Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(1,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1148.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1935333.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 8x^{3} + 10x^{2} + 13x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.10409\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.1 |
$q$-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 | ||||||||
\(3\) | −2.10409 | −1.21480 | −0.607399 | − | 0.794397i | \(-0.707787\pi\) | ||||
−0.607399 | + | 0.794397i | \(0.707787\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.26228 | −0.564509 | −0.282254 | − | 0.959340i | \(-0.591082\pi\) | ||||
−0.282254 | + | 0.959340i | \(0.591082\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.42721 | 0.475736 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.91823 | −1.18139 | −0.590696 | − | 0.806894i | \(-0.701147\pi\) | ||||
−0.590696 | + | 0.806894i | \(0.701147\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.38693 | 0.662016 | 0.331008 | − | 0.943628i | \(-0.392611\pi\) | ||||
0.331008 | + | 0.943628i | \(0.392611\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.65595 | 0.685764 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.14698 | −1.49086 | −0.745431 | − | 0.666583i | \(-0.767756\pi\) | ||||
−0.745431 | + | 0.666583i | \(0.767756\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.49103 | 1.25973 | 0.629864 | − | 0.776706i | \(-0.283111\pi\) | ||||
0.629864 | + | 0.776706i | \(0.283111\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.10409 | −0.459151 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.104093 | −0.0217050 | −0.0108525 | − | 0.999941i | \(-0.503455\pi\) | ||||
−0.0108525 | + | 0.999941i | \(0.503455\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.40665 | −0.681330 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.30930 | 0.636875 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.65595 | −0.493198 | −0.246599 | − | 0.969118i | \(-0.579313\pi\) | ||||
−0.246599 | + | 0.969118i | \(0.579313\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.26228 | 0.585923 | 0.292961 | − | 0.956124i | \(-0.405359\pi\) | ||||
0.292961 | + | 0.956124i | \(0.405359\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.24433 | 1.43515 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.26228 | −0.213364 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.993257 | 0.163290 | 0.0816452 | − | 0.996661i | \(-0.473983\pi\) | ||||
0.0816452 | + | 0.996661i | \(0.473983\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.02233 | −0.804216 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.14698 | 1.24240 | 0.621201 | − | 0.783651i | \(-0.286645\pi\) | ||||
0.621201 | + | 0.783651i | \(0.286645\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.80154 | −0.268557 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.90302 | 0.277584 | 0.138792 | − | 0.990322i | \(-0.455678\pi\) | ||||
0.138792 | + | 0.990322i | \(0.455678\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.9338 | 1.81110 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.26228 | 0.173387 | 0.0866937 | − | 0.996235i | \(-0.472370\pi\) | ||||
0.0866937 | + | 0.996235i | \(0.472370\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.94591 | 0.666906 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.5536 | −1.53032 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.24433 | 1.07332 | 0.536660 | − | 0.843798i | \(-0.319686\pi\) | ||||
0.536660 | + | 0.843798i | \(0.319686\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.89507 | 0.882823 | 0.441411 | − | 0.897305i | \(-0.354478\pi\) | ||||
0.441411 | + | 0.897305i | \(0.354478\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.42721 | 0.179811 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.01298 | −0.373714 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.69660 | 1.06246 | 0.531230 | − | 0.847228i | \(-0.321730\pi\) | ||||
0.531230 | + | 0.847228i | \(0.321730\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.219022 | 0.0263672 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.827998 | 0.0982653 | 0.0491326 | − | 0.998792i | \(-0.484354\pi\) | ||||
0.0491326 | + | 0.998792i | \(0.484354\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.44279 | 0.988154 | 0.494077 | − | 0.869418i | \(-0.335506\pi\) | ||||
0.494077 | + | 0.869418i | \(0.335506\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.16791 | 0.827679 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.91823 | −0.446524 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.27079 | −0.593010 | −0.296505 | − | 0.955031i | \(-0.595821\pi\) | ||||
−0.296505 | + | 0.955031i | \(0.595821\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2447 | −1.24941 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.82800 | 0.749470 | 0.374735 | − | 0.927132i | \(-0.377734\pi\) | ||||
0.374735 | + | 0.927132i | \(0.377734\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.75921 | 0.841604 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.58838 | 0.599137 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.9212 | 1.15765 | 0.578823 | − | 0.815453i | \(-0.303512\pi\) | ||||
0.578823 | + | 0.815453i | \(0.303512\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.38693 | 0.250218 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.86414 | −0.711778 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.93121 | −0.711127 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.31228 | 0.843984 | 0.421992 | − | 0.906600i | \(-0.361331\pi\) | ||||
0.421992 | + | 0.906600i | \(0.361331\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.59214 | −0.562031 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.13902 | 0.610856 | 0.305428 | − | 0.952215i | \(-0.401201\pi\) | ||||
0.305428 | + | 0.952215i | \(0.401201\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.28424 | −0.225072 | −0.112536 | − | 0.993648i | \(-0.535897\pi\) | ||||
−0.112536 | + | 0.993648i | \(0.535897\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.65595 | 0.259195 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.4995 | 1.49840 | 0.749198 | − | 0.662346i | \(-0.230439\pi\) | ||||
0.749198 | + | 0.662346i | \(0.230439\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.10372 | 0.105717 | 0.0528587 | − | 0.998602i | \(-0.483167\pi\) | ||||
0.0528587 | + | 0.998602i | \(0.483167\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.08991 | −0.198365 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.61893 | −0.622656 | −0.311328 | − | 0.950302i | \(-0.600774\pi\) | ||||
−0.311328 | + | 0.950302i | \(0.600774\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.131395 | 0.0122526 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.40665 | 0.314945 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.14698 | −0.563493 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.35256 | 0.395687 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.10409 | −0.189720 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.6115 | 0.949125 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.58163 | −0.761497 | −0.380748 | − | 0.924679i | \(-0.624334\pi\) | ||||
−0.380748 | + | 0.924679i | \(0.624334\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.1420 | −1.50927 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.751206 | 0.0656332 | 0.0328166 | − | 0.999461i | \(-0.489552\pi\) | ||||
0.0328166 | + | 0.999461i | \(0.489552\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.49103 | 0.476132 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.17726 | −0.359521 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.17651 | −0.100516 | −0.0502579 | − | 0.998736i | \(-0.516004\pi\) | ||||
−0.0502579 | + | 0.998736i | \(0.516004\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8173 | −1.42643 | −0.713213 | − | 0.700948i | \(-0.752761\pi\) | ||||
−0.713213 | + | 0.700948i | \(0.752761\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00413 | −0.337209 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.35256 | −0.782100 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.35256 | 0.278415 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.10409 | −0.173543 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.3431 | −1.42080 | −0.710400 | − | 0.703798i | \(-0.751486\pi\) | ||||
−0.710400 | + | 0.703798i | \(0.751486\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.5151 | 1.50674 | 0.753368 | − | 0.657599i | \(-0.228428\pi\) | ||||
0.753368 | + | 0.657599i | \(0.228428\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.77302 | −0.709257 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.11791 | −0.330758 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.3128 | −1.78076 | −0.890379 | − | 0.455220i | \(-0.849561\pi\) | ||||
−0.890379 | + | 0.455220i | \(0.849561\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.65595 | −0.210631 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.104093 | −0.00820370 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.444887 | −0.0348462 | −0.0174231 | − | 0.999848i | \(-0.505546\pi\) | ||||
−0.0174231 | + | 0.999848i | \(0.505546\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.4067 | −0.810157 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0924 | 0.935736 | 0.467868 | − | 0.883798i | \(-0.345022\pi\) | ||||
0.467868 | + | 0.883798i | \(0.345022\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.30256 | −0.561735 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.83684 | 0.599298 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.3598 | 1.09176 | 0.545878 | − | 0.837865i | \(-0.316196\pi\) | ||||
0.545878 | + | 0.837865i | \(0.316196\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.40665 | −0.257519 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.3468 | −1.30387 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.3740 | 0.999620 | 0.499810 | − | 0.866135i | \(-0.333403\pi\) | ||||
0.499810 | + | 0.866135i | \(0.333403\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.5977 | −0.787723 | −0.393861 | − | 0.919170i | \(-0.628861\pi\) | ||||
−0.393861 | + | 0.919170i | \(0.628861\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.5079 | −1.07245 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.25377 | −0.0921789 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.0853 | 1.76129 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.30930 | 0.240716 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.53879 | −0.473130 | −0.236565 | − | 0.971616i | \(-0.576022\pi\) | ||||
−0.236565 | + | 0.971616i | \(0.576022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.3398 | −1.89598 | −0.947991 | − | 0.318297i | \(-0.896889\pi\) | ||||
−0.947991 | + | 0.318297i | \(0.896889\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.33958 | 0.453987 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.21409 | 0.228994 | 0.114497 | − | 0.993424i | \(-0.463474\pi\) | ||||
0.114497 | + | 0.993424i | \(0.463474\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.75419 | −0.407903 | −0.203952 | − | 0.978981i | \(-0.565379\pi\) | ||||
−0.203952 | + | 0.978981i | \(0.565379\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.2985 | −1.29067 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.65595 | −0.186411 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.26228 | −0.0881614 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.148563 | −0.0103258 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.5151 | −1.48823 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.3573 | 0.850709 | 0.425355 | − | 0.905027i | \(-0.360149\pi\) | ||||
0.425355 | + | 0.905027i | \(0.360149\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.74218 | −0.119373 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.2838 | −0.701347 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.26228 | 0.221458 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.7644 | −1.20041 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.6724 | −0.986974 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7226 | 1.45465 | 0.727325 | − | 0.686293i | \(-0.240763\pi\) | ||||
0.727325 | + | 0.686293i | \(0.240763\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.86200 | −0.324133 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.38846 | −0.0921551 | −0.0460775 | − | 0.998938i | \(-0.514672\pi\) | ||||
−0.0460775 | + | 0.998938i | \(0.514672\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8059 | 0.978402 | 0.489201 | − | 0.872171i | \(-0.337288\pi\) | ||||
0.489201 | + | 0.872171i | \(0.337288\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.24433 | 0.542437 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.48963 | −0.163101 | −0.0815505 | − | 0.996669i | \(-0.525987\pi\) | ||||
−0.0815505 | + | 0.996669i | \(0.525987\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.40214 | −0.156699 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.0902 | 0.720388 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.69781 | −0.562615 | −0.281307 | − | 0.959618i | \(-0.590768\pi\) | ||||
−0.281307 | + | 0.959618i | \(0.590768\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.0312 | −1.03266 | −0.516329 | − | 0.856390i | \(-0.672702\pi\) | ||||
−0.516329 | + | 0.856390i | \(0.672702\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.7320 | 0.880908 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.26228 | −0.0806441 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.1067 | 0.833959 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.3667 | −0.910455 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.04065 | 0.255043 | 0.127522 | − | 0.991836i | \(-0.459298\pi\) | ||||
0.127522 | + | 0.991836i | \(0.459298\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.407862 | 0.0256421 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.3261 | −1.02238 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.2076 | 1.69716 | 0.848581 | − | 0.529065i | \(-0.177457\pi\) | ||||
0.848581 | + | 0.529065i | \(0.177457\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.993257 | 0.0617180 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.79060 | −0.234632 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.66066 | 0.225726 | 0.112863 | − | 0.993611i | \(-0.463998\pi\) | ||||
0.112863 | + | 0.993611i | \(0.463998\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.59335 | −0.0978787 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.9793 | −1.40631 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.87763 | −0.297394 | −0.148697 | − | 0.988883i | \(-0.547508\pi\) | ||||
−0.148697 | + | 0.988883i | \(0.547508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.18102 | 0.375470 | 0.187735 | − | 0.982220i | \(-0.439885\pi\) | ||||
0.187735 | + | 0.982220i | \(0.439885\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.02233 | −0.303965 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.3481 | 0.804918 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.69122 | −0.161699 | −0.0808497 | − | 0.996726i | \(-0.525763\pi\) | ||||
−0.0808497 | + | 0.996726i | \(0.525763\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.65595 | 0.278745 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.2070 | −1.32476 | −0.662379 | − | 0.749169i | \(-0.730453\pi\) | ||||
−0.662379 | + | 0.749169i | \(0.730453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.1955 | −1.02216 | −0.511082 | − | 0.859532i | \(-0.670755\pi\) | ||||
−0.511082 | + | 0.859532i | \(0.670755\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.5839 | 0.863876 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.00000 | 0.0590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.7854 | 1.22267 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.4898 | −1.02527 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.3426 | 1.71421 | 0.857107 | − | 0.515139i | \(-0.172260\pi\) | ||||
0.857107 | + | 0.515139i | \(0.172260\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.4067 | −0.605899 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.9666 | −0.752399 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.248464 | −0.0143690 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.14698 | 0.469584 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.9171 | −0.742067 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.70350 | −0.498361 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.4351 | 1.28044 | 0.640219 | − | 0.768193i | \(-0.278844\pi\) | ||||
0.640219 | + | 0.768193i | \(0.278844\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.80624 | 0.273418 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.1337 | −1.82214 | −0.911069 | − | 0.412255i | \(-0.864741\pi\) | ||||
−0.911069 | + | 0.412255i | \(0.864741\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.5982 | −0.994711 | −0.497356 | − | 0.867547i | \(-0.665696\pi\) | ||||
−0.497356 | + | 0.867547i | \(0.665696\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.80154 | −0.101505 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.6884 | 1.21814 | 0.609070 | − | 0.793116i | \(-0.291543\pi\) | ||||
0.609070 | + | 0.793116i | \(0.291543\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.4067 | 0.582661 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −32.6125 | −1.82025 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.7532 | −1.87808 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.13144 | −0.451051 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.32233 | −0.128425 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.90302 | 0.104917 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.3102 | −1.06139 | −0.530693 | − | 0.847564i | \(-0.678068\pi\) | ||||
−0.530693 | + | 0.847564i | \(0.678068\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.41759 | 0.0776832 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.9775 | −0.599767 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.2520 | 0.558460 | 0.279230 | − | 0.960224i | \(-0.409921\pi\) | ||||
0.279230 | + | 0.960224i | \(0.409921\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.9268 | 0.756402 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.7824 | −0.692204 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.276467 | −0.0148845 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.3334 | 1.09155 | 0.545777 | − | 0.837931i | \(-0.316235\pi\) | ||||
0.545777 | + | 0.837931i | \(0.316235\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.4518 | 1.04123 | 0.520616 | − | 0.853791i | \(-0.325702\pi\) | ||||
0.520616 | + | 0.853791i | \(0.325702\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.89907 | 0.421621 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.5318 | −1.03957 | −0.519787 | − | 0.854296i | \(-0.673989\pi\) | ||||
−0.519787 | + | 0.854296i | \(0.673989\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.04516 | −0.0554716 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.9338 | 0.684530 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.5680 | 0.557755 | 0.278878 | − | 0.960327i | \(-0.410038\pi\) | ||||
0.278878 | + | 0.960327i | \(0.410038\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.1514 | 0.586914 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.15819 | −0.480680 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.6572 | −0.557822 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.9662 | 1.35542 | 0.677712 | − | 0.735328i | \(-0.262972\pi\) | ||||
0.677712 | + | 0.735328i | \(0.262972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.42721 | 0.0742975 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.26228 | 0.0655343 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.6035 | 1.37748 | 0.688739 | − | 0.725010i | \(-0.258165\pi\) | ||||
0.688739 | + | 0.725010i | \(0.258165\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −22.3277 | −1.15300 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.33958 | −0.326505 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3871 | 0.533550 | 0.266775 | − | 0.963759i | \(-0.414042\pi\) | ||||
0.266775 | + | 0.963759i | \(0.414042\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.0566 | 0.925065 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.9970 | −1.48168 | −0.740838 | − | 0.671684i | \(-0.765571\pi\) | ||||
−0.740838 | + | 0.671684i | \(0.765571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.94591 | 0.252067 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.6274 | 0.591056 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.94763 | 0.250855 | 0.125428 | − | 0.992103i | \(-0.459970\pi\) | ||||
0.125428 | + | 0.992103i | \(0.459970\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.639860 | 0.0323591 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.58061 | −0.0797311 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.65321 | 0.334759 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.1987 | −0.562049 | −0.281025 | − | 0.959701i | \(-0.590674\pi\) | ||||
−0.281025 | + | 0.959701i | \(0.590674\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.5536 | −0.578405 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.8886 | 1.24288 | 0.621439 | − | 0.783463i | \(-0.286548\pi\) | ||||
0.621439 | + | 0.783463i | \(0.286548\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.78684 | 0.387890 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.1940 | 0.705303 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.89181 | −0.192910 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.3927 | 1.20614 | 0.603070 | − | 0.797688i | \(-0.293944\pi\) | ||||
0.603070 | + | 0.797688i | \(0.293944\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.47548 | 0.122107 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.24433 | 0.405677 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.61884 | −0.423082 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 35.3852 | 1.73282 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.48070 | −0.414309 | −0.207155 | − | 0.978308i | \(-0.566420\pi\) | ||||
−0.207155 | + | 0.978308i | \(0.566420\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.47164 | −0.120460 | −0.0602301 | − | 0.998185i | \(-0.519183\pi\) | ||||
−0.0602301 | + | 0.998185i | \(0.519183\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.71601 | 0.132057 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.9406 | 1.01577 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.89507 | 0.333676 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 19.6787 | 0.950094 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.3337 | 1.41295 | 0.706477 | − | 0.707736i | \(-0.250283\pi\) | ||||
0.706477 | + | 0.707736i | \(0.250283\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.80925 | 0.0869471 | 0.0434736 | − | 0.999055i | \(-0.486158\pi\) | ||||
0.0434736 | + | 0.999055i | \(0.486158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.05409 | −0.338218 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.571579 | −0.0273423 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.0164 | −1.19397 | −0.596984 | − | 0.802253i | \(-0.703635\pi\) | ||||
−0.596984 | + | 0.802253i | \(0.703635\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.42721 | 0.0679623 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.8846 | −1.08728 | −0.543639 | − | 0.839319i | \(-0.682954\pi\) | ||||
−0.543639 | + | 0.839319i | \(0.682954\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.7856 | −0.653501 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.4915 | 1.72599 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.6953 | 1.44860 | 0.724300 | − | 0.689484i | \(-0.242163\pi\) | ||||
0.724300 | + | 0.689484i | \(0.242163\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.91823 | −0.184502 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −38.9575 | −1.83038 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.01298 | −0.141250 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.0577 | 1.73349 | 0.866743 | − | 0.498756i | \(-0.166210\pi\) | ||||
0.866743 | + | 0.498756i | \(0.166210\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20.3422 | −0.949492 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.5555 | −0.491620 | −0.245810 | − | 0.969318i | \(-0.579054\pi\) | ||||
−0.245810 | + | 0.969318i | \(0.579054\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.95884 | 0.230457 | 0.115228 | − | 0.993339i | \(-0.463240\pi\) | ||||
0.115228 | + | 0.993339i | \(0.463240\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.66447 | 0.401805 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.65999 | −0.215639 | −0.107819 | − | 0.994171i | \(-0.534387\pi\) | ||||
−0.107819 | + | 0.994171i | \(0.534387\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.69660 | 0.401572 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 46.9483 | 2.16326 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.9218 | −1.46776 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.7060 | −0.858290 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.80154 | 0.0824867 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.2487 | −1.65625 | −0.828124 | − | 0.560545i | \(-0.810592\pi\) | ||||
−0.828124 | + | 0.560545i | \(0.810592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.37084 | 0.108101 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.219022 | 0.00996585 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.4924 | −0.476436 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.0988 | 1.54516 | 0.772582 | − | 0.634915i | \(-0.218965\pi\) | ||||
0.772582 | + | 0.634915i | \(0.218965\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.936084 | 0.0423312 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.6348 | −1.24714 | −0.623570 | − | 0.781767i | \(-0.714318\pi\) | ||||
−0.623570 | + | 0.781767i | \(0.714318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.3261 | 0.735290 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.05884 | 0.317271 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.827998 | 0.0371408 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.2386 | 0.503109 | 0.251554 | − | 0.967843i | \(-0.419058\pi\) | ||||
0.251554 | + | 0.967843i | \(0.419058\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.4435 | −1.13673 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.9283 | 0.621032 | 0.310516 | − | 0.950568i | \(-0.399498\pi\) | ||||
0.310516 | + | 0.950568i | \(0.399498\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.74917 | −0.344833 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.3653 | 0.682395 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.50363 | 0.376917 | 0.188458 | − | 0.982081i | \(-0.439651\pi\) | ||||
0.188458 | + | 0.982081i | \(0.439651\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.44279 | 0.373487 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.1714 | 0.802289 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.88334 | 0.127055 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.45648 | −0.327936 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.2144 | −1.32626 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.1843 | 0.709046 | 0.354523 | − | 0.935047i | \(-0.384643\pi\) | ||||
0.354523 | + | 0.935047i | \(0.384643\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.38373 | −0.0605061 | −0.0302531 | − | 0.999542i | \(-0.509631\pi\) | ||||
−0.0302531 | + | 0.999542i | \(0.509631\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.16791 | 0.312833 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.0532 | −0.873530 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9892 | −0.999529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.7664 | 0.510617 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.38693 | 0.103389 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.5647 | −0.845858 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.1401 | −1.21434 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.91823 | −0.168770 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −44.9258 | −1.93151 | −0.965756 | − | 0.259451i | \(-0.916458\pi\) | ||||
−0.965756 | + | 0.259451i | \(0.916458\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.2986 | 0.956925 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.39321 | −0.0596784 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.3783 | −1.85472 | −0.927360 | − | 0.374170i | \(-0.877928\pi\) | ||||
−0.927360 | + | 0.374170i | \(0.877928\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.84070 | 0.419991 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.5839 | −0.621296 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.27079 | −0.224137 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.63805 | 0.111979 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.217167 | −0.00920166 | −0.00460083 | − | 0.999989i | \(-0.501464\pi\) | ||||
−0.00460083 | + | 0.999989i | \(0.501464\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.4463 | 0.822490 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −50.6777 | −2.13962 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.67810 | −0.197158 | −0.0985791 | − | 0.995129i | \(-0.531430\pi\) | ||||
−0.0985791 | + | 0.995129i | \(0.531430\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.35494 | 0.351495 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.2447 | −0.472233 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.6044 | 0.486483 | 0.243241 | − | 0.969966i | \(-0.421789\pi\) | ||||
0.243241 | + | 0.969966i | \(0.421789\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.45201 | −0.0607646 | −0.0303823 | − | 0.999538i | \(-0.509672\pi\) | ||||
−0.0303823 | + | 0.999538i | \(0.509672\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.7582 | 0.574758 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.354610 | 0.0147882 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.2837 | 1.34399 | 0.671994 | − | 0.740557i | \(-0.265438\pi\) | ||||
0.671994 | + | 0.740557i | \(0.265438\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 55.4215 | 2.30324 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.82800 | 0.283273 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.94591 | −0.204839 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.30015 | −0.177789 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 46.4884 | 1.91878 | 0.959391 | − | 0.282081i | \(-0.0910248\pi\) | ||||
0.959391 | + | 0.282081i | \(0.0910248\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.9133 | 0.738103 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.76274 | −0.278182 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.63781 | −0.395777 | −0.197889 | − | 0.980225i | \(-0.563408\pi\) | ||||
−0.197889 | + | 0.980225i | \(0.563408\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.75921 | 0.318096 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.1073 | 0.495521 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.4339 | 1.40693 | 0.703466 | − | 0.710729i | \(-0.251635\pi\) | ||||
0.703466 | + | 0.710729i | \(0.251635\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.4941 | −1.20309 | −0.601545 | − | 0.798839i | \(-0.705448\pi\) | ||||
−0.601545 | + | 0.798839i | \(0.705448\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.4119 | 0.505450 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.49414 | −0.223369 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.6734 | 0.473809 | 0.236904 | − | 0.971533i | \(-0.423867\pi\) | ||||
0.236904 | + | 0.971533i | \(0.423867\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.58838 | 0.226452 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.54238 | 0.183765 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.0109 | 1.25252 | 0.626259 | − | 0.779615i | \(-0.284585\pi\) | ||||
0.626259 | + | 0.779615i | \(0.284585\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.65595 | 0.107098 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.2455 | 0.694277 | 0.347139 | − | 0.937814i | \(-0.387153\pi\) | ||||
0.347139 | + | 0.937814i | \(0.387153\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.24833 | −0.130561 | −0.0652806 | − | 0.997867i | \(-0.520794\pi\) | ||||
−0.0652806 | + | 0.997867i | \(0.520794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.344476 | −0.0138233 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.9212 | 0.437549 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.63851 | 0.145541 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 45.2698 | 1.80790 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.10553 | −0.243443 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.36377 | 0.173719 | 0.0868596 | − | 0.996221i | \(-0.472317\pi\) | ||||
0.0868596 | + | 0.996221i | \(0.472317\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.0008 | −1.03344 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.8324 | 0.429872 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.38693 | 0.0945737 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.18173 | 0.0467483 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.2389 | 1.23386 | 0.616931 | − | 0.787017i | \(-0.288376\pi\) | ||||
0.616931 | + | 0.787017i | \(0.288376\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5096 | −0.572202 | −0.286101 | − | 0.958199i | \(-0.592359\pi\) | ||||
−0.286101 | + | 0.958199i | \(0.592359\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.6380 | 0.851996 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.1309 | 0.516228 | 0.258114 | − | 0.966114i | \(-0.416899\pi\) | ||||
0.258114 | + | 0.966114i | \(0.416899\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.3032 | −1.26801 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.86414 | −0.269027 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.0021 | −1.68280 | −0.841401 | − | 0.540411i | \(-0.818269\pi\) | ||||
−0.841401 | + | 0.540411i | \(0.818269\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.948232 | −0.0370505 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.0496 | 0.470101 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.7392 | −1.11952 | −0.559760 | − | 0.828655i | \(-0.689107\pi\) | ||||
−0.559760 | + | 0.828655i | \(0.689107\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.01795 | 0.272967 | 0.136483 | − | 0.990642i | \(-0.456420\pi\) | ||||
0.136483 | + | 0.990642i | \(0.456420\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 30.8721 | 1.19897 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.93121 | −0.268781 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.276467 | 0.0107049 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −45.7063 | −1.76711 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27.0165 | −1.04296 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.21078 | −0.277955 | −0.138978 | − | 0.990296i | \(-0.544382\pi\) | ||||
−0.138978 | + | 0.990296i | \(0.544382\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.2736 | −0.433922 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.1112 | −0.734504 | −0.367252 | − | 0.930122i | \(-0.619701\pi\) | ||||
−0.367252 | + | 0.930122i | \(0.619701\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.31228 | 0.318996 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.92144 | 0.111950 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.29963 | 0.202785 | 0.101392 | − | 0.994847i | \(-0.467670\pi\) | ||||
0.101392 | + | 0.994847i | \(0.467670\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.48508 | 0.0567421 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −31.1530 | −1.18856 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.01298 | 0.114785 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.71386 | 0.369532 | 0.184766 | − | 0.982782i | \(-0.440847\pi\) | ||||
0.184766 | + | 0.982782i | \(0.440847\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.59214 | −0.212428 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.2281 | 0.805229 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.14698 | −0.232833 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.23841 | 0.198135 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.1661 | 0.459506 | 0.229753 | − | 0.973249i | \(-0.426208\pi\) | ||||
0.229753 | + | 0.973249i | \(0.426208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.45400 | 0.205702 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.05434 | 0.190357 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.13902 | 0.230882 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.2297 | −0.985076 | −0.492538 | − | 0.870291i | \(-0.663931\pi\) | ||||
−0.492538 | + | 0.870291i | \(0.663931\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.52252 | −0.282117 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.339582 | −0.0127174 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.8055 | 0.441502 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.3010 | 0.683464 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −49.3001 | −1.83858 | −0.919292 | − | 0.393576i | \(-0.871238\pi\) | ||||
−0.919292 | + | 0.393576i | \(0.871238\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.28424 | −0.0850694 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 33.7311 | 1.25447 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.04791 | 0.336031 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.6173 | 1.35806 | 0.679030 | − | 0.734111i | \(-0.262401\pi\) | ||||
0.679030 | + | 0.734111i | \(0.262401\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.84069 | 0.179285 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −50.0793 | −1.85225 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.6769 | 1.68712 | 0.843558 | − | 0.537038i | \(-0.180457\pi\) | ||||
0.843558 | + | 0.537038i | \(0.180457\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.65595 | 0.0979663 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −34.0753 | −1.25518 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.34456 | −0.196603 | −0.0983014 | − | 0.995157i | \(-0.531341\pi\) | ||||
−0.0983014 | + | 0.995157i | \(0.531341\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27.5777 | −1.01309 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.7658 | 1.20206 | 0.601031 | − | 0.799226i | \(-0.294757\pi\) | ||||
0.601031 | + | 0.799226i | \(0.294757\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.8918 | 0.802054 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.74498 | 0.356550 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.4995 | 0.566341 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.7261 | −1.70506 | −0.852529 | − | 0.522680i | \(-0.824932\pi\) | ||||
−0.852529 | + | 0.522680i | \(0.824932\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.50190 | −0.309827 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.3712 | −0.850565 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.0105 | 0.618257 | 0.309129 | − | 0.951020i | \(-0.399963\pi\) | ||||
0.309129 | + | 0.951020i | \(0.399963\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.858180 | −0.0311500 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.547716 | −0.0198547 | −0.00992735 | − | 0.999951i | \(-0.503160\pi\) | ||||
−0.00992735 | + | 0.999951i | \(0.503160\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.10372 | 0.0399574 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.0740 | 0.400382 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.6787 | 0.710555 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.04223 | −0.0736447 | −0.0368224 | − | 0.999322i | \(-0.511724\pi\) | ||||
−0.0368224 | + | 0.999322i | \(0.511724\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −57.2473 | −2.06171 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.5340 | 1.06226 | 0.531132 | − | 0.847289i | \(-0.321767\pi\) | ||||
0.531132 | + | 0.847289i | \(0.321767\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.1134 | −0.399207 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.08991 | −0.0749750 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.49103 | 0.196736 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.24429 | −0.116090 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.78935 | −0.314106 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.1650 | 1.00525 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.4181 | 1.29817 | 0.649083 | − | 0.760717i | \(-0.275153\pi\) | ||||
0.649083 | + | 0.760717i | \(0.275153\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.70237 | −0.274212 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.61893 | −0.235342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.4581 | 0.584443 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.35256 | 0.118903 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.2369 | 1.14189 | 0.570944 | − | 0.820989i | \(-0.306577\pi\) | ||||
0.570944 | + | 0.820989i | \(0.306577\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.6978 | −0.413840 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.5869 | 0.550734 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33.0808 | −1.16740 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.131395 | 0.00463106 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.2630 | 0.361274 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.23985 | −0.149065 | −0.0745327 | − | 0.997219i | \(-0.523747\pi\) | ||||
−0.0745327 | + | 0.997219i | \(0.523747\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.2040 | 0.885032 | 0.442516 | − | 0.896761i | \(-0.354086\pi\) | ||||
0.442516 | + | 0.896761i | \(0.354086\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.0055 | −0.456121 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.561572 | 0.0196710 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.7353 | 1.56509 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.40665 | 0.119038 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.9364 | 0.486383 | 0.243191 | − | 0.969978i | \(-0.421806\pi\) | ||||
0.243191 | + | 0.969978i | \(0.421806\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.9956 | 0.766718 | 0.383359 | − | 0.923599i | \(-0.374767\pi\) | ||||
0.383359 | + | 0.923599i | \(0.374767\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −28.0855 | −0.977813 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.75191 | 0.339107 | 0.169554 | − | 0.985521i | \(-0.445767\pi\) | ||||
0.169554 | + | 0.985521i | \(0.445767\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.58019 | −0.193808 | −0.0969040 | − | 0.995294i | \(-0.530894\pi\) | ||||
−0.0969040 | + | 0.995294i | \(0.530894\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.66257 | 0.196432 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.14698 | −0.212980 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.2640 | −0.528231 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.7959 | 0.373160 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.0940 | −1.34967 | −0.674837 | − | 0.737967i | \(-0.735786\pi\) | ||||
−0.674837 | + | 0.737967i | \(0.735786\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.9459 | −0.756755 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 46.7255 | 1.60931 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.21787 | 0.317104 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.35256 | 0.149556 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 36.1808 | 1.24172 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.103391 | −0.00354421 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.1285 | 1.13430 | 0.567149 | − | 0.823615i | \(-0.308047\pi\) | ||||
0.567149 | + | 0.823615i | \(0.308047\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.89228 | −0.338309 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.1806 | −0.723515 | −0.361758 | − | 0.932272i | \(-0.617823\pi\) | ||||
−0.361758 | + | 0.932272i | \(0.617823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.2122 | 0.860228 | 0.430114 | − | 0.902775i | \(-0.358473\pi\) | ||||
0.430114 | + | 0.902775i | \(0.358473\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.10409 | −0.0717073 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.69042 | −0.0915828 | −0.0457914 | − | 0.998951i | \(-0.514581\pi\) | ||||
−0.0457914 | + | 0.998951i | \(0.514581\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.1261 | −0.616306 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −43.7343 | −1.48530 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.6522 | 0.700578 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.7582 | 0.703365 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.8634 | 0.401514 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.6115 | 0.358736 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.60941 | 0.189416 | 0.0947081 | − | 0.995505i | \(-0.469808\pi\) | ||||
0.0947081 | + | 0.995505i | \(0.469808\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −61.7396 | −2.08242 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.6042 | 0.930009 | 0.465004 | − | 0.885308i | \(-0.346053\pi\) | ||||
0.465004 | + | 0.885308i | \(0.346053\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.26479 | −0.0425634 | −0.0212817 | − | 0.999774i | \(-0.506775\pi\) | ||||
−0.0212817 | + | 0.999774i | \(0.506775\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.8966 | 0.736045 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 59.3033 | 1.99121 | 0.995605 | − | 0.0936522i | \(-0.0298542\pi\) | ||||
0.995605 | + | 0.0936522i | \(0.0298542\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.58163 | −0.287819 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 44.0594 | 1.47604 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.4495 | 0.349680 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.8817 | −0.564294 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.522791 | 0.0174555 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.66447 | −0.288976 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.75921 | −0.258497 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.1420 | −0.570450 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.3773 | 0.444676 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.5275 | 1.37890 | 0.689450 | − | 0.724334i | \(-0.257852\pi\) | ||||
0.689450 | + | 0.724334i | \(0.257852\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.76167 | 0.290606 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.8723 | −1.51982 | −0.759908 | − | 0.650030i | \(-0.774756\pi\) | ||||
−0.759908 | + | 0.650030i | \(0.774756\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.7537 | −0.885418 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18.3130 | 0.605408 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.751206 | 0.0248070 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.3960 | 0.408905 | 0.204452 | − | 0.978876i | \(-0.434459\pi\) | ||||
0.204452 | + | 0.978876i | \(0.434459\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −47.2055 | −1.55547 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.97637 | 0.0650531 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.38368 | −0.111255 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.26008 | −0.107075 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.3588 | −0.897614 | −0.448807 | − | 0.893629i | \(-0.648151\pi\) | ||||
−0.448807 | + | 0.893629i | \(0.648151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.49103 | 0.179961 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 67.6124 | 2.21353 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −30.4024 | −0.994264 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.5181 | −1.65035 | −0.825177 | − | 0.564874i | \(-0.808925\pi\) | ||||
−0.825177 | + | 0.564874i | \(0.808925\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 37.0283 | 1.20837 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −59.8655 | −1.95156 | −0.975780 | − | 0.218752i | \(-0.929801\pi\) | ||||
−0.975780 | + | 0.218752i | \(0.929801\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.104093 | −0.00338975 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.17726 | −0.135886 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.6573 | −1.28869 | −0.644345 | − | 0.764735i | \(-0.722870\pi\) | ||||
−0.644345 | + | 0.764735i | \(0.722870\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.1524 | 0.654174 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.6344 | −1.47980 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.9581 | −0.549326 | −0.274663 | − | 0.961541i | \(-0.588566\pi\) | ||||
−0.274663 | + | 0.961541i | \(0.588566\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.25378 | 0.267086 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.8966 | −0.707815 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.17651 | −0.0379914 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.3575 | −0.656695 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.1211 | 0.712842 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33.2482 | 1.07030 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.8632 | −0.863861 | −0.431931 | − | 0.901907i | \(-0.642167\pi\) | ||||
−0.431931 | + | 0.901907i | \(0.642167\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 71.0199 | 2.28149 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.7252 | −1.46739 | −0.733696 | − | 0.679478i | \(-0.762206\pi\) | ||||
−0.733696 | + | 0.679478i | \(0.762206\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.8173 | −0.539138 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.1093 | 0.547936 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.7120 | −0.598651 | −0.299326 | − | 0.954151i | \(-0.596762\pi\) | ||||
−0.299326 | + | 0.954151i | \(0.596762\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.7919 | −1.36763 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.57524 | 0.0502936 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.7136 | −0.628766 | −0.314383 | − | 0.949296i | \(-0.601798\pi\) | ||||
−0.314383 | + | 0.949296i | \(0.601798\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.05708 | −0.129269 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.00413 | −0.127453 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.848046 | −0.0269663 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.8049 | 1.93153 | 0.965766 | − | 0.259414i | \(-0.0835294\pi\) | ||||
0.965766 | + | 0.259414i | \(0.0835294\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.6305 | 1.28937 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.26339 | 0.230265 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.5781 | −0.841738 | −0.420869 | − | 0.907121i | \(-0.638275\pi\) | ||||
−0.420869 | + | 0.907121i | \(0.638275\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.28699 | 0.103996 |
(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 | 1148.2.a.e.1.1 | ✓ | 5 | |
4.3 | odd | 2 | 4592.2.a.bd.1.5 | 5 | |||
7.6 | odd | 2 | 8036.2.a.j.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.a.e.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial | |
4592.2.a.bd.1.5 | 5 | 4.3 | odd | 2 | |||
8036.2.a.j.1.5 | 5 | 7.6 | odd | 2 |