Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, 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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.792287\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.792287 | 0.560232 | 0.280116 | − | 0.959966i | \(-0.409627\pi\) | ||||
0.280116 | + | 0.959966i | \(0.409627\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.37228 | −0.686141 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.792287 | 0.323450 | ||||||||
\(7\) | 2.52434 | 0.954110 | 0.477055 | − | 0.878873i | \(-0.341704\pi\) | ||||
0.477055 | + | 0.878873i | \(0.341704\pi\) | |||||||
\(8\) | −2.67181 | −0.944629 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.37228 | −0.396143 | ||||||||
\(13\) | 6.78073 | 1.88064 | 0.940318 | − | 0.340298i | \(-0.110528\pi\) | ||||
0.940318 | + | 0.340298i | \(0.110528\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.627719 | 0.156930 | ||||||||
\(17\) | 6.63325 | 1.60880 | 0.804400 | − | 0.594089i | \(-0.202487\pi\) | ||||
0.804400 | + | 0.594089i | \(0.202487\pi\) | |||||||
\(18\) | 0.792287 | 0.186744 | ||||||||
\(19\) | 7.72049 | 1.77120 | 0.885601 | − | 0.464447i | \(-0.153747\pi\) | ||||
0.885601 | + | 0.464447i | \(0.153747\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.52434 | 0.550856 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.00000 | −1.66812 | −0.834058 | − | 0.551677i | \(-0.813988\pi\) | ||||
−0.834058 | + | 0.551677i | \(0.813988\pi\) | |||||||
\(24\) | −2.67181 | −0.545382 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.37228 | 1.05359 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.46410 | −0.654654 | ||||||||
\(29\) | 3.16915 | 0.588496 | 0.294248 | − | 0.955729i | \(-0.404931\pi\) | ||||
0.294248 | + | 0.955729i | \(0.404931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.37228 | −0.605680 | −0.302840 | − | 0.953041i | \(-0.597935\pi\) | ||||
−0.302840 | + | 0.953041i | \(0.597935\pi\) | |||||||
\(32\) | 5.84096 | 1.03255 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.25544 | 0.901300 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.37228 | −0.228714 | ||||||||
\(37\) | −5.00000 | −0.821995 | −0.410997 | − | 0.911636i | \(-0.634819\pi\) | ||||
−0.410997 | + | 0.911636i | \(0.634819\pi\) | |||||||
\(38\) | 6.11684 | 0.992283 | ||||||||
\(39\) | 6.78073 | 1.08579 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.92820 | −1.08200 | −0.541002 | − | 0.841021i | \(-0.681955\pi\) | ||||
−0.541002 | + | 0.841021i | \(0.681955\pi\) | |||||||
\(42\) | 2.00000 | 0.308607 | ||||||||
\(43\) | 9.94987 | 1.51734 | 0.758671 | − | 0.651474i | \(-0.225849\pi\) | ||||
0.758671 | + | 0.651474i | \(0.225849\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.33830 | −0.934531 | ||||||||
\(47\) | −2.74456 | −0.400336 | −0.200168 | − | 0.979762i | \(-0.564149\pi\) | ||||
−0.200168 | + | 0.979762i | \(0.564149\pi\) | |||||||
\(48\) | 0.627719 | 0.0906034 | ||||||||
\(49\) | −0.627719 | −0.0896741 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.63325 | 0.928841 | ||||||||
\(52\) | −9.30506 | −1.29038 | ||||||||
\(53\) | 12.7446 | 1.75060 | 0.875300 | − | 0.483580i | \(-0.160664\pi\) | ||||
0.875300 | + | 0.483580i | \(0.160664\pi\) | |||||||
\(54\) | 0.792287 | 0.107817 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.74456 | −0.901280 | ||||||||
\(57\) | 7.72049 | 1.02260 | ||||||||
\(58\) | 2.51087 | 0.329694 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.67181 | −0.342091 | −0.171045 | − | 0.985263i | \(-0.554714\pi\) | ||||
−0.171045 | + | 0.985263i | \(0.554714\pi\) | |||||||
\(62\) | −2.67181 | −0.339321 | ||||||||
\(63\) | 2.52434 | 0.318037 | ||||||||
\(64\) | 3.37228 | 0.421535 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.11684 | −0.747291 | −0.373646 | − | 0.927571i | \(-0.621892\pi\) | ||||
−0.373646 | + | 0.927571i | \(0.621892\pi\) | |||||||
\(68\) | −9.10268 | −1.10386 | ||||||||
\(69\) | −8.00000 | −0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.744563 | −0.0883633 | −0.0441817 | − | 0.999024i | \(-0.514068\pi\) | ||||
−0.0441817 | + | 0.999024i | \(0.514068\pi\) | |||||||
\(72\) | −2.67181 | −0.314876 | ||||||||
\(73\) | 5.19615 | 0.608164 | 0.304082 | − | 0.952646i | \(-0.401650\pi\) | ||||
0.304082 | + | 0.952646i | \(0.401650\pi\) | |||||||
\(74\) | −3.96143 | −0.460507 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.5947 | −1.21529 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.37228 | 0.608291 | ||||||||
\(79\) | 0.147477 | 0.0165924 | 0.00829622 | − | 0.999966i | \(-0.497359\pi\) | ||||
0.00829622 | + | 0.999966i | \(0.497359\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.48913 | −0.606172 | ||||||||
\(83\) | −1.87953 | −0.206305 | −0.103152 | − | 0.994666i | \(-0.532893\pi\) | ||||
−0.103152 | + | 0.994666i | \(0.532893\pi\) | |||||||
\(84\) | −3.46410 | −0.377964 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.88316 | 0.850063 | ||||||||
\(87\) | 3.16915 | 0.339768 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.4891 | −1.85384 | −0.926922 | − | 0.375255i | \(-0.877555\pi\) | ||||
−0.926922 | + | 0.375255i | \(0.877555\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.1168 | 1.79433 | ||||||||
\(92\) | 10.9783 | 1.14456 | ||||||||
\(93\) | −3.37228 | −0.349689 | ||||||||
\(94\) | −2.17448 | −0.224281 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.84096 | 0.596141 | ||||||||
\(97\) | 3.62772 | 0.368339 | 0.184170 | − | 0.982894i | \(-0.441040\pi\) | ||||
0.184170 | + | 0.982894i | \(0.441040\pi\) | |||||||
\(98\) | −0.497333 | −0.0502383 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.2665 | −1.32007 | −0.660033 | − | 0.751237i | \(-0.729458\pi\) | ||||
−0.660033 | + | 0.751237i | \(0.729458\pi\) | |||||||
\(102\) | 5.25544 | 0.520366 | ||||||||
\(103\) | 7.74456 | 0.763094 | 0.381547 | − | 0.924349i | \(-0.375391\pi\) | ||||
0.381547 | + | 0.924349i | \(0.375391\pi\) | |||||||
\(104\) | −18.1168 | −1.77650 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0974 | 0.980741 | ||||||||
\(107\) | −11.6819 | −1.12933 | −0.564667 | − | 0.825319i | \(-0.690995\pi\) | ||||
−0.564667 | + | 0.825319i | \(0.690995\pi\) | |||||||
\(108\) | −1.37228 | −0.132048 | ||||||||
\(109\) | 5.98844 | 0.573588 | 0.286794 | − | 0.957992i | \(-0.407410\pi\) | ||||
0.286794 | + | 0.957992i | \(0.407410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.00000 | −0.474579 | ||||||||
\(112\) | 1.58457 | 0.149728 | ||||||||
\(113\) | 18.2337 | 1.71528 | 0.857641 | − | 0.514250i | \(-0.171930\pi\) | ||||
0.857641 | + | 0.514250i | \(0.171930\pi\) | |||||||
\(114\) | 6.11684 | 0.572895 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.34896 | −0.403791 | ||||||||
\(117\) | 6.78073 | 0.626878 | ||||||||
\(118\) | 3.16915 | 0.291744 | ||||||||
\(119\) | 16.7446 | 1.53497 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.11684 | −0.191650 | ||||||||
\(123\) | −6.92820 | −0.624695 | ||||||||
\(124\) | 4.62772 | 0.415581 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.00000 | 0.178174 | ||||||||
\(127\) | 3.61158 | 0.320476 | 0.160238 | − | 0.987078i | \(-0.448774\pi\) | ||||
0.160238 | + | 0.987078i | \(0.448774\pi\) | |||||||
\(128\) | −9.01011 | −0.796389 | ||||||||
\(129\) | 9.94987 | 0.876038 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.28962 | −0.112675 | −0.0563373 | − | 0.998412i | \(-0.517942\pi\) | ||||
−0.0563373 | + | 0.998412i | \(0.517942\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.4891 | 1.68992 | ||||||||
\(134\) | −4.84630 | −0.418656 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.7228 | −1.51972 | ||||||||
\(137\) | −10.7446 | −0.917970 | −0.458985 | − | 0.888444i | \(-0.651787\pi\) | ||||
−0.458985 | + | 0.888444i | \(0.651787\pi\) | |||||||
\(138\) | −6.33830 | −0.539552 | ||||||||
\(139\) | 10.3923 | 0.881464 | 0.440732 | − | 0.897639i | \(-0.354719\pi\) | ||||
0.440732 | + | 0.897639i | \(0.354719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.74456 | −0.231134 | ||||||||
\(142\) | −0.589907 | −0.0495039 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.627719 | 0.0523099 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.11684 | 0.340712 | ||||||||
\(147\) | −0.627719 | −0.0517734 | ||||||||
\(148\) | 6.86141 | 0.564004 | ||||||||
\(149\) | −18.6101 | −1.52460 | −0.762301 | − | 0.647223i | \(-0.775930\pi\) | ||||
−0.762301 | + | 0.647223i | \(0.775930\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.90653 | 0.317909 | 0.158955 | − | 0.987286i | \(-0.449188\pi\) | ||||
0.158955 | + | 0.987286i | \(0.449188\pi\) | |||||||
\(152\) | −20.6277 | −1.67313 | ||||||||
\(153\) | 6.63325 | 0.536266 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −9.30506 | −0.745001 | ||||||||
\(157\) | −2.62772 | −0.209715 | −0.104857 | − | 0.994487i | \(-0.533439\pi\) | ||||
−0.104857 | + | 0.994487i | \(0.533439\pi\) | |||||||
\(158\) | 0.116844 | 0.00929561 | ||||||||
\(159\) | 12.7446 | 1.01071 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.1947 | −1.59157 | ||||||||
\(162\) | 0.792287 | 0.0622479 | ||||||||
\(163\) | −8.62772 | −0.675775 | −0.337888 | − | 0.941186i | \(-0.609712\pi\) | ||||
−0.337888 | + | 0.941186i | \(0.609712\pi\) | |||||||
\(164\) | 9.50744 | 0.742407 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.48913 | −0.115579 | ||||||||
\(167\) | 1.58457 | 0.122618 | 0.0613090 | − | 0.998119i | \(-0.480472\pi\) | ||||
0.0613090 | + | 0.998119i | \(0.480472\pi\) | |||||||
\(168\) | −6.74456 | −0.520354 | ||||||||
\(169\) | 32.9783 | 2.53679 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.72049 | 0.590401 | ||||||||
\(172\) | −13.6540 | −1.04111 | ||||||||
\(173\) | 6.92820 | 0.526742 | 0.263371 | − | 0.964695i | \(-0.415166\pi\) | ||||
0.263371 | + | 0.964695i | \(0.415166\pi\) | |||||||
\(174\) | 2.51087 | 0.190349 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.00000 | 0.300658 | ||||||||
\(178\) | −13.8564 | −1.03858 | ||||||||
\(179\) | −3.48913 | −0.260789 | −0.130395 | − | 0.991462i | \(-0.541624\pi\) | ||||
−0.130395 | + | 0.991462i | \(0.541624\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.8614 | −1.10464 | −0.552320 | − | 0.833632i | \(-0.686257\pi\) | ||||
−0.552320 | + | 0.833632i | \(0.686257\pi\) | |||||||
\(182\) | 13.5615 | 1.00524 | ||||||||
\(183\) | −2.67181 | −0.197506 | ||||||||
\(184\) | 21.3745 | 1.57575 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.67181 | −0.195907 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.76631 | 0.274687 | ||||||||
\(189\) | 2.52434 | 0.183619 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.48913 | 0.397179 | 0.198590 | − | 0.980083i | \(-0.436364\pi\) | ||||
0.198590 | + | 0.980083i | \(0.436364\pi\) | |||||||
\(192\) | 3.37228 | 0.243373 | ||||||||
\(193\) | −2.08191 | −0.149859 | −0.0749295 | − | 0.997189i | \(-0.523873\pi\) | ||||
−0.0749295 | + | 0.997189i | \(0.523873\pi\) | |||||||
\(194\) | 2.87419 | 0.206355 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.861407 | 0.0615290 | ||||||||
\(197\) | −1.87953 | −0.133911 | −0.0669554 | − | 0.997756i | \(-0.521329\pi\) | ||||
−0.0669554 | + | 0.997756i | \(0.521329\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.8614 | −0.840833 | −0.420416 | − | 0.907331i | \(-0.638116\pi\) | ||||
−0.420416 | + | 0.907331i | \(0.638116\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.11684 | −0.431449 | ||||||||
\(202\) | −10.5109 | −0.739543 | ||||||||
\(203\) | 8.00000 | 0.561490 | ||||||||
\(204\) | −9.10268 | −0.637315 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.13592 | 0.427510 | ||||||||
\(207\) | −8.00000 | −0.556038 | ||||||||
\(208\) | 4.25639 | 0.295127 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.5012 | −0.998305 | −0.499152 | − | 0.866514i | \(-0.666355\pi\) | ||||
−0.499152 | + | 0.866514i | \(0.666355\pi\) | |||||||
\(212\) | −17.4891 | −1.20116 | ||||||||
\(213\) | −0.744563 | −0.0510166 | ||||||||
\(214\) | −9.25544 | −0.632689 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.67181 | −0.181794 | ||||||||
\(217\) | −8.51278 | −0.577885 | ||||||||
\(218\) | 4.74456 | 0.321342 | ||||||||
\(219\) | 5.19615 | 0.351123 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 44.9783 | 3.02556 | ||||||||
\(222\) | −3.96143 | −0.265874 | ||||||||
\(223\) | −4.86141 | −0.325544 | −0.162772 | − | 0.986664i | \(-0.552043\pi\) | ||||
−0.162772 | + | 0.986664i | \(0.552043\pi\) | |||||||
\(224\) | 14.7446 | 0.985163 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.4463 | 0.960954 | ||||||||
\(227\) | 17.3205 | 1.14960 | 0.574801 | − | 0.818293i | \(-0.305079\pi\) | ||||
0.574801 | + | 0.818293i | \(0.305079\pi\) | |||||||
\(228\) | −10.5947 | −0.701650 | ||||||||
\(229\) | 12.4891 | 0.825305 | 0.412652 | − | 0.910889i | \(-0.364602\pi\) | ||||
0.412652 | + | 0.910889i | \(0.364602\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.46738 | −0.555910 | ||||||||
\(233\) | 4.75372 | 0.311427 | 0.155713 | − | 0.987802i | \(-0.450232\pi\) | ||||
0.155713 | + | 0.987802i | \(0.450232\pi\) | |||||||
\(234\) | 5.37228 | 0.351197 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.48913 | −0.357312 | ||||||||
\(237\) | 0.147477 | 0.00957965 | ||||||||
\(238\) | 13.2665 | 0.859939 | ||||||||
\(239\) | 13.2665 | 0.858138 | 0.429069 | − | 0.903272i | \(-0.358842\pi\) | ||||
0.429069 | + | 0.903272i | \(0.358842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.6371 | 1.32935 | 0.664677 | − | 0.747131i | \(-0.268569\pi\) | ||||
0.664677 | + | 0.747131i | \(0.268569\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.66648 | 0.234722 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.48913 | −0.349974 | ||||||||
\(247\) | 52.3505 | 3.33098 | ||||||||
\(248\) | 9.01011 | 0.572143 | ||||||||
\(249\) | −1.87953 | −0.119110 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.4891 | −1.48262 | −0.741310 | − | 0.671163i | \(-0.765795\pi\) | ||||
−0.741310 | + | 0.671163i | \(0.765795\pi\) | |||||||
\(252\) | −3.46410 | −0.218218 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.86141 | 0.179541 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.8832 | −0.867697 | ||||||||
\(257\) | 5.48913 | 0.342402 | 0.171201 | − | 0.985236i | \(-0.445235\pi\) | ||||
0.171201 | + | 0.985236i | \(0.445235\pi\) | |||||||
\(258\) | 7.88316 | 0.490784 | ||||||||
\(259\) | −12.6217 | −0.784274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.16915 | 0.196165 | ||||||||
\(262\) | −1.02175 | −0.0631239 | ||||||||
\(263\) | −1.58457 | −0.0977090 | −0.0488545 | − | 0.998806i | \(-0.515557\pi\) | ||||
−0.0488545 | + | 0.998806i | \(0.515557\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.4410 | 0.946747 | ||||||||
\(267\) | −17.4891 | −1.07032 | ||||||||
\(268\) | 8.39403 | 0.512747 | ||||||||
\(269\) | 8.74456 | 0.533165 | 0.266583 | − | 0.963812i | \(-0.414105\pi\) | ||||
0.266583 | + | 0.963812i | \(0.414105\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.3923 | 0.631288 | 0.315644 | − | 0.948878i | \(-0.397780\pi\) | ||||
0.315644 | + | 0.948878i | \(0.397780\pi\) | |||||||
\(272\) | 4.16381 | 0.252468 | ||||||||
\(273\) | 17.1168 | 1.03596 | ||||||||
\(274\) | −8.51278 | −0.514276 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.9783 | 0.660813 | ||||||||
\(277\) | 29.2048 | 1.75475 | 0.877374 | − | 0.479808i | \(-0.159294\pi\) | ||||
0.877374 | + | 0.479808i | \(0.159294\pi\) | |||||||
\(278\) | 8.23369 | 0.493824 | ||||||||
\(279\) | −3.37228 | −0.201893 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.87953 | 0.112123 | 0.0560616 | − | 0.998427i | \(-0.482146\pi\) | ||||
0.0560616 | + | 0.998427i | \(0.482146\pi\) | |||||||
\(282\) | −2.17448 | −0.129488 | ||||||||
\(283\) | 18.4077 | 1.09423 | 0.547114 | − | 0.837058i | \(-0.315727\pi\) | ||||
0.547114 | + | 0.837058i | \(0.315727\pi\) | |||||||
\(284\) | 1.02175 | 0.0606297 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.4891 | −1.03235 | ||||||||
\(288\) | 5.84096 | 0.344182 | ||||||||
\(289\) | 27.0000 | 1.58824 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.62772 | 0.212661 | ||||||||
\(292\) | −7.13058 | −0.417286 | ||||||||
\(293\) | 26.1282 | 1.52643 | 0.763214 | − | 0.646146i | \(-0.223620\pi\) | ||||
0.763214 | + | 0.646146i | \(0.223620\pi\) | |||||||
\(294\) | −0.497333 | −0.0290051 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.3591 | 0.776480 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.7446 | −0.854130 | ||||||||
\(299\) | −54.2458 | −3.13712 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.1168 | 1.44771 | ||||||||
\(302\) | 3.09509 | 0.178103 | ||||||||
\(303\) | −13.2665 | −0.762140 | ||||||||
\(304\) | 4.84630 | 0.277954 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.25544 | 0.300433 | ||||||||
\(307\) | 9.89497 | 0.564736 | 0.282368 | − | 0.959306i | \(-0.408880\pi\) | ||||
0.282368 | + | 0.959306i | \(0.408880\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.74456 | 0.440573 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.2337 | 1.37417 | 0.687083 | − | 0.726579i | \(-0.258891\pi\) | ||||
0.687083 | + | 0.726579i | \(0.258891\pi\) | |||||||
\(312\) | −18.1168 | −1.02566 | ||||||||
\(313\) | −19.9783 | −1.12924 | −0.564619 | − | 0.825352i | \(-0.690977\pi\) | ||||
−0.564619 | + | 0.825352i | \(0.690977\pi\) | |||||||
\(314\) | −2.08191 | −0.117489 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.202380 | −0.0113847 | ||||||||
\(317\) | −26.9783 | −1.51525 | −0.757625 | − | 0.652690i | \(-0.773640\pi\) | ||||
−0.757625 | + | 0.652690i | \(0.773640\pi\) | |||||||
\(318\) | 10.0974 | 0.566231 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.6819 | −0.652021 | ||||||||
\(322\) | −16.0000 | −0.891645 | ||||||||
\(323\) | 51.2119 | 2.84951 | ||||||||
\(324\) | −1.37228 | −0.0762379 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.83563 | −0.378590 | ||||||||
\(327\) | 5.98844 | 0.331161 | ||||||||
\(328\) | 18.5109 | 1.02209 | ||||||||
\(329\) | −6.92820 | −0.381964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.2337 | −1.82669 | −0.913344 | − | 0.407188i | \(-0.866509\pi\) | ||||
−0.913344 | + | 0.407188i | \(0.866509\pi\) | |||||||
\(332\) | 2.57924 | 0.141554 | ||||||||
\(333\) | −5.00000 | −0.273998 | ||||||||
\(334\) | 1.25544 | 0.0686945 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.58457 | 0.0864456 | ||||||||
\(337\) | 19.2549 | 1.04888 | 0.524442 | − | 0.851446i | \(-0.324274\pi\) | ||||
0.524442 | + | 0.851446i | \(0.324274\pi\) | |||||||
\(338\) | 26.1282 | 1.42119 | ||||||||
\(339\) | 18.2337 | 0.990318 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 6.11684 | 0.330761 | ||||||||
\(343\) | −19.2549 | −1.03967 | ||||||||
\(344\) | −26.5842 | −1.43333 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.48913 | 0.295097 | ||||||||
\(347\) | 22.0742 | 1.18501 | 0.592503 | − | 0.805568i | \(-0.298140\pi\) | ||||
0.592503 | + | 0.805568i | \(0.298140\pi\) | |||||||
\(348\) | −4.34896 | −0.233129 | ||||||||
\(349\) | −8.66025 | −0.463573 | −0.231786 | − | 0.972767i | \(-0.574457\pi\) | ||||
−0.231786 | + | 0.972767i | \(0.574457\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.78073 | 0.361928 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.2337 | −0.970481 | −0.485241 | − | 0.874381i | \(-0.661268\pi\) | ||||
−0.485241 | + | 0.874381i | \(0.661268\pi\) | |||||||
\(354\) | 3.16915 | 0.168438 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 24.0000 | 1.27200 | ||||||||
\(357\) | 16.7446 | 0.886216 | ||||||||
\(358\) | −2.76439 | −0.146102 | ||||||||
\(359\) | 6.63325 | 0.350090 | 0.175045 | − | 0.984560i | \(-0.443993\pi\) | ||||
0.175045 | + | 0.984560i | \(0.443993\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.6060 | 2.13716 | ||||||||
\(362\) | −11.7745 | −0.618854 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −23.4891 | −1.23116 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.11684 | −0.110649 | ||||||||
\(367\) | 15.0000 | 0.782994 | 0.391497 | − | 0.920179i | \(-0.371957\pi\) | ||||
0.391497 | + | 0.920179i | \(0.371957\pi\) | |||||||
\(368\) | −5.02175 | −0.261777 | ||||||||
\(369\) | −6.92820 | −0.360668 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32.1716 | 1.67027 | ||||||||
\(372\) | 4.62772 | 0.239936 | ||||||||
\(373\) | 10.4472 | 0.540936 | 0.270468 | − | 0.962729i | \(-0.412822\pi\) | ||||
0.270468 | + | 0.962729i | \(0.412822\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.33296 | 0.378169 | ||||||||
\(377\) | 21.4891 | 1.10675 | ||||||||
\(378\) | 2.00000 | 0.102869 | ||||||||
\(379\) | −5.00000 | −0.256833 | −0.128416 | − | 0.991720i | \(-0.540989\pi\) | ||||
−0.128416 | + | 0.991720i | \(0.540989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.61158 | 0.185027 | ||||||||
\(382\) | 4.34896 | 0.222512 | ||||||||
\(383\) | −24.2337 | −1.23828 | −0.619142 | − | 0.785279i | \(-0.712519\pi\) | ||||
−0.619142 | + | 0.785279i | \(0.712519\pi\) | |||||||
\(384\) | −9.01011 | −0.459795 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.64947 | −0.0839557 | ||||||||
\(387\) | 9.94987 | 0.505781 | ||||||||
\(388\) | −4.97825 | −0.252732 | ||||||||
\(389\) | 21.2554 | 1.07769 | 0.538847 | − | 0.842404i | \(-0.318860\pi\) | ||||
0.538847 | + | 0.842404i | \(0.318860\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −53.0660 | −2.68366 | ||||||||
\(392\) | 1.67715 | 0.0847088 | ||||||||
\(393\) | −1.28962 | −0.0650527 | ||||||||
\(394\) | −1.48913 | −0.0750210 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.37228 | 0.420193 | 0.210096 | − | 0.977681i | \(-0.432622\pi\) | ||||
0.210096 | + | 0.977681i | \(0.432622\pi\) | |||||||
\(398\) | −9.39764 | −0.471061 | ||||||||
\(399\) | 19.4891 | 0.975677 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.9783 | 0.747978 | 0.373989 | − | 0.927433i | \(-0.377990\pi\) | ||||
0.373989 | + | 0.927433i | \(0.377990\pi\) | |||||||
\(402\) | −4.84630 | −0.241711 | ||||||||
\(403\) | −22.8665 | −1.13906 | ||||||||
\(404\) | 18.2054 | 0.905751 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.33830 | 0.314564 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −17.7228 | −0.877410 | ||||||||
\(409\) | −8.45787 | −0.418215 | −0.209107 | − | 0.977893i | \(-0.567056\pi\) | ||||
−0.209107 | + | 0.977893i | \(0.567056\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.7446 | −0.529990 | ||||||||
\(412\) | −10.6277 | −0.523590 | ||||||||
\(413\) | 10.0974 | 0.496858 | ||||||||
\(414\) | −6.33830 | −0.311510 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 39.6060 | 1.94184 | ||||||||
\(417\) | 10.3923 | 0.508913 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.2337 | 1.57472 | 0.787359 | − | 0.616494i | \(-0.211448\pi\) | ||||
0.787359 | + | 0.616494i | \(0.211448\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0000 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(422\) | −11.4891 | −0.559282 | ||||||||
\(423\) | −2.74456 | −0.133445 | ||||||||
\(424\) | −34.0511 | −1.65367 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.589907 | −0.0285811 | ||||||||
\(427\) | −6.74456 | −0.326392 | ||||||||
\(428\) | 16.0309 | 0.774882 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.87419 | 0.138445 | 0.0692225 | − | 0.997601i | \(-0.477948\pi\) | ||||
0.0692225 | + | 0.997601i | \(0.477948\pi\) | |||||||
\(432\) | 0.627719 | 0.0302011 | ||||||||
\(433\) | 23.0951 | 1.10988 | 0.554940 | − | 0.831891i | \(-0.312741\pi\) | ||||
0.554940 | + | 0.831891i | \(0.312741\pi\) | |||||||
\(434\) | −6.74456 | −0.323749 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.21782 | −0.393562 | ||||||||
\(437\) | −61.7639 | −2.95457 | ||||||||
\(438\) | 4.11684 | 0.196710 | ||||||||
\(439\) | 22.7190 | 1.08432 | 0.542160 | − | 0.840275i | \(-0.317607\pi\) | ||||
0.542160 | + | 0.840275i | \(0.317607\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.627719 | −0.0298914 | ||||||||
\(442\) | 35.6357 | 1.69502 | ||||||||
\(443\) | −20.7446 | −0.985604 | −0.492802 | − | 0.870142i | \(-0.664027\pi\) | ||||
−0.492802 | + | 0.870142i | \(0.664027\pi\) | |||||||
\(444\) | 6.86141 | 0.325628 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.85163 | −0.182380 | ||||||||
\(447\) | −18.6101 | −0.880229 | ||||||||
\(448\) | 8.51278 | 0.402191 | ||||||||
\(449\) | 1.25544 | 0.0592478 | 0.0296239 | − | 0.999561i | \(-0.490569\pi\) | ||||
0.0296239 | + | 0.999561i | \(0.490569\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −25.0217 | −1.17692 | ||||||||
\(453\) | 3.90653 | 0.183545 | ||||||||
\(454\) | 13.7228 | 0.644044 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −20.6277 | −0.965981 | ||||||||
\(457\) | −33.4612 | −1.56525 | −0.782624 | − | 0.622494i | \(-0.786119\pi\) | ||||
−0.782624 | + | 0.622494i | \(0.786119\pi\) | |||||||
\(458\) | 9.89497 | 0.462362 | ||||||||
\(459\) | 6.63325 | 0.309614 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.51278 | −0.396480 | −0.198240 | − | 0.980154i | \(-0.563522\pi\) | ||||
−0.198240 | + | 0.980154i | \(0.563522\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.9783 | 0.881994 | 0.440997 | − | 0.897509i | \(-0.354625\pi\) | ||||
0.440997 | + | 0.897509i | \(0.354625\pi\) | |||||||
\(464\) | 1.98933 | 0.0923525 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.76631 | 0.174471 | ||||||||
\(467\) | −21.4891 | −0.994398 | −0.497199 | − | 0.867636i | \(-0.665638\pi\) | ||||
−0.497199 | + | 0.867636i | \(0.665638\pi\) | |||||||
\(468\) | −9.30506 | −0.430127 | ||||||||
\(469\) | −15.4410 | −0.712998 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.62772 | −0.121079 | ||||||||
\(472\) | −10.6873 | −0.491921 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.116844 | 0.00536682 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −22.9783 | −1.05321 | ||||||||
\(477\) | 12.7446 | 0.583533 | ||||||||
\(478\) | 10.5109 | 0.480756 | ||||||||
\(479\) | 23.6588 | 1.08100 | 0.540499 | − | 0.841345i | \(-0.318235\pi\) | ||||
0.540499 | + | 0.841345i | \(0.318235\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.9036 | −1.54587 | ||||||||
\(482\) | 16.3505 | 0.744746 | ||||||||
\(483\) | −20.1947 | −0.918891 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.792287 | 0.0359389 | ||||||||
\(487\) | −9.97825 | −0.452158 | −0.226079 | − | 0.974109i | \(-0.572591\pi\) | ||||
−0.226079 | + | 0.974109i | \(0.572591\pi\) | |||||||
\(488\) | 7.13859 | 0.323149 | ||||||||
\(489\) | −8.62772 | −0.390159 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.63325 | −0.299354 | −0.149677 | − | 0.988735i | \(-0.547823\pi\) | ||||
−0.149677 | + | 0.988735i | \(0.547823\pi\) | |||||||
\(492\) | 9.50744 | 0.428629 | ||||||||
\(493\) | 21.0217 | 0.946772 | ||||||||
\(494\) | 41.4766 | 1.86612 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.11684 | −0.0950491 | ||||||||
\(497\) | −1.87953 | −0.0843083 | ||||||||
\(498\) | −1.48913 | −0.0667293 | ||||||||
\(499\) | 3.11684 | 0.139529 | 0.0697645 | − | 0.997563i | \(-0.477775\pi\) | ||||
0.0697645 | + | 0.997563i | \(0.477775\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.58457 | 0.0707935 | ||||||||
\(502\) | −18.6101 | −0.830611 | ||||||||
\(503\) | −10.0974 | −0.450219 | −0.225109 | − | 0.974334i | \(-0.572274\pi\) | ||||
−0.225109 | + | 0.974334i | \(0.572274\pi\) | |||||||
\(504\) | −6.74456 | −0.300427 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.9783 | 1.46462 | ||||||||
\(508\) | −4.95610 | −0.219891 | ||||||||
\(509\) | 14.9783 | 0.663899 | 0.331950 | − | 0.943297i | \(-0.392294\pi\) | ||||
0.331950 | + | 0.943297i | \(0.392294\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.1168 | 0.580255 | ||||||||
\(512\) | 7.02078 | 0.310277 | ||||||||
\(513\) | 7.72049 | 0.340868 | ||||||||
\(514\) | 4.34896 | 0.191825 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −13.6540 | −0.601085 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −10.0000 | −0.439375 | ||||||||
\(519\) | 6.92820 | 0.304114 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.2554 | −1.10646 | −0.553230 | − | 0.833028i | \(-0.686605\pi\) | ||||
−0.553230 | + | 0.833028i | \(0.686605\pi\) | |||||||
\(522\) | 2.51087 | 0.109898 | ||||||||
\(523\) | −37.0179 | −1.61868 | −0.809339 | − | 0.587341i | \(-0.800175\pi\) | ||||
−0.809339 | + | 0.587341i | \(0.800175\pi\) | |||||||
\(524\) | 1.76972 | 0.0773107 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.25544 | −0.0547397 | ||||||||
\(527\) | −22.3692 | −0.974417 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | −26.7446 | −1.15952 | ||||||||
\(533\) | −46.9783 | −2.03485 | ||||||||
\(534\) | −13.8564 | −0.599625 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 16.3431 | 0.705913 | ||||||||
\(537\) | −3.48913 | −0.150567 | ||||||||
\(538\) | 6.92820 | 0.298696 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.65492 | 0.415097 | 0.207549 | − | 0.978225i | \(-0.433451\pi\) | ||||
0.207549 | + | 0.978225i | \(0.433451\pi\) | |||||||
\(542\) | 8.23369 | 0.353667 | ||||||||
\(543\) | −14.8614 | −0.637764 | ||||||||
\(544\) | 38.7446 | 1.66116 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.5615 | 0.580377 | ||||||||
\(547\) | −40.6844 | −1.73954 | −0.869769 | − | 0.493459i | \(-0.835732\pi\) | ||||
−0.869769 | + | 0.493459i | \(0.835732\pi\) | |||||||
\(548\) | 14.7446 | 0.629857 | ||||||||
\(549\) | −2.67181 | −0.114030 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.4674 | 1.04235 | ||||||||
\(552\) | 21.3745 | 0.909760 | ||||||||
\(553\) | 0.372281 | 0.0158310 | ||||||||
\(554\) | 23.1386 | 0.983065 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.2612 | −0.604808 | ||||||||
\(557\) | −20.1947 | −0.855677 | −0.427839 | − | 0.903855i | \(-0.640725\pi\) | ||||
−0.427839 | + | 0.903855i | \(0.640725\pi\) | |||||||
\(558\) | −2.67181 | −0.113107 | ||||||||
\(559\) | 67.4674 | 2.85357 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.48913 | 0.0628150 | ||||||||
\(563\) | −9.21249 | −0.388260 | −0.194130 | − | 0.980976i | \(-0.562188\pi\) | ||||
−0.194130 | + | 0.980976i | \(0.562188\pi\) | |||||||
\(564\) | 3.76631 | 0.158590 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.5842 | 0.613020 | ||||||||
\(567\) | 2.52434 | 0.106012 | ||||||||
\(568\) | 1.98933 | 0.0834706 | ||||||||
\(569\) | 29.9971 | 1.25754 | 0.628772 | − | 0.777590i | \(-0.283558\pi\) | ||||
0.628772 | + | 0.777590i | \(0.283558\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.7446 | −1.66326 | −0.831630 | − | 0.555330i | \(-0.812592\pi\) | ||||
−0.831630 | + | 0.555330i | \(0.812592\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.48913 | 0.229311 | ||||||||
\(574\) | −13.8564 | −0.578355 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.37228 | 0.140512 | ||||||||
\(577\) | −39.0951 | −1.62755 | −0.813775 | − | 0.581180i | \(-0.802591\pi\) | ||||
−0.813775 | + | 0.581180i | \(0.802591\pi\) | |||||||
\(578\) | 21.3917 | 0.889779 | ||||||||
\(579\) | −2.08191 | −0.0865211 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.74456 | −0.196838 | ||||||||
\(582\) | 2.87419 | 0.119139 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −13.8832 | −0.574489 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.7011 | 0.855153 | ||||||||
\(587\) | −23.2554 | −0.959855 | −0.479927 | − | 0.877308i | \(-0.659337\pi\) | ||||
−0.479927 | + | 0.877308i | \(0.659337\pi\) | |||||||
\(588\) | 0.861407 | 0.0355238 | ||||||||
\(589\) | −26.0357 | −1.07278 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.87953 | −0.0773134 | ||||||||
\(592\) | −3.13859 | −0.128995 | ||||||||
\(593\) | −37.8102 | −1.55268 | −0.776339 | − | 0.630316i | \(-0.782925\pi\) | ||||
−0.776339 | + | 0.630316i | \(0.782925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 25.5383 | 1.04609 | ||||||||
\(597\) | −11.8614 | −0.485455 | ||||||||
\(598\) | −42.9783 | −1.75751 | ||||||||
\(599\) | −44.7446 | −1.82821 | −0.914107 | − | 0.405474i | \(-0.867107\pi\) | ||||
−0.914107 | + | 0.405474i | \(0.867107\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.08724 | 0.0443495 | 0.0221747 | − | 0.999754i | \(-0.492941\pi\) | ||||
0.0221747 | + | 0.999754i | \(0.492941\pi\) | |||||||
\(602\) | 19.8997 | 0.811053 | ||||||||
\(603\) | −6.11684 | −0.249097 | ||||||||
\(604\) | −5.36086 | −0.218130 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10.5109 | −0.426975 | ||||||||
\(607\) | −6.04334 | −0.245292 | −0.122646 | − | 0.992451i | \(-0.539138\pi\) | ||||
−0.122646 | + | 0.992451i | \(0.539138\pi\) | |||||||
\(608\) | 45.0951 | 1.82885 | ||||||||
\(609\) | 8.00000 | 0.324176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.6101 | −0.752885 | ||||||||
\(612\) | −9.10268 | −0.367954 | ||||||||
\(613\) | 11.5344 | 0.465872 | 0.232936 | − | 0.972492i | \(-0.425167\pi\) | ||||
0.232936 | + | 0.972492i | \(0.425167\pi\) | |||||||
\(614\) | 7.83966 | 0.316383 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.00000 | 0.0805170 | 0.0402585 | − | 0.999189i | \(-0.487182\pi\) | ||||
0.0402585 | + | 0.999189i | \(0.487182\pi\) | |||||||
\(618\) | 6.13592 | 0.246823 | ||||||||
\(619\) | −25.5109 | −1.02537 | −0.512684 | − | 0.858577i | \(-0.671349\pi\) | ||||
−0.512684 | + | 0.858577i | \(0.671349\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.00000 | −0.321029 | ||||||||
\(622\) | 19.2000 | 0.769851 | ||||||||
\(623\) | −44.1485 | −1.76877 | ||||||||
\(624\) | 4.25639 | 0.170392 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.8285 | −0.632634 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.60597 | 0.143894 | ||||||||
\(629\) | −33.1662 | −1.32242 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.5109 | −0.537859 | −0.268930 | − | 0.963160i | \(-0.586670\pi\) | ||||
−0.268930 | + | 0.963160i | \(0.586670\pi\) | |||||||
\(632\) | −0.394031 | −0.0156737 | ||||||||
\(633\) | −14.5012 | −0.576372 | ||||||||
\(634\) | −21.3745 | −0.848891 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −17.4891 | −0.693489 | ||||||||
\(637\) | −4.25639 | −0.168644 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.744563 | −0.0294544 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.9783 | −0.670601 | −0.335300 | − | 0.942111i | \(-0.608838\pi\) | ||||
−0.335300 | + | 0.942111i | \(0.608838\pi\) | |||||||
\(642\) | −9.25544 | −0.365283 | ||||||||
\(643\) | −25.2337 | −0.995120 | −0.497560 | − | 0.867430i | \(-0.665770\pi\) | ||||
−0.497560 | + | 0.867430i | \(0.665770\pi\) | |||||||
\(644\) | 27.7128 | 1.09204 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 40.5746 | 1.59638 | ||||||||
\(647\) | −2.00000 | −0.0786281 | −0.0393141 | − | 0.999227i | \(-0.512517\pi\) | ||||
−0.0393141 | + | 0.999227i | \(0.512517\pi\) | |||||||
\(648\) | −2.67181 | −0.104959 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.51278 | −0.333642 | ||||||||
\(652\) | 11.8397 | 0.463677 | ||||||||
\(653\) | −22.5109 | −0.880919 | −0.440459 | − | 0.897773i | \(-0.645184\pi\) | ||||
−0.440459 | + | 0.897773i | \(0.645184\pi\) | |||||||
\(654\) | 4.74456 | 0.185527 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.34896 | −0.169798 | ||||||||
\(657\) | 5.19615 | 0.202721 | ||||||||
\(658\) | −5.48913 | −0.213988 | ||||||||
\(659\) | 18.9051 | 0.736437 | 0.368219 | − | 0.929739i | \(-0.379968\pi\) | ||||
0.368219 | + | 0.929739i | \(0.379968\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.00000 | −0.116686 | −0.0583432 | − | 0.998297i | \(-0.518582\pi\) | ||||
−0.0583432 | + | 0.998297i | \(0.518582\pi\) | |||||||
\(662\) | −26.3306 | −1.02337 | ||||||||
\(663\) | 44.9783 | 1.74681 | ||||||||
\(664\) | 5.02175 | 0.194882 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.96143 | −0.153502 | ||||||||
\(667\) | −25.3532 | −0.981679 | ||||||||
\(668\) | −2.17448 | −0.0841332 | ||||||||
\(669\) | −4.86141 | −0.187953 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 14.7446 | 0.568784 | ||||||||
\(673\) | −2.32196 | −0.0895049 | −0.0447525 | − | 0.998998i | \(-0.514250\pi\) | ||||
−0.0447525 | + | 0.998998i | \(0.514250\pi\) | |||||||
\(674\) | 15.2554 | 0.587617 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −45.2554 | −1.74059 | ||||||||
\(677\) | 37.5152 | 1.44183 | 0.720913 | − | 0.693025i | \(-0.243723\pi\) | ||||
0.720913 | + | 0.693025i | \(0.243723\pi\) | |||||||
\(678\) | 14.4463 | 0.554807 | ||||||||
\(679\) | 9.15759 | 0.351436 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.3205 | 0.663723 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.0000 | −0.688751 | −0.344375 | − | 0.938832i | \(-0.611909\pi\) | ||||
−0.344375 | + | 0.938832i | \(0.611909\pi\) | |||||||
\(684\) | −10.5947 | −0.405098 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.2554 | −0.582455 | ||||||||
\(687\) | 12.4891 | 0.476490 | ||||||||
\(688\) | 6.24572 | 0.238116 | ||||||||
\(689\) | 86.4174 | 3.29224 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.7446 | −0.522868 | −0.261434 | − | 0.965221i | \(-0.584195\pi\) | ||||
−0.261434 | + | 0.965221i | \(0.584195\pi\) | |||||||
\(692\) | −9.50744 | −0.361419 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.4891 | 0.663878 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.46738 | −0.320955 | ||||||||
\(697\) | −45.9565 | −1.74073 | ||||||||
\(698\) | −6.86141 | −0.259708 | ||||||||
\(699\) | 4.75372 | 0.179802 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.5870 | 1.15526 | 0.577628 | − | 0.816300i | \(-0.303979\pi\) | ||||
0.577628 | + | 0.816300i | \(0.303979\pi\) | |||||||
\(702\) | 5.37228 | 0.202764 | ||||||||
\(703\) | −38.6025 | −1.45592 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.4463 | −0.543694 | ||||||||
\(707\) | −33.4891 | −1.25949 | ||||||||
\(708\) | −5.48913 | −0.206294 | ||||||||
\(709\) | 31.0000 | 1.16423 | 0.582115 | − | 0.813107i | \(-0.302225\pi\) | ||||
0.582115 | + | 0.813107i | \(0.302225\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.147477 | 0.00553081 | ||||||||
\(712\) | 46.7277 | 1.75119 | ||||||||
\(713\) | 26.9783 | 1.01034 | ||||||||
\(714\) | 13.2665 | 0.496486 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.78806 | 0.178938 | ||||||||
\(717\) | 13.2665 | 0.495446 | ||||||||
\(718\) | 5.25544 | 0.196131 | ||||||||
\(719\) | 14.0000 | 0.522112 | 0.261056 | − | 0.965324i | \(-0.415929\pi\) | ||||
0.261056 | + | 0.965324i | \(0.415929\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.5499 | 0.728076 | ||||||||
\(722\) | 32.1716 | 1.19730 | ||||||||
\(723\) | 20.6371 | 0.767503 | ||||||||
\(724\) | 20.3940 | 0.757938 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.4674 | 1.76047 | 0.880234 | − | 0.474540i | \(-0.157386\pi\) | ||||
0.880234 | + | 0.474540i | \(0.157386\pi\) | |||||||
\(728\) | −45.7330 | −1.69498 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 66.0000 | 2.44110 | ||||||||
\(732\) | 3.66648 | 0.135517 | ||||||||
\(733\) | 13.8564 | 0.511798 | 0.255899 | − | 0.966704i | \(-0.417629\pi\) | ||||
0.255899 | + | 0.966704i | \(0.417629\pi\) | |||||||
\(734\) | 11.8843 | 0.438658 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −46.7277 | −1.72241 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −5.48913 | −0.202057 | ||||||||
\(739\) | 12.8241 | 0.471741 | 0.235870 | − | 0.971784i | \(-0.424206\pi\) | ||||
0.235870 | + | 0.971784i | \(0.424206\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 52.3505 | 1.92314 | ||||||||
\(742\) | 25.4891 | 0.935735 | ||||||||
\(743\) | −17.7253 | −0.650277 | −0.325138 | − | 0.945666i | \(-0.605411\pi\) | ||||
−0.325138 | + | 0.945666i | \(0.605411\pi\) | |||||||
\(744\) | 9.01011 | 0.330327 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.27719 | 0.303049 | ||||||||
\(747\) | −1.87953 | −0.0687683 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.4891 | −1.07751 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.23369 | −0.190980 | −0.0954900 | − | 0.995430i | \(-0.530442\pi\) | ||||
−0.0954900 | + | 0.995430i | \(0.530442\pi\) | |||||||
\(752\) | −1.72281 | −0.0628245 | ||||||||
\(753\) | −23.4891 | −0.855991 | ||||||||
\(754\) | 17.0256 | 0.620034 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.46410 | −0.125988 | ||||||||
\(757\) | 19.3505 | 0.703307 | 0.351654 | − | 0.936130i | \(-0.385620\pi\) | ||||
0.351654 | + | 0.936130i | \(0.385620\pi\) | |||||||
\(758\) | −3.96143 | −0.143886 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.28962 | 0.0467487 | 0.0233744 | − | 0.999727i | \(-0.492559\pi\) | ||||
0.0233744 | + | 0.999727i | \(0.492559\pi\) | |||||||
\(762\) | 2.86141 | 0.103658 | ||||||||
\(763\) | 15.1168 | 0.547266 | ||||||||
\(764\) | −7.53262 | −0.272521 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.2000 | −0.693725 | ||||||||
\(767\) | 27.1229 | 0.979351 | ||||||||
\(768\) | −13.8832 | −0.500965 | ||||||||
\(769\) | 13.7638 | 0.496336 | 0.248168 | − | 0.968717i | \(-0.420171\pi\) | ||||
0.248168 | + | 0.968717i | \(0.420171\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.48913 | 0.197686 | ||||||||
\(772\) | 2.85696 | 0.102824 | ||||||||
\(773\) | −23.4891 | −0.844845 | −0.422423 | − | 0.906399i | \(-0.638820\pi\) | ||||
−0.422423 | + | 0.906399i | \(0.638820\pi\) | |||||||
\(774\) | 7.88316 | 0.283354 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.69259 | −0.347944 | ||||||||
\(777\) | −12.6217 | −0.452801 | ||||||||
\(778\) | 16.8404 | 0.603758 | ||||||||
\(779\) | −53.4891 | −1.91645 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −42.0435 | −1.50347 | ||||||||
\(783\) | 3.16915 | 0.113256 | ||||||||
\(784\) | −0.394031 | −0.0140725 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.02175 | −0.0364446 | ||||||||
\(787\) | −6.48577 | −0.231193 | −0.115596 | − | 0.993296i | \(-0.536878\pi\) | ||||
−0.115596 | + | 0.993296i | \(0.536878\pi\) | |||||||
\(788\) | 2.57924 | 0.0918816 | ||||||||
\(789\) | −1.58457 | −0.0564123 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 46.0280 | 1.63657 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.1168 | −0.643348 | ||||||||
\(794\) | 6.63325 | 0.235405 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.2772 | 0.576930 | ||||||||
\(797\) | −27.7228 | −0.981992 | −0.490996 | − | 0.871162i | \(-0.663367\pi\) | ||||
−0.490996 | + | 0.871162i | \(0.663367\pi\) | |||||||
\(798\) | 15.4410 | 0.546605 | ||||||||
\(799\) | −18.2054 | −0.644060 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.4891 | −0.617948 | ||||||||
\(802\) | 11.8671 | 0.419041 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 8.39403 | 0.296035 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18.1168 | −0.638139 | ||||||||
\(807\) | 8.74456 | 0.307823 | ||||||||
\(808\) | 35.4456 | 1.24697 | ||||||||
\(809\) | 7.22316 | 0.253953 | 0.126976 | − | 0.991906i | \(-0.459473\pi\) | ||||
0.126976 | + | 0.991906i | \(0.459473\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.7933 | −1.57290 | −0.786452 | − | 0.617651i | \(-0.788084\pi\) | ||||
−0.786452 | + | 0.617651i | \(0.788084\pi\) | |||||||
\(812\) | −10.9783 | −0.385261 | ||||||||
\(813\) | 10.3923 | 0.364474 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.16381 | 0.145763 | ||||||||
\(817\) | 76.8179 | 2.68752 | ||||||||
\(818\) | −6.70106 | −0.234297 | ||||||||
\(819\) | 17.1168 | 0.598111 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.8617 | 0.448878 | 0.224439 | − | 0.974488i | \(-0.427945\pi\) | ||||
0.224439 | + | 0.974488i | \(0.427945\pi\) | |||||||
\(822\) | −8.51278 | −0.296917 | ||||||||
\(823\) | 49.3505 | 1.72025 | 0.860126 | − | 0.510082i | \(-0.170385\pi\) | ||||
0.860126 | + | 0.510082i | \(0.170385\pi\) | |||||||
\(824\) | −20.6920 | −0.720841 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.00000 | 0.278356 | ||||||||
\(827\) | −36.9253 | −1.28402 | −0.642009 | − | 0.766697i | \(-0.721899\pi\) | ||||
−0.642009 | + | 0.766697i | \(0.721899\pi\) | |||||||
\(828\) | 10.9783 | 0.381521 | ||||||||
\(829\) | −27.4674 | −0.953981 | −0.476991 | − | 0.878908i | \(-0.658272\pi\) | ||||
−0.476991 | + | 0.878908i | \(0.658272\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.2048 | 1.01310 | ||||||||
\(832\) | 22.8665 | 0.792754 | ||||||||
\(833\) | −4.16381 | −0.144268 | ||||||||
\(834\) | 8.23369 | 0.285109 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.37228 | −0.116563 | ||||||||
\(838\) | 25.5383 | 0.882207 | ||||||||
\(839\) | 34.7446 | 1.19952 | 0.599758 | − | 0.800182i | \(-0.295264\pi\) | ||||
0.599758 | + | 0.800182i | \(0.295264\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9565 | −0.653672 | ||||||||
\(842\) | 14.2612 | 0.491472 | ||||||||
\(843\) | 1.87953 | 0.0647344 | ||||||||
\(844\) | 19.8997 | 0.684978 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.17448 | −0.0747602 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.00000 | 0.274721 | ||||||||
\(849\) | 18.4077 | 0.631752 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.0000 | 1.37118 | ||||||||
\(852\) | 1.02175 | 0.0350046 | ||||||||
\(853\) | 26.0357 | 0.891444 | 0.445722 | − | 0.895171i | \(-0.352947\pi\) | ||||
0.445722 | + | 0.895171i | \(0.352947\pi\) | |||||||
\(854\) | −5.34363 | −0.182855 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 31.2119 | 1.06680 | ||||||||
\(857\) | 9.39764 | 0.321017 | 0.160509 | − | 0.987034i | \(-0.448687\pi\) | ||||
0.160509 | + | 0.987034i | \(0.448687\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.7446 | −0.741915 | −0.370957 | − | 0.928650i | \(-0.620970\pi\) | ||||
−0.370957 | + | 0.928650i | \(0.620970\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.4891 | −0.596028 | ||||||||
\(862\) | 2.27719 | 0.0775613 | ||||||||
\(863\) | −14.2337 | −0.484520 | −0.242260 | − | 0.970211i | \(-0.577889\pi\) | ||||
−0.242260 | + | 0.970211i | \(0.577889\pi\) | |||||||
\(864\) | 5.84096 | 0.198714 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.2979 | 0.621789 | ||||||||
\(867\) | 27.0000 | 0.916968 | ||||||||
\(868\) | 11.6819 | 0.396510 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.4766 | −1.40538 | ||||||||
\(872\) | −16.0000 | −0.541828 | ||||||||
\(873\) | 3.62772 | 0.122780 | ||||||||
\(874\) | −48.9348 | −1.65524 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.13058 | −0.240920 | ||||||||
\(877\) | −10.0048 | −0.337837 | −0.168919 | − | 0.985630i | \(-0.554028\pi\) | ||||
−0.168919 | + | 0.985630i | \(0.554028\pi\) | |||||||
\(878\) | 18.0000 | 0.607471 | ||||||||
\(879\) | 26.1282 | 0.881284 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.4674 | −0.756945 | −0.378473 | − | 0.925613i | \(-0.623551\pi\) | ||||
−0.378473 | + | 0.925613i | \(0.623551\pi\) | |||||||
\(882\) | −0.497333 | −0.0167461 | ||||||||
\(883\) | −39.8614 | −1.34144 | −0.670722 | − | 0.741709i | \(-0.734015\pi\) | ||||
−0.670722 | + | 0.741709i | \(0.734015\pi\) | |||||||
\(884\) | −61.7228 | −2.07596 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.4356 | −0.552166 | ||||||||
\(887\) | 24.9484 | 0.837686 | 0.418843 | − | 0.908059i | \(-0.362436\pi\) | ||||
0.418843 | + | 0.908059i | \(0.362436\pi\) | |||||||
\(888\) | 13.3591 | 0.448301 | ||||||||
\(889\) | 9.11684 | 0.305769 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.67122 | 0.223369 | ||||||||
\(893\) | −21.1894 | −0.709075 | ||||||||
\(894\) | −14.7446 | −0.493132 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −22.7446 | −0.759843 | ||||||||
\(897\) | −54.2458 | −1.81121 | ||||||||
\(898\) | 0.994667 | 0.0331925 | ||||||||
\(899\) | −10.6873 | −0.356440 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 84.5379 | 2.81636 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.1168 | 0.835836 | ||||||||
\(904\) | −48.7170 | −1.62030 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.09509 | 0.102828 | ||||||||
\(907\) | −15.2337 | −0.505826 | −0.252913 | − | 0.967489i | \(-0.581389\pi\) | ||||
−0.252913 | + | 0.967489i | \(0.581389\pi\) | |||||||
\(908\) | −23.7686 | −0.788789 | ||||||||
\(909\) | −13.2665 | −0.440022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.4891 | 0.910755 | 0.455378 | − | 0.890298i | \(-0.349504\pi\) | ||||
0.455378 | + | 0.890298i | \(0.349504\pi\) | |||||||
\(912\) | 4.84630 | 0.160477 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −26.5109 | −0.876902 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.1386 | −0.566275 | ||||||||
\(917\) | −3.25544 | −0.107504 | ||||||||
\(918\) | 5.25544 | 0.173455 | ||||||||
\(919\) | 5.69349 | 0.187811 | 0.0939054 | − | 0.995581i | \(-0.470065\pi\) | ||||
0.0939054 | + | 0.995581i | \(0.470065\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.89497 | 0.326050 | ||||||||
\(922\) | −6.74456 | −0.222120 | ||||||||
\(923\) | −5.04868 | −0.166179 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.0362 | 0.494121 | ||||||||
\(927\) | 7.74456 | 0.254365 | ||||||||
\(928\) | 18.5109 | 0.607649 | ||||||||
\(929\) | 24.7446 | 0.811843 | 0.405921 | − | 0.913908i | \(-0.366951\pi\) | ||||
0.405921 | + | 0.913908i | \(0.366951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.84630 | −0.158831 | ||||||||
\(932\) | −6.52344 | −0.213683 | ||||||||
\(933\) | 24.2337 | 0.793375 | ||||||||
\(934\) | −17.0256 | −0.557093 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −18.1168 | −0.592168 | ||||||||
\(937\) | 24.8935 | 0.813236 | 0.406618 | − | 0.913598i | \(-0.366708\pi\) | ||||
0.406618 | + | 0.913598i | \(0.366708\pi\) | |||||||
\(938\) | −12.2337 | −0.399444 | ||||||||
\(939\) | −19.9783 | −0.651966 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.0256 | −0.555017 | −0.277509 | − | 0.960723i | \(-0.589509\pi\) | ||||
−0.277509 | + | 0.960723i | \(0.589509\pi\) | |||||||
\(942\) | −2.08191 | −0.0678322 | ||||||||
\(943\) | 55.4256 | 1.80491 | ||||||||
\(944\) | 2.51087 | 0.0817220 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.48913 | 0.0483901 | 0.0241950 | − | 0.999707i | \(-0.492298\pi\) | ||||
0.0241950 | + | 0.999707i | \(0.492298\pi\) | |||||||
\(948\) | −0.202380 | −0.00657299 | ||||||||
\(949\) | 35.2337 | 1.14373 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.9783 | −0.874830 | ||||||||
\(952\) | −44.7384 | −1.44998 | ||||||||
\(953\) | −7.92287 | −0.256647 | −0.128323 | − | 0.991732i | \(-0.540960\pi\) | ||||
−0.128323 | + | 0.991732i | \(0.540960\pi\) | |||||||
\(954\) | 10.0974 | 0.326914 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.2054 | −0.588804 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.7446 | 0.605609 | ||||||||
\(959\) | −27.1229 | −0.875844 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.6277 | −0.633152 | ||||||||
\(962\) | −26.8614 | −0.866047 | ||||||||
\(963\) | −11.6819 | −0.376445 | ||||||||
\(964\) | −28.3200 | −0.912124 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −16.0000 | −0.514792 | ||||||||
\(967\) | −54.3933 | −1.74917 | −0.874585 | − | 0.484872i | \(-0.838866\pi\) | ||||
−0.874585 | + | 0.484872i | \(0.838866\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 51.2119 | 1.64516 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.5109 | 0.850774 | 0.425387 | − | 0.905011i | \(-0.360138\pi\) | ||||
0.425387 | + | 0.905011i | \(0.360138\pi\) | |||||||
\(972\) | −1.37228 | −0.0440159 | ||||||||
\(973\) | 26.2337 | 0.841013 | ||||||||
\(974\) | −7.90564 | −0.253313 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.67715 | −0.0536842 | ||||||||
\(977\) | −27.2554 | −0.871979 | −0.435989 | − | 0.899952i | \(-0.643601\pi\) | ||||
−0.435989 | + | 0.899952i | \(0.643601\pi\) | |||||||
\(978\) | −6.83563 | −0.218579 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.98844 | 0.191196 | ||||||||
\(982\) | −5.25544 | −0.167708 | ||||||||
\(983\) | 14.5109 | 0.462825 | 0.231413 | − | 0.972856i | \(-0.425665\pi\) | ||||
0.231413 | + | 0.972856i | \(0.425665\pi\) | |||||||
\(984\) | 18.5109 | 0.590105 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 16.6553 | 0.530411 | ||||||||
\(987\) | −6.92820 | −0.220527 | ||||||||
\(988\) | −71.8397 | −2.28552 | ||||||||
\(989\) | −79.5990 | −2.53110 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.9565 | −1.42809 | −0.714045 | − | 0.700100i | \(-0.753139\pi\) | ||||
−0.714045 | + | 0.700100i | \(0.753139\pi\) | |||||||
\(992\) | −19.6974 | −0.625392 | ||||||||
\(993\) | −33.2337 | −1.05464 | ||||||||
\(994\) | −1.48913 | −0.0472322 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.57924 | 0.0817264 | ||||||||
\(997\) | −52.5138 | −1.66313 | −0.831564 | − | 0.555429i | \(-0.812554\pi\) | ||||
−0.831564 | + | 0.555429i | \(0.812554\pi\) | |||||||
\(998\) | 2.46943 | 0.0781686 | ||||||||
\(999\) | −5.00000 | −0.158193 |
(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 | 9075.2.a.db.1.3 | yes | 4 | |
5.4 | even | 2 | 9075.2.a.cw.1.2 | ✓ | 4 | ||
11.10 | odd | 2 | inner | 9075.2.a.db.1.2 | yes | 4 | |
55.54 | odd | 2 | 9075.2.a.cw.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9075.2.a.cw.1.2 | ✓ | 4 | 5.4 | even | 2 | ||
9075.2.a.cw.1.3 | yes | 4 | 55.54 | odd | 2 | ||
9075.2.a.db.1.2 | yes | 4 | 11.10 | odd | 2 | inner | |
9075.2.a.db.1.3 | yes | 4 | 1.1 | even | 1 | trivial |