Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.239575536.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 12x^{4} + 8x^{3} + 35x^{2} - 15x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.04302\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-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 | ||||||||
\(3\) | −3.04302 | −1.75689 | −0.878444 | − | 0.477846i | \(-0.841418\pi\) | ||||
−0.878444 | + | 0.477846i | \(0.841418\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.25996 | 2.08665 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.20055 | 0.965002 | 0.482501 | − | 0.875895i | \(-0.339728\pi\) | ||||
0.482501 | + | 0.875895i | \(0.339728\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.25996 | −1.73620 | −0.868100 | − | 0.496389i | \(-0.834659\pi\) | ||||
−0.868100 | + | 0.496389i | \(0.834659\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.78144 | 0.432064 | 0.216032 | − | 0.976386i | \(-0.430689\pi\) | ||||
0.216032 | + | 0.976386i | \(0.430689\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.67654 | −0.843457 | −0.421728 | − | 0.906722i | \(-0.638576\pi\) | ||||
−0.421728 | + | 0.906722i | \(0.638576\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.21694 | 0.670778 | 0.335389 | − | 0.942080i | \(-0.391132\pi\) | ||||
0.335389 | + | 0.942080i | \(0.391132\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9.92011 | −1.90913 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.88463 | 0.535662 | 0.267831 | − | 0.963466i | \(-0.413693\pi\) | ||||
0.267831 | + | 0.963466i | \(0.413693\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.81854 | 0.506226 | 0.253113 | − | 0.967437i | \(-0.418546\pi\) | ||||
0.253113 | + | 0.967437i | \(0.418546\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.73933 | −1.69540 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.08265 | 0.835583 | 0.417792 | − | 0.908543i | \(-0.362804\pi\) | ||||
0.417792 | + | 0.908543i | \(0.362804\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 19.0492 | 3.05031 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.899340 | −0.140453 | −0.0702266 | − | 0.997531i | \(-0.522372\pi\) | ||||
−0.0702266 | + | 0.997531i | \(0.522372\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.26767 | −1.10831 | −0.554155 | − | 0.832414i | \(-0.686959\pi\) | ||||
−0.554155 | + | 0.832414i | \(0.686959\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.52063 | −0.367671 | −0.183836 | − | 0.982957i | \(-0.558851\pi\) | ||||
−0.183836 | + | 0.982957i | \(0.558851\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.42097 | −0.759087 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.04054 | −1.24181 | −0.620907 | − | 0.783884i | \(-0.713236\pi\) | ||||
−0.620907 | + | 0.783884i | \(0.713236\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.1878 | 1.48186 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.58427 | −0.727011 | −0.363505 | − | 0.931592i | \(-0.618420\pi\) | ||||
−0.363505 | + | 0.931592i | \(0.618420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9028 | 1.39596 | 0.697979 | − | 0.716118i | \(-0.254083\pi\) | ||||
0.697979 | + | 0.716118i | \(0.254083\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.40019 | 0.171061 | 0.0855305 | − | 0.996336i | \(-0.472741\pi\) | ||||
0.0855305 | + | 0.996336i | \(0.472741\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.78921 | −1.17848 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.3970 | −1.82729 | −0.913644 | − | 0.406514i | \(-0.866744\pi\) | ||||
−0.913644 | + | 0.406514i | \(0.866744\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.01571 | −0.821127 | −0.410564 | − | 0.911832i | \(-0.634668\pi\) | ||||
−0.410564 | + | 0.911832i | \(0.634668\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.186696 | 0.0210050 | 0.0105025 | − | 0.999945i | \(-0.496657\pi\) | ||||
0.0105025 | + | 0.999945i | \(0.496657\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.4072 | 1.26747 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.134286 | −0.0147398 | −0.00736988 | − | 0.999973i | \(-0.502346\pi\) | ||||
−0.00736988 | + | 0.999973i | \(0.502346\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.77797 | −0.941097 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.4329 | 1.95388 | 0.976941 | − | 0.213509i | \(-0.0684891\pi\) | ||||
0.976941 | + | 0.213509i | \(0.0684891\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.57688 | −0.889381 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.75419 | 0.990388 | 0.495194 | − | 0.868783i | \(-0.335097\pi\) | ||||
0.495194 | + | 0.868783i | \(0.335097\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.0353 | 2.01362 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.01385 | 0.200386 | 0.100193 | − | 0.994968i | \(-0.468054\pi\) | ||||
0.100193 | + | 0.994968i | \(0.468054\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0070 | 1.08455 | 0.542276 | − | 0.840200i | \(-0.317563\pi\) | ||||
0.542276 | + | 0.840200i | \(0.317563\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.20223 | −0.116224 | −0.0581118 | − | 0.998310i | \(-0.518508\pi\) | ||||
−0.0581118 | + | 0.998310i | \(0.518508\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.55494 | 0.819414 | 0.409707 | − | 0.912217i | \(-0.365631\pi\) | ||||
0.409707 | + | 0.912217i | \(0.365631\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.4666 | −1.46803 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.56879 | 0.617940 | 0.308970 | − | 0.951072i | \(-0.400016\pi\) | ||||
0.308970 | + | 0.951072i | \(0.400016\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −39.1871 | −3.62285 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.756478 | −0.0687707 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.73671 | 0.246761 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0999 | −1.16243 | −0.581214 | − | 0.813751i | \(-0.697422\pi\) | ||||
−0.581214 | + | 0.813751i | \(0.697422\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 22.1157 | 1.94718 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.54839 | −0.659506 | −0.329753 | − | 0.944067i | \(-0.606966\pi\) | ||||
−0.329753 | + | 0.944067i | \(0.606966\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.54631 | 0.473854 | 0.236927 | − | 0.971528i | \(-0.423860\pi\) | ||||
0.236927 | + | 0.971528i | \(0.423860\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.2856 | −1.29651 | −0.648256 | − | 0.761423i | \(-0.724501\pi\) | ||||
−0.648256 | + | 0.761423i | \(0.724501\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.67031 | 0.645957 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.0353 | −1.67544 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.74119 | −0.716106 | −0.358053 | − | 0.933701i | \(-0.616559\pi\) | ||||
−0.358053 | + | 0.933701i | \(0.616559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1042 | 1.14778 | 0.573891 | − | 0.818931i | \(-0.305433\pi\) | ||||
0.573891 | + | 0.818931i | \(0.305433\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.1518 | 0.901567 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.910583 | −0.0726724 | −0.0363362 | − | 0.999340i | \(-0.511569\pi\) | ||||
−0.0363362 | + | 0.999340i | \(0.511569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 27.5105 | 2.18173 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.3923 | −0.813991 | −0.406996 | − | 0.913430i | \(-0.633424\pi\) | ||||
−0.406996 | + | 0.913430i | \(0.633424\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.35994 | −0.569529 | −0.284765 | − | 0.958597i | \(-0.591915\pi\) | ||||
−0.284765 | + | 0.958597i | \(0.591915\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.1871 | 2.01439 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23.0150 | −1.76000 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.38925 | 0.333708 | 0.166854 | − | 0.985982i | \(-0.446639\pi\) | ||||
0.166854 | + | 0.985982i | \(0.446639\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.9930 | 1.27728 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.98085 | 0.521774 | 0.260887 | − | 0.965369i | \(-0.415985\pi\) | ||||
0.260887 | + | 0.965369i | \(0.415985\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5217 | 0.782073 | 0.391036 | − | 0.920375i | \(-0.372117\pi\) | ||||
0.391036 | + | 0.920375i | \(0.372117\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −33.1774 | −2.45254 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.70160 | 0.416942 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.29282 | 0.0935450 | 0.0467725 | − | 0.998906i | \(-0.485106\pi\) | ||||
0.0467725 | + | 0.998906i | \(0.485106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.5051 | 0.900134 | 0.450067 | − | 0.892995i | \(-0.351400\pi\) | ||||
0.450067 | + | 0.892995i | \(0.351400\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.2608 | −1.22978 | −0.614891 | − | 0.788612i | \(-0.710800\pi\) | ||||
−0.614891 | + | 0.788612i | \(0.710800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.9502 | −1.41423 | −0.707117 | − | 0.707097i | \(-0.750004\pi\) | ||||
−0.707117 | + | 0.707097i | \(0.750004\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.26082 | −0.300535 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.1379 | 1.39968 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.7670 | −0.813938 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.53377 | 0.518646 | 0.259323 | − | 0.965791i | \(-0.416501\pi\) | ||||
0.259323 | + | 0.965791i | \(0.416501\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 46.8534 | 3.21034 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.3489 | 1.44263 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.1518 | −0.750149 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.2471 | 1.48977 | 0.744887 | − | 0.667191i | \(-0.232504\pi\) | ||||
0.744887 | + | 0.667191i | \(0.232504\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.4944 | 0.829281 | 0.414640 | − | 0.909985i | \(-0.363907\pi\) | ||||
0.414640 | + | 0.909985i | \(0.363907\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.75196 | 0.181854 | 0.0909272 | − | 0.995858i | \(-0.471017\pi\) | ||||
0.0909272 | + | 0.995858i | \(0.471017\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.0742 | 1.57715 | 0.788577 | − | 0.614936i | \(-0.210818\pi\) | ||||
0.788577 | + | 0.614936i | \(0.210818\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.568120 | −0.0369033 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0011 | −0.776290 | −0.388145 | − | 0.921598i | \(-0.626884\pi\) | ||||
−0.388145 | + | 0.921598i | \(0.626884\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.4468 | −0.737355 | −0.368677 | − | 0.929557i | \(-0.620189\pi\) | ||||
−0.368677 | + | 0.929557i | \(0.620189\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.95199 | −0.317670 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.0150 | 1.46441 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.408633 | 0.0258961 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.13791 | 0.261183 | 0.130591 | − | 0.991436i | \(-0.458312\pi\) | ||||
0.130591 | + | 0.991436i | \(0.458312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.2960 | 0.647303 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.2697 | 1.26439 | 0.632196 | − | 0.774809i | \(-0.282154\pi\) | ||||
0.632196 | + | 0.774809i | \(0.282154\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.0576 | 1.11774 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.9590 | 0.984074 | 0.492037 | − | 0.870574i | \(-0.336253\pi\) | ||||
0.492037 | + | 0.870574i | \(0.336253\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −56.0916 | −3.43275 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.6587 | −0.649872 | −0.324936 | − | 0.945736i | \(-0.605343\pi\) | ||||
−0.324936 | + | 0.945736i | \(0.605343\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.3420 | 1.96464 | 0.982318 | − | 0.187221i | \(-0.0599481\pi\) | ||||
0.982318 | + | 0.187221i | \(0.0599481\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.3636 | 0.682770 | 0.341385 | − | 0.939924i | \(-0.389104\pi\) | ||||
0.341385 | + | 0.939924i | \(0.389104\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.6440 | 1.05632 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.49337 | 0.148742 | 0.0743709 | − | 0.997231i | \(-0.476305\pi\) | ||||
0.0743709 | + | 0.997231i | \(0.476305\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.7882 | −1.05740 | −0.528700 | − | 0.848809i | \(-0.677320\pi\) | ||||
−0.528700 | + | 0.848809i | \(0.677320\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.8265 | −0.813321 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −29.6822 | −1.74000 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.0630 | −0.821570 | −0.410785 | − | 0.911732i | \(-0.634745\pi\) | ||||
−0.410785 | + | 0.911732i | \(0.634745\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −31.7498 | −1.84231 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.1379 | −1.16461 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.12819 | −0.352056 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.1448 | 0.578992 | 0.289496 | − | 0.957179i | \(-0.406512\pi\) | ||||
0.289496 | + | 0.957179i | \(0.406512\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −33.4945 | −1.90544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.13868 | 0.291388 | 0.145694 | − | 0.989330i | \(-0.453459\pi\) | ||||
0.145694 | + | 0.989330i | \(0.453459\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.22113 | −0.182069 | −0.0910347 | − | 0.995848i | \(-0.529017\pi\) | ||||
−0.0910347 | + | 0.995848i | \(0.529017\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.7919 | −0.662301 | −0.331150 | − | 0.943578i | \(-0.607437\pi\) | ||||
−0.331150 | + | 0.943578i | \(0.607437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.23239 | 0.516915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.65840 | 0.204192 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.54956 | −0.364427 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −26.0328 | −1.43962 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.2514 | −1.11312 | −0.556560 | − | 0.830808i | \(-0.687879\pi\) | ||||
−0.556560 | + | 0.830808i | \(0.687879\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 31.8172 | 1.74357 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.6086 | 1.28604 | 0.643022 | − | 0.765848i | \(-0.277680\pi\) | ||||
0.643022 | + | 0.765848i | \(0.277680\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.9889 | −1.08565 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.02089 | 0.488509 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.8844 | −1.87269 | −0.936346 | − | 0.351078i | \(-0.885815\pi\) | ||||
−0.936346 | + | 0.351078i | \(0.885815\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.4410 | 1.79006 | 0.895028 | − | 0.446010i | \(-0.147155\pi\) | ||||
0.895028 | + | 0.446010i | \(0.147155\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 62.0995 | 3.31462 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.5633 | −0.721904 | −0.360952 | − | 0.932584i | \(-0.617548\pi\) | ||||
−0.360952 | + | 0.932584i | \(0.617548\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.9079 | −1.10348 | −0.551739 | − | 0.834017i | \(-0.686036\pi\) | ||||
−0.551739 | + | 0.834017i | \(0.686036\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.48303 | −0.288581 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.30198 | 0.120822 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.7555 | −1.03123 | −0.515615 | − | 0.856820i | \(-0.672436\pi\) | ||||
−0.515615 | + | 0.856820i | \(0.672436\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.62983 | −0.293077 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.06795 | 0.417743 | 0.208871 | − | 0.977943i | \(-0.433021\pi\) | ||||
0.208871 | + | 0.977943i | \(0.433021\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.0576 | −0.930016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.1761 | 1.44731 | 0.723655 | − | 0.690162i | \(-0.242461\pi\) | ||||
0.723655 | + | 0.690162i | \(0.242461\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 39.8632 | 2.04225 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.3412 | −1.49926 | −0.749632 | − | 0.661855i | \(-0.769769\pi\) | ||||
−0.749632 | + | 0.661855i | \(0.769769\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −45.4953 | −2.31266 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.52293 | −0.229322 | −0.114661 | − | 0.993405i | \(-0.536578\pi\) | ||||
−0.114661 | + | 0.993405i | \(0.536578\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.73080 | 0.289819 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.9699 | 1.15868 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.0352 | −1.25648 | −0.628239 | − | 0.778020i | \(-0.716224\pi\) | ||||
−0.628239 | + | 0.778020i | \(0.716224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.5942 | 1.37799 | 0.688995 | − | 0.724766i | \(-0.258052\pi\) | ||||
0.688995 | + | 0.724766i | \(0.258052\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.6440 | −0.878909 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.2673 | 0.806340 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.5428 | −1.55969 | −0.779846 | − | 0.625971i | \(-0.784703\pi\) | ||||
−0.779846 | + | 0.625971i | \(0.784703\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.8775 | −0.832507 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 46.5145 | 2.27782 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.8997 | −1.65611 | −0.828055 | − | 0.560647i | \(-0.810552\pi\) | ||||
−0.828055 | + | 0.560647i | \(0.810552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.93350 | −0.435392 | −0.217696 | − | 0.976017i | \(-0.569854\pi\) | ||||
−0.217696 | + | 0.976017i | \(0.569854\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.7790 | −0.767202 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 60.9678 | 2.94355 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.10828 | −0.438731 | −0.219365 | − | 0.975643i | \(-0.570399\pi\) | ||||
−0.219365 | + | 0.975643i | \(0.570399\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.2953 | −1.84035 | −0.920177 | − | 0.391504i | \(-0.871955\pi\) | ||||
−0.920177 | + | 0.391504i | \(0.871955\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.8272 | −0.565773 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.14647 | −0.436537 | −0.218269 | − | 0.975889i | \(-0.570041\pi\) | ||||
−0.218269 | + | 0.975889i | \(0.570041\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.81570 | 0.181289 | 0.0906447 | − | 0.995883i | \(-0.471107\pi\) | ||||
0.0906447 | + | 0.995883i | \(0.471107\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26.5996 | 1.25812 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.1990 | −1.75553 | −0.877764 | − | 0.479092i | \(-0.840966\pi\) | ||||
−0.877764 | + | 0.479092i | \(0.840966\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.87838 | −0.135538 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −42.9193 | −2.01652 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.77887 | −0.223546 | −0.111773 | − | 0.993734i | \(-0.535653\pi\) | ||||
−0.111773 | + | 0.993734i | \(0.535653\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.6721 | −0.824864 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.6903 | 1.52254 | 0.761269 | − | 0.648436i | \(-0.224577\pi\) | ||||
0.761269 | + | 0.648436i | \(0.224577\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.36482 | −0.295798 | −0.147899 | − | 0.989002i | \(-0.547251\pi\) | ||||
−0.147899 | + | 0.989002i | \(0.547251\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.0339 | −1.20470 | −0.602352 | − | 0.798231i | \(-0.705769\pi\) | ||||
−0.602352 | + | 0.798231i | \(0.705769\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.77092 | 0.127677 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.2606 | −1.06952 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −56.5934 | −2.59123 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.66850 | −0.0762357 | −0.0381178 | − | 0.999273i | \(-0.512136\pi\) | ||||
−0.0381178 | + | 0.999273i | \(0.512136\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.8172 | −1.45074 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.58671 | 0.0719006 | 0.0359503 | − | 0.999354i | \(-0.488554\pi\) | ||||
0.0359503 | + | 0.999354i | \(0.488554\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31.6241 | 1.43009 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.8237 | −1.21054 | −0.605269 | − | 0.796021i | \(-0.706934\pi\) | ||||
−0.605269 | + | 0.796021i | \(0.706934\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.13880 | 0.231440 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.0985 | −0.989263 | −0.494631 | − | 0.869103i | \(-0.664697\pi\) | ||||
−0.494631 | + | 0.869103i | \(0.664697\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.3964 | 1.00060 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.937839 | −0.0418162 | −0.0209081 | − | 0.999781i | \(-0.506656\pi\) | ||||
−0.0209081 | + | 0.999781i | \(0.506656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −79.6877 | −3.53906 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.7200 | 0.475157 | 0.237578 | − | 0.971368i | \(-0.423646\pi\) | ||||
0.237578 | + | 0.971368i | \(0.423646\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 36.4717 | 1.61027 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.06739 | −0.354803 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.3566 | −0.586288 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −43.4900 | −1.90533 | −0.952666 | − | 0.304018i | \(-0.901672\pi\) | ||||
−0.952666 | + | 0.304018i | \(0.901672\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.58671 | −0.0693819 | −0.0346909 | − | 0.999398i | \(-0.511045\pi\) | ||||
−0.0346909 | + | 0.999398i | \(0.511045\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.02108 | 0.218722 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.6513 | −0.550056 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −34.9573 | −1.51702 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.62983 | 0.243855 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.2429 | −0.916697 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.70954 | 0.288466 | 0.144233 | − | 0.989544i | \(-0.453929\pi\) | ||||
0.144233 | + | 0.989544i | \(0.453929\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.0178 | −1.37401 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.34916 | −0.271470 | −0.135735 | − | 0.990745i | \(-0.543340\pi\) | ||||
−0.135735 | + | 0.990745i | \(0.543340\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 68.2510 | 2.91288 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.6055 | −0.451807 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −40.8845 | −1.73233 | −0.866166 | − | 0.499756i | \(-0.833423\pi\) | ||||
−0.866166 | + | 0.499756i | \(0.833423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.4953 | 1.92425 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.3501 | −0.732521 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.3938 | 1.57596 | 0.787981 | − | 0.615700i | \(-0.211127\pi\) | ||||
0.787981 | + | 0.615700i | \(0.211127\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.893881 | −0.0374734 | −0.0187367 | − | 0.999824i | \(-0.505964\pi\) | ||||
−0.0187367 | + | 0.999824i | \(0.505964\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.1786 | 0.969994 | 0.484997 | − | 0.874516i | \(-0.338821\pi\) | ||||
0.484997 | + | 0.874516i | \(0.338821\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.93407 | −0.164348 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.25249 | 0.177033 | 0.0885166 | − | 0.996075i | \(-0.471787\pi\) | ||||
0.0885166 | + | 0.996075i | \(0.471787\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −38.0531 | −1.58143 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.9347 | −1.19835 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.3127 | −0.962218 | −0.481109 | − | 0.876661i | \(-0.659766\pi\) | ||||
−0.481109 | + | 0.876661i | \(0.659766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.3625 | −0.426979 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 52.5250 | 2.16059 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.347733 | 0.0142797 | 0.00713984 | − | 0.999975i | \(-0.497727\pi\) | ||||
0.00713984 | + | 0.999975i | \(0.497727\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 60.7089 | 2.48465 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.1256 | −1.27176 | −0.635880 | − | 0.771788i | \(-0.719363\pi\) | ||||
−0.635880 | + | 0.771788i | \(0.719363\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.9573 | −1.18119 | −0.590597 | − | 0.806967i | \(-0.701108\pi\) | ||||
−0.590597 | + | 0.806967i | \(0.701108\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.76516 | 0.356945 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.0209 | −0.893799 | −0.446900 | − | 0.894584i | \(-0.647472\pi\) | ||||
−0.446900 | + | 0.894584i | \(0.647472\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.7790 | 0.638351 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.18218 | 0.128527 | 0.0642636 | − | 0.997933i | \(-0.479530\pi\) | ||||
0.0642636 | + | 0.997933i | \(0.479530\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.7426 | −1.64024 | −0.820119 | − | 0.572194i | \(-0.806093\pi\) | ||||
−0.820119 | + | 0.572194i | \(0.806093\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.5019 | 0.623075 | 0.311537 | − | 0.950234i | \(-0.399156\pi\) | ||||
0.311537 | + | 0.950234i | \(0.399156\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −31.9124 | −1.28060 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 35.8071 | 1.43000 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.05446 | 0.361025 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.15519 | 0.364462 | 0.182231 | − | 0.983256i | \(-0.441668\pi\) | ||||
0.182231 | + | 0.983256i | \(0.441668\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.9254 | −0.911203 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −96.3846 | −3.81292 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.41967 | 0.135069 | 0.0675343 | − | 0.997717i | \(-0.478487\pi\) | ||||
0.0675343 | + | 0.997717i | \(0.478487\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.9753 | −1.73421 | −0.867107 | − | 0.498121i | \(-0.834023\pi\) | ||||
−0.867107 | + | 0.498121i | \(0.834023\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.5869 | 0.573470 | 0.286735 | − | 0.958010i | \(-0.407430\pi\) | ||||
0.286735 | + | 0.958010i | \(0.407430\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.8728 | −0.701567 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.6812 | 0.926715 | 0.463358 | − | 0.886171i | \(-0.346645\pi\) | ||||
0.463358 | + | 0.886171i | \(0.346645\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −43.9181 | −1.71341 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.0130 | −0.857503 | −0.428751 | − | 0.903422i | \(-0.641046\pi\) | ||||
−0.428751 | + | 0.903422i | \(0.641046\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.1884 | −0.785239 | −0.392619 | − | 0.919701i | \(-0.628431\pi\) | ||||
−0.392619 | + | 0.919701i | \(0.628431\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 33.9350 | 1.31793 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.27967 | 0.359310 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −67.6982 | −2.61736 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.8949 | 1.34710 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.7957 | 1.26418 | 0.632091 | − | 0.774894i | \(-0.282197\pi\) | ||||
0.632091 | + | 0.774894i | \(0.282197\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.98825 | −0.307013 | −0.153507 | − | 0.988148i | \(-0.549057\pi\) | ||||
−0.153507 | + | 0.988148i | \(0.549057\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −38.0206 | −1.45695 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.0090 | 0.995207 | 0.497604 | − | 0.867405i | \(-0.334213\pi\) | ||||
0.497604 | + | 0.867405i | \(0.334213\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.37425 | −0.319498 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 56.5934 | 2.15604 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.63696 | 0.366607 | 0.183304 | − | 0.983056i | \(-0.441321\pi\) | ||||
0.183304 | + | 0.983056i | \(0.441321\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.60212 | −0.0606847 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −73.2583 | −2.77088 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.3814 | −1.41188 | −0.705938 | − | 0.708274i | \(-0.749474\pi\) | ||||
−0.705938 | + | 0.708274i | \(0.749474\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.6866 | −0.704778 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.21700 | −0.271040 | −0.135520 | − | 0.990775i | \(-0.543270\pi\) | ||||
−0.135520 | + | 0.990775i | \(0.543270\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.16871 | 0.0438301 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.06709 | 0.339565 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 36.5197 | 1.36385 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.3761 | 1.69224 | 0.846121 | − | 0.532991i | \(-0.178932\pi\) | ||||
0.846121 | + | 0.532991i | \(0.178932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.8329 | 1.29545 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.3119 | −0.604976 | −0.302488 | − | 0.953153i | \(-0.597817\pi\) | ||||
−0.302488 | + | 0.953153i | \(0.597817\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.1526 | −0.709356 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.9470 | −0.478860 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.1208 | −1.07560 | −0.537801 | − | 0.843072i | \(-0.680745\pi\) | ||||
−0.537801 | + | 0.843072i | \(0.680745\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.48139 | 0.165074 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.5275 | −1.45404 | −0.727021 | − | 0.686616i | \(-0.759096\pi\) | ||||
−0.727021 | + | 0.686616i | \(0.759096\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −70.0351 | −2.57280 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.7213 | 0.576759 | 0.288379 | − | 0.957516i | \(-0.406884\pi\) | ||||
0.288379 | + | 0.957516i | \(0.406884\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.840622 | −0.0307568 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.2601 | −1.21368 | −0.606840 | − | 0.794824i | \(-0.707563\pi\) | ||||
−0.606840 | + | 0.794824i | \(0.707563\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.5917 | −0.458868 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.5431 | −1.29183 | −0.645917 | − | 0.763407i | \(-0.723525\pi\) | ||||
−0.645917 | + | 0.763407i | \(0.723525\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31.3308 | −1.13724 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.5071 | 0.453384 | 0.226692 | − | 0.973967i | \(-0.427209\pi\) | ||||
0.226692 | + | 0.973967i | \(0.427209\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.9573 | 1.26224 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.2730 | 0.695003 | 0.347501 | − | 0.937679i | \(-0.387030\pi\) | ||||
0.347501 | + | 0.937679i | \(0.387030\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −61.6812 | −2.22139 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.9871 | 0.431146 | 0.215573 | − | 0.976488i | \(-0.430838\pi\) | ||||
0.215573 | + | 0.976488i | \(0.430838\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.30646 | 0.118466 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −49.2789 | −1.76334 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.6158 | −1.02265 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.0423 | −0.999599 | −0.499800 | − | 0.866141i | \(-0.666593\pi\) | ||||
−0.499800 | + | 0.866141i | \(0.666593\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −48.5635 | −1.72891 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −68.2510 | −2.42366 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.4252 | 0.510967 | 0.255484 | − | 0.966813i | \(-0.417765\pi\) | ||||
0.255484 | + | 0.966813i | \(0.417765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.49035 | −0.158857 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 115.389 | 4.07707 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.4541 | −0.792390 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.4346 | 1.14175 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.8536 | −0.627698 | −0.313849 | − | 0.949473i | \(-0.601619\pi\) | ||||
−0.313849 | + | 0.949473i | \(0.601619\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0944 | 0.389576 | 0.194788 | − | 0.980845i | \(-0.437598\pi\) | ||||
0.194788 | + | 0.980845i | \(0.437598\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −98.4172 | −3.45164 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.7199 | 0.934812 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.7820 | −1.42330 | −0.711650 | − | 0.702534i | \(-0.752052\pi\) | ||||
−0.711650 | + | 0.702534i | \(0.752052\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.57749 | 0.229277 | 0.114638 | − | 0.993407i | \(-0.463429\pi\) | ||||
0.114638 | + | 0.993407i | \(0.463429\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.3109 | 0.984468 | 0.492234 | − | 0.870463i | \(-0.336180\pi\) | ||||
0.492234 | + | 0.870463i | \(0.336180\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.95880 | 0.276421 | 0.138210 | − | 0.990403i | \(-0.455865\pi\) | ||||
0.138210 | + | 0.990403i | \(0.455865\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −34.5795 | −1.19955 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.9603 | −0.966449 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.8178 | −1.37466 | −0.687331 | − | 0.726344i | \(-0.741218\pi\) | ||||
−0.687331 | + | 0.726344i | \(0.741218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.6789 | −0.713067 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.58736 | −0.261323 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 54.1298 | 1.85773 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.3506 | 0.560491 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.5544 | 0.738007 | 0.369004 | − | 0.929428i | \(-0.379699\pi\) | ||||
0.369004 | + | 0.929428i | \(0.379699\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.01622 | −0.0347133 | −0.0173566 | − | 0.999849i | \(-0.505525\pi\) | ||||
−0.0173566 | + | 0.999849i | \(0.505525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.9605 | −1.09048 | −0.545240 | − | 0.838280i | \(-0.683561\pi\) | ||||
−0.545240 | + | 0.838280i | \(0.683561\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.9315 | 0.848679 | 0.424339 | − | 0.905503i | \(-0.360506\pi\) | ||||
0.424339 | + | 0.905503i | \(0.360506\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.0742 | 1.42891 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.597531 | 0.0202698 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.76516 | −0.296996 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 61.0608 | 2.06659 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.9702 | −1.55230 | −0.776151 | − | 0.630547i | \(-0.782831\pi\) | ||||
−0.776151 | + | 0.630547i | \(0.782831\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 42.7940 | 1.44341 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.7324 | 0.698493 | 0.349247 | − | 0.937031i | \(-0.386438\pi\) | ||||
0.349247 | + | 0.937031i | \(0.386438\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.32252 | 0.0781589 | 0.0390795 | − | 0.999236i | \(-0.487557\pi\) | ||||
0.0390795 | + | 0.999236i | \(0.487557\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.2867 | −0.479702 | −0.239851 | − | 0.970810i | \(-0.577099\pi\) | ||||
−0.239851 | + | 0.970810i | \(0.577099\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36.5093 | 1.22311 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.26719 | 0.310115 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 61.2800 | 2.04608 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.13045 | 0.271166 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.1052 | −0.536543 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.0737 | 1.23101 | 0.615506 | − | 0.788132i | \(-0.288951\pi\) | ||||
0.615506 | + | 0.788132i | \(0.288951\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.6066 | 0.418136 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.9023 | 0.559999 | 0.280000 | − | 0.960000i | \(-0.409666\pi\) | ||||
0.280000 | + | 0.960000i | \(0.409666\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.429788 | −0.0142239 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.01558 | −0.0335010 | −0.0167505 | − | 0.999860i | \(-0.505332\pi\) | ||||
−0.0167505 | + | 0.999860i | \(0.505332\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.8707 | −1.01722 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 96.3846 | 3.17254 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 68.9034 | 2.26308 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.1114 | −1.57848 | −0.789242 | − | 0.614083i | \(-0.789526\pi\) | ||||
−0.789242 | + | 0.614083i | \(0.789526\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.6371 | −0.511936 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.00982 | −0.0983267 | −0.0491633 | − | 0.998791i | \(-0.515655\pi\) | ||||
−0.0491633 | + | 0.998791i | \(0.515655\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.80197 | 0.319875 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.5682 | 0.637904 | 0.318952 | − | 0.947771i | \(-0.396669\pi\) | ||||
0.318952 | + | 0.947771i | \(0.396669\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.89312 | −0.0942130 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.5651 | 0.343321 | 0.171661 | − | 0.985156i | \(-0.445087\pi\) | ||||
0.171661 | + | 0.985156i | \(0.445087\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.9181 | 1.42564 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 35.8830 | 1.16359 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.3529 | −1.56630 | −0.783152 | − | 0.621830i | \(-0.786389\pi\) | ||||
−0.783152 | + | 0.621830i | \(0.786389\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −28.0943 | −0.908161 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0558 | −0.743736 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.52589 | −0.242518 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.4047 | 1.23501 | 0.617506 | − | 0.786566i | \(-0.288143\pi\) | ||||
0.617506 | + | 0.786566i | \(0.288143\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.9304 | 0.640257 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.71416 | 0.311742 | 0.155871 | − | 0.987777i | \(-0.450182\pi\) | ||||
0.155871 | + | 0.987777i | \(0.450182\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.3191 | 0.586080 | 0.293040 | − | 0.956100i | \(-0.405333\pi\) | ||||
0.293040 | + | 0.956100i | \(0.405333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.9954 | 1.88550 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 53.5535 | 1.70983 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.9575 | 0.413280 | 0.206640 | − | 0.978417i | \(-0.433747\pi\) | ||||
0.206640 | + | 0.978417i | \(0.433747\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.3797 | −0.743430 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4708 | −0.809107 | −0.404553 | − | 0.914514i | \(-0.632573\pi\) | ||||
−0.404553 | + | 0.914514i | \(0.632573\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 61.6255 | 1.95563 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.7938 | 1.57699 | 0.788493 | − | 0.615043i | \(-0.210862\pi\) | ||||
0.788493 | + | 0.615043i | \(0.210862\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −50.4205 | −1.59523 |
(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 | 9800.2.a.cv.1.1 | 6 | ||
5.2 | odd | 4 | 1960.2.g.f.1569.12 | 12 | |||
5.3 | odd | 4 | 1960.2.g.f.1569.1 | 12 | |||
5.4 | even | 2 | 9800.2.a.cx.1.6 | 6 | |||
7.2 | even | 3 | 1400.2.q.o.1201.6 | 12 | |||
7.4 | even | 3 | 1400.2.q.o.401.6 | 12 | |||
7.6 | odd | 2 | 9800.2.a.cy.1.6 | 6 | |||
35.2 | odd | 12 | 280.2.bg.a.249.1 | yes | 24 | ||
35.4 | even | 6 | 1400.2.q.n.401.1 | 12 | |||
35.9 | even | 6 | 1400.2.q.n.1201.1 | 12 | |||
35.13 | even | 4 | 1960.2.g.e.1569.12 | 12 | |||
35.18 | odd | 12 | 280.2.bg.a.9.1 | ✓ | 24 | ||
35.23 | odd | 12 | 280.2.bg.a.249.12 | yes | 24 | ||
35.27 | even | 4 | 1960.2.g.e.1569.1 | 12 | |||
35.32 | odd | 12 | 280.2.bg.a.9.12 | yes | 24 | ||
35.34 | odd | 2 | 9800.2.a.cw.1.1 | 6 | |||
140.23 | even | 12 | 560.2.bw.f.529.1 | 24 | |||
140.67 | even | 12 | 560.2.bw.f.289.1 | 24 | |||
140.107 | even | 12 | 560.2.bw.f.529.12 | 24 | |||
140.123 | even | 12 | 560.2.bw.f.289.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bg.a.9.1 | ✓ | 24 | 35.18 | odd | 12 | ||
280.2.bg.a.9.12 | yes | 24 | 35.32 | odd | 12 | ||
280.2.bg.a.249.1 | yes | 24 | 35.2 | odd | 12 | ||
280.2.bg.a.249.12 | yes | 24 | 35.23 | odd | 12 | ||
560.2.bw.f.289.1 | 24 | 140.67 | even | 12 | |||
560.2.bw.f.289.12 | 24 | 140.123 | even | 12 | |||
560.2.bw.f.529.1 | 24 | 140.23 | even | 12 | |||
560.2.bw.f.529.12 | 24 | 140.107 | even | 12 | |||
1400.2.q.n.401.1 | 12 | 35.4 | even | 6 | |||
1400.2.q.n.1201.1 | 12 | 35.9 | even | 6 | |||
1400.2.q.o.401.6 | 12 | 7.4 | even | 3 | |||
1400.2.q.o.1201.6 | 12 | 7.2 | even | 3 | |||
1960.2.g.e.1569.1 | 12 | 35.27 | even | 4 | |||
1960.2.g.e.1569.12 | 12 | 35.13 | even | 4 | |||
1960.2.g.f.1569.1 | 12 | 5.3 | odd | 4 | |||
1960.2.g.f.1569.12 | 12 | 5.2 | odd | 4 | |||
9800.2.a.cv.1.1 | 6 | 1.1 | even | 1 | trivial | ||
9800.2.a.cw.1.1 | 6 | 35.34 | odd | 2 | |||
9800.2.a.cx.1.6 | 6 | 5.4 | even | 2 | |||
9800.2.a.cy.1.6 | 6 | 7.6 | odd | 2 |