Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | 0.268328 | 0.134164 | − | 0.990959i | \(-0.457165\pi\) | ||||
0.134164 | + | 0.990959i | \(0.457165\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.0000 | 0.411152 | 0.205576 | − | 0.978641i | \(-0.434093\pi\) | ||||
0.205576 | + | 0.978641i | \(0.434093\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 64.0000 | 1.36542 | 0.682708 | − | 0.730691i | \(-0.260802\pi\) | ||||
0.682708 | + | 0.730691i | \(0.260802\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.00000 | 0.154919 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −84.0000 | −1.19841 | −0.599206 | − | 0.800595i | \(-0.704517\pi\) | ||||
−0.599206 | + | 0.800595i | \(0.704517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.0000 | −0.193192 | −0.0965961 | − | 0.995324i | \(-0.530796\pi\) | ||||
−0.0965961 | + | 0.995324i | \(0.530796\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 84.0000 | 0.761531 | 0.380765 | − | 0.924672i | \(-0.375661\pi\) | ||||
0.380765 | + | 0.924672i | \(0.375661\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −116.000 | −0.928000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −297.000 | −1.90178 | −0.950888 | − | 0.309535i | \(-0.899827\pi\) | ||||
−0.950888 | + | 0.309535i | \(0.899827\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −253.000 | −1.46581 | −0.732906 | − | 0.680330i | \(-0.761836\pi\) | ||||
−0.732906 | + | 0.680330i | \(0.761836\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 45.0000 | 0.237379 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −316.000 | −1.40406 | −0.702028 | − | 0.712149i | \(-0.747722\pi\) | ||||
−0.702028 | + | 0.712149i | \(0.747722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 192.000 | 0.788323 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −360.000 | −1.37128 | −0.685641 | − | 0.727940i | \(-0.740478\pi\) | ||||
−0.685641 | + | 0.727940i | \(0.740478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −26.0000 | −0.0922084 | −0.0461042 | − | 0.998937i | \(-0.514681\pi\) | ||||
−0.0461042 | + | 0.998937i | \(0.514681\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 27.0000 | 0.0894427 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −30.0000 | −0.0931053 | −0.0465527 | − | 0.998916i | \(-0.514824\pi\) | ||||
−0.0465527 | + | 0.998916i | \(0.514824\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −252.000 | −0.691903 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 363.000 | 0.940790 | 0.470395 | − | 0.882456i | \(-0.344111\pi\) | ||||
0.470395 | + | 0.882456i | \(0.344111\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 45.0000 | 0.110324 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −48.0000 | −0.111540 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −15.0000 | −0.0330989 | −0.0165494 | − | 0.999863i | \(-0.505268\pi\) | ||||
−0.0165494 | + | 0.999863i | \(0.505268\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 118.000 | 0.247678 | 0.123839 | − | 0.992302i | \(-0.460479\pi\) | ||||
0.123839 | + | 0.992302i | \(0.460479\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 192.000 | 0.366380 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 370.000 | 0.674667 | 0.337334 | − | 0.941385i | \(-0.390475\pi\) | ||||
0.337334 | + | 0.941385i | \(0.390475\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 252.000 | 0.439670 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 342.000 | 0.571661 | 0.285831 | − | 0.958280i | \(-0.407731\pi\) | ||||
0.285831 | + | 0.958280i | \(0.407731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −362.000 | −0.580396 | −0.290198 | − | 0.956967i | \(-0.593721\pi\) | ||||
−0.290198 | + | 0.956967i | \(0.593721\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −348.000 | −0.535781 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −467.000 | −0.665084 | −0.332542 | − | 0.943089i | \(-0.607906\pi\) | ||||
−0.332542 | + | 0.943089i | \(0.607906\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 477.000 | 0.630814 | 0.315407 | − | 0.948957i | \(-0.397859\pi\) | ||||
0.315407 | + | 0.948957i | \(0.397859\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −252.000 | −0.321568 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −891.000 | −1.09799 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −906.000 | −1.07905 | −0.539527 | − | 0.841968i | \(-0.681397\pi\) | ||||
−0.539527 | + | 0.841968i | \(0.681397\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −759.000 | −0.846286 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −48.0000 | −0.0518389 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −503.000 | −0.526515 | −0.263257 | − | 0.964726i | \(-0.584797\pi\) | ||||
−0.263257 | + | 0.964726i | \(0.584797\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 135.000 | 0.137051 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1086.00 | 1.06991 | 0.534956 | − | 0.844880i | \(-0.320328\pi\) | ||||
0.534956 | + | 0.844880i | \(0.320328\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1736.00 | 1.66071 | 0.830355 | − | 0.557235i | \(-0.188138\pi\) | ||||
0.830355 | + | 0.557235i | \(0.188138\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1353.00 | 1.22242 | 0.611212 | − | 0.791467i | \(-0.290682\pi\) | ||||
0.611212 | + | 0.791467i | \(0.290682\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −370.000 | −0.325134 | −0.162567 | − | 0.986698i | \(-0.551977\pi\) | ||||
−0.162567 | + | 0.986698i | \(0.551977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −948.000 | −0.810632 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −648.000 | −0.539458 | −0.269729 | − | 0.962936i | \(-0.586934\pi\) | ||||
−0.269729 | + | 0.962936i | \(0.586934\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 252.000 | 0.204340 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 576.000 | 0.455139 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1106.00 | −0.830954 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1080.00 | −0.791710 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −723.000 | −0.517337 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −377.000 | −0.263412 | −0.131706 | − | 0.991289i | \(-0.542046\pi\) | ||||
−0.131706 | + | 0.991289i | \(0.542046\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −78.0000 | −0.0532366 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −651.000 | −0.434184 | −0.217092 | − | 0.976151i | \(-0.569657\pi\) | ||||
−0.217092 | + | 0.976151i | \(0.569657\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 81.0000 | 0.0516398 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1770.00 | −1.10381 | −0.551903 | − | 0.833909i | \(-0.686098\pi\) | ||||
−0.551903 | + | 0.833909i | \(0.686098\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1558.00 | −0.950704 | −0.475352 | − | 0.879796i | \(-0.657679\pi\) | ||||
−0.475352 | + | 0.879796i | \(0.657679\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −90.0000 | −0.0537544 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 960.000 | 0.561393 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −891.000 | −0.510300 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2454.00 | 1.34926 | 0.674629 | − | 0.738157i | \(-0.264304\pi\) | ||||
0.674629 | + | 0.738157i | \(0.264304\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1259.00 | −0.678516 | −0.339258 | − | 0.940693i | \(-0.610176\pi\) | ||||
−0.339258 | + | 0.940693i | \(0.610176\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −756.000 | −0.399470 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −759.000 | −0.393318 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 196.000 | 0.0996338 | 0.0498169 | − | 0.998758i | \(-0.484136\pi\) | ||||
0.0498169 | + | 0.998758i | \(0.484136\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1089.00 | 0.543166 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1252.00 | 0.601621 | 0.300810 | − | 0.953684i | \(-0.402743\pi\) | ||||
0.300810 | + | 0.953684i | \(0.402743\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 135.000 | 0.0636954 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2646.00 | −1.22607 | −0.613035 | − | 0.790056i | \(-0.710051\pi\) | ||||
−0.613035 | + | 0.790056i | \(0.710051\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1899.00 | 0.864360 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −144.000 | −0.0643974 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 786.000 | 0.345425 | 0.172712 | − | 0.984972i | \(-0.444747\pi\) | ||||
0.172712 | + | 0.984972i | \(0.444747\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −45.0000 | −0.0191096 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2892.00 | −1.20759 | −0.603794 | − | 0.797140i | \(-0.706345\pi\) | ||||
−0.603794 | + | 0.797140i | \(0.706345\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1352.00 | −0.555212 | −0.277606 | − | 0.960695i | \(-0.589541\pi\) | ||||
−0.277606 | + | 0.960695i | \(0.589541\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 354.000 | 0.142997 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −948.000 | −0.376748 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1260.00 | −0.492729 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3912.00 | −1.48200 | −0.741001 | − | 0.671504i | \(-0.765649\pi\) | ||||
−0.741001 | + | 0.671504i | \(0.765649\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1493.00 | 0.556832 | 0.278416 | − | 0.960461i | \(-0.410191\pi\) | ||||
0.278416 | + | 0.960461i | \(0.410191\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 576.000 | 0.211529 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4086.00 | −1.47774 | −0.738872 | − | 0.673846i | \(-0.764641\pi\) | ||||
−0.738872 | + | 0.673846i | \(0.764641\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3556.00 | −1.26672 | −0.633362 | − | 0.773855i | \(-0.718326\pi\) | ||||
−0.633362 | + | 0.773855i | \(0.718326\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1110.00 | 0.389519 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1080.00 | −0.367954 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 756.000 | 0.253844 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −240.000 | −0.0794313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1250.00 | −0.407837 | −0.203918 | − | 0.978988i | \(-0.565368\pi\) | ||||
−0.203918 | + | 0.978988i | \(0.565368\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1026.00 | 0.330049 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −78.0000 | −0.0247421 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1086.00 | −0.335092 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5376.00 | −1.63633 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 425.000 | 0.127624 | 0.0638119 | − | 0.997962i | \(-0.479674\pi\) | ||||
0.0638119 | + | 0.997962i | \(0.479674\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1044.00 | −0.309333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3855.00 | 1.12716 | 0.563580 | − | 0.826061i | \(-0.309424\pi\) | ||||
0.563580 | + | 0.826061i | \(0.309424\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2188.00 | 0.631385 | 0.315692 | − | 0.948862i | \(-0.397763\pi\) | ||||
0.315692 | + | 0.948862i | \(0.397763\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 852.000 | 0.239555 | 0.119778 | − | 0.992801i | \(-0.461782\pi\) | ||||
0.119778 | + | 0.992801i | \(0.461782\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −90.0000 | −0.0249828 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1401.00 | −0.383986 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5508.00 | −1.49072 | −0.745362 | − | 0.666660i | \(-0.767723\pi\) | ||||
−0.745362 | + | 0.666660i | \(0.767723\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −791.000 | −0.211422 | −0.105711 | − | 0.994397i | \(-0.533712\pi\) | ||||
−0.105711 | + | 0.994397i | \(0.533712\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1024.00 | −0.263788 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1431.00 | 0.364201 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5265.00 | 1.32400 | 0.662000 | − | 0.749504i | \(-0.269708\pi\) | ||||
0.662000 | + | 0.749504i | \(0.269708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1260.00 | 0.313105 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −756.000 | −0.185657 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6870.00 | 1.66747 | 0.833733 | − | 0.552168i | \(-0.186199\pi\) | ||||
0.833733 | + | 0.552168i | \(0.186199\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2673.00 | −0.633925 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 222.000 | 0.0520498 | 0.0260249 | − | 0.999661i | \(-0.491715\pi\) | ||||
0.0260249 | + | 0.999661i | \(0.491715\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1089.00 | 0.252441 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2718.00 | −0.622992 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7851.00 | −1.77949 | −0.889747 | − | 0.456454i | \(-0.849119\pi\) | ||||
−0.889747 | + | 0.456454i | \(0.849119\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5183.00 | 1.16179 | 0.580895 | − | 0.813979i | \(-0.302703\pi\) | ||||
0.580895 | + | 0.813979i | \(0.302703\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1740.00 | −0.381549 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4960.00 | −1.07588 | −0.537938 | − | 0.842985i | \(-0.680796\pi\) | ||||
−0.537938 | + | 0.842985i | \(0.680796\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2277.00 | −0.488604 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −774.000 | −0.164317 | −0.0821583 | − | 0.996619i | \(-0.526181\pi\) | ||||
−0.0821583 | + | 0.996619i | \(0.526181\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3698.00 | 0.776761 | 0.388380 | − | 0.921499i | \(-0.373035\pi\) | ||||
0.388380 | + | 0.921499i | \(0.373035\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −144.000 | −0.0299292 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2143.00 | 0.436190 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1509.00 | −0.303983 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6273.00 | 1.25076 | 0.625380 | − | 0.780321i | \(-0.284944\pi\) | ||||
0.625380 | + | 0.780321i | \(0.284944\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −45.0000 | −0.00888136 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 405.000 | 0.0791262 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5376.00 | 1.03981 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3258.00 | 0.617714 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 354.000 | 0.0664590 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1684.00 | −0.313065 | −0.156533 | − | 0.987673i | \(-0.550032\pi\) | ||||
−0.156533 | + | 0.987673i | \(0.550032\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5208.00 | 0.958812 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1320.00 | −0.240676 | −0.120338 | − | 0.992733i | \(-0.538398\pi\) | ||||
−0.120338 | + | 0.992733i | \(0.538398\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8503.00 | 1.53552 | 0.767760 | − | 0.640737i | \(-0.221371\pi\) | ||||
0.767760 | + | 0.640737i | \(0.221371\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2577.00 | −0.456589 | −0.228295 | − | 0.973592i | \(-0.573315\pi\) | ||||
−0.228295 | + | 0.973592i | \(0.573315\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4455.00 | −0.781919 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4059.00 | 0.705767 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1344.00 | 0.231524 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7424.00 | −1.26711 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1110.00 | −0.187716 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 484.000 | 0.0803717 | 0.0401859 | − | 0.999192i | \(-0.487205\pi\) | ||||
0.0401859 | + | 0.999192i | \(0.487205\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2844.00 | −0.468019 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1110.00 | 0.181032 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8359.00 | −1.35117 | −0.675584 | − | 0.737283i | \(-0.736109\pi\) | ||||
−0.675584 | + | 0.737283i | \(0.736109\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1944.00 | −0.311456 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3795.00 | −0.602671 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 756.000 | 0.117976 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1860.00 | 0.287752 | 0.143876 | − | 0.989596i | \(-0.454043\pi\) | ||||
0.143876 | + | 0.989596i | \(0.454043\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1918.00 | 0.294178 | 0.147089 | − | 0.989123i | \(-0.453010\pi\) | ||||
0.147089 | + | 0.989123i | \(0.453010\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1728.00 | 0.262774 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3048.00 | 0.459571 | 0.229786 | − | 0.973241i | \(-0.426197\pi\) | ||||
0.229786 | + | 0.973241i | \(0.426197\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1026.00 | 0.153393 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.0000 | 0.00441042 | 0.00220521 | − | 0.999998i | \(-0.499298\pi\) | ||||
0.00220521 | + | 0.999998i | \(0.499298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6603.00 | −0.962677 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3318.00 | −0.479752 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1086.00 | −0.155737 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11311.0 | −1.60880 | −0.804400 | − | 0.594088i | \(-0.797513\pi\) | ||||
−0.804400 | + | 0.594088i | \(0.797513\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3240.00 | −0.457094 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1208.00 | 0.167689 | 0.0838443 | − | 0.996479i | \(-0.473280\pi\) | ||||
0.0838443 | + | 0.996479i | \(0.473280\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2169.00 | −0.298684 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19008.0 | −2.59672 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7640.00 | −1.03546 | −0.517731 | − | 0.855543i | \(-0.673223\pi\) | ||||
−0.517731 | + | 0.855543i | \(0.673223\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1131.00 | −0.152081 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12750.0 | 1.70103 | 0.850515 | − | 0.525951i | \(-0.176290\pi\) | ||||
0.850515 | + | 0.525951i | \(0.176290\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −234.000 | −0.0307361 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3126.00 | 0.407441 | 0.203720 | − | 0.979029i | \(-0.434697\pi\) | ||||
0.203720 | + | 0.979029i | \(0.434697\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7056.00 | −0.912627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1953.00 | −0.250676 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1401.00 | −0.178461 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5932.00 | 0.749921 | 0.374960 | − | 0.927041i | \(-0.377656\pi\) | ||||
0.374960 | + | 0.927041i | \(0.377656\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1608.00 | 0.200249 | 0.100124 | − | 0.994975i | \(-0.468076\pi\) | ||||
0.100124 | + | 0.994975i | \(0.468076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16192.0 | −2.00144 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 243.000 | 0.0298142 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4740.00 | −0.577280 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4465.00 | 0.539805 | 0.269902 | − | 0.962888i | \(-0.413009\pi\) | ||||
0.269902 | + | 0.962888i | \(0.413009\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5310.00 | −0.637282 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1431.00 | 0.169265 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4674.00 | −0.548889 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1584.00 | −0.184686 | −0.0923430 | − | 0.995727i | \(-0.529436\pi\) | ||||
−0.0923430 | + | 0.995727i | \(0.529436\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1330.00 | −0.153967 | −0.0769837 | − | 0.997032i | \(-0.524529\pi\) | ||||
−0.0769837 | + | 0.997032i | \(0.524529\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −270.000 | −0.0310351 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9744.00 | 1.11213 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2880.00 | 0.324121 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9588.00 | −1.07155 | −0.535775 | − | 0.844361i | \(-0.679980\pi\) | ||||
−0.535775 | + | 0.844361i | \(0.679980\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −494.000 | −0.0548271 | −0.0274135 | − | 0.999624i | \(-0.508727\pi\) | ||||
−0.0274135 | + | 0.999624i | \(0.508727\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2673.00 | −0.294622 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1344.00 | −0.147122 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16009.0 | −1.74047 | −0.870237 | − | 0.492634i | \(-0.836034\pi\) | ||||
−0.870237 | + | 0.492634i | \(0.836034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7773.00 | −0.833649 | −0.416824 | − | 0.908987i | \(-0.636857\pi\) | ||||
−0.416824 | + | 0.908987i | \(0.636857\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2718.00 | −0.289541 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7362.00 | 0.778995 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 864.000 | 0.0908122 | 0.0454061 | − | 0.998969i | \(-0.485542\pi\) | ||||
0.0454061 | + | 0.998969i | \(0.485542\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5400.00 | −0.563805 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3777.00 | −0.391742 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2519.00 | 0.257842 | 0.128921 | − | 0.991655i | \(-0.458849\pi\) | ||||
0.128921 | + | 0.991655i | \(0.458849\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2268.00 | −0.230634 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 342.000 | 0.0345521 | 0.0172761 | − | 0.999851i | \(-0.494501\pi\) | ||||
0.0172761 | + | 0.999851i | \(0.494501\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4336.00 | 0.435229 | 0.217614 | − | 0.976035i | \(-0.430172\pi\) | ||||
0.217614 | + | 0.976035i | \(0.430172\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2277.00 | −0.227082 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18636.0 | 1.84662 | 0.923310 | − | 0.384056i | \(-0.125473\pi\) | ||||
0.923310 | + | 0.384056i | \(0.125473\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 588.000 | 0.0575236 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −390.000 | −0.0379117 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1856.00 | 0.179282 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3267.00 | 0.313597 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15078.0 | 1.43827 | 0.719135 | − | 0.694870i | \(-0.244538\pi\) | ||||
0.719135 | + | 0.694870i | \(0.244538\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20224.0 | −1.91712 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1509.00 | −0.141279 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6221.00 | −0.578851 | −0.289425 | − | 0.957201i | \(-0.593464\pi\) | ||||
−0.289425 | + | 0.957201i | \(0.593464\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3756.00 | 0.347346 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7371.00 | 0.677492 | 0.338746 | − | 0.940878i | \(-0.389997\pi\) | ||||
0.338746 | + | 0.940878i | \(0.389997\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24948.0 | 2.27911 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 405.000 | 0.0367745 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4274.00 | −0.383428 | −0.191714 | − | 0.981451i | \(-0.561405\pi\) | ||||
−0.191714 | + | 0.981451i | \(0.561405\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7938.00 | −0.707872 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2520.00 | −0.223382 | −0.111691 | − | 0.993743i | \(-0.535627\pi\) | ||||
−0.111691 | + | 0.993743i | \(0.535627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3258.00 | 0.287087 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5697.00 | 0.499039 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14277.0 | 1.24326 | 0.621628 | − | 0.783313i | \(-0.286472\pi\) | ||||
0.621628 | + | 0.783313i | \(0.286472\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −432.000 | −0.0371799 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5208.00 | 0.445615 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −450.000 | −0.0382804 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2358.00 | 0.199431 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6306.00 | 0.530270 | 0.265135 | − | 0.964211i | \(-0.414583\pi\) | ||||
0.265135 | + | 0.964211i | \(0.414583\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8072.00 | 0.674883 | 0.337442 | − | 0.941346i | \(-0.390438\pi\) | ||||
0.337442 | + | 0.941346i | \(0.390438\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21252.0 | 1.75664 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5111.00 | −0.420071 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −135.000 | −0.0110330 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23040.0 | −1.87237 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4059.00 | 0.328011 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8676.00 | −0.697201 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22858.0 | −1.81653 | −0.908264 | − | 0.418396i | \(-0.862592\pi\) | ||||
−0.908264 | + | 0.418396i | \(0.862592\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4056.00 | −0.320552 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1110.00 | −0.0872425 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24724.0 | 1.93258 | 0.966291 | − | 0.257454i | \(-0.0828835\pi\) | ||||
0.966291 | + | 0.257454i | \(0.0828835\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1062.00 | 0.0825593 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4752.00 | 0.367408 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2844.00 | −0.217515 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9843.00 | −0.748764 | −0.374382 | − | 0.927275i | \(-0.622145\pi\) | ||||
−0.374382 | + | 0.927275i | \(0.622145\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1664.00 | −0.125903 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3780.00 | −0.284477 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13371.0 | −1.00092 | −0.500462 | − | 0.865758i | \(-0.666837\pi\) | ||||
−0.500462 | + | 0.865758i | \(0.666837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1944.00 | −0.144752 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5232.00 | −0.385478 | −0.192739 | − | 0.981250i | \(-0.561737\pi\) | ||||
−0.192739 | + | 0.981250i | \(0.561737\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14398.0 | 1.05523 | 0.527616 | − | 0.849483i | \(-0.323086\pi\) | ||||
0.527616 | + | 0.849483i | \(0.323086\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11736.0 | −0.855634 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9744.00 | −0.706701 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19871.0 | −1.43369 | −0.716846 | − | 0.697231i | \(-0.754415\pi\) | ||||
−0.716846 | + | 0.697231i | \(0.754415\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4479.00 | 0.321487 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5445.00 | 0.386808 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1728.00 | 0.122127 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16137.0 | −1.13466 | −0.567330 | − | 0.823491i | \(-0.692024\pi\) | ||||
−0.567330 | + | 0.823491i | \(0.692024\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4048.00 | 0.283183 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12258.0 | −0.853176 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21324.0 | 1.47668 | 0.738340 | − | 0.674428i | \(-0.235610\pi\) | ||||
0.738340 | + | 0.674428i | \(0.235610\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10668.0 | −0.731344 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8646.00 | 0.589760 | 0.294880 | − | 0.955534i | \(-0.404720\pi\) | ||||
0.294880 | + | 0.955534i | \(0.404720\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11195.0 | −0.759823 | −0.379911 | − | 0.925023i | \(-0.624046\pi\) | ||||
−0.379911 | + | 0.925023i | \(0.624046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3330.00 | 0.224889 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3318.00 | −0.222968 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8971.00 | −0.599871 | −0.299935 | − | 0.953959i | \(-0.596965\pi\) | ||||
−0.299935 | + | 0.953959i | \(0.596965\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1920.00 | −0.127127 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12772.0 | −0.841527 | −0.420764 | − | 0.907170i | \(-0.638238\pi\) | ||||
−0.420764 | + | 0.907170i | \(0.638238\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3240.00 | −0.212438 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12762.0 | 0.832705 | 0.416352 | − | 0.909203i | \(-0.363308\pi\) | ||||
0.416352 | + | 0.909203i | \(0.363308\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12842.0 | 0.833867 | 0.416933 | − | 0.908937i | \(-0.363105\pi\) | ||||
0.416933 | + | 0.908937i | \(0.363105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2268.00 | 0.146557 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12331.0 | 0.789184 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −720.000 | −0.0458597 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26544.0 | 1.68264 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21365.0 | −1.34790 | −0.673952 | − | 0.738775i | \(-0.735404\pi\) | ||||
−0.673952 | + | 0.738775i | \(0.735404\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3750.00 | −0.235465 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1131.00 | −0.0706809 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3078.00 | 0.190554 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8274.00 | 0.509834 | 0.254917 | − | 0.966963i | \(-0.417952\pi\) | ||||
0.254917 | + | 0.966963i | \(0.417952\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27998.0 | 1.71716 | 0.858580 | − | 0.512680i | \(-0.171347\pi\) | ||||
0.858580 | + | 0.512680i | \(0.171347\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −234.000 | −0.0142849 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17466.0 | −1.06130 | −0.530649 | − | 0.847592i | \(-0.678052\pi\) | ||||
−0.530649 | + | 0.847592i | \(0.678052\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −225.000 | −0.0136087 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2157.00 | 0.129265 | 0.0646324 | − | 0.997909i | \(-0.479413\pi\) | ||||
0.0646324 | + | 0.997909i | \(0.479413\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1953.00 | −0.116504 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3258.00 | −0.193465 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19944.0 | −1.17892 | −0.589460 | − | 0.807798i | \(-0.700659\pi\) | ||||
−0.589460 | + | 0.807798i | \(0.700659\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27506.0 | −1.61855 | −0.809273 | − | 0.587432i | \(-0.800139\pi\) | ||||
−0.809273 | + | 0.587432i | \(0.800139\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16128.0 | −0.944735 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24948.0 | −1.44826 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1275.00 | 0.0736836 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1770.00 | 0.101833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19123.0 | −1.09530 | −0.547650 | − | 0.836707i | \(-0.684478\pi\) | ||||
−0.547650 | + | 0.836707i | \(0.684478\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3132.00 | −0.178594 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13857.0 | −0.786658 | −0.393329 | − | 0.919398i | \(-0.628677\pi\) | ||||
−0.393329 | + | 0.919398i | \(0.628677\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11565.0 | 0.650766 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22245.0 | 1.24624 | 0.623120 | − | 0.782127i | \(-0.285865\pi\) | ||||
0.623120 | + | 0.782127i | \(0.285865\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5310.00 | −0.296182 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6564.00 | 0.364530 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23232.0 | 1.28457 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −640.000 | −0.0352341 | −0.0176170 | − | 0.999845i | \(-0.505608\pi\) | ||||
−0.0176170 | + | 0.999845i | \(0.505608\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4674.00 | −0.255101 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30240.0 | 1.64336 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2556.00 | 0.138307 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15561.0 | −0.838418 | −0.419209 | − | 0.907890i | \(-0.637693\pi\) | ||||
−0.419209 | + | 0.907890i | \(0.637693\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5056.00 | 0.271253 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −270.000 | −0.0144238 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5534.00 | 0.293136 | 0.146568 | − | 0.989201i | \(-0.453177\pi\) | ||||
0.146568 | + | 0.989201i | \(0.453177\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4203.00 | −0.221695 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21252.0 | −1.11626 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2880.00 | 0.150638 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16524.0 | −0.860670 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21846.0 | −1.13313 | −0.566564 | − | 0.824018i | \(-0.691727\pi\) | ||||
−0.566564 | + | 0.824018i | \(0.691727\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2373.00 | −0.122065 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34452.0 | 1.76485 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11089.0 | −0.565706 | −0.282853 | − | 0.959163i | \(-0.591281\pi\) | ||||
−0.282853 | + | 0.959163i | \(0.591281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2184.00 | 0.110504 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11762.0 | −0.592687 | −0.296343 | − | 0.955081i | \(-0.595767\pi\) | ||||
−0.296343 | + | 0.955081i | \(0.595767\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5550.00 | 0.277391 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22726.0 | 1.13124 | 0.565622 | − | 0.824665i | \(-0.308636\pi\) | ||||
0.565622 | + | 0.824665i | \(0.308636\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3072.00 | −0.152298 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6678.00 | −0.329734 | −0.164867 | − | 0.986316i | \(-0.552719\pi\) | ||||
−0.164867 | + | 0.986316i | \(0.552719\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7362.00 | 0.362044 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4293.00 | 0.210271 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19987.0 | 0.971153 | 0.485577 | − | 0.874194i | \(-0.338610\pi\) | ||||
0.485577 | + | 0.874194i | \(0.338610\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15795.0 | 0.764411 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3777.00 | −0.182065 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 314.000 | 0.0150760 | 0.00753799 | − | 0.999972i | \(-0.497601\pi\) | ||||
0.00753799 | + | 0.999972i | \(0.497601\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3780.00 | 0.180771 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11496.0 | 0.547608 | 0.273804 | − | 0.961786i | \(-0.411718\pi\) | ||||
0.273804 | + | 0.961786i | \(0.411718\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2268.00 | −0.107189 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −960.000 | −0.0451937 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2765.00 | −0.129660 | −0.0648299 | − | 0.997896i | \(-0.520650\pi\) | ||||
−0.0648299 | + | 0.997896i | \(0.520650\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20610.0 | 0.962712 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14046.0 | 0.653557 | 0.326778 | − | 0.945101i | \(-0.394037\pi\) | ||||
0.326778 | + | 0.945101i | \(0.394037\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29348.0 | 1.36027 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5760.00 | 0.264921 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5130.00 | 0.235039 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8019.00 | −0.365997 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 588.000 | 0.0267345 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18514.0 | −0.838568 | −0.419284 | − | 0.907855i | \(-0.637719\pi\) | ||||
−0.419284 | + | 0.907855i | \(0.637719\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 666.000 | 0.0300510 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7552.00 | 0.338183 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3267.00 | 0.145747 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27495.0 | 1.22199 | 0.610993 | − | 0.791636i | \(-0.290770\pi\) | ||||
0.610993 | + | 0.791636i | \(0.290770\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2520.00 | 0.111578 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8154.00 | −0.359685 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5430.00 | −0.238631 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23553.0 | −1.02739 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7944.00 | −0.345236 | −0.172618 | − | 0.984989i | \(-0.555223\pi\) | ||||
−0.172618 | + | 0.984989i | \(0.555223\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28942.0 | −1.25313 | −0.626567 | − | 0.779368i | \(-0.715540\pi\) | ||||
−0.626567 | + | 0.779368i | \(0.715540\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15549.0 | 0.670759 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3756.00 | 0.161432 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 416.000 | 0.0178140 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8187.00 | 0.348025 | 0.174012 | − | 0.984743i | \(-0.444327\pi\) | ||||
0.174012 | + | 0.984743i | \(0.444327\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 280.000 | 0.0118593 | 0.00592964 | − | 0.999982i | \(-0.498113\pi\) | ||||
0.00592964 | + | 0.999982i | \(0.498113\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5220.00 | −0.220287 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25317.0 | −1.06452 | −0.532260 | − | 0.846581i | \(-0.678657\pi\) | ||||
−0.532260 | + | 0.846581i | \(0.678657\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15320.0 | −0.641840 | −0.320920 | − | 0.947106i | \(-0.603992\pi\) | ||||
−0.320920 | + | 0.947106i | \(0.603992\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14880.0 | −0.621157 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7938.00 | −0.328989 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6831.00 | −0.282095 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34092.0 | 1.40284 | 0.701422 | − | 0.712746i | \(-0.252549\pi\) | ||||
0.701422 | + | 0.712746i | \(0.252549\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 63820.0 | 2.61675 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2322.00 | −0.0948682 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5697.00 | 0.231932 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11094.0 | 0.448463 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26544.0 | −1.06923 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7378.00 | 0.296152 | 0.148076 | − | 0.988976i | \(-0.452692\pi\) | ||||
0.148076 | + | 0.988976i | \(0.452692\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −432.000 | −0.0172796 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15594.0 | 0.621565 | 0.310782 | − | 0.950481i | \(-0.399409\pi\) | ||||
0.310782 | + | 0.950481i | \(0.399409\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30538.0 | −1.21297 | −0.606486 | − | 0.795094i | \(-0.707421\pi\) | ||||
−0.606486 | + | 0.795094i | \(0.707421\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 822.000 | 0.0324232 | 0.0162116 | − | 0.999869i | \(-0.494839\pi\) | ||||
0.0162116 | + | 0.999869i | \(0.494839\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2358.00 | 0.0926872 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6429.00 | 0.251834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7005.00 | −0.273450 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23680.0 | 0.921201 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4527.00 | −0.175505 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41824.0 | −1.61037 | −0.805186 | − | 0.593022i | \(-0.797935\pi\) | ||||
−0.805186 | + | 0.593022i | \(0.797935\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18819.0 | 0.722126 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46098.0 | 1.76286 | 0.881431 | − | 0.472313i | \(-0.156581\pi\) | ||||
0.881431 | + | 0.472313i | \(0.156581\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21008.0 | −0.800652 | −0.400326 | − | 0.916373i | \(-0.631103\pi\) | ||||
−0.400326 | + | 0.916373i | \(0.631103\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −135.000 | −0.00512766 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24036.0 | 0.909865 | 0.454932 | − | 0.890526i | \(-0.349663\pi\) | ||||
0.454932 | + | 0.890526i | \(0.349663\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1215.00 | 0.0456835 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 480.000 | 0.0179872 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8676.00 | −0.324030 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16128.0 | 0.600332 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 75141.0 | 2.78764 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30492.0 | −1.12745 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4056.00 | −0.148979 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13292.0 | −0.486608 | −0.243304 | − | 0.969950i | \(-0.578231\pi\) | ||||
−0.243304 | + | 0.969950i | \(0.578231\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9774.00 | 0.356637 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9306.00 | 0.338443 | 0.169221 | − | 0.985578i | \(-0.445875\pi\) | ||||
0.169221 | + | 0.985578i | \(0.445875\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7155.00 | 0.259360 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1062.00 | 0.0383701 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16496.0 | −0.592114 | −0.296057 | − | 0.955170i | \(-0.595672\pi\) | ||||
−0.296057 | + | 0.955170i | \(0.595672\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5052.00 | −0.180748 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21888.0 | 0.780555 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36656.0 | 1.30296 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15624.0 | 0.553570 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14154.0 | −0.499868 | −0.249934 | − | 0.968263i | \(-0.580409\pi\) | ||||
−0.249934 | + | 0.968263i | \(0.580409\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3960.00 | −0.138955 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3780.00 | −0.132213 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3781.00 | 0.131825 | 0.0659124 | − | 0.997825i | \(-0.479004\pi\) | ||||
0.0659124 | + | 0.997825i | \(0.479004\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25509.0 | 0.886533 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25863.0 | 0.895972 | 0.447986 | − | 0.894041i | \(-0.352141\pi\) | ||||
0.447986 | + | 0.894041i | \(0.352141\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30240.0 | −1.04427 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42384.0 | 1.45438 | 0.727188 | − | 0.686438i | \(-0.240827\pi\) | ||||
0.727188 | + | 0.686438i | \(0.240827\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23168.0 | −0.792482 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7731.00 | −0.263612 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10530.0 | 0.357923 | 0.178961 | − | 0.983856i | \(-0.442726\pi\) | ||||
0.178961 | + | 0.983856i | \(0.442726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11736.0 | −0.397663 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13365.0 | −0.451441 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34218.0 | 1.14860 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12177.0 | 0.407475 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4479.00 | 0.149414 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38341.0 | 1.27504 | 0.637520 | − | 0.770434i | \(-0.279960\pi\) | ||||
0.637520 | + | 0.770434i | \(0.279960\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4032.00 | 0.133670 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1923.00 | 0.0635551 | 0.0317776 | − | 0.999495i | \(-0.489883\pi\) | ||||
0.0317776 | + | 0.999495i | \(0.489883\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22272.0 | −0.731564 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 57090.0 | 1.86947 | 0.934734 | − | 0.355347i | \(-0.115637\pi\) | ||||
0.934734 | + | 0.355347i | \(0.115637\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13590.0 | −0.443655 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3330.00 | −0.108378 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5484.00 | 0.177937 | 0.0889687 | − | 0.996034i | \(-0.471643\pi\) | ||||
0.0889687 | + | 0.996034i | \(0.471643\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12258.0 | −0.396520 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2184.00 | −0.0702196 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22465.0 | 0.720105 | 0.360053 | − | 0.932932i | \(-0.382759\pi\) | ||||
0.360053 | + | 0.932932i | \(0.382759\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1452.00 | 0.0464026 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10668.0 | −0.339898 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29366.0 | −0.932829 | −0.466415 | − | 0.884566i | \(-0.654454\pi\) | ||||
−0.466415 | + | 0.884566i | \(0.654454\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8532.00 | −0.270211 |
(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 | 2352.4.a.bd.1.1 | 1 | ||
4.3 | odd | 2 | 147.4.a.a.1.1 | 1 | |||
7.3 | odd | 6 | 336.4.q.e.289.1 | 2 | |||
7.5 | odd | 6 | 336.4.q.e.193.1 | 2 | |||
7.6 | odd | 2 | 2352.4.a.i.1.1 | 1 | |||
12.11 | even | 2 | 441.4.a.k.1.1 | 1 | |||
28.3 | even | 6 | 21.4.e.a.16.1 | yes | 2 | ||
28.11 | odd | 6 | 147.4.e.h.79.1 | 2 | |||
28.19 | even | 6 | 21.4.e.a.4.1 | ✓ | 2 | ||
28.23 | odd | 6 | 147.4.e.h.67.1 | 2 | |||
28.27 | even | 2 | 147.4.a.b.1.1 | 1 | |||
84.11 | even | 6 | 441.4.e.c.226.1 | 2 | |||
84.23 | even | 6 | 441.4.e.c.361.1 | 2 | |||
84.47 | odd | 6 | 63.4.e.a.46.1 | 2 | |||
84.59 | odd | 6 | 63.4.e.a.37.1 | 2 | |||
84.83 | odd | 2 | 441.4.a.l.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.e.a.4.1 | ✓ | 2 | 28.19 | even | 6 | ||
21.4.e.a.16.1 | yes | 2 | 28.3 | even | 6 | ||
63.4.e.a.37.1 | 2 | 84.59 | odd | 6 | |||
63.4.e.a.46.1 | 2 | 84.47 | odd | 6 | |||
147.4.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
147.4.a.b.1.1 | 1 | 28.27 | even | 2 | |||
147.4.e.h.67.1 | 2 | 28.23 | odd | 6 | |||
147.4.e.h.79.1 | 2 | 28.11 | odd | 6 | |||
336.4.q.e.193.1 | 2 | 7.5 | odd | 6 | |||
336.4.q.e.289.1 | 2 | 7.3 | odd | 6 | |||
441.4.a.k.1.1 | 1 | 12.11 | even | 2 | |||
441.4.a.l.1.1 | 1 | 84.83 | odd | 2 | |||
441.4.e.c.226.1 | 2 | 84.11 | even | 6 | |||
441.4.e.c.361.1 | 2 | 84.23 | even | 6 | |||
2352.4.a.i.1.1 | 1 | 7.6 | odd | 2 | |||
2352.4.a.bd.1.1 | 1 | 1.1 | even | 1 | trivial |