Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1734,2,Mod(829,1734)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1734, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1734.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1734 = 2 \cdot 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1734.f (of order \(4\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(13.8460597105\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.722204136308736.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 18x^{8} + 69x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1483.4 | ||
Root | \(1.32893 + 1.32893i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1734.1483 |
Dual form | 1734.2.f.n.829.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times\).
\(n\) | \(1157\) | \(1159\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.49756 | + | 2.49756i | −1.11694 | + | 1.11694i | −0.124757 | + | 0.992187i | \(0.539815\pi\) |
−0.992187 | + | 0.124757i | \(0.960185\pi\) | |||||||
\(6\) | −0.707107 | − | 0.707107i | −0.288675 | − | 0.288675i | ||||
\(7\) | 1.95075 | + | 1.95075i | 0.737312 | + | 0.737312i | 0.972057 | − | 0.234745i | \(-0.0754254\pi\) |
−0.234745 | + | 0.972057i | \(0.575425\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 2.49756 | + | 2.49756i | 0.789799 | + | 0.789799i | ||||
\(11\) | −2.08141 | − | 2.08141i | −0.627570 | − | 0.627570i | 0.319886 | − | 0.947456i | \(-0.396355\pi\) |
−0.947456 | + | 0.319886i | \(0.896355\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | −5.06418 | −1.40455 | −0.702275 | − | 0.711906i | \(-0.747832\pi\) | ||||
−0.702275 | + | 0.711906i | \(0.747832\pi\) | |||||||
\(14\) | 1.95075 | − | 1.95075i | 0.521359 | − | 0.521359i | ||||
\(15\) | 3.53209i | 0.911981i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | − | 4.36959i | − | 1.00245i | −0.865317 | − | 0.501226i | \(-0.832883\pi\) | ||
0.865317 | − | 0.501226i | \(-0.167117\pi\) | |||||||
\(20\) | 2.49756 | − | 2.49756i | 0.558472 | − | 0.558472i | ||||
\(21\) | 2.75877 | 0.602013 | ||||||||
\(22\) | −2.08141 | + | 2.08141i | −0.443759 | + | 0.443759i | ||||
\(23\) | 4.24264 | + | 4.24264i | 0.884652 | + | 0.884652i | 0.994003 | − | 0.109351i | \(-0.0348774\pi\) |
−0.109351 | + | 0.994003i | \(0.534877\pi\) | |||||||
\(24\) | 0.707107 | + | 0.707107i | 0.144338 | + | 0.144338i | ||||
\(25\) | − | 7.47565i | − | 1.49513i | ||||||
\(26\) | 5.06418i | 0.993167i | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | −1.95075 | − | 1.95075i | −0.368656 | − | 0.368656i | ||||
\(29\) | 3.39458 | − | 3.39458i | 0.630357 | − | 0.630357i | −0.317800 | − | 0.948158i | \(-0.602944\pi\) |
0.948158 | + | 0.317800i | \(0.102944\pi\) | |||||||
\(30\) | 3.53209 | 0.644868 | ||||||||
\(31\) | 0.506912 | − | 0.506912i | 0.0910440 | − | 0.0910440i | −0.660118 | − | 0.751162i | \(-0.729494\pi\) |
0.751162 | + | 0.660118i | \(0.229494\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −2.94356 | −0.512409 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.74422 | −1.64707 | ||||||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | 7.22107 | − | 7.22107i | 1.18714 | − | 1.18714i | 0.209281 | − | 0.977856i | \(-0.432888\pi\) |
0.977856 | − | 0.209281i | \(-0.0671123\pi\) | |||||||
\(38\) | −4.36959 | −0.708840 | ||||||||
\(39\) | −3.58091 | + | 3.58091i | −0.573405 | + | 0.573405i | ||||
\(40\) | −2.49756 | − | 2.49756i | −0.394900 | − | 0.394900i | ||||
\(41\) | −8.89662 | − | 8.89662i | −1.38942 | − | 1.38942i | −0.826539 | − | 0.562879i | \(-0.809694\pi\) |
−0.562879 | − | 0.826539i | \(-0.690306\pi\) | |||||||
\(42\) | − | 2.75877i | − | 0.425688i | ||||||
\(43\) | − | 10.9067i | − | 1.66326i | −0.555330 | − | 0.831630i | \(-0.687408\pi\) | ||
0.555330 | − | 0.831630i | \(-0.312592\pi\) | |||||||
\(44\) | 2.08141 | + | 2.08141i | 0.313785 | + | 0.313785i | ||||
\(45\) | 2.49756 | + | 2.49756i | 0.372315 | + | 0.372315i | ||||
\(46\) | 4.24264 | − | 4.24264i | 0.625543 | − | 0.625543i | ||||
\(47\) | −5.14796 | −0.750907 | −0.375453 | − | 0.926841i | \(-0.622513\pi\) | ||||
−0.375453 | + | 0.926841i | \(0.622513\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | 0.610815i | 0.0872592i | ||||||||
\(50\) | −7.47565 | −1.05722 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.06418 | 0.702275 | ||||||||
\(53\) | 4.57398i | 0.628284i | 0.949376 | + | 0.314142i | \(0.101717\pi\) | ||||
−0.949376 | + | 0.314142i | \(0.898283\pi\) | |||||||
\(54\) | −0.707107 | + | 0.707107i | −0.0962250 | + | 0.0962250i | ||||
\(55\) | 10.3969 | 1.40192 | ||||||||
\(56\) | −1.95075 | + | 1.95075i | −0.260679 | + | 0.260679i | ||||
\(57\) | −3.08976 | − | 3.08976i | −0.409249 | − | 0.409249i | ||||
\(58\) | −3.39458 | − | 3.39458i | −0.445730 | − | 0.445730i | ||||
\(59\) | − | 5.53209i | − | 0.720217i | −0.932911 | − | 0.360108i | \(-0.882740\pi\) | ||
0.932911 | − | 0.360108i | \(-0.117260\pi\) | |||||||
\(60\) | − | 3.53209i | − | 0.455991i | ||||||
\(61\) | 4.41322 | + | 4.41322i | 0.565054 | + | 0.565054i | 0.930739 | − | 0.365685i | \(-0.119165\pi\) |
−0.365685 | + | 0.930739i | \(0.619165\pi\) | |||||||
\(62\) | −0.506912 | − | 0.506912i | −0.0643779 | − | 0.0643779i | ||||
\(63\) | 1.95075 | − | 1.95075i | 0.245771 | − | 0.245771i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 12.6481 | − | 12.6481i | 1.56880 | − | 1.56880i | ||||
\(66\) | 2.94356i | 0.362328i | ||||||||
\(67\) | 5.67499 | 0.693311 | 0.346655 | − | 0.937993i | \(-0.387317\pi\) | ||||
0.346655 | + | 0.937993i | \(0.387317\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 9.74422i | 1.16466i | ||||||||
\(71\) | −6.93201 | + | 6.93201i | −0.822679 | + | 0.822679i | −0.986491 | − | 0.163813i | \(-0.947621\pi\) |
0.163813 | + | 0.986491i | \(0.447621\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 6.39358 | − | 6.39358i | 0.748312 | − | 0.748312i | −0.225850 | − | 0.974162i | \(-0.572516\pi\) |
0.974162 | + | 0.225850i | \(0.0725159\pi\) | |||||||
\(74\) | −7.22107 | − | 7.22107i | −0.839432 | − | 0.839432i | ||||
\(75\) | −5.28608 | − | 5.28608i | −0.610384 | − | 0.610384i | ||||
\(76\) | 4.36959i | 0.501226i | ||||||||
\(77\) | − | 8.12061i | − | 0.925430i | ||||||
\(78\) | 3.58091 | + | 3.58091i | 0.405459 | + | 0.405459i | ||||
\(79\) | −4.68003 | − | 4.68003i | −0.526544 | − | 0.526544i | 0.392996 | − | 0.919540i | \(-0.371439\pi\) |
−0.919540 | + | 0.392996i | \(0.871439\pi\) | |||||||
\(80\) | −2.49756 | + | 2.49756i | −0.279236 | + | 0.279236i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −8.89662 | + | 8.89662i | −0.982467 | + | 0.982467i | ||||
\(83\) | − | 3.32501i | − | 0.364967i | −0.983209 | − | 0.182484i | \(-0.941586\pi\) | ||
0.983209 | − | 0.182484i | \(-0.0584136\pi\) | |||||||
\(84\) | −2.75877 | −0.301007 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.9067 | −1.17610 | ||||||||
\(87\) | − | 4.80066i | − | 0.514685i | ||||||
\(88\) | 2.08141 | − | 2.08141i | 0.221879 | − | 0.221879i | ||||
\(89\) | −13.8425 | −1.46731 | −0.733654 | − | 0.679524i | \(-0.762186\pi\) | ||||
−0.733654 | + | 0.679524i | \(0.762186\pi\) | |||||||
\(90\) | 2.49756 | − | 2.49756i | 0.263266 | − | 0.263266i | ||||
\(91\) | −9.87892 | − | 9.87892i | −1.03559 | − | 1.03559i | ||||
\(92\) | −4.24264 | − | 4.24264i | −0.442326 | − | 0.442326i | ||||
\(93\) | − | 0.716881i | − | 0.0743371i | ||||||
\(94\) | 5.14796i | 0.530971i | ||||||||
\(95\) | 10.9133 | + | 10.9133i | 1.11968 | + | 1.11968i | ||||
\(96\) | −0.707107 | − | 0.707107i | −0.0721688 | − | 0.0721688i | ||||
\(97\) | 7.79751 | − | 7.79751i | 0.791717 | − | 0.791717i | −0.190056 | − | 0.981773i | \(-0.560867\pi\) |
0.981773 | + | 0.190056i | \(0.0608670\pi\) | |||||||
\(98\) | 0.610815 | 0.0617016 | ||||||||
\(99\) | −2.08141 | + | 2.08141i | −0.209190 | + | 0.209190i | ||||
\(100\) | 7.47565i | 0.747565i | ||||||||
\(101\) | 0.921274 | 0.0916702 | 0.0458351 | − | 0.998949i | \(-0.485405\pi\) | ||||
0.0458351 | + | 0.998949i | \(0.485405\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.9736 | −1.67246 | −0.836229 | − | 0.548381i | \(-0.815245\pi\) | ||||
−0.836229 | + | 0.548381i | \(0.815245\pi\) | |||||||
\(104\) | − | 5.06418i | − | 0.496583i | ||||||
\(105\) | −6.89021 | + | 6.89021i | −0.672415 | + | 0.672415i | ||||
\(106\) | 4.57398 | 0.444264 | ||||||||
\(107\) | 2.18246 | − | 2.18246i | 0.210987 | − | 0.210987i | −0.593700 | − | 0.804686i | \(-0.702333\pi\) |
0.804686 | + | 0.593700i | \(0.202333\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 1.58479 | + | 1.58479i | 0.151795 | + | 0.151795i | 0.778919 | − | 0.627124i | \(-0.215768\pi\) |
−0.627124 | + | 0.778919i | \(0.715768\pi\) | |||||||
\(110\) | − | 10.3969i | − | 0.991308i | ||||||
\(111\) | − | 10.2121i | − | 0.969293i | ||||||
\(112\) | 1.95075 | + | 1.95075i | 0.184328 | + | 0.184328i | ||||
\(113\) | 8.08489 | + | 8.08489i | 0.760563 | + | 0.760563i | 0.976424 | − | 0.215861i | \(-0.0692559\pi\) |
−0.215861 | + | 0.976424i | \(0.569256\pi\) | |||||||
\(114\) | −3.08976 | + | 3.08976i | −0.289383 | + | 0.289383i | ||||
\(115\) | −21.1925 | −1.97621 | ||||||||
\(116\) | −3.39458 | + | 3.39458i | −0.315179 | + | 0.315179i | ||||
\(117\) | 5.06418i | 0.468183i | ||||||||
\(118\) | −5.53209 | −0.509270 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.53209 | −0.322434 | ||||||||
\(121\) | − | 2.33544i | − | 0.212312i | ||||||
\(122\) | 4.41322 | − | 4.41322i | 0.399554 | − | 0.399554i | ||||
\(123\) | −12.5817 | −1.13446 | ||||||||
\(124\) | −0.506912 | + | 0.506912i | −0.0455220 | + | 0.0455220i | ||||
\(125\) | 6.18310 | + | 6.18310i | 0.553033 | + | 0.553033i | ||||
\(126\) | −1.95075 | − | 1.95075i | −0.173786 | − | 0.173786i | ||||
\(127\) | 8.75877i | 0.777215i | 0.921403 | + | 0.388608i | \(0.127044\pi\) | ||||
−0.921403 | + | 0.388608i | \(0.872956\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −7.71222 | − | 7.71222i | −0.679023 | − | 0.679023i | ||||
\(130\) | −12.6481 | − | 12.6481i | −1.10931 | − | 1.10931i | ||||
\(131\) | −0.909203 | + | 0.909203i | −0.0794374 | + | 0.0794374i | −0.745709 | − | 0.666272i | \(-0.767889\pi\) |
0.666272 | + | 0.745709i | \(0.267889\pi\) | |||||||
\(132\) | 2.94356 | 0.256204 | ||||||||
\(133\) | 8.52395 | − | 8.52395i | 0.739120 | − | 0.739120i | ||||
\(134\) | − | 5.67499i | − | 0.490245i | ||||||
\(135\) | 3.53209 | 0.303994 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.36959 | 0.202447 | 0.101224 | − | 0.994864i | \(-0.467724\pi\) | ||||
0.101224 | + | 0.994864i | \(0.467724\pi\) | |||||||
\(138\) | − | 6.00000i | − | 0.510754i | ||||||
\(139\) | 3.99225 | − | 3.99225i | 0.338618 | − | 0.338618i | −0.517229 | − | 0.855847i | \(-0.673036\pi\) |
0.855847 | + | 0.517229i | \(0.173036\pi\) | |||||||
\(140\) | 9.74422 | 0.823537 | ||||||||
\(141\) | −3.64015 | + | 3.64015i | −0.306556 | + | 0.306556i | ||||
\(142\) | 6.93201 | + | 6.93201i | 0.581722 | + | 0.581722i | ||||
\(143\) | 10.5406 | + | 10.5406i | 0.881453 | + | 0.881453i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 16.9564i | 1.40815i | ||||||||
\(146\) | −6.39358 | − | 6.39358i | −0.529137 | − | 0.529137i | ||||
\(147\) | 0.431911 | + | 0.431911i | 0.0356234 | + | 0.0356234i | ||||
\(148\) | −7.22107 | + | 7.22107i | −0.593568 | + | 0.593568i | ||||
\(149\) | −11.4260 | −0.936056 | −0.468028 | − | 0.883714i | \(-0.655035\pi\) | ||||
−0.468028 | + | 0.883714i | \(0.655035\pi\) | |||||||
\(150\) | −5.28608 | + | 5.28608i | −0.431607 | + | 0.431607i | ||||
\(151\) | 11.7510i | 0.956285i | 0.878282 | + | 0.478143i | \(0.158690\pi\) | ||||
−0.878282 | + | 0.478143i | \(0.841310\pi\) | |||||||
\(152\) | 4.36959 | 0.354420 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.12061 | −0.654378 | ||||||||
\(155\) | 2.53209i | 0.203382i | ||||||||
\(156\) | 3.58091 | − | 3.58091i | 0.286703 | − | 0.286703i | ||||
\(157\) | 3.51754 | 0.280730 | 0.140365 | − | 0.990100i | \(-0.455172\pi\) | ||||
0.140365 | + | 0.990100i | \(0.455172\pi\) | |||||||
\(158\) | −4.68003 | + | 4.68003i | −0.372323 | + | 0.372323i | ||||
\(159\) | 3.23429 | + | 3.23429i | 0.256496 | + | 0.256496i | ||||
\(160\) | 2.49756 | + | 2.49756i | 0.197450 | + | 0.197450i | ||||
\(161\) | 16.5526i | 1.30453i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 4.47246 | + | 4.47246i | 0.350310 | + | 0.350310i | 0.860225 | − | 0.509915i | \(-0.170323\pi\) |
−0.509915 | + | 0.860225i | \(0.670323\pi\) | |||||||
\(164\) | 8.89662 | + | 8.89662i | 0.694709 | + | 0.694709i | ||||
\(165\) | 7.35174 | − | 7.35174i | 0.572332 | − | 0.572332i | ||||
\(166\) | −3.32501 | −0.258071 | ||||||||
\(167\) | −10.1403 | + | 10.1403i | −0.784677 | + | 0.784677i | −0.980616 | − | 0.195939i | \(-0.937224\pi\) |
0.195939 | + | 0.980616i | \(0.437224\pi\) | |||||||
\(168\) | 2.75877i | 0.212844i | ||||||||
\(169\) | 12.6459 | 0.972761 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.36959 | −0.334151 | ||||||||
\(172\) | 10.9067i | 0.831630i | ||||||||
\(173\) | −0.576439 | + | 0.576439i | −0.0438258 | + | 0.0438258i | −0.728680 | − | 0.684854i | \(-0.759866\pi\) |
0.684854 | + | 0.728680i | \(0.259866\pi\) | |||||||
\(174\) | −4.80066 | −0.363937 | ||||||||
\(175\) | 14.5831 | − | 14.5831i | 1.10238 | − | 1.10238i | ||||
\(176\) | −2.08141 | − | 2.08141i | −0.156892 | − | 0.156892i | ||||
\(177\) | −3.91178 | − | 3.91178i | −0.294027 | − | 0.294027i | ||||
\(178\) | 13.8425i | 1.03754i | ||||||||
\(179\) | − | 14.0642i | − | 1.05121i | −0.850730 | − | 0.525603i | \(-0.823840\pi\) | ||
0.850730 | − | 0.525603i | \(-0.176160\pi\) | |||||||
\(180\) | −2.49756 | − | 2.49756i | −0.186157 | − | 0.186157i | ||||
\(181\) | −14.3829 | − | 14.3829i | −1.06907 | − | 1.06907i | −0.997430 | − | 0.0716420i | \(-0.977176\pi\) |
−0.0716420 | − | 0.997430i | \(-0.522824\pi\) | |||||||
\(182\) | −9.87892 | + | 9.87892i | −0.732274 | + | 0.732274i | ||||
\(183\) | 6.24123 | 0.461365 | ||||||||
\(184\) | −4.24264 | + | 4.24264i | −0.312772 | + | 0.312772i | ||||
\(185\) | 36.0702i | 2.65193i | ||||||||
\(186\) | −0.716881 | −0.0525643 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.14796 | 0.375453 | ||||||||
\(189\) | − | 2.75877i | − | 0.200671i | ||||||
\(190\) | 10.9133 | − | 10.9133i | 0.791735 | − | 0.791735i | ||||
\(191\) | −15.6459 | −1.13210 | −0.566049 | − | 0.824372i | \(-0.691529\pi\) | ||||
−0.566049 | + | 0.824372i | \(0.691529\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | 7.26288 | + | 7.26288i | 0.522793 | + | 0.522793i | 0.918414 | − | 0.395621i | \(-0.129471\pi\) |
−0.395621 | + | 0.918414i | \(0.629471\pi\) | |||||||
\(194\) | −7.79751 | − | 7.79751i | −0.559828 | − | 0.559828i | ||||
\(195\) | − | 17.8871i | − | 1.28092i | ||||||
\(196\) | − | 0.610815i | − | 0.0436296i | ||||||
\(197\) | 6.17281 | + | 6.17281i | 0.439795 | + | 0.439795i | 0.891943 | − | 0.452148i | \(-0.149342\pi\) |
−0.452148 | + | 0.891943i | \(0.649342\pi\) | |||||||
\(198\) | 2.08141 | + | 2.08141i | 0.147920 | + | 0.147920i | ||||
\(199\) | −11.9446 | + | 11.9446i | −0.846728 | + | 0.846728i | −0.989723 | − | 0.142995i | \(-0.954327\pi\) |
0.142995 | + | 0.989723i | \(0.454327\pi\) | |||||||
\(200\) | 7.47565 | 0.528608 | ||||||||
\(201\) | 4.01283 | − | 4.01283i | 0.283043 | − | 0.283043i | ||||
\(202\) | − | 0.921274i | − | 0.0648206i | ||||||
\(203\) | 13.2439 | 0.929541 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 44.4397 | 3.10381 | ||||||||
\(206\) | 16.9736i | 1.18261i | ||||||||
\(207\) | 4.24264 | − | 4.24264i | 0.294884 | − | 0.294884i | ||||
\(208\) | −5.06418 | −0.351138 | ||||||||
\(209\) | −9.09491 | + | 9.09491i | −0.629108 | + | 0.629108i | ||||
\(210\) | 6.89021 | + | 6.89021i | 0.475469 | + | 0.475469i | ||||
\(211\) | 9.96968 | + | 9.96968i | 0.686341 | + | 0.686341i | 0.961421 | − | 0.275080i | \(-0.0887044\pi\) |
−0.275080 | + | 0.961421i | \(0.588704\pi\) | |||||||
\(212\) | − | 4.57398i | − | 0.314142i | ||||||
\(213\) | 9.80335i | 0.671714i | ||||||||
\(214\) | −2.18246 | − | 2.18246i | −0.149190 | − | 0.149190i | ||||
\(215\) | 27.2402 | + | 27.2402i | 1.85777 | + | 1.85777i | ||||
\(216\) | 0.707107 | − | 0.707107i | 0.0481125 | − | 0.0481125i | ||||
\(217\) | 1.97771 | 0.134256 | ||||||||
\(218\) | 1.58479 | − | 1.58479i | 0.107335 | − | 0.107335i | ||||
\(219\) | − | 9.04189i | − | 0.610994i | ||||||
\(220\) | −10.3969 | −0.700961 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.2121 | −0.685394 | ||||||||
\(223\) | − | 26.3037i | − | 1.76142i | −0.473653 | − | 0.880711i | \(-0.657065\pi\) | ||
0.473653 | − | 0.880711i | \(-0.342935\pi\) | |||||||
\(224\) | 1.95075 | − | 1.95075i | 0.130340 | − | 0.130340i | ||||
\(225\) | −7.47565 | −0.498377 | ||||||||
\(226\) | 8.08489 | − | 8.08489i | 0.537799 | − | 0.537799i | ||||
\(227\) | −4.28802 | − | 4.28802i | −0.284606 | − | 0.284606i | 0.550337 | − | 0.834943i | \(-0.314499\pi\) |
−0.834943 | + | 0.550337i | \(0.814499\pi\) | |||||||
\(228\) | 3.08976 | + | 3.08976i | 0.204625 | + | 0.204625i | ||||
\(229\) | − | 8.56624i | − | 0.566073i | −0.959109 | − | 0.283036i | \(-0.908658\pi\) | ||
0.959109 | − | 0.283036i | \(-0.0913417\pi\) | |||||||
\(230\) | 21.1925i | 1.39739i | ||||||||
\(231\) | −5.74214 | − | 5.74214i | −0.377805 | − | 0.377805i | ||||
\(232\) | 3.39458 | + | 3.39458i | 0.222865 | + | 0.222865i | ||||
\(233\) | −8.63528 | + | 8.63528i | −0.565716 | + | 0.565716i | −0.930925 | − | 0.365209i | \(-0.880997\pi\) |
0.365209 | + | 0.930925i | \(0.380997\pi\) | |||||||
\(234\) | 5.06418 | 0.331056 | ||||||||
\(235\) | 12.8573 | − | 12.8573i | 0.838721 | − | 0.838721i | ||||
\(236\) | 5.53209i | 0.360108i | ||||||||
\(237\) | −6.61856 | −0.429921 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.8716 | 0.767913 | 0.383956 | − | 0.923351i | \(-0.374561\pi\) | ||||
0.383956 | + | 0.923351i | \(0.374561\pi\) | |||||||
\(240\) | 3.53209i | 0.227995i | ||||||||
\(241\) | −16.9120 | + | 16.9120i | −1.08940 | + | 1.08940i | −0.0938061 | + | 0.995590i | \(0.529903\pi\) |
−0.995590 | + | 0.0938061i | \(0.970097\pi\) | |||||||
\(242\) | −2.33544 | −0.150128 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | −4.41322 | − | 4.41322i | −0.282527 | − | 0.282527i | ||||
\(245\) | −1.52555 | − | 1.52555i | −0.0974637 | − | 0.0974637i | ||||
\(246\) | 12.5817i | 0.802181i | ||||||||
\(247\) | 22.1284i | 1.40799i | ||||||||
\(248\) | 0.506912 | + | 0.506912i | 0.0321889 | + | 0.0321889i | ||||
\(249\) | −2.35114 | − | 2.35114i | −0.148997 | − | 0.148997i | ||||
\(250\) | 6.18310 | − | 6.18310i | 0.391054 | − | 0.391054i | ||||
\(251\) | 18.6040 | 1.17427 | 0.587137 | − | 0.809487i | \(-0.300255\pi\) | ||||
0.587137 | + | 0.809487i | \(0.300255\pi\) | |||||||
\(252\) | −1.95075 | + | 1.95075i | −0.122885 | + | 0.122885i | ||||
\(253\) | − | 17.6614i | − | 1.11036i | ||||||
\(254\) | 8.75877 | 0.549574 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 4.16756i | − | 0.259965i | −0.991516 | − | 0.129983i | \(-0.958508\pi\) | ||
0.991516 | − | 0.129983i | \(-0.0414921\pi\) | |||||||
\(258\) | −7.71222 | + | 7.71222i | −0.480142 | + | 0.480142i | ||||
\(259\) | 28.1729 | 1.75058 | ||||||||
\(260\) | −12.6481 | + | 12.6481i | −0.784402 | + | 0.784402i | ||||
\(261\) | −3.39458 | − | 3.39458i | −0.210119 | − | 0.210119i | ||||
\(262\) | 0.909203 | + | 0.909203i | 0.0561707 | + | 0.0561707i | ||||
\(263\) | − | 7.97090i | − | 0.491507i | −0.969332 | − | 0.245754i | \(-0.920965\pi\) | ||
0.969332 | − | 0.245754i | \(-0.0790354\pi\) | |||||||
\(264\) | − | 2.94356i | − | 0.181164i | ||||||
\(265\) | −11.4238 | − | 11.4238i | −0.701759 | − | 0.701759i | ||||
\(266\) | −8.52395 | − | 8.52395i | −0.522637 | − | 0.522637i | ||||
\(267\) | −9.78816 | + | 9.78816i | −0.599026 | + | 0.599026i | ||||
\(268\) | −5.67499 | −0.346655 | ||||||||
\(269\) | −4.21659 | + | 4.21659i | −0.257090 | + | 0.257090i | −0.823870 | − | 0.566779i | \(-0.808189\pi\) |
0.566779 | + | 0.823870i | \(0.308189\pi\) | |||||||
\(270\) | − | 3.53209i | − | 0.214956i | ||||||
\(271\) | −3.07098 | −0.186549 | −0.0932745 | − | 0.995640i | \(-0.529733\pi\) | ||||
−0.0932745 | + | 0.995640i | \(0.529733\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.9709 | −0.845558 | ||||||||
\(274\) | − | 2.36959i | − | 0.143152i | ||||||
\(275\) | −15.5599 | + | 15.5599i | −0.938299 | + | 0.938299i | ||||
\(276\) | −6.00000 | −0.361158 | ||||||||
\(277\) | 16.4383 | − | 16.4383i | 0.987680 | − | 0.987680i | −0.0122455 | − | 0.999925i | \(-0.503898\pi\) |
0.999925 | + | 0.0122455i | \(0.00389795\pi\) | |||||||
\(278\) | −3.99225 | − | 3.99225i | −0.239439 | − | 0.239439i | ||||
\(279\) | −0.506912 | − | 0.506912i | −0.0303480 | − | 0.0303480i | ||||
\(280\) | − | 9.74422i | − | 0.582329i | ||||||
\(281\) | − | 21.7297i | − | 1.29628i | −0.761520 | − | 0.648142i | \(-0.775546\pi\) | ||
0.761520 | − | 0.648142i | \(-0.224454\pi\) | |||||||
\(282\) | 3.64015 | + | 3.64015i | 0.216768 | + | 0.216768i | ||||
\(283\) | −12.1570 | − | 12.1570i | −0.722656 | − | 0.722656i | 0.246489 | − | 0.969145i | \(-0.420723\pi\) |
−0.969145 | + | 0.246489i | \(0.920723\pi\) | |||||||
\(284\) | 6.93201 | − | 6.93201i | 0.411339 | − | 0.411339i | ||||
\(285\) | 15.4338 | 0.914217 | ||||||||
\(286\) | 10.5406 | − | 10.5406i | 0.623282 | − | 0.623282i | ||||
\(287\) | − | 34.7101i | − | 2.04887i | ||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 16.9564 | 0.995712 | ||||||||
\(291\) | − | 11.0273i | − | 0.646434i | ||||||
\(292\) | −6.39358 | + | 6.39358i | −0.374156 | + | 0.374156i | ||||
\(293\) | 9.20708 | 0.537883 | 0.268942 | − | 0.963156i | \(-0.413326\pi\) | ||||
0.268942 | + | 0.963156i | \(0.413326\pi\) | |||||||
\(294\) | 0.431911 | − | 0.431911i | 0.0251896 | − | 0.0251896i | ||||
\(295\) | 13.8167 | + | 13.8167i | 0.804442 | + | 0.804442i | ||||
\(296\) | 7.22107 | + | 7.22107i | 0.419716 | + | 0.419716i | ||||
\(297\) | 2.94356i | 0.170803i | ||||||||
\(298\) | 11.4260i | 0.661892i | ||||||||
\(299\) | −21.4855 | − | 21.4855i | −1.24254 | − | 1.24254i | ||||
\(300\) | 5.28608 | + | 5.28608i | 0.305192 | + | 0.305192i | ||||
\(301\) | 21.2762 | − | 21.2762i | 1.22634 | − | 1.22634i | ||||
\(302\) | 11.7510 | 0.676196 | ||||||||
\(303\) | 0.651439 | − | 0.651439i | 0.0374242 | − | 0.0374242i | ||||
\(304\) | − | 4.36959i | − | 0.250613i | ||||||
\(305\) | −22.0446 | −1.26227 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.90673 | 0.165896 | 0.0829478 | − | 0.996554i | \(-0.473567\pi\) | ||||
0.0829478 | + | 0.996554i | \(0.473567\pi\) | |||||||
\(308\) | 8.12061i | 0.462715i | ||||||||
\(309\) | −12.0021 | + | 12.0021i | −0.682778 | + | 0.682778i | ||||
\(310\) | 2.53209 | 0.143813 | ||||||||
\(311\) | 9.21719 | − | 9.21719i | 0.522659 | − | 0.522659i | −0.395714 | − | 0.918374i | \(-0.629503\pi\) |
0.918374 | + | 0.395714i | \(0.129503\pi\) | |||||||
\(312\) | −3.58091 | − | 3.58091i | −0.202729 | − | 0.202729i | ||||
\(313\) | −2.27804 | − | 2.27804i | −0.128762 | − | 0.128762i | 0.639789 | − | 0.768551i | \(-0.279022\pi\) |
−0.768551 | + | 0.639789i | \(0.779022\pi\) | |||||||
\(314\) | − | 3.51754i | − | 0.198506i | ||||||
\(315\) | 9.74422i | 0.549025i | ||||||||
\(316\) | 4.68003 | + | 4.68003i | 0.263272 | + | 0.263272i | ||||
\(317\) | −13.4943 | − | 13.4943i | −0.757914 | − | 0.757914i | 0.218029 | − | 0.975942i | \(-0.430037\pi\) |
−0.975942 | + | 0.218029i | \(0.930037\pi\) | |||||||
\(318\) | 3.23429 | − | 3.23429i | 0.181370 | − | 0.181370i | ||||
\(319\) | −14.1310 | −0.791187 | ||||||||
\(320\) | 2.49756 | − | 2.49756i | 0.139618 | − | 0.139618i | ||||
\(321\) | − | 3.08647i | − | 0.172270i | ||||||
\(322\) | 16.5526 | 0.922442 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 37.8580i | 2.09999i | ||||||||
\(326\) | 4.47246 | − | 4.47246i | 0.247706 | − | 0.247706i | ||||
\(327\) | 2.24123 | 0.123940 | ||||||||
\(328\) | 8.89662 | − | 8.89662i | 0.491234 | − | 0.491234i | ||||
\(329\) | −10.0424 | − | 10.0424i | −0.553653 | − | 0.553653i | ||||
\(330\) | −7.35174 | − | 7.35174i | −0.404700 | − | 0.404700i | ||||
\(331\) | − | 3.43376i | − | 0.188737i | −0.995537 | − | 0.0943683i | \(-0.969917\pi\) | ||
0.995537 | − | 0.0943683i | \(-0.0300831\pi\) | |||||||
\(332\) | 3.32501i | 0.182484i | ||||||||
\(333\) | −7.22107 | − | 7.22107i | −0.395712 | − | 0.395712i | ||||
\(334\) | 10.1403 | + | 10.1403i | 0.554850 | + | 0.554850i | ||||
\(335\) | −14.1737 | + | 14.1737i | −0.774390 | + | 0.774390i | ||||
\(336\) | 2.75877 | 0.150503 | ||||||||
\(337\) | −25.2580 | + | 25.2580i | −1.37589 | + | 1.37589i | −0.524446 | + | 0.851443i | \(0.675728\pi\) |
−0.851443 | + | 0.524446i | \(0.824272\pi\) | |||||||
\(338\) | − | 12.6459i | − | 0.687846i | ||||||
\(339\) | 11.4338 | 0.620997 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.11019 | −0.114273 | ||||||||
\(342\) | 4.36959i | 0.236280i | ||||||||
\(343\) | 12.4637 | − | 12.4637i | 0.672975 | − | 0.672975i | ||||
\(344\) | 10.9067 | 0.588051 | ||||||||
\(345\) | −14.9854 | + | 14.9854i | −0.806786 | + | 0.806786i | ||||
\(346\) | 0.576439 | + | 0.576439i | 0.0309895 | + | 0.0309895i | ||||
\(347\) | 0.783348 | + | 0.783348i | 0.0420523 | + | 0.0420523i | 0.727820 | − | 0.685768i | \(-0.240534\pi\) |
−0.685768 | + | 0.727820i | \(0.740534\pi\) | |||||||
\(348\) | 4.80066i | 0.257342i | ||||||||
\(349\) | − | 11.2371i | − | 0.601509i | −0.953702 | − | 0.300754i | \(-0.902762\pi\) | ||
0.953702 | − | 0.300754i | \(-0.0972384\pi\) | |||||||
\(350\) | −14.5831 | − | 14.5831i | −0.779499 | − | 0.779499i | ||||
\(351\) | 3.58091 | + | 3.58091i | 0.191135 | + | 0.191135i | ||||
\(352\) | −2.08141 | + | 2.08141i | −0.110940 | + | 0.110940i | ||||
\(353\) | 11.2608 | 0.599353 | 0.299677 | − | 0.954041i | \(-0.403121\pi\) | ||||
0.299677 | + | 0.954041i | \(0.403121\pi\) | |||||||
\(354\) | −3.91178 | + | 3.91178i | −0.207909 | + | 0.207909i | ||||
\(355\) | − | 34.6263i | − | 1.83777i | ||||||
\(356\) | 13.8425 | 0.733654 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.0642 | −0.743315 | ||||||||
\(359\) | 2.04458i | 0.107909i | 0.998543 | + | 0.0539543i | \(0.0171825\pi\) | ||||
−0.998543 | + | 0.0539543i | \(0.982817\pi\) | |||||||
\(360\) | −2.49756 | + | 2.49756i | −0.131633 | + | 0.131633i | ||||
\(361\) | −0.0932736 | −0.00490914 | ||||||||
\(362\) | −14.3829 | + | 14.3829i | −0.755948 | + | 0.755948i | ||||
\(363\) | −1.65140 | − | 1.65140i | −0.0866762 | − | 0.0866762i | ||||
\(364\) | 9.87892 | + | 9.87892i | 0.517796 | + | 0.517796i | ||||
\(365\) | 31.9368i | 1.67165i | ||||||||
\(366\) | − | 6.24123i | − | 0.326234i | ||||||
\(367\) | −17.2603 | − | 17.2603i | −0.900979 | − | 0.900979i | 0.0945417 | − | 0.995521i | \(-0.469861\pi\) |
−0.995521 | + | 0.0945417i | \(0.969861\pi\) | |||||||
\(368\) | 4.24264 | + | 4.24264i | 0.221163 | + | 0.221163i | ||||
\(369\) | −8.89662 | + | 8.89662i | −0.463139 | + | 0.463139i | ||||
\(370\) | 36.0702 | 1.87520 | ||||||||
\(371\) | −8.92267 | + | 8.92267i | −0.463242 | + | 0.463242i | ||||
\(372\) | 0.716881i | 0.0371686i | ||||||||
\(373\) | 27.3756 | 1.41745 | 0.708727 | − | 0.705483i | \(-0.249270\pi\) | ||||
0.708727 | + | 0.705483i | \(0.249270\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.74422 | 0.451550 | ||||||||
\(376\) | − | 5.14796i | − | 0.265486i | ||||||
\(377\) | −17.1908 | + | 17.1908i | −0.885369 | + | 0.885369i | ||||
\(378\) | −2.75877 | −0.141896 | ||||||||
\(379\) | −15.9084 | + | 15.9084i | −0.817162 | + | 0.817162i | −0.985696 | − | 0.168534i | \(-0.946097\pi\) |
0.168534 | + | 0.985696i | \(0.446097\pi\) | |||||||
\(380\) | −10.9133 | − | 10.9133i | −0.559841 | − | 0.559841i | ||||
\(381\) | 6.19339 | + | 6.19339i | 0.317297 | + | 0.317297i | ||||
\(382\) | 15.6459i | 0.800514i | ||||||||
\(383\) | − | 16.5972i | − | 0.848077i | −0.905644 | − | 0.424039i | \(-0.860612\pi\) | ||
0.905644 | − | 0.424039i | \(-0.139388\pi\) | |||||||
\(384\) | 0.707107 | + | 0.707107i | 0.0360844 | + | 0.0360844i | ||||
\(385\) | 20.2818 | + | 20.2818i | 1.03365 | + | 1.03365i | ||||
\(386\) | 7.26288 | − | 7.26288i | 0.369671 | − | 0.369671i | ||||
\(387\) | −10.9067 | −0.554420 | ||||||||
\(388\) | −7.79751 | + | 7.79751i | −0.395858 | + | 0.395858i | ||||
\(389\) | − | 17.2249i | − | 0.873338i | −0.899622 | − | 0.436669i | \(-0.856158\pi\) | ||
0.899622 | − | 0.436669i | \(-0.143842\pi\) | |||||||
\(390\) | −17.8871 | −0.905750 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.610815 | −0.0308508 | ||||||||
\(393\) | 1.28581i | 0.0648604i | ||||||||
\(394\) | 6.17281 | − | 6.17281i | 0.310982 | − | 0.310982i | ||||
\(395\) | 23.3773 | 1.17624 | ||||||||
\(396\) | 2.08141 | − | 2.08141i | 0.104595 | − | 0.104595i | ||||
\(397\) | 3.18052 | + | 3.18052i | 0.159626 | + | 0.159626i | 0.782401 | − | 0.622775i | \(-0.213995\pi\) |
−0.622775 | + | 0.782401i | \(0.713995\pi\) | |||||||
\(398\) | 11.9446 | + | 11.9446i | 0.598727 | + | 0.598727i | ||||
\(399\) | − | 12.0547i | − | 0.603489i | ||||||
\(400\) | − | 7.47565i | − | 0.373783i | ||||||
\(401\) | −1.44573 | − | 1.44573i | −0.0721965 | − | 0.0721965i | 0.670086 | − | 0.742283i | \(-0.266257\pi\) |
−0.742283 | + | 0.670086i | \(0.766257\pi\) | |||||||
\(402\) | −4.01283 | − | 4.01283i | −0.200142 | − | 0.200142i | ||||
\(403\) | −2.56709 | + | 2.56709i | −0.127876 | + | 0.127876i | ||||
\(404\) | −0.921274 | −0.0458351 | ||||||||
\(405\) | 2.49756 | − | 2.49756i | 0.124105 | − | 0.124105i | ||||
\(406\) | − | 13.2439i | − | 0.657285i | ||||||
\(407\) | −30.0601 | −1.49002 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.2841 | 1.15132 | 0.575661 | − | 0.817688i | \(-0.304745\pi\) | ||||
0.575661 | + | 0.817688i | \(0.304745\pi\) | |||||||
\(410\) | − | 44.4397i | − | 2.19472i | ||||||
\(411\) | 1.67555 | − | 1.67555i | 0.0826488 | − | 0.0826488i | ||||
\(412\) | 16.9736 | 0.836229 | ||||||||
\(413\) | 10.7917 | − | 10.7917i | 0.531025 | − | 0.531025i | ||||
\(414\) | −4.24264 | − | 4.24264i | −0.208514 | − | 0.208514i | ||||
\(415\) | 8.30442 | + | 8.30442i | 0.407648 | + | 0.407648i | ||||
\(416\) | 5.06418i | 0.248292i | ||||||||
\(417\) | − | 5.64590i | − | 0.276481i | ||||||
\(418\) | 9.09491 | + | 9.09491i | 0.444847 | + | 0.444847i | ||||
\(419\) | 1.06278 | + | 1.06278i | 0.0519200 | + | 0.0519200i | 0.732590 | − | 0.680670i | \(-0.238311\pi\) |
−0.680670 | + | 0.732590i | \(0.738311\pi\) | |||||||
\(420\) | 6.89021 | − | 6.89021i | 0.336208 | − | 0.336208i | ||||
\(421\) | −18.1438 | −0.884277 | −0.442138 | − | 0.896947i | \(-0.645780\pi\) | ||||
−0.442138 | + | 0.896947i | \(0.645780\pi\) | |||||||
\(422\) | 9.96968 | − | 9.96968i | 0.485317 | − | 0.485317i | ||||
\(423\) | 5.14796i | 0.250302i | ||||||||
\(424\) | −4.57398 | −0.222132 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9.80335 | 0.474974 | ||||||||
\(427\) | 17.2181i | 0.833243i | ||||||||
\(428\) | −2.18246 | + | 2.18246i | −0.105493 | + | 0.105493i | ||||
\(429\) | 14.9067 | 0.719704 | ||||||||
\(430\) | 27.2402 | − | 27.2402i | 1.31364 | − | 1.31364i | ||||
\(431\) | 18.5457 | + | 18.5457i | 0.893316 | + | 0.893316i | 0.994834 | − | 0.101518i | \(-0.0323698\pi\) |
−0.101518 | + | 0.994834i | \(0.532370\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 27.6604i | 1.32928i | 0.747165 | + | 0.664638i | \(0.231414\pi\) | ||||
−0.747165 | + | 0.664638i | \(0.768586\pi\) | |||||||
\(434\) | − | 1.97771i | − | 0.0949332i | ||||||
\(435\) | 11.9900 | + | 11.9900i | 0.574874 | + | 0.574874i | ||||
\(436\) | −1.58479 | − | 1.58479i | −0.0758976 | − | 0.0758976i | ||||
\(437\) | 18.5386 | − | 18.5386i | 0.886821 | − | 0.886821i | ||||
\(438\) | −9.04189 | −0.432038 | ||||||||
\(439\) | 20.9628 | − | 20.9628i | 1.00050 | − | 1.00050i | 0.000500672 | − | 1.00000i | \(-0.499841\pi\) |
1.00000 | 0.000500672i | \(-0.000159369\pi\) | ||||||||
\(440\) | 10.3969i | 0.495654i | ||||||||
\(441\) | 0.610815 | 0.0290864 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.3209 | −1.63063 | −0.815317 | − | 0.579014i | \(-0.803437\pi\) | ||||
−0.815317 | + | 0.579014i | \(0.803437\pi\) | |||||||
\(444\) | 10.2121i | 0.484646i | ||||||||
\(445\) | 34.5727 | − | 34.5727i | 1.63890 | − | 1.63890i | ||||
\(446\) | −26.3037 | −1.24551 | ||||||||
\(447\) | −8.07942 | + | 8.07942i | −0.382143 | + | 0.382143i | ||||
\(448\) | −1.95075 | − | 1.95075i | −0.0921641 | − | 0.0921641i | ||||
\(449\) | 16.8425 | + | 16.8425i | 0.794845 | + | 0.794845i | 0.982277 | − | 0.187433i | \(-0.0600167\pi\) |
−0.187433 | + | 0.982277i | \(0.560017\pi\) | |||||||
\(450\) | 7.47565i | 0.352406i | ||||||||
\(451\) | 37.0351i | 1.74391i | ||||||||
\(452\) | −8.08489 | − | 8.08489i | −0.380281 | − | 0.380281i | ||||
\(453\) | 8.30923 | + | 8.30923i | 0.390402 | + | 0.390402i | ||||
\(454\) | −4.28802 | + | 4.28802i | −0.201247 | + | 0.201247i | ||||
\(455\) | 49.3465 | 2.31340 | ||||||||
\(456\) | 3.08976 | − | 3.08976i | 0.144691 | − | 0.144691i | ||||
\(457\) | − | 21.4662i | − | 1.00414i | −0.864826 | − | 0.502072i | \(-0.832571\pi\) | ||
0.864826 | − | 0.502072i | \(-0.167429\pi\) | |||||||
\(458\) | −8.56624 | −0.400274 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 21.1925 | 0.988107 | ||||||||
\(461\) | − | 16.8898i | − | 0.786637i | −0.919402 | − | 0.393319i | \(-0.871327\pi\) | ||
0.919402 | − | 0.393319i | \(-0.128673\pi\) | |||||||
\(462\) | −5.74214 | + | 5.74214i | −0.267149 | + | 0.267149i | ||||
\(463\) | 3.75784 | 0.174641 | 0.0873207 | − | 0.996180i | \(-0.472169\pi\) | ||||
0.0873207 | + | 0.996180i | \(0.472169\pi\) | |||||||
\(464\) | 3.39458 | − | 3.39458i | 0.157589 | − | 0.157589i | ||||
\(465\) | 1.79046 | + | 1.79046i | 0.0830305 | + | 0.0830305i | ||||
\(466\) | 8.63528 | + | 8.63528i | 0.400022 | + | 0.400022i | ||||
\(467\) | − | 12.4311i | − | 0.575242i | −0.957744 | − | 0.287621i | \(-0.907136\pi\) | ||
0.957744 | − | 0.287621i | \(-0.0928643\pi\) | |||||||
\(468\) | − | 5.06418i | − | 0.234092i | ||||||
\(469\) | 11.0705 | + | 11.0705i | 0.511187 | + | 0.511187i | ||||
\(470\) | −12.8573 | − | 12.8573i | −0.593065 | − | 0.593065i | ||||
\(471\) | 2.48728 | − | 2.48728i | 0.114608 | − | 0.114608i | ||||
\(472\) | 5.53209 | 0.254635 | ||||||||
\(473\) | −22.7014 | + | 22.7014i | −1.04381 | + | 1.04381i | ||||
\(474\) | 6.61856i | 0.304000i | ||||||||
\(475\) | −32.6655 | −1.49880 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.57398 | 0.209428 | ||||||||
\(478\) | − | 11.8716i | − | 0.542996i | ||||||
\(479\) | 8.26641 | − | 8.26641i | 0.377702 | − | 0.377702i | −0.492570 | − | 0.870273i | \(-0.663943\pi\) |
0.870273 | + | 0.492570i | \(0.163943\pi\) | |||||||
\(480\) | 3.53209 | 0.161217 | ||||||||
\(481\) | −36.5688 | + | 36.5688i | −1.66739 | + | 1.66739i | ||||
\(482\) | 16.9120 | + | 16.9120i | 0.770320 | + | 0.770320i | ||||
\(483\) | 11.7045 | + | 11.7045i | 0.532572 | + | 0.532572i | ||||
\(484\) | 2.33544i | 0.106156i | ||||||||
\(485\) | 38.9495i | 1.76861i | ||||||||
\(486\) | 0.707107 | + | 0.707107i | 0.0320750 | + | 0.0320750i | ||||
\(487\) | −5.18694 | − | 5.18694i | −0.235043 | − | 0.235043i | 0.579751 | − | 0.814794i | \(-0.303150\pi\) |
−0.814794 | + | 0.579751i | \(0.803150\pi\) | |||||||
\(488\) | −4.41322 | + | 4.41322i | −0.199777 | + | 0.199777i | ||||
\(489\) | 6.32501 | 0.286027 | ||||||||
\(490\) | −1.52555 | + | 1.52555i | −0.0689173 | + | 0.0689173i | ||||
\(491\) | 2.27126i | 0.102500i | 0.998686 | + | 0.0512502i | \(0.0163206\pi\) | ||||
−0.998686 | + | 0.0512502i | \(0.983679\pi\) | |||||||
\(492\) | 12.5817 | 0.567228 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 22.1284 | 0.995602 | ||||||||
\(495\) | − | 10.3969i | − | 0.467307i | ||||||
\(496\) | 0.506912 | − | 0.506912i | 0.0227610 | − | 0.0227610i | ||||
\(497\) | −27.0452 | −1.21314 | ||||||||
\(498\) | −2.35114 | + | 2.35114i | −0.105357 | + | 0.105357i | ||||
\(499\) | −6.87277 | − | 6.87277i | −0.307668 | − | 0.307668i | 0.536337 | − | 0.844004i | \(-0.319808\pi\) |
−0.844004 | + | 0.536337i | \(0.819808\pi\) | |||||||
\(500\) | −6.18310 | − | 6.18310i | −0.276517 | − | 0.276517i | ||||
\(501\) | 14.3405i | 0.640686i | ||||||||
\(502\) | − | 18.6040i | − | 0.830337i | ||||||
\(503\) | 12.5573 | + | 12.5573i | 0.559904 | + | 0.559904i | 0.929280 | − | 0.369376i | \(-0.120428\pi\) |
−0.369376 | + | 0.929280i | \(0.620428\pi\) | |||||||
\(504\) | 1.95075 | + | 1.95075i | 0.0868931 | + | 0.0868931i | ||||
\(505\) | −2.30094 | + | 2.30094i | −0.102391 | + | 0.102391i | ||||
\(506\) | −17.6614 | −0.785144 | ||||||||
\(507\) | 8.94200 | − | 8.94200i | 0.397128 | − | 0.397128i | ||||
\(508\) | − | 8.75877i | − | 0.388608i | ||||||
\(509\) | −7.39786 | −0.327904 | −0.163952 | − | 0.986468i | \(-0.552424\pi\) | ||||
−0.163952 | + | 0.986468i | \(0.552424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.9445 | 1.10348 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −3.08976 | + | 3.08976i | −0.136416 | + | 0.136416i | ||||
\(514\) | −4.16756 | −0.183823 | ||||||||
\(515\) | 42.3926 | − | 42.3926i | 1.86804 | − | 1.86804i | ||||
\(516\) | 7.71222 | + | 7.71222i | 0.339512 | + | 0.339512i | ||||
\(517\) | 10.7150 | + | 10.7150i | 0.471246 | + | 0.471246i | ||||
\(518\) | − | 28.1729i | − | 1.23785i | ||||||
\(519\) | 0.815207i | 0.0357836i | ||||||||
\(520\) | 12.6481 | + | 12.6481i | 0.554656 | + | 0.554656i | ||||
\(521\) | −2.91539 | − | 2.91539i | −0.127725 | − | 0.127725i | 0.640354 | − | 0.768080i | \(-0.278788\pi\) |
−0.768080 | + | 0.640354i | \(0.778788\pi\) | |||||||
\(522\) | −3.39458 | + | 3.39458i | −0.148577 | + | 0.148577i | ||||
\(523\) | 36.5134 | 1.59662 | 0.798310 | − | 0.602246i | \(-0.205728\pi\) | ||||
0.798310 | + | 0.602246i | \(0.205728\pi\) | |||||||
\(524\) | 0.909203 | − | 0.909203i | 0.0397187 | − | 0.0397187i | ||||
\(525\) | − | 20.6236i | − | 0.900088i | ||||||
\(526\) | −7.97090 | −0.347548 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.94356 | −0.128102 | ||||||||
\(529\) | 13.0000i | 0.565217i | ||||||||
\(530\) | −11.4238 | + | 11.4238i | −0.496218 | + | 0.496218i | ||||
\(531\) | −5.53209 | −0.240072 | ||||||||
\(532\) | −8.52395 | + | 8.52395i | −0.369560 | + | 0.369560i | ||||
\(533\) | 45.0541 | + | 45.0541i | 1.95151 | + | 1.95151i | ||||
\(534\) | 9.78816 | + | 9.78816i | 0.423575 | + | 0.423575i | ||||
\(535\) | 10.9017i | 0.471320i | ||||||||
\(536\) | 5.67499i | 0.245122i | ||||||||
\(537\) | −9.94488 | − | 9.94488i | −0.429153 | − | 0.429153i | ||||
\(538\) | 4.21659 | + | 4.21659i | 0.181790 | + | 0.181790i | ||||
\(539\) | 1.27136 | − | 1.27136i | 0.0547612 | − | 0.0547612i | ||||
\(540\) | −3.53209 | −0.151997 | ||||||||
\(541\) | −31.6740 | + | 31.6740i | −1.36177 | + | 1.36177i | −0.490116 | + | 0.871657i | \(0.663046\pi\) |
−0.871657 | + | 0.490116i | \(0.836954\pi\) | |||||||
\(542\) | 3.07098i | 0.131910i | ||||||||
\(543\) | −20.3405 | −0.872894 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.91622 | −0.339094 | ||||||||
\(546\) | 13.9709i | 0.597900i | ||||||||
\(547\) | −15.6265 | + | 15.6265i | −0.668142 | + | 0.668142i | −0.957286 | − | 0.289143i | \(-0.906630\pi\) |
0.289143 | + | 0.957286i | \(0.406630\pi\) | |||||||
\(548\) | −2.36959 | −0.101224 | ||||||||
\(549\) | 4.41322 | − | 4.41322i | 0.188351 | − | 0.188351i | ||||
\(550\) | 15.5599 | + | 15.5599i | 0.663477 | + | 0.663477i | ||||
\(551\) | −14.8329 | − | 14.8329i | −0.631903 | − | 0.631903i | ||||
\(552\) | 6.00000i | 0.255377i | ||||||||
\(553\) | − | 18.2591i | − | 0.776455i | ||||||
\(554\) | −16.4383 | − | 16.4383i | −0.698395 | − | 0.698395i | ||||
\(555\) | 25.5055 | + | 25.5055i | 1.08265 | + | 1.08265i | ||||
\(556\) | −3.99225 | + | 3.99225i | −0.169309 | + | 0.169309i | ||||
\(557\) | −21.9905 | −0.931768 | −0.465884 | − | 0.884846i | \(-0.654264\pi\) | ||||
−0.465884 | + | 0.884846i | \(0.654264\pi\) | |||||||
\(558\) | −0.506912 | + | 0.506912i | −0.0214593 | + | 0.0214593i | ||||
\(559\) | 55.2336i | 2.33613i | ||||||||
\(560\) | −9.74422 | −0.411769 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −21.7297 | −0.916611 | ||||||||
\(563\) | − | 31.9486i | − | 1.34647i | −0.739427 | − | 0.673237i | \(-0.764903\pi\) | ||
0.739427 | − | 0.673237i | \(-0.235097\pi\) | |||||||
\(564\) | 3.64015 | − | 3.64015i | 0.153278 | − | 0.153278i | ||||
\(565\) | −40.3851 | −1.69901 | ||||||||
\(566\) | −12.1570 | + | 12.1570i | −0.510995 | + | 0.510995i | ||||
\(567\) | −1.95075 | − | 1.95075i | −0.0819236 | − | 0.0819236i | ||||
\(568\) | −6.93201 | − | 6.93201i | −0.290861 | − | 0.290861i | ||||
\(569\) | 30.9614i | 1.29797i | 0.760801 | + | 0.648985i | \(0.224806\pi\) | ||||
−0.760801 | + | 0.648985i | \(0.775194\pi\) | |||||||
\(570\) | − | 15.4338i | − | 0.646449i | ||||||
\(571\) | 11.6730 | + | 11.6730i | 0.488498 | + | 0.488498i | 0.907832 | − | 0.419334i | \(-0.137736\pi\) |
−0.419334 | + | 0.907832i | \(0.637736\pi\) | |||||||
\(572\) | −10.5406 | − | 10.5406i | −0.440727 | − | 0.440727i | ||||
\(573\) | −11.0633 | + | 11.0633i | −0.462177 | + | 0.462177i | ||||
\(574\) | −34.7101 | −1.44877 | ||||||||
\(575\) | 31.7165 | − | 31.7165i | 1.32267 | − | 1.32267i | ||||
\(576\) | 1.00000i | 0.0416667i | ||||||||
\(577\) | −18.9026 | −0.786926 | −0.393463 | − | 0.919340i | \(-0.628723\pi\) | ||||
−0.393463 | + | 0.919340i | \(0.628723\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.2713 | 0.426859 | ||||||||
\(580\) | − | 16.9564i | − | 0.704074i | ||||||
\(581\) | 6.48624 | − | 6.48624i | 0.269095 | − | 0.269095i | ||||
\(582\) | −11.0273 | −0.457098 | ||||||||
\(583\) | 9.52034 | − | 9.52034i | 0.394292 | − | 0.394292i | ||||
\(584\) | 6.39358 | + | 6.39358i | 0.264568 | + | 0.264568i | ||||
\(585\) | −12.6481 | − | 12.6481i | −0.522935 | − | 0.522935i | ||||
\(586\) | − | 9.20708i | − | 0.380341i | ||||||
\(587\) | − | 7.17799i | − | 0.296267i | −0.988967 | − | 0.148134i | \(-0.952673\pi\) | ||
0.988967 | − | 0.148134i | \(-0.0473266\pi\) | |||||||
\(588\) | −0.431911 | − | 0.431911i | −0.0178117 | − | 0.0178117i | ||||
\(589\) | −2.21499 | − | 2.21499i | −0.0912672 | − | 0.0912672i | ||||
\(590\) | 13.8167 | − | 13.8167i | 0.568826 | − | 0.568826i | ||||
\(591\) | 8.72967 | 0.359091 | ||||||||
\(592\) | 7.22107 | − | 7.22107i | 0.296784 | − | 0.296784i | ||||
\(593\) | 26.2823i | 1.07928i | 0.841894 | + | 0.539642i | \(0.181441\pi\) | ||||
−0.841894 | + | 0.539642i | \(0.818559\pi\) | |||||||
\(594\) | 2.94356 | 0.120776 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.4260 | 0.468028 | ||||||||
\(597\) | 16.8922i | 0.691351i | ||||||||
\(598\) | −21.4855 | + | 21.4855i | −0.878607 | + | 0.878607i | ||||
\(599\) | 28.3114 | 1.15677 | 0.578386 | − | 0.815763i | \(-0.303683\pi\) | ||||
0.578386 | + | 0.815763i | \(0.303683\pi\) | |||||||
\(600\) | 5.28608 | − | 5.28608i | 0.215803 | − | 0.215803i | ||||
\(601\) | −8.08970 | − | 8.08970i | −0.329986 | − | 0.329986i | 0.522595 | − | 0.852581i | \(-0.324964\pi\) |
−0.852581 | + | 0.522595i | \(0.824964\pi\) | |||||||
\(602\) | −21.2762 | − | 21.2762i | −0.867155 | − | 0.867155i | ||||
\(603\) | − | 5.67499i | − | 0.231104i | ||||||
\(604\) | − | 11.7510i | − | 0.478143i | ||||||
\(605\) | 5.83290 | + | 5.83290i | 0.237141 | + | 0.237141i | ||||
\(606\) | −0.651439 | − | 0.651439i | −0.0264629 | − | 0.0264629i | ||||
\(607\) | −22.9747 | + | 22.9747i | −0.932514 | + | 0.932514i | −0.997863 | − | 0.0653482i | \(-0.979184\pi\) |
0.0653482 | + | 0.997863i | \(0.479184\pi\) | |||||||
\(608\) | −4.36959 | −0.177210 | ||||||||
\(609\) | 9.36486 | − | 9.36486i | 0.379483 | − | 0.379483i | ||||
\(610\) | 22.0446i | 0.892559i | ||||||||
\(611\) | 26.0702 | 1.05469 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.2959 | −0.577406 | −0.288703 | − | 0.957419i | \(-0.593224\pi\) | ||||
−0.288703 | + | 0.957419i | \(0.593224\pi\) | |||||||
\(614\) | − | 2.90673i | − | 0.117306i | ||||||
\(615\) | 31.4236 | − | 31.4236i | 1.26712 | − | 1.26712i | ||||
\(616\) | 8.12061 | 0.327189 | ||||||||
\(617\) | −29.2994 | + | 29.2994i | −1.17955 | + | 1.17955i | −0.199691 | + | 0.979859i | \(0.563994\pi\) |
−0.979859 | + | 0.199691i | \(0.936006\pi\) | |||||||
\(618\) | 12.0021 | + | 12.0021i | 0.482797 | + | 0.482797i | ||||
\(619\) | 5.69552 | + | 5.69552i | 0.228922 | + | 0.228922i | 0.812242 | − | 0.583320i | \(-0.198247\pi\) |
−0.583320 | + | 0.812242i | \(0.698247\pi\) | |||||||
\(620\) | − | 2.53209i | − | 0.101691i | ||||||
\(621\) | − | 6.00000i | − | 0.240772i | ||||||
\(622\) | −9.21719 | − | 9.21719i | −0.369576 | − | 0.369576i | ||||
\(623\) | −27.0033 | − | 27.0033i | −1.08186 | − | 1.08186i | ||||
\(624\) | −3.58091 | + | 3.58091i | −0.143351 | + | 0.143351i | ||||
\(625\) | 6.49289 | 0.259716 | ||||||||
\(626\) | −2.27804 | + | 2.27804i | −0.0910486 | + | 0.0910486i | ||||
\(627\) | 12.8621i | 0.513665i | ||||||||
\(628\) | −3.51754 | −0.140365 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 9.74422 | 0.388219 | ||||||||
\(631\) | 10.5885i | 0.421523i | 0.977538 | + | 0.210761i | \(0.0675943\pi\) | ||||
−0.977538 | + | 0.210761i | \(0.932406\pi\) | |||||||
\(632\) | 4.68003 | − | 4.68003i | 0.186161 | − | 0.186161i | ||||
\(633\) | 14.0993 | 0.560395 | ||||||||
\(634\) | −13.4943 | + | 13.4943i | −0.535926 | + | 0.535926i | ||||
\(635\) | −21.8756 | − | 21.8756i | −0.868106 | − | 0.868106i | ||||
\(636\) | −3.23429 | − | 3.23429i | −0.128248 | − | 0.128248i | ||||
\(637\) | − | 3.09327i | − | 0.122560i | ||||||
\(638\) | 14.1310i | 0.559453i | ||||||||
\(639\) | 6.93201 | + | 6.93201i | 0.274226 | + | 0.274226i | ||||
\(640\) | −2.49756 | − | 2.49756i | −0.0987249 | − | 0.0987249i | ||||
\(641\) | 23.0182 | − | 23.0182i | 0.909163 | − | 0.909163i | −0.0870412 | − | 0.996205i | \(-0.527741\pi\) |
0.996205 | + | 0.0870412i | \(0.0277412\pi\) | |||||||
\(642\) | −3.08647 | −0.121813 | ||||||||
\(643\) | 7.48241 | − | 7.48241i | 0.295077 | − | 0.295077i | −0.544005 | − | 0.839082i | \(-0.683093\pi\) |
0.839082 | + | 0.544005i | \(0.183093\pi\) | |||||||
\(644\) | − | 16.5526i | − | 0.652265i | ||||||
\(645\) | 38.5235 | 1.51686 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.4884 | −1.00205 | −0.501027 | − | 0.865432i | \(-0.667044\pi\) | ||||
−0.501027 | + | 0.865432i | \(0.667044\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −11.5146 | + | 11.5146i | −0.451986 | + | 0.451986i | ||||
\(650\) | 37.8580 | 1.48491 | ||||||||
\(651\) | 1.39845 | − | 1.39845i | 0.0548097 | − | 0.0548097i | ||||
\(652\) | −4.47246 | − | 4.47246i | −0.175155 | − | 0.175155i | ||||
\(653\) | 14.5740 | + | 14.5740i | 0.570327 | + | 0.570327i | 0.932220 | − | 0.361893i | \(-0.117869\pi\) |
−0.361893 | + | 0.932220i | \(0.617869\pi\) | |||||||
\(654\) | − | 2.24123i | − | 0.0876390i | ||||||
\(655\) | − | 4.54158i | − | 0.177454i | ||||||
\(656\) | −8.89662 | − | 8.89662i | −0.347355 | − | 0.347355i | ||||
\(657\) | −6.39358 | − | 6.39358i | −0.249437 | − | 0.249437i | ||||
\(658\) | −10.0424 | + | 10.0424i | −0.391492 | + | 0.391492i | ||||
\(659\) | 41.5117 | 1.61706 | 0.808532 | − | 0.588452i | \(-0.200262\pi\) | ||||
0.808532 | + | 0.588452i | \(0.200262\pi\) | |||||||
\(660\) | −7.35174 | + | 7.35174i | −0.286166 | + | 0.286166i | ||||
\(661\) | − | 17.0060i | − | 0.661456i | −0.943726 | − | 0.330728i | \(-0.892706\pi\) | ||
0.943726 | − | 0.330728i | \(-0.107294\pi\) | |||||||
\(662\) | −3.43376 | −0.133457 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.32501 | 0.129035 | ||||||||
\(665\) | 42.5782i | 1.65111i | ||||||||
\(666\) | −7.22107 | + | 7.22107i | −0.279811 | + | 0.279811i | ||||
\(667\) | 28.8040 | 1.11529 | ||||||||
\(668\) | 10.1403 | − | 10.1403i | 0.392338 | − | 0.392338i | ||||
\(669\) | −18.5995 | − | 18.5995i | −0.719098 | − | 0.719098i | ||||
\(670\) | 14.1737 | + | 14.1737i | 0.547576 | + | 0.547576i | ||||
\(671\) | − | 18.3715i | − | 0.709222i | ||||||
\(672\) | − | 2.75877i | − | 0.106422i | ||||||
\(673\) | −14.1699 | − | 14.1699i | −0.546208 | − | 0.546208i | 0.379134 | − | 0.925342i | \(-0.376222\pi\) |
−0.925342 | + | 0.379134i | \(0.876222\pi\) | |||||||
\(674\) | 25.2580 | + | 25.2580i | 0.972901 | + | 0.972901i | ||||
\(675\) | −5.28608 | + | 5.28608i | −0.203461 | + | 0.203461i | ||||
\(676\) | −12.6459 | −0.486381 | ||||||||
\(677\) | −33.9286 | + | 33.9286i | −1.30398 | + | 1.30398i | −0.378297 | + | 0.925684i | \(0.623490\pi\) |
−0.925684 | + | 0.378297i | \(0.876510\pi\) | |||||||
\(678\) | − | 11.4338i | − | 0.439111i | ||||||
\(679\) | 30.4219 | 1.16749 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.06418 | −0.232380 | ||||||||
\(682\) | 2.11019i | 0.0808032i | ||||||||
\(683\) | 23.6696 | − | 23.6696i | 0.905693 | − | 0.905693i | −0.0902283 | − | 0.995921i | \(-0.528760\pi\) |
0.995921 | + | 0.0902283i | \(0.0287597\pi\) | |||||||
\(684\) | 4.36959 | 0.167075 | ||||||||
\(685\) | −5.91819 | + | 5.91819i | −0.226122 | + | 0.226122i | ||||
\(686\) | −12.4637 | − | 12.4637i | −0.475865 | − | 0.475865i | ||||
\(687\) | −6.05724 | − | 6.05724i | −0.231098 | − | 0.231098i | ||||
\(688\) | − | 10.9067i | − | 0.415815i | ||||||
\(689\) | − | 23.1634i | − | 0.882457i | ||||||
\(690\) | 14.9854 | + | 14.9854i | 0.570484 | + | 0.570484i | ||||
\(691\) | 14.4942 | + | 14.4942i | 0.551387 | + | 0.551387i | 0.926841 | − | 0.375454i | \(-0.122513\pi\) |
−0.375454 | + | 0.926841i | \(0.622513\pi\) | |||||||
\(692\) | 0.576439 | − | 0.576439i | 0.0219129 | − | 0.0219129i | ||||
\(693\) | −8.12061 | −0.308477 | ||||||||
\(694\) | 0.783348 | − | 0.783348i | 0.0297355 | − | 0.0297355i | ||||
\(695\) | 19.9418i | 0.756436i | ||||||||
\(696\) | 4.80066 | 0.181969 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −11.2371 | −0.425331 | ||||||||
\(699\) | 12.2121i | 0.461905i | ||||||||
\(700\) | −14.5831 | + | 14.5831i | −0.551189 | + | 0.551189i | ||||
\(701\) | −51.4415 | −1.94292 | −0.971459 | − | 0.237206i | \(-0.923768\pi\) | ||||
−0.971459 | + | 0.237206i | \(0.923768\pi\) | |||||||
\(702\) | 3.58091 | − | 3.58091i | 0.135153 | − | 0.135153i | ||||
\(703\) | −31.5531 | − | 31.5531i | −1.19005 | − | 1.19005i | ||||
\(704\) | 2.08141 | + | 2.08141i | 0.0784462 | + | 0.0784462i | ||||
\(705\) | − | 18.1830i | − | 0.684813i | ||||||
\(706\) | − | 11.2608i | − | 0.423807i | ||||||
\(707\) | 1.79717 | + | 1.79717i | 0.0675896 | + | 0.0675896i | ||||
\(708\) | 3.91178 | + | 3.91178i | 0.147014 | + | 0.147014i | ||||
\(709\) | 7.17278 | − | 7.17278i | 0.269379 | − | 0.269379i | −0.559471 | − | 0.828850i | \(-0.688996\pi\) |
0.828850 | + | 0.559471i | \(0.188996\pi\) | |||||||
\(710\) | −34.6263 | −1.29950 | ||||||||
\(711\) | −4.68003 | + | 4.68003i | −0.175515 | + | 0.175515i | ||||
\(712\) | − | 13.8425i | − | 0.518771i | ||||||
\(713\) | 4.30129 | 0.161085 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −52.6519 | −1.96907 | ||||||||
\(716\) | 14.0642i | 0.525603i | ||||||||
\(717\) | 8.39452 | − | 8.39452i | 0.313499 | − | 0.313499i | ||||
\(718\) | 2.04458 | 0.0763030 | ||||||||
\(719\) | 10.8927 | − | 10.8927i | 0.406231 | − | 0.406231i | −0.474191 | − | 0.880422i | \(-0.657259\pi\) |
0.880422 | + | 0.474191i | \(0.157259\pi\) | |||||||
\(720\) | 2.49756 | + | 2.49756i | 0.0930787 | + | 0.0930787i | ||||
\(721\) | −33.1112 | − | 33.1112i | −1.23312 | − | 1.23312i | ||||
\(722\) | 0.0932736i | 0.00347128i | ||||||||
\(723\) | 23.9172i | 0.889489i | ||||||||
\(724\) | 14.3829 | + | 14.3829i | 0.534536 | + | 0.534536i | ||||
\(725\) | −25.3767 | − | 25.3767i | −0.942467 | − | 0.942467i | ||||
\(726\) | −1.65140 | + | 1.65140i | −0.0612893 | + | 0.0612893i | ||||
\(727\) | 23.1097 | 0.857091 | 0.428545 | − | 0.903520i | \(-0.359026\pi\) | ||||
0.428545 | + | 0.903520i | \(0.359026\pi\) | |||||||
\(728\) | 9.87892 | − | 9.87892i | 0.366137 | − | 0.366137i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 31.9368 | 1.18203 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −6.24123 | −0.230682 | ||||||||
\(733\) | − | 4.20676i | − | 0.155380i | −0.996978 | − | 0.0776901i | \(-0.975246\pi\) | ||
0.996978 | − | 0.0776901i | \(-0.0247545\pi\) | |||||||
\(734\) | −17.2603 | + | 17.2603i | −0.637088 | + | 0.637088i | ||||
\(735\) | −2.15745 | −0.0795788 | ||||||||
\(736\) | 4.24264 | − | 4.24264i | 0.156386 | − | 0.156386i | ||||
\(737\) | −11.8120 | − | 11.8120i | −0.435101 | − | 0.435101i | ||||
\(738\) | 8.89662 | + | 8.89662i | 0.327489 | + | 0.327489i | ||||
\(739\) | − | 7.79797i | − | 0.286853i | −0.989661 | − | 0.143427i | \(-0.954188\pi\) | ||
0.989661 | − | 0.143427i | \(-0.0458121\pi\) | |||||||
\(740\) | − | 36.0702i | − | 1.32597i | ||||||
\(741\) | 15.6471 | + | 15.6471i | 0.574811 | + | 0.574811i | ||||
\(742\) | 8.92267 | + | 8.92267i | 0.327561 | + | 0.327561i | ||||
\(743\) | 8.17185 | − | 8.17185i | 0.299796 | − | 0.299796i | −0.541138 | − | 0.840934i | \(-0.682006\pi\) |
0.840934 | + | 0.541138i | \(0.182006\pi\) | |||||||
\(744\) | 0.716881 | 0.0262821 | ||||||||
\(745\) | 28.5372 | − | 28.5372i | 1.04552 | − | 1.04552i | ||||
\(746\) | − | 27.3756i | − | 1.00229i | ||||||
\(747\) | −3.32501 | −0.121656 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.51485 | 0.311126 | ||||||||
\(750\) | − | 8.74422i | − | 0.319294i | ||||||
\(751\) | −9.84092 | + | 9.84092i | −0.359100 | + | 0.359100i | −0.863481 | − | 0.504381i | \(-0.831721\pi\) |
0.504381 | + | 0.863481i | \(0.331721\pi\) | |||||||
\(752\) | −5.14796 | −0.187727 | ||||||||
\(753\) | 13.1550 | − | 13.1550i | 0.479396 | − | 0.479396i | ||||
\(754\) | 17.1908 | + | 17.1908i | 0.626050 | + | 0.626050i | ||||
\(755\) | −29.3489 | − | 29.3489i | −1.06812 | − | 1.06812i | ||||
\(756\) | 2.75877i | 0.100336i | ||||||||
\(757\) | 18.0702i | 0.656771i | 0.944544 | + | 0.328386i | \(0.106505\pi\) | ||||
−0.944544 | + | 0.328386i | \(0.893495\pi\) | |||||||
\(758\) | 15.9084 | + | 15.9084i | 0.577821 | + | 0.577821i | ||||
\(759\) | −12.4885 | − | 12.4885i | −0.453303 | − | 0.453303i | ||||
\(760\) | −10.9133 | + | 10.9133i | −0.395868 | + | 0.395868i | ||||
\(761\) | 0.241230 | 0.00874456 | 0.00437228 | − | 0.999990i | \(-0.498608\pi\) | ||||
0.00437228 | + | 0.999990i | \(0.498608\pi\) | |||||||
\(762\) | 6.19339 | − | 6.19339i | 0.224363 | − | 0.224363i | ||||
\(763\) | 6.18304i | 0.223841i | ||||||||
\(764\) | 15.6459 | 0.566049 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.5972 | −0.599681 | ||||||||
\(767\) | 28.0155i | 1.01158i | ||||||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | −12.5963 | −0.454233 | −0.227116 | − | 0.973868i | \(-0.572930\pi\) | ||||
−0.227116 | + | 0.973868i | \(0.572930\pi\) | |||||||
\(770\) | 20.2818 | − | 20.2818i | 0.730904 | − | 0.730904i | ||||
\(771\) | −2.94691 | − | 2.94691i | −0.106130 | − | 0.106130i | ||||
\(772\) | −7.26288 | − | 7.26288i | −0.261397 | − | 0.261397i | ||||
\(773\) | − | 33.4807i | − | 1.20422i | −0.798414 | − | 0.602109i | \(-0.794327\pi\) | ||
0.798414 | − | 0.602109i | \(-0.205673\pi\) | |||||||
\(774\) | 10.9067i | 0.392034i | ||||||||
\(775\) | −3.78950 | − | 3.78950i | −0.136123 | − | 0.136123i | ||||
\(776\) | 7.79751 | + | 7.79751i | 0.279914 | + | 0.279914i | ||||
\(777\) | 19.9213 | − | 19.9213i | 0.714672 | − | 0.714672i | ||||
\(778\) | −17.2249 | −0.617544 | ||||||||
\(779\) | −38.8745 | + | 38.8745i | −1.39282 | + | 1.39282i | ||||
\(780\) | 17.8871i | 0.640462i | ||||||||
\(781\) | 28.8568 | 1.03258 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.80066 | −0.171562 | ||||||||
\(784\) | 0.610815i | 0.0218148i | ||||||||
\(785\) | −8.78528 | + | 8.78528i | −0.313560 | + | 0.313560i | ||||
\(786\) | 1.28581 | 0.0458632 | ||||||||
\(787\) | −18.3269 | + | 18.3269i | −0.653282 | + | 0.653282i | −0.953782 | − | 0.300500i | \(-0.902846\pi\) |
0.300500 | + | 0.953782i | \(0.402846\pi\) | |||||||
\(788\) | −6.17281 | − | 6.17281i | −0.219897 | − | 0.219897i | ||||
\(789\) | −5.63628 | − | 5.63628i | −0.200657 | − | 0.200657i | ||||
\(790\) | − | 23.3773i | − | 0.831728i | ||||||
\(791\) | 31.5431i | 1.12154i | ||||||||
\(792\) | −2.08141 | − | 2.08141i | −0.0739598 | − | 0.0739598i | ||||
\(793\) | −22.3493 | − | 22.3493i | −0.793647 | − | 0.793647i | ||||
\(794\) | 3.18052 | − | 3.18052i | 0.112873 | − | 0.112873i | ||||
\(795\) | −16.1557 | −0.572984 | ||||||||
\(796\) | 11.9446 | − | 11.9446i | 0.423364 | − | 0.423364i | ||||
\(797\) | 55.5580i | 1.96797i | 0.178264 | + | 0.983983i | \(0.442952\pi\) | ||||
−0.178264 | + | 0.983983i | \(0.557048\pi\) | |||||||
\(798\) | −12.0547 | −0.426731 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −7.47565 | −0.264304 | ||||||||
\(801\) | 13.8425i | 0.489102i | ||||||||
\(802\) | −1.44573 | + | 1.44573i | −0.0510507 | + | 0.0510507i | ||||
\(803\) | −26.6154 | −0.939236 | ||||||||
\(804\) | −4.01283 | + | 4.01283i | −0.141521 | + | 0.141521i | ||||
\(805\) | −41.3412 | − | 41.3412i | −1.45709 | − | 1.45709i | ||||
\(806\) | 2.56709 | + | 2.56709i | 0.0904219 | + | 0.0904219i | ||||
\(807\) | 5.96316i | 0.209913i | ||||||||
\(808\) | 0.921274i | 0.0324103i | ||||||||
\(809\) | 12.6796 | + | 12.6796i | 0.445792 | + | 0.445792i | 0.893953 | − | 0.448161i | \(-0.147921\pi\) |
−0.448161 | + | 0.893953i | \(0.647921\pi\) | |||||||
\(810\) | −2.49756 | − | 2.49756i | −0.0877555 | − | 0.0877555i | ||||
\(811\) | 17.8525 | − | 17.8525i | 0.626885 | − | 0.626885i | −0.320398 | − | 0.947283i | \(-0.603817\pi\) |
0.947283 | + | 0.320398i | \(0.103817\pi\) | |||||||
\(812\) | −13.2439 | −0.464770 | ||||||||
\(813\) | −2.17151 | + | 2.17151i | −0.0761583 | + | 0.0761583i | ||||
\(814\) | 30.0601i | 1.05360i | ||||||||
\(815\) | −22.3405 | −0.782553 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.6579 | −1.66734 | ||||||||
\(818\) | − | 23.2841i | − | 0.814108i | ||||||
\(819\) | −9.87892 | + | 9.87892i | −0.345197 | + | 0.345197i | ||||
\(820\) | −44.4397 | −1.55190 | ||||||||
\(821\) | −1.89574 | + | 1.89574i | −0.0661617 | + | 0.0661617i | −0.739413 | − | 0.673252i | \(-0.764897\pi\) |
0.673252 | + | 0.739413i | \(0.264897\pi\) | |||||||
\(822\) | −1.67555 | − | 1.67555i | −0.0584415 | − | 0.0584415i | ||||
\(823\) | −17.7987 | − | 17.7987i | −0.620424 | − | 0.620424i | 0.325216 | − | 0.945640i | \(-0.394563\pi\) |
−0.945640 | + | 0.325216i | \(0.894563\pi\) | |||||||
\(824\) | − | 16.9736i | − | 0.591303i | ||||||
\(825\) | 22.0051i | 0.766118i | ||||||||
\(826\) | −10.7917 | − | 10.7917i | −0.375491 | − | 0.375491i | ||||
\(827\) | −8.10613 | − | 8.10613i | −0.281878 | − | 0.281878i | 0.551980 | − | 0.833857i | \(-0.313873\pi\) |
−0.833857 | + | 0.551980i | \(0.813873\pi\) | |||||||
\(828\) | −4.24264 | + | 4.24264i | −0.147442 | + | 0.147442i | ||||
\(829\) | −49.4593 | −1.71779 | −0.858897 | − | 0.512148i | \(-0.828850\pi\) | ||||
−0.858897 | + | 0.512148i | \(0.828850\pi\) | |||||||
\(830\) | 8.30442 | − | 8.30442i | 0.288251 | − | 0.288251i | ||||
\(831\) | − | 23.2472i | − | 0.806437i | ||||||
\(832\) | 5.06418 | 0.175569 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5.64590 | −0.195501 | ||||||||
\(835\) | − | 50.6519i | − | 1.75288i | ||||||
\(836\) | 9.09491 | − | 9.09491i | 0.314554 | − | 0.314554i | ||||
\(837\) | −0.716881 | −0.0247790 | ||||||||
\(838\) | 1.06278 | − | 1.06278i | 0.0367130 | − | 0.0367130i | ||||
\(839\) | −23.7984 | − | 23.7984i | −0.821612 | − | 0.821612i | 0.164728 | − | 0.986339i | \(-0.447326\pi\) |
−0.986339 | + | 0.164728i | \(0.947326\pi\) | |||||||
\(840\) | −6.89021 | − | 6.89021i | −0.237735 | − | 0.237735i | ||||
\(841\) | 5.95367i | 0.205299i | ||||||||
\(842\) | 18.1438i | 0.625278i | ||||||||
\(843\) | −15.3652 | − | 15.3652i | −0.529206 | − | 0.529206i | ||||
\(844\) | −9.96968 | − | 9.96968i | −0.343171 | − | 0.343171i | ||||
\(845\) | −31.5839 | + | 31.5839i | −1.08652 | + | 1.08652i | ||||
\(846\) | 5.14796 | 0.176990 | ||||||||
\(847\) | 4.55584 | − | 4.55584i | 0.156541 | − | 0.156541i | ||||
\(848\) | 4.57398i | 0.157071i | ||||||||
\(849\) | −17.1925 | −0.590046 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 61.2728 | 2.10040 | ||||||||
\(852\) | − | 9.80335i | − | 0.335857i | ||||||
\(853\) | −1.71422 | + | 1.71422i | −0.0586936 | + | 0.0586936i | −0.735844 | − | 0.677151i | \(-0.763215\pi\) |
0.677151 | + | 0.735844i | \(0.263215\pi\) | |||||||
\(854\) | 17.2181 | 0.589192 | ||||||||
\(855\) | 10.9133 | − | 10.9133i | 0.373228 | − | 0.373228i | ||||
\(856\) | 2.18246 | + | 2.18246i | 0.0745950 | + | 0.0745950i | ||||
\(857\) | −2.27423 | − | 2.27423i | −0.0776864 | − | 0.0776864i | 0.667196 | − | 0.744882i | \(-0.267494\pi\) |
−0.744882 | + | 0.667196i | \(0.767494\pi\) | |||||||
\(858\) | − | 14.9067i | − | 0.508907i | ||||||
\(859\) | − | 23.4831i | − | 0.801232i | −0.916246 | − | 0.400616i | \(-0.868796\pi\) | ||
0.916246 | − | 0.400616i | \(-0.131204\pi\) | |||||||
\(860\) | −27.2402 | − | 27.2402i | −0.928885 | − | 0.928885i | ||||
\(861\) | −24.5437 | − | 24.5437i | −0.836448 | − | 0.836448i | ||||
\(862\) | 18.5457 | − | 18.5457i | 0.631670 | − | 0.631670i | ||||
\(863\) | −44.4344 | −1.51256 | −0.756282 | − | 0.654246i | \(-0.772986\pi\) | ||||
−0.756282 | + | 0.654246i | \(0.772986\pi\) | |||||||
\(864\) | −0.707107 | + | 0.707107i | −0.0240563 | + | 0.0240563i | ||||
\(865\) | − | 2.87939i | − | 0.0979020i | ||||||
\(866\) | 27.6604 | 0.939940 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.97771 | −0.0671279 | ||||||||
\(869\) | 19.4821i | 0.660886i | ||||||||
\(870\) | 11.9900 | − | 11.9900i | 0.406498 | − | 0.406498i | ||||
\(871\) | −28.7392 | −0.973790 | ||||||||
\(872\) | −1.58479 | + | 1.58479i | −0.0536677 | + | 0.0536677i | ||||
\(873\) | −7.79751 | − | 7.79751i | −0.263906 | − | 0.263906i | ||||
\(874\) | −18.5386 | − | 18.5386i | −0.627077 | − | 0.627077i | ||||
\(875\) | 24.1233i | 0.815516i | ||||||||
\(876\) | 9.04189i | 0.305497i | ||||||||
\(877\) | −6.42029 | − | 6.42029i | −0.216798 | − | 0.216798i | 0.590350 | − | 0.807148i | \(-0.298990\pi\) |
−0.807148 | + | 0.590350i | \(0.798990\pi\) | |||||||
\(878\) | −20.9628 | − | 20.9628i | −0.707461 | − | 0.707461i | ||||
\(879\) | 6.51039 | − | 6.51039i | 0.219590 | − | 0.219590i | ||||
\(880\) | 10.3969 | 0.350480 | ||||||||
\(881\) | 18.0957 | − | 18.0957i | 0.609660 | − | 0.609660i | −0.333197 | − | 0.942857i | \(-0.608127\pi\) |
0.942857 | + | 0.333197i | \(0.108127\pi\) | |||||||
\(882\) | − | 0.610815i | − | 0.0205672i | ||||||
\(883\) | −22.3506 | −0.752157 | −0.376079 | − | 0.926588i | \(-0.622728\pi\) | ||||
−0.376079 | + | 0.926588i | \(0.622728\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.5398 | 0.656824 | ||||||||
\(886\) | 34.3209i | 1.15303i | ||||||||
\(887\) | 18.7163 | − | 18.7163i | 0.628432 | − | 0.628432i | −0.319242 | − | 0.947673i | \(-0.603428\pi\) |
0.947673 | + | 0.319242i | \(0.103428\pi\) | |||||||
\(888\) | 10.2121 | 0.342697 | ||||||||
\(889\) | −17.0861 | + | 17.0861i | −0.573050 | + | 0.573050i | ||||
\(890\) | −34.5727 | − | 34.5727i | −1.15888 | − | 1.15888i | ||||
\(891\) | 2.08141 | + | 2.08141i | 0.0697300 | + | 0.0697300i | ||||
\(892\) | 26.3037i | 0.880711i | ||||||||
\(893\) | 22.4944i | 0.752747i | ||||||||
\(894\) | 8.07942 | + | 8.07942i | 0.270216 | + | 0.270216i | ||||
\(895\) | 35.1262 | + | 35.1262i | 1.17414 | + | 1.17414i | ||||
\(896\) | −1.95075 | + | 1.95075i | −0.0651698 | + | 0.0651698i | ||||
\(897\) | −30.3851 | −1.01453 | ||||||||
\(898\) | 16.8425 | − | 16.8425i | 0.562040 | − | 0.562040i | ||||
\(899\) | − | 3.44150i | − | 0.114781i | ||||||
\(900\) | 7.47565 | 0.249188 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 37.0351 | 1.23313 | ||||||||
\(903\) | − | 30.0892i | − | 1.00130i | ||||||
\(904\) | −8.08489 | + | 8.08489i | −0.268899 | + | 0.268899i | ||||
\(905\) | 71.8444 | 2.38819 | ||||||||
\(906\) | 8.30923 | − | 8.30923i | 0.276056 | − | 0.276056i | ||||
\(907\) | 39.2955 | + | 39.2955i | 1.30479 | + | 1.30479i | 0.925126 | + | 0.379659i | \(0.123959\pi\) |
0.379659 | + | 0.925126i | \(0.376041\pi\) | |||||||
\(908\) | 4.28802 | + | 4.28802i | 0.142303 | + | 0.142303i | ||||
\(909\) | − | 0.921274i | − | 0.0305567i | ||||||
\(910\) | − | 49.3465i | − | 1.63582i | ||||||
\(911\) | 34.6840 | + | 34.6840i | 1.14913 | + | 1.14913i | 0.986724 | + | 0.162408i | \(0.0519261\pi\) |
0.162408 | + | 0.986724i | \(0.448074\pi\) | |||||||
\(912\) | −3.08976 | − | 3.08976i | −0.102312 | − | 0.102312i | ||||
\(913\) | −6.92072 | + | 6.92072i | −0.229042 | + | 0.229042i | ||||
\(914\) | −21.4662 | −0.710037 | ||||||||
\(915\) | −15.5879 | + | 15.5879i | −0.515319 | + | 0.515319i | ||||
\(916\) | 8.56624i | 0.283036i | ||||||||
\(917\) | −3.54725 | −0.117140 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.2020 | −0.501469 | −0.250734 | − | 0.968056i | \(-0.580672\pi\) | ||||
−0.250734 | + | 0.968056i | \(0.580672\pi\) | |||||||
\(920\) | − | 21.1925i | − | 0.698697i | ||||||
\(921\) | 2.05537 | − | 2.05537i | 0.0677266 | − | 0.0677266i | ||||
\(922\) | −16.8898 | −0.556236 | ||||||||
\(923\) | 35.1050 | − | 35.1050i | 1.15549 | − | 1.15549i | ||||
\(924\) | 5.74214 | + | 5.74214i | 0.188903 | + | 0.188903i | ||||
\(925\) | −53.9822 | − | 53.9822i | −1.77492 | − | 1.77492i | ||||
\(926\) | − | 3.75784i | − | 0.123490i | ||||||
\(927\) | 16.9736i | 0.557486i | ||||||||
\(928\) | −3.39458 | − | 3.39458i | −0.111433 | − | 0.111433i | ||||
\(929\) | 16.1904 | + | 16.1904i | 0.531188 | + | 0.531188i | 0.920926 | − | 0.389738i | \(-0.127434\pi\) |
−0.389738 | + | 0.920926i | \(0.627434\pi\) | |||||||
\(930\) | 1.79046 | − | 1.79046i | 0.0587114 | − | 0.0587114i | ||||
\(931\) | 2.66901 | 0.0874731 | ||||||||
\(932\) | 8.63528 | − | 8.63528i | 0.282858 | − | 0.282858i | ||||
\(933\) | − | 13.0351i | − | 0.426749i | ||||||
\(934\) | −12.4311 | −0.406757 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.06418 | −0.165528 | ||||||||
\(937\) | 3.34554i | 0.109294i | 0.998506 | + | 0.0546470i | \(0.0174034\pi\) | ||||
−0.998506 | + | 0.0546470i | \(0.982597\pi\) | |||||||
\(938\) | 11.0705 | − | 11.0705i | 0.361463 | − | 0.361463i | ||||
\(939\) | −3.22163 | −0.105134 | ||||||||
\(940\) | −12.8573 | + | 12.8573i | −0.419360 | + | 0.419360i | ||||
\(941\) | 8.19374 | + | 8.19374i | 0.267108 | + | 0.267108i | 0.827934 | − | 0.560826i | \(-0.189516\pi\) |
−0.560826 | + | 0.827934i | \(0.689516\pi\) | |||||||
\(942\) | −2.48728 | − | 2.48728i | −0.0810399 | − | 0.0810399i | ||||
\(943\) | − | 75.4903i | − | 2.45830i | ||||||
\(944\) | − | 5.53209i | − | 0.180054i | ||||||
\(945\) | 6.89021 | + | 6.89021i | 0.224138 | + | 0.224138i | ||||
\(946\) | 22.7014 | + | 22.7014i | 0.738086 | + | 0.738086i | ||||
\(947\) | −23.8148 | + | 23.8148i | −0.773877 | + | 0.773877i | −0.978782 | − | 0.204905i | \(-0.934312\pi\) |
0.204905 | + | 0.978782i | \(0.434312\pi\) | |||||||
\(948\) | 6.61856 | 0.214961 | ||||||||
\(949\) | −32.3782 | + | 32.3782i | −1.05104 | + | 1.05104i | ||||
\(950\) | 32.6655i | 1.05981i | ||||||||
\(951\) | −19.0838 | −0.618834 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.9655 | −0.452388 | −0.226194 | − | 0.974082i | \(-0.572628\pi\) | ||||
−0.226194 | + | 0.974082i | \(0.572628\pi\) | |||||||
\(954\) | − | 4.57398i | − | 0.148088i | ||||||
\(955\) | 39.0766 | − | 39.0766i | 1.26449 | − | 1.26449i | ||||
\(956\) | −11.8716 | −0.383956 | ||||||||
\(957\) | −9.99216 | + | 9.99216i | −0.323001 | + | 0.323001i | ||||
\(958\) | −8.26641 | − | 8.26641i | −0.267076 | − | 0.267076i | ||||
\(959\) | 4.62246 | + | 4.62246i | 0.149267 | + | 0.149267i | ||||
\(960\) | − | 3.53209i | − | 0.113998i | ||||||
\(961\) | 30.4861i | 0.983422i | ||||||||
\(962\) | 36.5688 | + | 36.5688i | 1.17902 | + | 1.17902i | ||||
\(963\) | −2.18246 | − | 2.18246i | −0.0703288 | − | 0.0703288i | ||||
\(964\) | 16.9120 | − | 16.9120i | 0.544698 | − | 0.544698i | ||||
\(965\) | −36.2790 | −1.16786 | ||||||||
\(966\) | 11.7045 | − | 11.7045i | 0.376585 | − | 0.376585i | ||||
\(967\) | 47.0515i | 1.51307i | 0.653951 | + | 0.756537i | \(0.273110\pi\) | ||||
−0.653951 | + | 0.756537i | \(0.726890\pi\) | |||||||
\(968\) | 2.33544 | 0.0750638 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 38.9495 | 1.25059 | ||||||||
\(971\) | 30.2044i | 0.969305i | 0.874707 | + | 0.484653i | \(0.161054\pi\) | ||||
−0.874707 | + | 0.484653i | \(0.838946\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 15.5757 | 0.499335 | ||||||||
\(974\) | −5.18694 | + | 5.18694i | −0.166200 | + | 0.166200i | ||||
\(975\) | 26.7697 | + | 26.7697i | 0.857316 | + | 0.857316i | ||||
\(976\) | 4.41322 | + | 4.41322i | 0.141264 | + | 0.141264i | ||||
\(977\) | − | 12.4534i | − | 0.398418i | −0.979957 | − | 0.199209i | \(-0.936163\pi\) | ||
0.979957 | − | 0.199209i | \(-0.0638373\pi\) | |||||||
\(978\) | − | 6.32501i | − | 0.202251i | ||||||
\(979\) | 28.8121 | + | 28.8121i | 0.920838 | + | 0.920838i | ||||
\(980\) | 1.52555 | + | 1.52555i | 0.0487319 | + | 0.0487319i | ||||
\(981\) | 1.58479 | − | 1.58479i | 0.0505984 | − | 0.0505984i | ||||
\(982\) | 2.27126 | 0.0724788 | ||||||||
\(983\) | 30.3893 | − | 30.3893i | 0.969267 | − | 0.969267i | −0.0302750 | − | 0.999542i | \(-0.509638\pi\) |
0.999542 | + | 0.0302750i | \(0.00963832\pi\) | |||||||
\(984\) | − | 12.5817i | − | 0.401091i | ||||||
\(985\) | −30.8340 | −0.982453 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.2020 | −0.452056 | ||||||||
\(988\) | − | 22.1284i | − | 0.703997i | ||||||
\(989\) | 46.2733 | − | 46.2733i | 1.47141 | − | 1.47141i | ||||
\(990\) | −10.3969 | −0.330436 | ||||||||
\(991\) | 6.53454 | − | 6.53454i | 0.207576 | − | 0.207576i | −0.595660 | − | 0.803237i | \(-0.703109\pi\) |
0.803237 | + | 0.595660i | \(0.203109\pi\) | |||||||
\(992\) | −0.506912 | − | 0.506912i | −0.0160945 | − | 0.0160945i | ||||
\(993\) | −2.42804 | − | 2.42804i | −0.0770514 | − | 0.0770514i | ||||
\(994\) | 27.0452i | 0.857821i | ||||||||
\(995\) | − | 59.6647i | − | 1.89150i | ||||||
\(996\) | 2.35114 | + | 2.35114i | 0.0744986 | + | 0.0744986i | ||||
\(997\) | 19.9805 | + | 19.9805i | 0.632789 | + | 0.632789i | 0.948767 | − | 0.315978i | \(-0.102332\pi\) |
−0.315978 | + | 0.948767i | \(0.602332\pi\) | |||||||
\(998\) | −6.87277 | + | 6.87277i | −0.217554 | + | 0.217554i | ||||
\(999\) | −10.2121 | −0.323098 |
(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 | 1734.2.f.n.1483.4 | 12 | ||
17.2 | even | 8 | 1734.2.b.j.577.1 | 6 | |||
17.4 | even | 4 | inner | 1734.2.f.n.829.3 | 12 | ||
17.8 | even | 8 | 1734.2.a.p.1.1 | ✓ | 3 | ||
17.9 | even | 8 | 1734.2.a.q.1.3 | yes | 3 | ||
17.13 | even | 4 | inner | 1734.2.f.n.829.4 | 12 | ||
17.15 | even | 8 | 1734.2.b.j.577.6 | 6 | |||
17.16 | even | 2 | inner | 1734.2.f.n.1483.3 | 12 | ||
51.8 | odd | 8 | 5202.2.a.bp.1.3 | 3 | |||
51.26 | odd | 8 | 5202.2.a.bm.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1734.2.a.p.1.1 | ✓ | 3 | 17.8 | even | 8 | ||
1734.2.a.q.1.3 | yes | 3 | 17.9 | even | 8 | ||
1734.2.b.j.577.1 | 6 | 17.2 | even | 8 | |||
1734.2.b.j.577.6 | 6 | 17.15 | even | 8 | |||
1734.2.f.n.829.3 | 12 | 17.4 | even | 4 | inner | ||
1734.2.f.n.829.4 | 12 | 17.13 | even | 4 | inner | ||
1734.2.f.n.1483.3 | 12 | 17.16 | even | 2 | inner | ||
1734.2.f.n.1483.4 | 12 | 1.1 | even | 1 | trivial | ||
5202.2.a.bm.1.1 | 3 | 51.26 | odd | 8 | |||
5202.2.a.bp.1.3 | 3 | 51.8 | odd | 8 |