Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,4,Mod(1,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, 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("720.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.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: | \(42.4813752041\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 180) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 720.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | −0.107990 | −0.0539949 | − | 0.998541i | \(-0.517195\pi\) | ||||
−0.0539949 | + | 0.998541i | \(0.517195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 30.0000 | 0.822304 | 0.411152 | − | 0.911567i | \(-0.365127\pi\) | ||||
0.411152 | + | 0.911567i | \(0.365127\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −0.0853385 | −0.0426692 | − | 0.999089i | \(-0.513586\pi\) | ||||
−0.0426692 | + | 0.999089i | \(0.513586\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −90.0000 | −1.28401 | −0.642006 | − | 0.766700i | \(-0.721898\pi\) | ||||
−0.642006 | + | 0.766700i | \(0.721898\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.0000 | 0.338086 | 0.169043 | − | 0.985609i | \(-0.445932\pi\) | ||||
0.169043 | + | 0.985609i | \(0.445932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 120.000 | 1.08790 | 0.543951 | − | 0.839117i | \(-0.316928\pi\) | ||||
0.543951 | + | 0.839117i | \(0.316928\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −210.000 | −1.34469 | −0.672345 | − | 0.740238i | \(-0.734713\pi\) | ||||
−0.672345 | + | 0.740238i | \(0.734713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.0231749 | 0.0115874 | − | 0.999933i | \(-0.496312\pi\) | ||||
0.0115874 | + | 0.999933i | \(0.496312\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.0000 | 0.0482945 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 200.000 | 0.888643 | 0.444322 | − | 0.895867i | \(-0.353445\pi\) | ||||
0.444322 | + | 0.895867i | \(0.353445\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −240.000 | −0.914188 | −0.457094 | − | 0.889418i | \(-0.651110\pi\) | ||||
−0.457094 | + | 0.889418i | \(0.651110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 136.000 | 0.482321 | 0.241161 | − | 0.970485i | \(-0.422472\pi\) | ||||
0.241161 | + | 0.970485i | \(0.422472\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −120.000 | −0.372421 | −0.186211 | − | 0.982510i | \(-0.559621\pi\) | ||||
−0.186211 | + | 0.982510i | \(0.559621\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −339.000 | −0.988338 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 30.0000 | 0.0777513 | 0.0388756 | − | 0.999244i | \(-0.487622\pi\) | ||||
0.0388756 | + | 0.999244i | \(0.487622\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −150.000 | −0.367745 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −450.000 | −0.992966 | −0.496483 | − | 0.868046i | \(-0.665376\pi\) | ||||
−0.496483 | + | 0.868046i | \(0.665376\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −166.000 | −0.348428 | −0.174214 | − | 0.984708i | \(-0.555738\pi\) | ||||
−0.174214 | + | 0.984708i | \(0.555738\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20.0000 | 0.0381645 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −908.000 | −1.65567 | −0.827835 | − | 0.560972i | \(-0.810428\pi\) | ||||
−0.827835 | + | 0.560972i | \(0.810428\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1020.00 | −1.70495 | −0.852477 | − | 0.522765i | \(-0.824901\pi\) | ||||
−0.852477 | + | 0.522765i | \(0.824901\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −250.000 | −0.400826 | −0.200413 | − | 0.979712i | \(-0.564228\pi\) | ||||
−0.200413 | + | 0.979712i | \(0.564228\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −60.0000 | −0.0888004 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 916.000 | 1.30453 | 0.652266 | − | 0.757990i | \(-0.273818\pi\) | ||||
0.652266 | + | 0.757990i | \(0.273818\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1140.00 | −1.50761 | −0.753803 | − | 0.657101i | \(-0.771783\pi\) | ||||
−0.753803 | + | 0.657101i | \(0.771783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 450.000 | 0.574228 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 420.000 | 0.500224 | 0.250112 | − | 0.968217i | \(-0.419533\pi\) | ||||
0.250112 | + | 0.968217i | \(0.419533\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | 0.00921569 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −140.000 | −0.151197 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1538.00 | 1.60990 | 0.804950 | − | 0.593343i | \(-0.202192\pi\) | ||||
0.804950 | + | 0.593343i | \(0.202192\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −450.000 | −0.443333 | −0.221667 | − | 0.975122i | \(-0.571150\pi\) | ||||
−0.221667 | + | 0.975122i | \(0.571150\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1150.00 | 1.10012 | 0.550062 | − | 0.835124i | \(-0.314604\pi\) | ||||
0.550062 | + | 0.835124i | \(0.314604\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1620.00 | −1.46366 | −0.731829 | − | 0.681489i | \(-0.761333\pi\) | ||||
−0.731829 | + | 0.681489i | \(0.761333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1702.00 | −1.49561 | −0.747807 | − | 0.663916i | \(-0.768893\pi\) | ||||
−0.747807 | + | 0.663916i | \(0.768893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1350.00 | −1.12387 | −0.561935 | − | 0.827181i | \(-0.689943\pi\) | ||||
−0.561935 | + | 0.827181i | \(0.689943\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −600.000 | −0.486524 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 180.000 | 0.138660 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −431.000 | −0.323817 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2450.00 | −1.71183 | −0.855915 | − | 0.517117i | \(-0.827005\pi\) | ||||
−0.855915 | + | 0.517117i | \(0.827005\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 690.000 | 0.460195 | 0.230098 | − | 0.973168i | \(-0.426095\pi\) | ||||
0.230098 | + | 0.973168i | \(0.426095\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −56.0000 | −0.0365099 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2070.00 | −1.29089 | −0.645445 | − | 0.763806i | \(-0.723328\pi\) | ||||
−0.645445 | + | 0.763806i | \(0.723328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1924.00 | 1.17404 | 0.587020 | − | 0.809572i | \(-0.300301\pi\) | ||||
0.587020 | + | 0.809572i | \(0.300301\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −120.000 | −0.0701742 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1050.00 | 0.601364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2910.00 | −1.59998 | −0.799988 | − | 0.600016i | \(-0.795161\pi\) | ||||
−0.799988 | + | 0.600016i | \(0.795161\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −176.000 | −0.0948522 | −0.0474261 | − | 0.998875i | \(-0.515102\pi\) | ||||
−0.0474261 | + | 0.998875i | \(0.515102\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.0000 | −0.0103641 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2348.00 | 1.19357 | 0.596786 | − | 0.802400i | \(-0.296444\pi\) | ||||
0.596786 | + | 0.802400i | \(0.296444\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −240.000 | −0.117482 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1996.00 | 0.959134 | 0.479567 | − | 0.877505i | \(-0.340794\pi\) | ||||
0.479567 | + | 0.877505i | \(0.340794\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3120.00 | 1.44571 | 0.722853 | − | 0.691002i | \(-0.242830\pi\) | ||||
0.722853 | + | 0.691002i | \(0.242830\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2181.00 | −0.992717 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1770.00 | −0.777865 | −0.388932 | − | 0.921266i | \(-0.627156\pi\) | ||||
−0.388932 | + | 0.921266i | \(0.627156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −50.0000 | −0.0215980 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2130.00 | −0.889406 | −0.444703 | − | 0.895678i | \(-0.646691\pi\) | ||||
−0.444703 | + | 0.895678i | \(0.646691\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1654.00 | −0.679231 | −0.339616 | − | 0.940564i | \(-0.610297\pi\) | ||||
−0.339616 | + | 0.940564i | \(0.610297\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1000.00 | −0.397413 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2700.00 | −1.05585 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1740.00 | 0.659173 | 0.329586 | − | 0.944125i | \(-0.393091\pi\) | ||||
0.329586 | + | 0.944125i | \(0.393091\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 86.0000 | 0.0320747 | 0.0160373 | − | 0.999871i | \(-0.494895\pi\) | ||||
0.0160373 | + | 0.999871i | \(0.494895\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2490.00 | 0.900534 | 0.450267 | − | 0.892894i | \(-0.351329\pi\) | ||||
0.450267 | + | 0.892894i | \(0.351329\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 832.000 | 0.296376 | 0.148188 | − | 0.988959i | \(-0.452656\pi\) | ||||
0.148188 | + | 0.988959i | \(0.452656\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 420.000 | 0.145213 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1200.00 | 0.408837 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 840.000 | 0.278010 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2084.00 | −0.679945 | −0.339973 | − | 0.940435i | \(-0.610418\pi\) | ||||
−0.339973 | + | 0.940435i | \(0.610418\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −680.000 | −0.215701 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00000 | −0.00250265 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 360.000 | 0.109576 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1174.00 | 0.352542 | 0.176271 | − | 0.984342i | \(-0.443597\pi\) | ||||
0.176271 | + | 0.984342i | \(0.443597\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3120.00 | −0.912254 | −0.456127 | − | 0.889915i | \(-0.650764\pi\) | ||||
−0.456127 | + | 0.889915i | \(0.650764\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −58.0000 | −0.0167369 | −0.00836845 | − | 0.999965i | \(-0.502664\pi\) | ||||
−0.00836845 | + | 0.999965i | \(0.502664\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5910.00 | 1.66170 | 0.830852 | − | 0.556494i | \(-0.187854\pi\) | ||||
0.830852 | + | 0.556494i | \(0.187854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 600.000 | 0.166552 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3300.00 | 0.893135 | 0.446567 | − | 0.894750i | \(-0.352646\pi\) | ||||
0.446567 | + | 0.894750i | \(0.352646\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2986.00 | −0.798113 | −0.399056 | − | 0.916926i | \(-0.630662\pi\) | ||||
−0.399056 | + | 0.916926i | \(0.630662\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1695.00 | 0.441998 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −112.000 | −0.0288518 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6630.00 | −1.66726 | −0.833629 | − | 0.552324i | \(-0.813741\pi\) | ||||
−0.833629 | + | 0.552324i | \(0.813741\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3600.00 | 0.894585 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1530.00 | 0.371357 | 0.185679 | − | 0.982611i | \(-0.440552\pi\) | ||||
0.185679 | + | 0.982611i | \(0.440552\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −400.000 | −0.0959644 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2640.00 | 0.618971 | 0.309486 | − | 0.950904i | \(-0.399843\pi\) | ||||
0.309486 | + | 0.950904i | \(0.399843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −150.000 | −0.0347714 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7350.00 | 1.66594 | 0.832969 | − | 0.553319i | \(-0.186639\pi\) | ||||
0.832969 | + | 0.553319i | \(0.186639\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3512.00 | −0.787228 | −0.393614 | − | 0.919276i | \(-0.628775\pi\) | ||||
−0.393614 | + | 0.919276i | \(0.628775\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 750.000 | 0.164461 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5368.00 | −1.16437 | −0.582187 | − | 0.813055i | \(-0.697803\pi\) | ||||
−0.582187 | + | 0.813055i | \(0.697803\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3060.00 | 0.649624 | 0.324812 | − | 0.945779i | \(-0.394699\pi\) | ||||
0.324812 | + | 0.945779i | \(0.394699\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5044.00 | 1.05949 | 0.529743 | − | 0.848158i | \(-0.322288\pi\) | ||||
0.529743 | + | 0.848158i | \(0.322288\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 480.000 | 0.0987230 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3187.00 | 0.648687 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2010.00 | 0.400769 | 0.200385 | − | 0.979717i | \(-0.435781\pi\) | ||||
0.200385 | + | 0.979717i | \(0.435781\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2250.00 | 0.444068 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −480.000 | −0.0928399 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −272.000 | −0.0520858 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 830.000 | 0.155822 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2752.00 | 0.511612 | 0.255806 | − | 0.966728i | \(-0.417659\pi\) | ||||
0.255806 | + | 0.966728i | \(0.417659\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9540.00 | 1.73943 | 0.869717 | − | 0.493551i | \(-0.164301\pi\) | ||||
0.869717 | + | 0.493551i | \(0.164301\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9254.00 | 1.67114 | 0.835570 | − | 0.549384i | \(-0.185137\pi\) | ||||
0.835570 | + | 0.549384i | \(0.185137\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −150.000 | −0.0265768 | −0.0132884 | − | 0.999912i | \(-0.504230\pi\) | ||||
−0.0132884 | + | 0.999912i | \(0.504230\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6300.00 | −1.10574 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2520.00 | −0.434107 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −100.000 | −0.0170677 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 240.000 | 0.0402177 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1892.00 | −0.314180 | −0.157090 | − | 0.987584i | \(-0.550211\pi\) | ||||
−0.157090 | + | 0.987584i | \(0.550211\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4540.00 | 0.740438 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7378.00 | −1.19260 | −0.596299 | − | 0.802763i | \(-0.703363\pi\) | ||||
−0.596299 | + | 0.802763i | \(0.703363\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 120.000 | 0.0190568 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1364.00 | 0.214720 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6720.00 | 1.03962 | 0.519811 | − | 0.854282i | \(-0.326003\pi\) | ||||
0.519811 | + | 0.854282i | \(0.326003\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5186.00 | 0.795416 | 0.397708 | − | 0.917512i | \(-0.369806\pi\) | ||||
0.397708 | + | 0.917512i | \(0.369806\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3330.00 | −0.502091 | −0.251045 | − | 0.967975i | \(-0.580774\pi\) | ||||
−0.251045 | + | 0.967975i | \(0.580774\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5100.00 | 0.762479 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9000.00 | 1.32312 | 0.661562 | − | 0.749890i | \(-0.269894\pi\) | ||||
0.661562 | + | 0.749890i | \(0.269894\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6075.00 | −0.885698 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1250.00 | 0.179255 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8758.00 | 1.24568 | 0.622839 | − | 0.782350i | \(-0.285979\pi\) | ||||
0.622839 | + | 0.782350i | \(0.285979\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −60.0000 | −0.00839635 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4724.00 | 0.655763 | 0.327881 | − | 0.944719i | \(-0.393665\pi\) | ||||
0.327881 | + | 0.944719i | \(0.393665\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 840.000 | 0.114754 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7292.00 | −0.988298 | −0.494149 | − | 0.869377i | \(-0.664520\pi\) | ||||
−0.494149 | + | 0.869377i | \(0.664520\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14520.0 | 1.93717 | 0.968587 | − | 0.248676i | \(-0.0799956\pi\) | ||||
0.968587 | + | 0.248676i | \(0.0799956\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 300.000 | 0.0397128 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7110.00 | −0.926713 | −0.463356 | − | 0.886172i | \(-0.653355\pi\) | ||||
−0.463356 | + | 0.886172i | \(0.653355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10800.0 | −1.39688 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4580.00 | −0.583405 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11488.0 | −1.45231 | −0.726154 | − | 0.687532i | \(-0.758694\pi\) | ||||
−0.726154 | + | 0.687532i | \(0.758694\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −780.000 | −0.0971355 | −0.0485678 | − | 0.998820i | \(-0.515466\pi\) | ||||
−0.0485678 | + | 0.998820i | \(0.515466\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.0000 | −0.00197771 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6000.00 | 0.730735 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5402.00 | 0.653085 | 0.326542 | − | 0.945183i | \(-0.394116\pi\) | ||||
0.326542 | + | 0.945183i | \(0.394116\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 900.000 | 0.107230 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5700.00 | 0.674222 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2190.00 | −0.255342 | −0.127671 | − | 0.991817i | \(-0.540750\pi\) | ||||
−0.127671 | + | 0.991817i | \(0.540750\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7162.00 | −0.829108 | −0.414554 | − | 0.910025i | \(-0.636062\pi\) | ||||
−0.414554 | + | 0.910025i | \(0.636062\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2250.00 | −0.256802 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 332.000 | 0.0376267 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9360.00 | 1.04607 | 0.523034 | − | 0.852312i | \(-0.324800\pi\) | ||||
0.523034 | + | 0.852312i | \(0.324800\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12806.0 | 1.42129 | 0.710643 | − | 0.703552i | \(-0.248404\pi\) | ||||
0.710643 | + | 0.703552i | \(0.248404\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3360.00 | 0.367805 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11288.0 | −1.22721 | −0.613607 | − | 0.789612i | \(-0.710282\pi\) | ||||
−0.613607 | + | 0.789612i | \(0.710282\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8520.00 | −0.913764 | −0.456882 | − | 0.889527i | \(-0.651034\pi\) | ||||
−0.456882 | + | 0.889527i | \(0.651034\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2100.00 | −0.223707 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1260.00 | 0.132434 | 0.0662172 | − | 0.997805i | \(-0.478907\pi\) | ||||
0.0662172 | + | 0.997805i | \(0.478907\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7200.00 | −0.751740 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −40.0000 | −0.00412138 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13750.0 | −1.40744 | −0.703718 | − | 0.710480i | \(-0.748478\pi\) | ||||
−0.703718 | + | 0.710480i | \(0.748478\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3210.00 | 0.324305 | 0.162152 | − | 0.986766i | \(-0.448156\pi\) | ||||
0.162152 | + | 0.986766i | \(0.448156\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12850.0 | 1.28983 | 0.644914 | − | 0.764255i | \(-0.276893\pi\) | ||||
0.644914 | + | 0.764255i | \(0.276893\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8220.00 | −0.814510 | −0.407255 | − | 0.913314i | \(-0.633514\pi\) | ||||
−0.407255 | + | 0.913314i | \(0.633514\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1816.00 | 0.178795 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4080.00 | 0.396614 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 700.000 | 0.0676173 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7020.00 | −0.669628 | −0.334814 | − | 0.942284i | \(-0.608674\pi\) | ||||
−0.334814 | + | 0.942284i | \(0.608674\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −800.000 | −0.0758355 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7690.00 | −0.719969 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8122.00 | 0.755735 | 0.377868 | − | 0.925860i | \(-0.376657\pi\) | ||||
0.377868 | + | 0.925860i | \(0.376657\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13470.0 | −1.23807 | −0.619035 | − | 0.785363i | \(-0.712476\pi\) | ||||
−0.619035 | + | 0.785363i | \(0.712476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18900.0 | 1.72660 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2040.00 | 0.184118 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2468.00 | −0.221409 | −0.110704 | − | 0.993853i | \(-0.535311\pi\) | ||||
−0.110704 | + | 0.993853i | \(0.535311\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4440.00 | −0.393578 | −0.196789 | − | 0.980446i | \(-0.563051\pi\) | ||||
−0.196789 | + | 0.980446i | \(0.563051\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2250.00 | 0.198265 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11190.0 | 0.974436 | 0.487218 | − | 0.873280i | \(-0.338012\pi\) | ||||
0.487218 | + | 0.873280i | \(0.338012\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 500.000 | 0.0432851 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5750.00 | −0.491991 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3600.00 | −0.306243 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4020.00 | 0.338041 | 0.169021 | − | 0.985613i | \(-0.445940\pi\) | ||||
0.169021 | + | 0.985613i | \(0.445940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9076.00 | 0.758826 | 0.379413 | − | 0.925228i | \(-0.376126\pi\) | ||||
0.379413 | + | 0.925228i | \(0.376126\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −360.000 | −0.0297568 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2233.00 | 0.183529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 960.000 | 0.0780154 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8100.00 | 0.654567 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10170.0 | −0.812714 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7486.00 | −0.594914 | −0.297457 | − | 0.954735i | \(-0.596138\pi\) | ||||
−0.297457 | + | 0.954735i | \(0.596138\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8510.00 | 0.668859 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7400.00 | −0.578430 | −0.289215 | − | 0.957264i | \(-0.593394\pi\) | ||||
−0.289215 | + | 0.957264i | \(0.593394\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5880.00 | −0.454621 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1832.00 | −0.140876 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11490.0 | −0.874052 | −0.437026 | − | 0.899449i | \(-0.643968\pi\) | ||||
−0.437026 | + | 0.899449i | \(0.643968\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −544.000 | −0.0411606 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19320.0 | −1.44625 | −0.723127 | − | 0.690715i | \(-0.757296\pi\) | ||||
−0.723127 | + | 0.690715i | \(0.757296\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6750.00 | 0.502610 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8340.00 | −0.614466 | −0.307233 | − | 0.951634i | \(-0.599403\pi\) | ||||
−0.307233 | + | 0.951634i | \(0.599403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21044.0 | −1.54232 | −0.771159 | − | 0.636642i | \(-0.780323\pi\) | ||||
−0.771159 | + | 0.636642i | \(0.780323\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3000.00 | 0.217580 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1418.00 | 0.102309 | 0.0511543 | − | 0.998691i | \(-0.483710\pi\) | ||||
0.0511543 | + | 0.998691i | \(0.483710\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2280.00 | 0.162806 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 900.000 | 0.0639351 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22020.0 | −1.54832 | −0.774159 | − | 0.632991i | \(-0.781827\pi\) | ||||
−0.774159 | + | 0.632991i | \(0.781827\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 112.000 | 0.00783511 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25230.0 | −1.74717 | −0.873585 | − | 0.486671i | \(-0.838211\pi\) | ||||
−0.873585 | + | 0.486671i | \(0.838211\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −900.000 | −0.0620108 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8280.00 | 0.564794 | 0.282397 | − | 0.959298i | \(-0.408870\pi\) | ||||
0.282397 | + | 0.959298i | \(0.408870\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18874.0 | −1.28101 | −0.640505 | − | 0.767954i | \(-0.721275\pi\) | ||||
−0.640505 | + | 0.767954i | \(0.721275\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2155.00 | 0.144815 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10550.0 | −0.705455 | −0.352728 | − | 0.935726i | \(-0.614746\pi\) | ||||
−0.352728 | + | 0.935726i | \(0.614746\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 480.000 | 0.0317819 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11000.0 | 0.724773 | 0.362386 | − | 0.932028i | \(-0.381962\pi\) | ||||
0.362386 | + | 0.932028i | \(0.381962\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11310.0 | 0.737963 | 0.368982 | − | 0.929437i | \(-0.379706\pi\) | ||||
0.368982 | + | 0.929437i | \(0.379706\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17572.0 | 1.14100 | 0.570499 | − | 0.821298i | \(-0.306750\pi\) | ||||
0.570499 | + | 0.821298i | \(0.306750\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −840.000 | −0.0540191 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18000.0 | −1.14103 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1604.00 | −0.101195 | −0.0505976 | − | 0.998719i | \(-0.516113\pi\) | ||||
−0.0505976 | + | 0.998719i | \(0.516113\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12250.0 | 0.765553 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1356.00 | 0.0843433 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31320.0 | −1.92990 | −0.964950 | − | 0.262435i | \(-0.915475\pi\) | ||||
−0.964950 | + | 0.262435i | \(0.915475\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31300.0 | 1.91968 | 0.959838 | − | 0.280555i | \(-0.0905186\pi\) | ||||
0.959838 | + | 0.280555i | \(0.0905186\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10920.0 | 0.663539 | 0.331769 | − | 0.943361i | \(-0.392354\pi\) | ||||
0.331769 | + | 0.943361i | \(0.392354\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13500.0 | −0.816520 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3210.00 | 0.192369 | 0.0961845 | − | 0.995364i | \(-0.469336\pi\) | ||||
0.0961845 | + | 0.995364i | \(0.469336\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3450.00 | −0.205806 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11910.0 | −0.704018 | −0.352009 | − | 0.935997i | \(-0.614501\pi\) | ||||
−0.352009 | + | 0.935997i | \(0.614501\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3382.00 | −0.199008 | −0.0995042 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995042 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 280.000 | 0.0163277 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25200.0 | −1.46289 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4980.00 | −0.286514 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15950.0 | 0.913562 | 0.456781 | − | 0.889579i | \(-0.349002\pi\) | ||||
0.456781 | + | 0.889579i | \(0.349002\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32190.0 | −1.82742 | −0.913709 | − | 0.406369i | \(-0.866795\pi\) | ||||
−0.913709 | + | 0.406369i | \(0.866795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3076.00 | −0.173853 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22140.0 | 1.24036 | 0.620178 | − | 0.784461i | \(-0.287060\pi\) | ||||
0.620178 | + | 0.784461i | \(0.287060\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10350.0 | 0.577304 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −120.000 | −0.00663518 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6172.00 | 0.339789 | 0.169894 | − | 0.985462i | \(-0.445657\pi\) | ||||
0.169894 | + | 0.985462i | \(0.445657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9620.00 | −0.525047 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21600.0 | 1.17383 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19170.0 | −1.03287 | −0.516434 | − | 0.856327i | \(-0.672741\pi\) | ||||
−0.516434 | + | 0.856327i | \(0.672741\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5600.00 | 0.300438 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 900.000 | 0.0478755 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21898.0 | −1.15994 | −0.579969 | − | 0.814638i | \(-0.696936\pi\) | ||||
−0.579969 | + | 0.814638i | \(0.696936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 480.000 | 0.0252120 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 600.000 | 0.0313828 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16680.0 | 0.865173 | 0.432586 | − | 0.901593i | \(-0.357601\pi\) | ||||
0.432586 | + | 0.901593i | \(0.357601\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2300.00 | −0.118802 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5250.00 | −0.268938 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6518.00 | −0.332516 | −0.166258 | − | 0.986082i | \(-0.553168\pi\) | ||||
−0.166258 | + | 0.986082i | \(0.553168\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12240.0 | −0.619306 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23200.0 | −1.16905 | −0.584524 | − | 0.811377i | \(-0.698719\pi\) | ||||
−0.584524 | + | 0.811377i | \(0.698719\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27240.0 | −1.36146 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16324.0 | 0.812568 | 0.406284 | − | 0.913747i | \(-0.366824\pi\) | ||||
0.406284 | + | 0.913747i | \(0.366824\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −120.000 | −0.00592513 | −0.00296257 | − | 0.999996i | \(-0.500943\pi\) | ||||
−0.00296257 | + | 0.999996i | \(0.500943\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14550.0 | 0.715531 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3240.00 | 0.158060 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30548.0 | −1.48430 | −0.742152 | − | 0.670232i | \(-0.766195\pi\) | ||||
−0.742152 | + | 0.670232i | \(0.766195\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 880.000 | 0.0424192 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16952.0 | 0.813911 | 0.406956 | − | 0.913448i | \(-0.366590\pi\) | ||||
0.406956 | + | 0.913448i | \(0.366590\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20220.0 | 0.963173 | 0.481586 | − | 0.876399i | \(-0.340061\pi\) | ||||
0.481586 | + | 0.876399i | \(0.340061\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3404.00 | 0.161511 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1800.00 | 0.0847382 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20722.0 | −0.971722 | −0.485861 | − | 0.874036i | \(-0.661494\pi\) | ||||
−0.485861 | + | 0.874036i | \(0.661494\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4350.00 | −0.202404 | −0.101202 | − | 0.994866i | \(-0.532269\pi\) | ||||
−0.101202 | + | 0.994866i | \(0.532269\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 100.000 | 0.00463498 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6720.00 | −0.309074 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30600.0 | −1.40199 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11740.0 | −0.533782 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41972.0 | −1.90107 | −0.950534 | − | 0.310621i | \(-0.899463\pi\) | ||||
−0.950534 | + | 0.310621i | \(0.899463\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2700.00 | 0.121367 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 664.000 | 0.0297343 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39510.0 | 1.75598 | 0.877990 | − | 0.478679i | \(-0.158884\pi\) | ||||
0.877990 | + | 0.478679i | \(0.158884\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10800.0 | 0.478193 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7500.00 | −0.329601 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1200.00 | 0.0525397 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16680.0 | −0.724892 | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||||
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15484.0 | 0.670428 | 0.335214 | − | 0.942142i | \(-0.391191\pi\) | ||||
0.335214 | + | 0.942142i | \(0.391191\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9980.00 | −0.428938 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3808.00 | 0.163066 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4170.00 | −0.177264 | −0.0886322 | − | 0.996064i | \(-0.528250\pi\) | ||||
−0.0886322 | + | 0.996064i | \(0.528250\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30226.0 | 1.28021 | 0.640105 | − | 0.768288i | \(-0.278891\pi\) | ||||
0.640105 | + | 0.768288i | \(0.278891\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14760.0 | −0.620623 | −0.310312 | − | 0.950635i | \(-0.600433\pi\) | ||||
−0.310312 | + | 0.950635i | \(0.600433\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9934.00 | −0.416191 | −0.208095 | − | 0.978109i | \(-0.566726\pi\) | ||||
−0.208095 | + | 0.978109i | \(0.566726\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30510.0 | 1.26904 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15600.0 | −0.646539 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23520.0 | −0.967820 | −0.483910 | − | 0.875118i | \(-0.660784\pi\) | ||||
−0.483910 | + | 0.875118i | \(0.660784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19711.0 | 0.808192 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10905.0 | 0.443957 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 862.000 | 0.0349689 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24000.0 | 0.966756 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29816.0 | 1.19681 | 0.598406 | − | 0.801193i | \(-0.295801\pi\) | ||||
0.598406 | + | 0.801193i | \(0.295801\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35430.0 | 1.41221 | 0.706106 | − | 0.708106i | \(-0.250450\pi\) | ||||
0.706106 | + | 0.708106i | \(0.250450\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36196.0 | 1.43771 | 0.718854 | − | 0.695161i | \(-0.244667\pi\) | ||||
0.718854 | + | 0.695161i | \(0.244667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 480.000 | 0.0189332 | 0.00946662 | − | 0.999955i | \(-0.496987\pi\) | ||||
0.00946662 | + | 0.999955i | \(0.496987\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8850.00 | 0.347872 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27480.0 | 1.07272 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3632.00 | 0.141292 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 250.000 | 0.00965891 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28532.0 | 1.09858 | 0.549291 | − | 0.835631i | \(-0.314898\pi\) | ||||
0.549291 | + | 0.835631i | \(0.314898\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20340.0 | 0.777834 | 0.388917 | − | 0.921273i | \(-0.372849\pi\) | ||||
0.388917 | + | 0.921273i | \(0.372849\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10756.0 | 0.409930 | 0.204965 | − | 0.978769i | \(-0.434292\pi\) | ||||
0.204965 | + | 0.978769i | \(0.434292\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 600.000 | 0.0227125 | 0.0113563 | − | 0.999936i | \(-0.496385\pi\) | ||||
0.0113563 | + | 0.999936i | \(0.496385\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4900.00 | 0.184860 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3360.00 | −0.125911 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10650.0 | 0.397754 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −840.000 | −0.0311630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2700.00 | −0.0998336 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8270.00 | 0.303761 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25400.0 | −0.929871 | −0.464936 | − | 0.885345i | \(-0.653923\pi\) | ||||
−0.464936 | + | 0.885345i | \(0.653923\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36240.0 | −1.31799 | −0.658993 | − | 0.752149i | \(-0.729017\pi\) | ||||
−0.658993 | + | 0.752149i | \(0.729017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34200.0 | −1.23971 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1380.00 | −0.0496964 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6572.00 | −0.235898 | −0.117949 | − | 0.993020i | \(-0.537632\pi\) | ||||
−0.117949 | + | 0.993020i | \(0.537632\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4080.00 | 0.145498 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5000.00 | 0.177729 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2340.00 | −0.0826404 | −0.0413202 | − | 0.999146i | \(-0.513156\pi\) | ||||
−0.0413202 | + | 0.999146i | \(0.513156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9492.00 | −0.334144 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13500.0 | 0.472190 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2522.00 | 0.0879297 | 0.0439649 | − | 0.999033i | \(-0.486001\pi\) | ||||
0.0439649 | + | 0.999033i | \(0.486001\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52770.0 | 1.82811 | 0.914056 | − | 0.405589i | \(-0.132933\pi\) | ||||
0.914056 | + | 0.405589i | \(0.132933\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28800.0 | −0.994546 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28200.0 | 0.967663 | 0.483832 | − | 0.875161i | \(-0.339245\pi\) | ||||
0.483832 | + | 0.875161i | \(0.339245\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1000.00 | 0.0342059 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15570.0 | 0.529236 | 0.264618 | − | 0.964353i | \(-0.414754\pi\) | ||||
0.264618 | + | 0.964353i | \(0.414754\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8700.00 | −0.294791 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4140.00 | 0.139403 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29775.0 | −0.999463 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −430.000 | −0.0143442 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8350.00 | 0.277681 | 0.138841 | − | 0.990315i | \(-0.455662\pi\) | ||||
0.138841 | + | 0.990315i | \(0.455662\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43650.0 | 1.44263 | 0.721316 | − | 0.692606i | \(-0.243538\pi\) | ||||
0.721316 | + | 0.692606i | \(0.243538\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3848.00 | −0.126784 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18810.0 | −0.615952 | −0.307976 | − | 0.951394i | \(-0.599652\pi\) | ||||
−0.307976 | + | 0.951394i | \(0.599652\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12600.0 | 0.411336 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25320.0 | −0.821549 | −0.410774 | − | 0.911737i | \(-0.634742\pi\) | ||||
−0.410774 | + | 0.911737i | \(0.634742\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12450.0 | −0.402731 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16320.0 | 0.524718 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6736.00 | 0.215919 | 0.107960 | − | 0.994155i | \(-0.465568\pi\) | ||||
0.107960 | + | 0.994155i | \(0.465568\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4160.00 | −0.132544 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20500.0 | −0.651195 | −0.325598 | − | 0.945508i | \(-0.605565\pi\) | ||||
−0.325598 | + | 0.945508i | \(0.605565\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 720.4.a.h.1.1 | 1 | ||
3.2 | odd | 2 | 720.4.a.w.1.1 | 1 | |||
4.3 | odd | 2 | 180.4.a.b.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 180.4.a.e.1.1 | yes | 1 | ||
20.3 | even | 4 | 900.4.d.d.649.1 | 2 | |||
20.7 | even | 4 | 900.4.d.d.649.2 | 2 | |||
20.19 | odd | 2 | 900.4.a.i.1.1 | 1 | |||
36.7 | odd | 6 | 1620.4.i.i.1081.1 | 2 | |||
36.11 | even | 6 | 1620.4.i.c.1081.1 | 2 | |||
36.23 | even | 6 | 1620.4.i.c.541.1 | 2 | |||
36.31 | odd | 6 | 1620.4.i.i.541.1 | 2 | |||
60.23 | odd | 4 | 900.4.d.i.649.1 | 2 | |||
60.47 | odd | 4 | 900.4.d.i.649.2 | 2 | |||
60.59 | even | 2 | 900.4.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.4.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
180.4.a.e.1.1 | yes | 1 | 12.11 | even | 2 | ||
720.4.a.h.1.1 | 1 | 1.1 | even | 1 | trivial | ||
720.4.a.w.1.1 | 1 | 3.2 | odd | 2 | |||
900.4.a.i.1.1 | 1 | 20.19 | odd | 2 | |||
900.4.a.j.1.1 | 1 | 60.59 | even | 2 | |||
900.4.d.d.649.1 | 2 | 20.3 | even | 4 | |||
900.4.d.d.649.2 | 2 | 20.7 | even | 4 | |||
900.4.d.i.649.1 | 2 | 60.23 | odd | 4 | |||
900.4.d.i.649.2 | 2 | 60.47 | odd | 4 | |||
1620.4.i.c.541.1 | 2 | 36.23 | even | 6 | |||
1620.4.i.c.1081.1 | 2 | 36.11 | even | 6 | |||
1620.4.i.i.541.1 | 2 | 36.31 | odd | 6 | |||
1620.4.i.i.1081.1 | 2 | 36.7 | odd | 6 |