0.808587i | \(0.299767\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 38.9122 | 0.00966952 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1332.79 | 0.327305 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2223.42 | 0.539663 | 0.269831 | − | 0.962908i | \(-0.413032\pi\) | ||||
0.269831 | + | 0.962908i | \(0.413032\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3564.27 | −0.855107 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1589.02 | 0.376850 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6720.95 | −1.57579 | −0.787893 | − | 0.615813i | \(-0.788828\pi\) | ||||
−0.787893 | + | 0.615813i | \(0.788828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1117.95 | 0.259150 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12571.4 | 2.88148 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2842.85 | 0.644356 | 0.322178 | − | 0.946679i | \(-0.395585\pi\) | ||||
0.322178 | + | 0.946679i | \(0.395585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3793.02 | 0.850219 | 0.425109 | − | 0.905142i | \(-0.360236\pi\) | ||||
0.425109 | + | 0.905142i | \(0.360236\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16432.5 | −3.64300 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 42.3005 | 0.00927569 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6698.19 | −1.45291 | −0.726453 | − | 0.687216i | \(-0.758833\pi\) | ||||
−0.726453 | + | 0.687216i | \(0.758833\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14150.8 | 3.03652 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8532.95 | 1.81151 | 0.905753 | − | 0.423807i | \(-0.139306\pi\) | ||||
0.905753 | + | 0.423807i | \(0.139306\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9100.83 | −1.91162 | −0.955810 | − | 0.293986i | \(-0.905018\pi\) | ||||
−0.955810 | + | 0.293986i | \(0.905018\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1752.15 | −0.364170 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7866.66 | −1.61796 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −244.069 | −0.0496781 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11108.7 | 2.23782 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6416.32 | −1.27934 | −0.639668 | − | 0.768651i | \(-0.720928\pi\) | ||||
−0.639668 | + | 0.768651i | \(0.720928\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 220.734 | 0.0435649 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −88.3511 | −0.0172615 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7236.50 | −1.39966 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9431.99 | −1.80615 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9860.20 | −1.86948 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1708.04 | −0.320663 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9836.12 | 1.82859 | 0.914295 | − | 0.405050i | \(-0.132746\pi\) | ||||
0.914295 | + | 0.405050i | \(0.132746\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11096.5 | 2.04291 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6806.95 | −1.24112 | −0.620558 | − | 0.784161i | \(-0.713094\pi\) | ||||
−0.620558 | + | 0.784161i | \(0.713094\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1860.04 | 0.335896 | 0.167948 | − | 0.985796i | \(-0.446286\pi\) | ||||
0.167948 | + | 0.985796i | \(0.446286\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3284.90 | 0.587565 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2326.51 | −0.412208 | −0.206104 | − | 0.978530i | \(-0.566078\pi\) | ||||
−0.206104 | + | 0.978530i | \(0.566078\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.1930 | −0.00178902 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3303.98 | −0.574487 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6137.99 | −1.05736 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7866.61 | −1.34265 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15913.4 | 2.69116 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4098.79 | −0.686850 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1668.98 | −0.277146 | −0.138573 | − | 0.990352i | \(-0.544252\pi\) | ||||
−0.138573 | + | 0.990352i | \(0.544252\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7025.95 | 1.15622 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −619.682 | −0.101065 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9794.95 | −1.58328 | −0.791639 | − | 0.610989i | \(-0.790772\pi\) | ||||
−0.791639 | + | 0.610989i | \(0.790772\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15957.8 | −2.55667 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −90.7726 | −0.0144153 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2409.09 | −0.379238 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2159.41 | 0.336982 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2296.52 | −0.355285 | −0.177642 | − | 0.984095i | \(-0.556847\pi\) | ||||
−0.177642 | + | 0.984095i | \(0.556847\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9856.35 | −1.51174 | −0.755871 | − | 0.654720i | \(-0.772786\pi\) | ||||
−0.755871 | + | 0.654720i | \(0.772786\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16430.7 | 2.49858 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10005.5 | −1.50860 | −0.754301 | − | 0.656528i | \(-0.772024\pi\) | ||||
−0.754301 | + | 0.656528i | \(0.772024\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1179.37 | −0.176323 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17177.7 | 2.54661 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −176.590 | −0.0259612 | −0.0129806 | − | 0.999916i | \(-0.504132\pi\) | ||||
−0.0129806 | + | 0.999916i | \(0.504132\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1210.28 | 0.176451 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12036.4 | −1.74036 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 561.057 | 0.0804577 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −50.2297 | −0.00714433 | −0.00357216 | − | 0.999994i | \(-0.501137\pi\) | ||||
−0.00357216 | + | 0.999994i | \(0.501137\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15506.9 | 2.18769 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14408.6 | 2.01633 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10666.6 | 1.48068 | 0.740340 | − | 0.672232i | \(-0.234664\pi\) | ||||
0.740340 | + | 0.672232i | \(0.234664\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4785.61 | 0.659008 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1895.59 | 0.258960 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4158.76 | −0.563644 | −0.281822 | − | 0.959467i | \(-0.590939\pi\) | ||||
−0.281822 | + | 0.959467i | \(0.590939\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10140.9 | 1.36361 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10572.2 | 1.41049 | 0.705243 | − | 0.708965i | \(-0.250838\pi\) | ||||
0.705243 | + | 0.708965i | \(0.250838\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.0714 | −0.00278935 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18592.5 | 2.44215 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8211.23 | 1.07025 | 0.535123 | − | 0.844774i | \(-0.320265\pi\) | ||||
0.535123 | + | 0.844774i | \(0.320265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7564.68 | 0.978420 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11543.0 | 1.48160 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −441.045 | −0.0561807 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4879.38 | −0.616849 | −0.308424 | − | 0.951249i | \(-0.599802\pi\) | ||||
−0.308424 | + | 0.951249i | \(0.599802\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22582.6 | −2.83344 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7570.58 | 0.942785 | 0.471393 | − | 0.881923i | \(-0.343751\pi\) | ||||
0.471393 | + | 0.881923i | \(0.343751\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16881.0 | 2.08660 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1712.28 | −0.210084 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −45.0690 | −0.00548891 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11758.1 | −1.42152 | −0.710760 | − | 0.703435i | \(-0.751649\pi\) | ||||
−0.710760 | + | 0.703435i | \(0.751649\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14149.2 | −1.69812 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2844.93 | 0.338959 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2046.73 | 0.242097 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20184.6 | 2.37037 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10150.6 | 1.18351 | 0.591755 | − | 0.806118i | \(-0.298435\pi\) | ||||
0.591755 | + | 0.806118i | \(0.298435\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2822.78 | −0.326779 | −0.163390 | − | 0.986562i | \(-0.552243\pi\) | ||||
−0.163390 | + | 0.986562i | \(0.552243\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8079.62 | 0.928710 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8223.37 | 0.938569 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22014.1 | −2.49494 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −207.784 | −0.0233843 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6663.84 | 0.744747 | 0.372373 | − | 0.928083i | \(-0.378544\pi\) | ||||
0.372373 | + | 0.928083i | \(0.378544\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6591.27 | −0.731539 | −0.365769 | − | 0.930706i | \(-0.619194\pi\) | ||||
−0.365769 | + | 0.930706i | \(0.619194\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −565.656 | −0.0623474 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9944.87 | −1.08862 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12121.1 | −1.31778 | −0.658891 | − | 0.752238i | \(-0.728974\pi\) | ||||
−0.658891 | + | 0.752238i | \(0.728974\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 23543.1 | 2.54218 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9017.80 | 0.967152 | 0.483576 | − | 0.875302i | \(-0.339338\pi\) | ||||
0.483576 | + | 0.875302i | \(0.339338\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2997.89 | −0.319357 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31427.5 | 3.32543 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4485.59 | −0.471466 | −0.235733 | − | 0.971818i | \(-0.575749\pi\) | ||||
−0.235733 | + | 0.971818i | \(0.575749\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −99.4714 | −0.0103856 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9601.11 | −0.995805 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3918.66 | 0.403757 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7305.52 | 0.747785 | 0.373893 | − | 0.927472i | \(-0.378023\pi\) | ||||
0.373893 | + | 0.927472i | \(0.378023\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17175.8 | −1.74662 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1174.43 | −0.118652 | −0.0593259 | − | 0.998239i | \(-0.518895\pi\) | ||||
−0.0593259 | + | 0.998239i | \(0.518895\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7866.43 | −0.789598 | −0.394799 | − | 0.918768i | \(-0.629186\pi\) | ||||
−0.394799 | + | 0.918768i | \(0.629186\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5037.38 | −0.502372 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12691.8 | 1.25762 | 0.628810 | − | 0.777559i | \(-0.283542\pi\) | ||||
0.628810 | + | 0.777559i | \(0.283542\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7986.78 | −0.786344 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15052.8 | 1.47260 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −119.265 | −0.0115936 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10810.8 | −1.04428 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28402.6 | −2.72634 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11226.1 | −1.07084 | −0.535420 | − | 0.844586i | \(-0.679847\pi\) | ||||
−0.535420 | + | 0.844586i | \(0.679847\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8381.48 | 0.794516 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 27831.6 | 2.62191 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2649.10 | −0.248020 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2493.14 | −0.231981 | −0.115991 | − | 0.993250i | \(-0.537004\pi\) | ||||
−0.115991 | + | 0.993250i | \(0.537004\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2163.00 | −0.200029 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11346.8 | 1.04292 | 0.521458 | − | 0.853277i | \(-0.325388\pi\) | ||||
0.521458 | + | 0.853277i | \(0.325388\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1981.56 | −0.181024 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 41.5364 | 0.00377156 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15200.4 | −1.37189 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19216.1 | −1.72391 | −0.861956 | − | 0.506982i | \(-0.830761\pi\) | ||||
−0.861956 | + | 0.506982i | \(0.830761\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12032.4 | −1.07299 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9284.26 | 0.822991 | 0.411496 | − | 0.911412i | \(-0.365007\pi\) | ||||
0.411496 | + | 0.911412i | \(0.365007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2351.36 | 0.207196 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18771.8 | 1.64435 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2987.03 | −0.260113 | −0.130057 | − | 0.991507i | \(-0.541516\pi\) | ||||
−0.130057 | + | 0.991507i | \(0.541516\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7231.19 | 0.626006 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22580.1 | 1.94334 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2646.19 | −0.226418 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −51.8279 | −0.00440887 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27198.5 | −2.30035 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11082.9 | 0.931962 | 0.465981 | − | 0.884795i | \(-0.345702\pi\) | ||||
0.465981 | + | 0.884795i | \(0.345702\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13718.6 | 1.14698 | 0.573492 | − | 0.819211i | \(-0.305588\pi\) | ||||
0.573492 | + | 0.819211i | \(0.305588\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 30255.0 | 2.51512 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17646.5 | −1.45862 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 89.4044 | 0.00734811 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5607.99 | −0.458316 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18498.7 | 1.50332 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 787.901 | 0.0636709 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6532.40 | 0.524942 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −151.021 | −0.0120685 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9946.06 | −0.790415 | −0.395207 | − | 0.918592i | \(-0.629327\pi\) | ||||
−0.395207 | + | 0.918592i | \(0.629327\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24996.8 | −1.97553 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3794.86 | −0.298264 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14925.2 | −1.16665 | −0.583325 | − | 0.812239i | \(-0.698248\pi\) | ||||
−0.583325 | + | 0.812239i | \(0.698248\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 43394.7 | 3.37348 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2605.05 | 0.201413 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5684.40 | −0.437117 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2501.08 | −0.191288 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12187.8 | −0.927136 | −0.463568 | − | 0.886061i | \(-0.653431\pi\) | ||||
−0.463568 | + | 0.886061i | \(0.653431\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22179.6 | 1.67817 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 217.207 | 0.0163467 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25198.0 | −1.88627 | −0.943133 | − | 0.332415i | \(-0.892136\pi\) | ||||
−0.943133 | + | 0.332415i | \(0.892136\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3805.47 | 0.283358 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22068.7 | −1.63457 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14101.5 | −1.03895 | −0.519477 | − | 0.854485i | \(-0.673873\pi\) | ||||
−0.519477 | + | 0.854485i | \(0.673873\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21762.0 | 1.59494 | 0.797472 | − | 0.603356i | \(-0.206170\pi\) | ||||
0.797472 | + | 0.603356i | \(0.206170\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6511.31 | −0.474719 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13323.6 | 0.966319 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17435.4 | −1.25796 | −0.628982 | − | 0.777420i | \(-0.716528\pi\) | ||||
−0.628982 | + | 0.777420i | \(0.716528\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9225.63 | 0.662183 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26379.3 | 1.88365 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 182.193 | 0.0129428 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7724.53 | −0.545932 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18080.4 | −1.27131 | −0.635655 | − | 0.771974i | \(-0.719270\pi\) | ||||
−0.635655 | + | 0.771974i | \(0.719270\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23198.9 | 1.62291 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1649.16 | −0.114784 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24509.3 | −1.69726 | −0.848630 | − | 0.528987i | \(-0.822572\pi\) | ||||
−0.848630 | + | 0.528987i | \(0.822572\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4096.37 | −0.282243 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 28494.0 | 1.95340 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9457.05 | 0.645083 | 0.322541 | − | 0.946555i | \(-0.395463\pi\) | ||||
0.322541 | + | 0.946555i | \(0.395463\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11759.8 | −0.798158 | −0.399079 | − | 0.916917i | \(-0.630670\pi\) | ||||
−0.399079 | + | 0.916917i | \(0.630670\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15743.7 | 1.06324 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2870.33 | 0.192885 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17929.0 | −1.19887 | −0.599435 | − | 0.800424i | \(-0.704608\pi\) | ||||
−0.599435 | + | 0.800424i | \(0.704608\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7290.45 | −0.485097 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9638.43 | 0.638182 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −334.350 | −0.0220298 | −0.0110149 | − | 0.999939i | \(-0.503506\pi\) | ||||
−0.0110149 | + | 0.999939i | \(0.503506\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5520.12 | −0.361939 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23637.6 | 1.54233 | 0.771163 | − | 0.636638i | \(-0.219675\pi\) | ||||
0.771163 | + | 0.636638i | \(0.219675\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12855.8 | 0.834763 | 0.417381 | − | 0.908731i | \(-0.362948\pi\) | ||||
0.417381 | + | 0.908731i | \(0.362948\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27828.5 | −1.79826 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −38638.4 | −2.48477 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13902.3 | 0.889750 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −285.550 | −0.0181878 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8761.58 | −0.555401 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15364.3 | 0.969321 | 0.484660 | − | 0.874702i | \(-0.338943\pi\) | ||||
0.484660 | + | 0.874702i | \(0.338943\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18344.5 | 1.15186 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2418.31 | −0.151130 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28085.3 | 1.74691 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29963.2 | 1.85497 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4238.75 | 0.261186 | 0.130593 | − | 0.991436i | \(-0.458312\pi\) | ||||
0.130593 | + | 0.991436i | \(0.458312\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2694.68 | −0.165269 | −0.0826345 | − | 0.996580i | \(-0.526333\pi\) | ||||
−0.0826345 | + | 0.996580i | \(0.526333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6618.53 | −0.404037 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4728.45 | −0.287318 | −0.143659 | − | 0.989627i | \(-0.545887\pi\) | ||||
−0.143659 | + | 0.989627i | \(0.545887\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.9733 | 0.00217577 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −64924.3 | −3.90873 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2902.87 | 0.173963 | 0.0869817 | − | 0.996210i | \(-0.472278\pi\) | ||||
0.0869817 | + | 0.996210i | \(0.472278\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2752.66 | −0.164207 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14254.3 | −0.846440 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3791.51 | 0.224122 | 0.112061 | − | 0.993701i | \(-0.464255\pi\) | ||||
0.112061 | + | 0.993701i | \(0.464255\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7566.63 | −0.445246 | −0.222623 | − | 0.974905i | \(-0.571462\pi\) | ||||
−0.222623 | + | 0.974905i | \(0.571462\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −40393.9 | −2.36617 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5385.27 | 0.314033 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3210.55 | −0.186376 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17565.4 | 1.01513 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −278.362 | −0.0160150 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18220.4 | 1.04360 | 0.521801 | − | 0.853067i | \(-0.325260\pi\) | ||||
0.521801 | + | 0.853067i | \(0.325260\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −30251.6 | −1.72502 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24827.8 | −1.40947 | −0.704735 | − | 0.709470i | \(-0.748934\pi\) | ||||
−0.704735 | + | 0.709470i | \(0.748934\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34143.0 | −1.92973 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31440.6 | 1.76917 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7554.87 | −0.423249 | −0.211625 | − | 0.977351i | \(-0.567875\pi\) | ||||
−0.211625 | + | 0.977351i | \(0.567875\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3374.16 | 0.188205 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27270.3 | −1.51445 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33882.4 | −1.87346 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11730.1 | −0.645780 | −0.322890 | − | 0.946437i | \(-0.604654\pi\) | ||||
−0.322890 | + | 0.946437i | \(0.604654\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 535.343 | 0.0293449 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4813.43 | −0.262711 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19337.6 | −1.05088 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 49834.2 | 2.69657 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13791.3 | 0.743065 | 0.371533 | − | 0.928420i | \(-0.378832\pi\) | ||||
0.371533 | + | 0.928420i | \(0.378832\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11518.4 | 0.617957 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2876.16 | −0.153649 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30305.5 | 1.61210 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3236.05 | −0.171414 | −0.0857068 | − | 0.996320i | \(-0.527315\pi\) | ||||
−0.0857068 | + | 0.996320i | \(0.527315\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11205.2 | 0.591038 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28591.2 | −1.50175 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 49.5501 | 0.00259171 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15763.0 | −0.821030 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5692.08 | 0.295241 | 0.147621 | − | 0.989044i | \(-0.452839\pi\) | ||||
0.147621 | + | 0.989044i | \(0.452839\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34105.4 | −1.76165 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10750.1 | −0.552975 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3490.11 | −0.178785 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24211.1 | 1.23513 | 0.617565 | − | 0.786520i | \(-0.288119\pi\) | ||||
0.617565 | + | 0.786520i | \(0.288119\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17878.4 | −0.908318 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23185.5 | −1.17311 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35957.5 | −1.81190 | −0.905948 | − | 0.423390i | \(-0.860840\pi\) | ||||
−0.905948 | + | 0.423390i | \(0.860840\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8380.82 | −0.420587 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −100.990 | −0.00504752 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15533.2 | 0.773206 | 0.386603 | − | 0.922246i | \(-0.373648\pi\) | ||||
0.386603 | + | 0.922246i | \(0.373648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 53103.7 | 2.63267 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7606.78 | −0.375593 | −0.187797 | − | 0.982208i | \(-0.560135\pi\) | ||||
−0.187797 | + | 0.982208i | \(0.560135\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7494.50 | −0.368560 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −51999.5 | −2.54694 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10154.9 | 0.495395 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29108.6 | 1.41437 | 0.707183 | − | 0.707030i | \(-0.249965\pi\) | ||||
0.707183 | + | 0.707030i | \(0.249965\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 42321.1 | 2.04816 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2289.58 | 0.110366 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3291.98 | −0.158057 | −0.0790284 | − | 0.996872i | \(-0.525182\pi\) | ||||
−0.0790284 | + | 0.996872i | \(0.525182\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 351.922 | 0.0168300 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4341.98 | −0.206829 | −0.103414 | − | 0.994638i | \(-0.532977\pi\) | ||||
−0.103414 | + | 0.994638i | \(0.532977\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −48910.0 | −2.32066 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8074.84 | 0.381629 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6689.95 | −0.314941 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13820.2 | 0.648075 | 0.324038 | − | 0.946044i | \(-0.394960\pi\) | ||||
0.324038 | + | 0.946044i | \(0.394960\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20108.6 | 0.939292 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19762.4 | −0.919539 | −0.459769 | − | 0.888038i | \(-0.652068\pi\) | ||||
−0.459769 | + | 0.888038i | \(0.652068\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31080.8 | −1.44059 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −32235.2 | −1.48833 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25422.1 | 1.16924 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −192.204 | −0.00880613 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7289.64 | 0.332708 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3589.64 | −0.163210 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12090.5 | 0.547622 | 0.273811 | − | 0.961784i | \(-0.411716\pi\) | ||||
0.273811 | + | 0.961784i | \(0.411716\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −60784.2 | −2.74268 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 49046.8 | 2.20468 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 51766.9 | 2.31815 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10110.7 | 0.451056 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26490.3 | 1.17733 | 0.588667 | − | 0.808376i | \(-0.299653\pi\) | ||||
0.588667 | + | 0.808376i | \(0.299653\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10075.5 | −0.446116 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 76164.7 | 3.35973 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 91.4360 | 0.00401832 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6637.00 | −0.290588 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25710.7 | 1.12151 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21825.5 | −0.948508 | −0.474254 | − | 0.880388i | \(-0.657282\pi\) | ||||
−0.474254 | + | 0.880388i | \(0.657282\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28758.7 | 1.24520 | 0.622599 | − | 0.782541i | \(-0.286077\pi\) | ||||
0.622599 | + | 0.782541i | \(0.286077\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34304.0 | 1.47982 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 515.809 | 0.0221693 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30480.7 | 1.30524 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −99557.6 | −4.24765 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3491.27 | −0.148412 | −0.0742060 | − | 0.997243i | \(-0.523642\pi\) | ||||
−0.0742060 | + | 0.997243i | \(0.523642\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1472.33 | 0.0623597 | 0.0311799 | − | 0.999514i | \(-0.490074\pi\) | ||||
0.0311799 | + | 0.999514i | \(0.490074\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 382.565 | 0.0161445 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17843.8 | −0.750289 | −0.375145 | − | 0.926966i | \(-0.622407\pi\) | ||||
−0.375145 | + | 0.926966i | \(0.622407\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19574.7 | −0.820093 | −0.410047 | − | 0.912065i | \(-0.634488\pi\) | ||||
−0.410047 | + | 0.912065i | \(0.634488\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −60578.4 | −2.52881 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29359.0 | −1.22116 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2869.36 | 0.118920 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 64917.0 | 2.68084 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26014.0 | 1.07045 | 0.535223 | − | 0.844711i | \(-0.320228\pi\) | ||||
0.535223 | + | 0.844711i | \(0.320228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 77171.9 | 3.15296 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4476.52 | −0.182245 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36994.2 | 1.50075 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −82307.8 | −3.32721 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14195.6 | −0.571822 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17613.3 | −0.706996 | −0.353498 | − | 0.935435i | \(-0.615008\pi\) | ||||
−0.353498 | + | 0.935435i | \(0.615008\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10615.6 | −0.424613 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40047.5 | −1.59626 | −0.798130 | − | 0.602485i | \(-0.794177\pi\) | ||||
−0.798130 | + | 0.602485i | \(0.794177\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10686.0 | 0.424448 | 0.212224 | − | 0.977221i | \(-0.431929\pi\) | ||||
0.212224 | + | 0.977221i | \(0.431929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −71146.0 | −2.81609 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24243.4 | −0.956263 | −0.478131 | − | 0.878288i | \(-0.658686\pi\) | ||||
−0.478131 | + | 0.878288i | \(0.658686\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6486.02 | 0.254950 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2207.36 | −0.0864656 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −71.8775 | −0.00280584 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18781.1 | 0.730626 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 67303.3 | 2.60924 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14708.7 | −0.568279 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32542.0 | −1.25298 | −0.626491 | − | 0.779429i | \(-0.715509\pi\) | ||||
−0.626491 | + | 0.779429i | \(0.715509\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −58029.2 | −2.22671 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28538.8 | 1.09137 | 0.545686 | − | 0.837990i | \(-0.316269\pi\) | ||||
0.545686 | + | 0.837990i | \(0.316269\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3707.98 | −0.141317 | −0.0706587 | − | 0.997501i | \(-0.522510\pi\) | ||||
−0.0706587 | + | 0.997501i | \(0.522510\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1996.32 | 0.0758254 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4461.95 | −0.168904 | −0.0844519 | − | 0.996428i | \(-0.526914\pi\) | ||||
−0.0844519 | + | 0.996428i | \(0.526914\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31168.4 | −1.17588 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −279.052 | −0.0104922 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13245.8 | 0.496363 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1557.78 | −0.0581798 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −65446.8 | −2.43613 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7489.43 | 0.277849 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35418.9 | 1.30963 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −85302.9 | −3.14363 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5960.99 | 0.218950 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30719.9 | 1.12463 | 0.562313 | − | 0.826924i | \(-0.309912\pi\) | ||||
0.562313 | + | 0.826924i | \(0.309912\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −59738.9 | −2.17977 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22983.9 | −0.835886 | −0.417943 | − | 0.908473i | \(-0.637249\pi\) | ||||
−0.417943 | + | 0.908473i | \(0.637249\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 333.558 | 0.0120911 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15447.5 | −0.558120 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35477.7 | −1.27762 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52064.7 | 1.86883 | 0.934416 | − | 0.356183i | \(-0.115922\pi\) | ||||
0.934416 | + | 0.356183i | \(0.115922\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 88957.8 | 3.18269 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35744.1 | 1.27468 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15431.7 | −0.548532 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 67229.3 | 2.38199 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48448.1 | −1.71101 | −0.855506 | − | 0.517793i | \(-0.826754\pi\) | ||||
−0.855506 | + | 0.517793i | \(0.826754\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38596.7 | 1.35871 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −61562.0 | −2.16018 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −51.7973 | −0.00181171 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20972.3 | 0.731199 | 0.365600 | − | 0.930772i | \(-0.380864\pi\) | ||||
0.365600 | + | 0.930772i | \(0.380864\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16822.2 | 0.584633 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19883.9 | 0.688840 | 0.344420 | − | 0.938816i | \(-0.388076\pi\) | ||||
0.344420 | + | 0.938816i | \(0.388076\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31331.1 | −1.08195 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15069.5 | 0.518741 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45811.5 | −1.57199 | −0.785995 | − | 0.618233i | \(-0.787849\pi\) | ||||
−0.785995 | + | 0.618233i | \(0.787849\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17004.3 | −0.581649 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21040.9 | −0.717454 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24303.7 | −0.826101 | −0.413050 | − | 0.910708i | \(-0.635537\pi\) | ||||
−0.413050 | + | 0.910708i | \(0.635537\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1552.75 | 0.0526135 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −92.1854 | −0.00311383 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43487.9 | 1.46434 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36905.3 | 1.23881 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20017.5 | −0.669838 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2200.04 | −0.0733903 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46462.1 | −1.54511 | −0.772555 | − | 0.634948i | \(-0.781021\pi\) | ||||
−0.772555 | + | 0.634948i | \(0.781021\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −55511.9 | −1.84035 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5526.77 | −0.182660 | −0.0913298 | − | 0.995821i | \(-0.529112\pi\) | ||||
−0.0913298 | + | 0.995821i | \(0.529112\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −62037.9 | −2.04403 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −71145.6 | −2.33690 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12957.3 | 0.424300 | 0.212150 | − | 0.977237i | \(-0.431953\pi\) | ||||
0.212150 | + | 0.977237i | \(0.431953\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −488.570 | −0.0159497 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 96412.4 | 3.13783 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −57988.1 | −1.88152 | −0.940759 | − | 0.339076i | \(-0.889886\pi\) | ||||
−0.940759 | + | 0.339076i | \(0.889886\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 393.275 | 0.0127216 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −37069.4 | −1.19547 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −37565.5 | −1.20780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33344.7 | 1.06885 | 0.534425 | − | 0.845216i | \(-0.320528\pi\) | ||||
0.534425 | + | 0.845216i | \(0.320528\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15094.2 | −0.482378 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6794.96 | −0.216497 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13474.8 | 0.428034 | 0.214017 | − | 0.976830i | \(-0.431345\pi\) | ||||
0.214017 | + | 0.976830i | \(0.431345\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32231.6 | 1.02078 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1856.4.a.u.1.3 | 3 | ||
4.3 | odd | 2 | 1856.4.a.p.1.1 | 3 | |||
8.3 | odd | 2 | 232.4.a.b.1.3 | ✓ | 3 | ||
8.5 | even | 2 | 464.4.a.g.1.1 | 3 | |||
24.11 | even | 2 | 2088.4.a.b.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.4.a.b.1.3 | ✓ | 3 | 8.3 | odd | 2 | ||
464.4.a.g.1.1 | 3 | 8.5 | even | 2 | |||
1856.4.a.p.1.1 | 3 | 4.3 | odd | 2 | |||
1856.4.a.u.1.3 | 3 | 1.1 | even | 1 | trivial | ||
2088.4.a.b.1.2 | 3 | 24.11 | even | 2 |