Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(1,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, 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("1638.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.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: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.37228 | −1.06092 | −0.530458 | − | 0.847711i | \(-0.677980\pi\) | ||||
−0.530458 | + | 0.847711i | \(0.677980\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.37228 | −0.750181 | ||||||||
\(11\) | 2.37228 | 0.715270 | 0.357635 | − | 0.933862i | \(-0.383583\pi\) | ||||
0.357635 | + | 0.933862i | \(0.383583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.37228 | 1.06043 | 0.530217 | − | 0.847862i | \(-0.322110\pi\) | ||||
0.530217 | + | 0.847862i | \(0.322110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.62772 | 0.373424 | 0.186712 | − | 0.982415i | \(-0.440217\pi\) | ||||
0.186712 | + | 0.982415i | \(0.440217\pi\) | |||||||
\(20\) | −2.37228 | −0.530458 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.37228 | 0.505772 | ||||||||
\(23\) | 3.62772 | 0.756432 | 0.378216 | − | 0.925717i | \(-0.376538\pi\) | ||||
0.378216 | + | 0.925717i | \(0.376538\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.627719 | 0.125544 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 6.37228 | 1.18330 | 0.591651 | − | 0.806194i | \(-0.298476\pi\) | ||||
0.591651 | + | 0.806194i | \(0.298476\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.74456 | −0.852149 | −0.426074 | − | 0.904688i | \(-0.640104\pi\) | ||||
−0.426074 | + | 0.904688i | \(0.640104\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.37228 | 0.749840 | ||||||||
\(35\) | 2.37228 | 0.400989 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.37228 | −0.718799 | −0.359399 | − | 0.933184i | \(-0.617018\pi\) | ||||
−0.359399 | + | 0.933184i | \(0.617018\pi\) | |||||||
\(38\) | 1.62772 | 0.264051 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.37228 | −0.375091 | ||||||||
\(41\) | 8.74456 | 1.36567 | 0.682836 | − | 0.730572i | \(-0.260747\pi\) | ||||
0.682836 | + | 0.730572i | \(0.260747\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.1168 | 1.69530 | 0.847651 | − | 0.530554i | \(-0.178016\pi\) | ||||
0.847651 | + | 0.530554i | \(0.178016\pi\) | |||||||
\(44\) | 2.37228 | 0.357635 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.62772 | 0.534878 | ||||||||
\(47\) | 1.25544 | 0.183124 | 0.0915622 | − | 0.995799i | \(-0.470814\pi\) | ||||
0.0915622 | + | 0.995799i | \(0.470814\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.627719 | 0.0887728 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 8.74456 | 1.20116 | 0.600579 | − | 0.799565i | \(-0.294937\pi\) | ||||
0.600579 | + | 0.799565i | \(0.294937\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.62772 | −0.758841 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.37228 | 0.836722 | ||||||||
\(59\) | 2.00000 | 0.260378 | 0.130189 | − | 0.991489i | \(-0.458442\pi\) | ||||
0.130189 | + | 0.991489i | \(0.458442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.11684 | 0.655145 | 0.327572 | − | 0.944826i | \(-0.393769\pi\) | ||||
0.327572 | + | 0.944826i | \(0.393769\pi\) | |||||||
\(62\) | −4.74456 | −0.602560 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.37228 | 0.294245 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.48913 | 1.15928 | 0.579641 | − | 0.814872i | \(-0.303193\pi\) | ||||
0.579641 | + | 0.814872i | \(0.303193\pi\) | |||||||
\(68\) | 4.37228 | 0.530217 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.37228 | 0.283542 | ||||||||
\(71\) | −4.74456 | −0.563076 | −0.281538 | − | 0.959550i | \(-0.590845\pi\) | ||||
−0.281538 | + | 0.959550i | \(0.590845\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.37228 | −0.979901 | −0.489951 | − | 0.871750i | \(-0.662985\pi\) | ||||
−0.489951 | + | 0.871750i | \(0.662985\pi\) | |||||||
\(74\) | −4.37228 | −0.508267 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.62772 | 0.186712 | ||||||||
\(77\) | −2.37228 | −0.270347 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.74456 | 0.533805 | 0.266903 | − | 0.963724i | \(-0.414000\pi\) | ||||
0.266903 | + | 0.963724i | \(0.414000\pi\) | |||||||
\(80\) | −2.37228 | −0.265229 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.74456 | 0.965675 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.3723 | −1.12503 | ||||||||
\(86\) | 11.1168 | 1.19876 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.37228 | 0.252886 | ||||||||
\(89\) | −3.25544 | −0.345076 | −0.172538 | − | 0.985003i | \(-0.555197\pi\) | ||||
−0.172538 | + | 0.985003i | \(0.555197\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 3.62772 | 0.378216 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.25544 | 0.129488 | ||||||||
\(95\) | −3.86141 | −0.396172 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.48913 | 0.760405 | 0.380203 | − | 0.924903i | \(-0.375854\pi\) | ||||
0.380203 | + | 0.924903i | \(0.375854\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.627719 | 0.0627719 | ||||||||
\(101\) | −2.00000 | −0.199007 | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995037 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.8614 | −1.16874 | −0.584370 | − | 0.811488i | \(-0.698658\pi\) | ||||
−0.584370 | + | 0.811488i | \(0.698658\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.74456 | 0.849347 | ||||||||
\(107\) | 2.00000 | 0.193347 | 0.0966736 | − | 0.995316i | \(-0.469180\pi\) | ||||
0.0966736 | + | 0.995316i | \(0.469180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.62772 | −0.347472 | −0.173736 | − | 0.984792i | \(-0.555584\pi\) | ||||
−0.173736 | + | 0.984792i | \(0.555584\pi\) | |||||||
\(110\) | −5.62772 | −0.536582 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 20.0000 | 1.88144 | 0.940721 | − | 0.339182i | \(-0.110150\pi\) | ||||
0.940721 | + | 0.339182i | \(0.110150\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.60597 | −0.802511 | ||||||||
\(116\) | 6.37228 | 0.591651 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.00000 | 0.184115 | ||||||||
\(119\) | −4.37228 | −0.400806 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.37228 | −0.488389 | ||||||||
\(122\) | 5.11684 | 0.463257 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.74456 | −0.426074 | ||||||||
\(125\) | 10.3723 | 0.927725 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.37228 | 0.208063 | ||||||||
\(131\) | −11.1168 | −0.971283 | −0.485642 | − | 0.874158i | \(-0.661414\pi\) | ||||
−0.485642 | + | 0.874158i | \(0.661414\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.62772 | −0.141141 | ||||||||
\(134\) | 9.48913 | 0.819736 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.37228 | 0.374920 | ||||||||
\(137\) | 1.11684 | 0.0954184 | 0.0477092 | − | 0.998861i | \(-0.484808\pi\) | ||||
0.0477092 | + | 0.998861i | \(0.484808\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.744563 | 0.0631530 | 0.0315765 | − | 0.999501i | \(-0.489947\pi\) | ||||
0.0315765 | + | 0.999501i | \(0.489947\pi\) | |||||||
\(140\) | 2.37228 | 0.200494 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.74456 | −0.398155 | ||||||||
\(143\) | −2.37228 | −0.198380 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.1168 | −1.25539 | ||||||||
\(146\) | −8.37228 | −0.692895 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.37228 | −0.359399 | ||||||||
\(149\) | −20.2337 | −1.65761 | −0.828804 | − | 0.559539i | \(-0.810978\pi\) | ||||
−0.828804 | + | 0.559539i | \(0.810978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.1168 | 1.55571 | 0.777853 | − | 0.628446i | \(-0.216309\pi\) | ||||
0.777853 | + | 0.628446i | \(0.216309\pi\) | |||||||
\(152\) | 1.62772 | 0.132025 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.37228 | −0.191164 | ||||||||
\(155\) | 11.2554 | 0.904058 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.3723 | −1.62589 | −0.812943 | − | 0.582344i | \(-0.802136\pi\) | ||||
−0.812943 | + | 0.582344i | \(0.802136\pi\) | |||||||
\(158\) | 4.74456 | 0.377457 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.37228 | −0.187545 | ||||||||
\(161\) | −3.62772 | −0.285904 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.2337 | −1.42817 | −0.714086 | − | 0.700058i | \(-0.753158\pi\) | ||||
−0.714086 | + | 0.700058i | \(0.753158\pi\) | |||||||
\(164\) | 8.74456 | 0.682836 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | 13.1168 | 1.01501 | 0.507506 | − | 0.861648i | \(-0.330568\pi\) | ||||
0.507506 | + | 0.861648i | \(0.330568\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −10.3723 | −0.795518 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.1168 | 0.847651 | ||||||||
\(173\) | −10.0000 | −0.760286 | −0.380143 | − | 0.924928i | \(-0.624125\pi\) | ||||
−0.380143 | + | 0.924928i | \(0.624125\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.627719 | −0.0474511 | ||||||||
\(176\) | 2.37228 | 0.178817 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.25544 | −0.244005 | ||||||||
\(179\) | −2.74456 | −0.205138 | −0.102569 | − | 0.994726i | \(-0.532706\pi\) | ||||
−0.102569 | + | 0.994726i | \(0.532706\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.4891 | −1.74593 | −0.872966 | − | 0.487780i | \(-0.837807\pi\) | ||||
−0.872966 | + | 0.487780i | \(0.837807\pi\) | |||||||
\(182\) | 1.00000 | 0.0741249 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.62772 | 0.267439 | ||||||||
\(185\) | 10.3723 | 0.762585 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.3723 | 0.758496 | ||||||||
\(188\) | 1.25544 | 0.0915622 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.86141 | −0.280136 | ||||||||
\(191\) | 5.11684 | 0.370242 | 0.185121 | − | 0.982716i | \(-0.440732\pi\) | ||||
0.185121 | + | 0.982716i | \(0.440732\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | 0.143963 | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) | ||||
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 7.48913 | 0.537688 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.8614 | 0.840833 | 0.420416 | − | 0.907331i | \(-0.361884\pi\) | ||||
0.420416 | + | 0.907331i | \(0.361884\pi\) | |||||||
\(200\) | 0.627719 | 0.0443864 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.00000 | −0.140720 | ||||||||
\(203\) | −6.37228 | −0.447246 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.7446 | −1.44886 | ||||||||
\(206\) | −11.8614 | −0.826423 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 3.86141 | 0.267099 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.6277 | −1.21354 | −0.606771 | − | 0.794877i | \(-0.707536\pi\) | ||||
−0.606771 | + | 0.794877i | \(0.707536\pi\) | |||||||
\(212\) | 8.74456 | 0.600579 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.00000 | 0.136717 | ||||||||
\(215\) | −26.3723 | −1.79857 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.74456 | 0.322082 | ||||||||
\(218\) | −3.62772 | −0.245700 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.62772 | −0.379421 | ||||||||
\(221\) | −4.37228 | −0.294111 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.4891 | −1.17116 | −0.585579 | − | 0.810615i | \(-0.699133\pi\) | ||||
−0.585579 | + | 0.810615i | \(0.699133\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.0000 | 1.33038 | ||||||||
\(227\) | 11.4891 | 0.762560 | 0.381280 | − | 0.924460i | \(-0.375483\pi\) | ||||
0.381280 | + | 0.924460i | \(0.375483\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000 | 0.396491 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(230\) | −8.60597 | −0.567461 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.37228 | 0.418361 | ||||||||
\(233\) | −1.48913 | −0.0975558 | −0.0487779 | − | 0.998810i | \(-0.515533\pi\) | ||||
−0.0487779 | + | 0.998810i | \(0.515533\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.97825 | −0.194280 | ||||||||
\(236\) | 2.00000 | 0.130189 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.37228 | −0.283413 | ||||||||
\(239\) | −5.48913 | −0.355062 | −0.177531 | − | 0.984115i | \(-0.556811\pi\) | ||||
−0.177531 | + | 0.984115i | \(0.556811\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.00000 | −0.386494 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(242\) | −5.37228 | −0.345343 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.11684 | 0.327572 | ||||||||
\(245\) | −2.37228 | −0.151559 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.62772 | −0.103569 | ||||||||
\(248\) | −4.74456 | −0.301280 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.3723 | 0.656001 | ||||||||
\(251\) | −13.6277 | −0.860174 | −0.430087 | − | 0.902787i | \(-0.641517\pi\) | ||||
−0.430087 | + | 0.902787i | \(0.641517\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.60597 | 0.541053 | ||||||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.4891 | 0.716672 | 0.358336 | − | 0.933593i | \(-0.383344\pi\) | ||||
0.358336 | + | 0.933593i | \(0.383344\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.37228 | 0.271680 | ||||||||
\(260\) | 2.37228 | 0.147123 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.1168 | −0.686801 | ||||||||
\(263\) | 9.25544 | 0.570715 | 0.285357 | − | 0.958421i | \(-0.407888\pi\) | ||||
0.285357 | + | 0.958421i | \(0.407888\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.7446 | −1.27433 | ||||||||
\(266\) | −1.62772 | −0.0998018 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.48913 | 0.579641 | ||||||||
\(269\) | 0.510875 | 0.0311486 | 0.0155743 | − | 0.999879i | \(-0.495042\pi\) | ||||
0.0155743 | + | 0.999879i | \(0.495042\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.2337 | 1.83657 | 0.918283 | − | 0.395925i | \(-0.129576\pi\) | ||||
0.918283 | + | 0.395925i | \(0.129576\pi\) | |||||||
\(272\) | 4.37228 | 0.265108 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.11684 | 0.0674710 | ||||||||
\(275\) | 1.48913 | 0.0897976 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.7446 | 1.60693 | 0.803463 | − | 0.595355i | \(-0.202989\pi\) | ||||
0.803463 | + | 0.595355i | \(0.202989\pi\) | |||||||
\(278\) | 0.744563 | 0.0446559 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.37228 | 0.141771 | ||||||||
\(281\) | 10.0000 | 0.596550 | 0.298275 | − | 0.954480i | \(-0.403589\pi\) | ||||
0.298275 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9783 | 0.890365 | 0.445182 | − | 0.895440i | \(-0.353139\pi\) | ||||
0.445182 | + | 0.895440i | \(0.353139\pi\) | |||||||
\(284\) | −4.74456 | −0.281538 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.37228 | −0.140276 | ||||||||
\(287\) | −8.74456 | −0.516175 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.11684 | 0.124520 | ||||||||
\(290\) | −15.1168 | −0.887692 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.37228 | −0.489951 | ||||||||
\(293\) | −28.7446 | −1.67928 | −0.839638 | − | 0.543147i | \(-0.817233\pi\) | ||||
−0.839638 | + | 0.543147i | \(0.817233\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.74456 | −0.276239 | ||||||||
\(296\) | −4.37228 | −0.254134 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.2337 | −1.17211 | ||||||||
\(299\) | −3.62772 | −0.209796 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.1168 | −0.640764 | ||||||||
\(302\) | 19.1168 | 1.10005 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.62772 | 0.0933561 | ||||||||
\(305\) | −12.1386 | −0.695054 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | −2.37228 | −0.135173 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11.2554 | 0.639266 | ||||||||
\(311\) | 17.4891 | 0.991717 | 0.495859 | − | 0.868403i | \(-0.334853\pi\) | ||||
0.495859 | + | 0.868403i | \(0.334853\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.9783 | 0.733574 | 0.366787 | − | 0.930305i | \(-0.380458\pi\) | ||||
0.366787 | + | 0.930305i | \(0.380458\pi\) | |||||||
\(314\) | −20.3723 | −1.14967 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.74456 | 0.266903 | ||||||||
\(317\) | −28.9783 | −1.62758 | −0.813790 | − | 0.581159i | \(-0.802600\pi\) | ||||
−0.813790 | + | 0.581159i | \(0.802600\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.1168 | 0.846381 | ||||||||
\(320\) | −2.37228 | −0.132615 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.62772 | −0.202165 | ||||||||
\(323\) | 7.11684 | 0.395992 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.627719 | −0.0348196 | ||||||||
\(326\) | −18.2337 | −1.00987 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.74456 | 0.482838 | ||||||||
\(329\) | −1.25544 | −0.0692145 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.7446 | 0.920364 | 0.460182 | − | 0.887824i | \(-0.347784\pi\) | ||||
0.460182 | + | 0.887824i | \(0.347784\pi\) | |||||||
\(332\) | −6.00000 | −0.329293 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.1168 | 0.717722 | ||||||||
\(335\) | −22.5109 | −1.22990 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.86141 | −0.101397 | −0.0506986 | − | 0.998714i | \(-0.516145\pi\) | ||||
−0.0506986 | + | 0.998714i | \(0.516145\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.3723 | −0.562516 | ||||||||
\(341\) | −11.2554 | −0.609516 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 11.1168 | 0.599380 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.0000 | −0.537603 | ||||||||
\(347\) | 25.7228 | 1.38087 | 0.690436 | − | 0.723393i | \(-0.257418\pi\) | ||||
0.690436 | + | 0.723393i | \(0.257418\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.7446 | −1.21749 | −0.608744 | − | 0.793367i | \(-0.708326\pi\) | ||||
−0.608744 | + | 0.793367i | \(0.708326\pi\) | |||||||
\(350\) | −0.627719 | −0.0335530 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.37228 | 0.126443 | ||||||||
\(353\) | −4.74456 | −0.252528 | −0.126264 | − | 0.991997i | \(-0.540299\pi\) | ||||
−0.126264 | + | 0.991997i | \(0.540299\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.2554 | 0.597377 | ||||||||
\(356\) | −3.25544 | −0.172538 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.74456 | −0.145055 | ||||||||
\(359\) | −3.25544 | −0.171815 | −0.0859077 | − | 0.996303i | \(-0.527379\pi\) | ||||
−0.0859077 | + | 0.996303i | \(0.527379\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.3505 | −0.860554 | ||||||||
\(362\) | −23.4891 | −1.23456 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.00000 | 0.0524142 | ||||||||
\(365\) | 19.8614 | 1.03959 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.51087 | 0.131067 | 0.0655333 | − | 0.997850i | \(-0.479125\pi\) | ||||
0.0655333 | + | 0.997850i | \(0.479125\pi\) | |||||||
\(368\) | 3.62772 | 0.189108 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.3723 | 0.539229 | ||||||||
\(371\) | −8.74456 | −0.453995 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.4891 | −0.801997 | −0.400998 | − | 0.916079i | \(-0.631337\pi\) | ||||
−0.400998 | + | 0.916079i | \(0.631337\pi\) | |||||||
\(374\) | 10.3723 | 0.536338 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.25544 | 0.0647442 | ||||||||
\(377\) | −6.37228 | −0.328189 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.7446 | −1.47651 | −0.738255 | − | 0.674522i | \(-0.764350\pi\) | ||||
−0.738255 | + | 0.674522i | \(0.764350\pi\) | |||||||
\(380\) | −3.86141 | −0.198086 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.11684 | 0.261801 | ||||||||
\(383\) | 6.60597 | 0.337549 | 0.168775 | − | 0.985655i | \(-0.446019\pi\) | ||||
0.168775 | + | 0.985655i | \(0.446019\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.62772 | 0.286815 | ||||||||
\(386\) | 2.00000 | 0.101797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.48913 | 0.380203 | ||||||||
\(389\) | 3.25544 | 0.165057 | 0.0825286 | − | 0.996589i | \(-0.473700\pi\) | ||||
0.0825286 | + | 0.996589i | \(0.473700\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.8614 | 0.802146 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | −11.2554 | −0.566323 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.25544 | 0.263763 | 0.131881 | − | 0.991265i | \(-0.457898\pi\) | ||||
0.131881 | + | 0.991265i | \(0.457898\pi\) | |||||||
\(398\) | 11.8614 | 0.594559 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.627719 | 0.0313859 | ||||||||
\(401\) | −35.4891 | −1.77224 | −0.886121 | − | 0.463454i | \(-0.846610\pi\) | ||||
−0.886121 | + | 0.463454i | \(0.846610\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.74456 | 0.236343 | ||||||||
\(404\) | −2.00000 | −0.0995037 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.37228 | −0.316251 | ||||||||
\(407\) | −10.3723 | −0.514135 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.8614 | 1.27876 | 0.639382 | − | 0.768889i | \(-0.279190\pi\) | ||||
0.639382 | + | 0.768889i | \(0.279190\pi\) | |||||||
\(410\) | −20.7446 | −1.02450 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.8614 | −0.584370 | ||||||||
\(413\) | −2.00000 | −0.0984136 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.2337 | 0.698704 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.86141 | 0.188868 | ||||||||
\(419\) | −3.86141 | −0.188642 | −0.0943210 | − | 0.995542i | \(-0.530068\pi\) | ||||
−0.0943210 | + | 0.995542i | \(0.530068\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.48913 | −0.364998 | −0.182499 | − | 0.983206i | \(-0.558419\pi\) | ||||
−0.182499 | + | 0.983206i | \(0.558419\pi\) | |||||||
\(422\) | −17.6277 | −0.858104 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.74456 | 0.424674 | ||||||||
\(425\) | 2.74456 | 0.133131 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.11684 | −0.247621 | ||||||||
\(428\) | 2.00000 | 0.0966736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.3723 | −1.27178 | ||||||||
\(431\) | −32.7446 | −1.57725 | −0.788625 | − | 0.614874i | \(-0.789207\pi\) | ||||
−0.788625 | + | 0.614874i | \(0.789207\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0000 | 0.480569 | 0.240285 | − | 0.970702i | \(-0.422759\pi\) | ||||
0.240285 | + | 0.970702i | \(0.422759\pi\) | |||||||
\(434\) | 4.74456 | 0.227746 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.62772 | −0.173736 | ||||||||
\(437\) | 5.90491 | 0.282470 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.62772 | 0.459506 | 0.229753 | − | 0.973249i | \(-0.426208\pi\) | ||||
0.229753 | + | 0.973249i | \(0.426208\pi\) | |||||||
\(440\) | −5.62772 | −0.268291 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.37228 | −0.207968 | ||||||||
\(443\) | 16.9783 | 0.806661 | 0.403331 | − | 0.915054i | \(-0.367852\pi\) | ||||
0.403331 | + | 0.915054i | \(0.367852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.72281 | 0.366096 | ||||||||
\(446\) | −17.4891 | −0.828134 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −0.372281 | −0.0175690 | −0.00878452 | − | 0.999961i | \(-0.502796\pi\) | ||||
−0.00878452 | + | 0.999961i | \(0.502796\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.7446 | 0.976823 | ||||||||
\(452\) | 20.0000 | 0.940721 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.4891 | 0.539211 | ||||||||
\(455\) | −2.37228 | −0.111214 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.2337 | 0.572268 | 0.286134 | − | 0.958190i | \(-0.407630\pi\) | ||||
0.286134 | + | 0.958190i | \(0.407630\pi\) | |||||||
\(458\) | 6.00000 | 0.280362 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.60597 | −0.401255 | ||||||||
\(461\) | −36.6060 | −1.70491 | −0.852455 | − | 0.522801i | \(-0.824887\pi\) | ||||
−0.852455 | + | 0.522801i | \(0.824887\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.3505 | −0.806348 | −0.403174 | − | 0.915123i | \(-0.632093\pi\) | ||||
−0.403174 | + | 0.915123i | \(0.632093\pi\) | |||||||
\(464\) | 6.37228 | 0.295826 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.48913 | −0.0689824 | ||||||||
\(467\) | −34.0951 | −1.57773 | −0.788866 | − | 0.614565i | \(-0.789332\pi\) | ||||
−0.788866 | + | 0.614565i | \(0.789332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.48913 | −0.438167 | ||||||||
\(470\) | −2.97825 | −0.137376 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.00000 | 0.0920575 | ||||||||
\(473\) | 26.3723 | 1.21260 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.02175 | 0.0468811 | ||||||||
\(476\) | −4.37228 | −0.200403 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.48913 | −0.251067 | ||||||||
\(479\) | 39.3505 | 1.79797 | 0.898986 | − | 0.437978i | \(-0.144305\pi\) | ||||
0.898986 | + | 0.437978i | \(0.144305\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.37228 | 0.199359 | ||||||||
\(482\) | −6.00000 | −0.273293 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.37228 | −0.244195 | ||||||||
\(485\) | −17.7663 | −0.806727 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.4674 | −1.47124 | −0.735619 | − | 0.677396i | \(-0.763108\pi\) | ||||
−0.735619 | + | 0.677396i | \(0.763108\pi\) | |||||||
\(488\) | 5.11684 | 0.231629 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.37228 | −0.107169 | ||||||||
\(491\) | 25.2554 | 1.13976 | 0.569881 | − | 0.821727i | \(-0.306989\pi\) | ||||
0.569881 | + | 0.821727i | \(0.306989\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.8614 | 1.25481 | ||||||||
\(494\) | −1.62772 | −0.0732345 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.74456 | −0.213037 | ||||||||
\(497\) | 4.74456 | 0.212823 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | 10.3723 | 0.463863 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.6277 | −0.608235 | ||||||||
\(503\) | 21.4891 | 0.958153 | 0.479076 | − | 0.877773i | \(-0.340972\pi\) | ||||
0.479076 | + | 0.877773i | \(0.340972\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.74456 | 0.211130 | ||||||||
\(506\) | 8.60597 | 0.382582 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.00000 | −0.354943 | ||||||||
\(509\) | −26.0951 | −1.15664 | −0.578322 | − | 0.815808i | \(-0.696292\pi\) | ||||
−0.578322 | + | 0.815808i | \(0.696292\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.37228 | 0.370368 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.4891 | 0.506764 | ||||||||
\(515\) | 28.1386 | 1.23993 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.97825 | 0.130983 | ||||||||
\(518\) | 4.37228 | 0.192107 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.37228 | 0.104031 | ||||||||
\(521\) | −28.3723 | −1.24301 | −0.621506 | − | 0.783409i | \(-0.713479\pi\) | ||||
−0.621506 | + | 0.783409i | \(0.713479\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.23369 | 0.0976724 | 0.0488362 | − | 0.998807i | \(-0.484449\pi\) | ||||
0.0488362 | + | 0.998807i | \(0.484449\pi\) | |||||||
\(524\) | −11.1168 | −0.485642 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.25544 | 0.403556 | ||||||||
\(527\) | −20.7446 | −0.903647 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.83966 | −0.427811 | ||||||||
\(530\) | −20.7446 | −0.901086 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.62772 | −0.0705706 | ||||||||
\(533\) | −8.74456 | −0.378769 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.74456 | −0.205125 | ||||||||
\(536\) | 9.48913 | 0.409868 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.510875 | 0.0220254 | ||||||||
\(539\) | 2.37228 | 0.102181 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.3505 | 1.00392 | 0.501959 | − | 0.864891i | \(-0.332613\pi\) | ||||
0.501959 | + | 0.864891i | \(0.332613\pi\) | |||||||
\(542\) | 30.2337 | 1.29865 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.37228 | 0.187460 | ||||||||
\(545\) | 8.60597 | 0.368639 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | 1.11684 | 0.0477092 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.48913 | 0.0634965 | ||||||||
\(551\) | 10.3723 | 0.441874 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.74456 | −0.201759 | ||||||||
\(554\) | 26.7446 | 1.13627 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.744563 | 0.0315765 | ||||||||
\(557\) | 11.4891 | 0.486810 | 0.243405 | − | 0.969925i | \(-0.421736\pi\) | ||||
0.243405 | + | 0.969925i | \(0.421736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.1168 | −0.470192 | ||||||||
\(560\) | 2.37228 | 0.100247 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.0000 | 0.421825 | ||||||||
\(563\) | −11.1168 | −0.468519 | −0.234260 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234260 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −47.4456 | −1.99605 | ||||||||
\(566\) | 14.9783 | 0.629583 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.74456 | −0.199077 | ||||||||
\(569\) | 12.7446 | 0.534280 | 0.267140 | − | 0.963658i | \(-0.413921\pi\) | ||||
0.267140 | + | 0.963658i | \(0.413921\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | −2.37228 | −0.0991901 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.74456 | −0.364991 | ||||||||
\(575\) | 2.27719 | 0.0949653 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.510875 | −0.0212680 | −0.0106340 | − | 0.999943i | \(-0.503385\pi\) | ||||
−0.0106340 | + | 0.999943i | \(0.503385\pi\) | |||||||
\(578\) | 2.11684 | 0.0880491 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15.1168 | −0.627693 | ||||||||
\(581\) | 6.00000 | 0.248922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.7446 | 0.859152 | ||||||||
\(584\) | −8.37228 | −0.346447 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.7446 | −1.18743 | ||||||||
\(587\) | −27.4891 | −1.13460 | −0.567299 | − | 0.823512i | \(-0.692012\pi\) | ||||
−0.567299 | + | 0.823512i | \(0.692012\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.72281 | −0.318213 | ||||||||
\(590\) | −4.74456 | −0.195331 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.37228 | −0.179700 | ||||||||
\(593\) | −4.00000 | −0.164260 | −0.0821302 | − | 0.996622i | \(-0.526172\pi\) | ||||
−0.0821302 | + | 0.996622i | \(0.526172\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.3723 | 0.425222 | ||||||||
\(596\) | −20.2337 | −0.828804 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.62772 | −0.148348 | ||||||||
\(599\) | −21.1168 | −0.862811 | −0.431405 | − | 0.902158i | \(-0.641982\pi\) | ||||
−0.431405 | + | 0.902158i | \(0.641982\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.4674 | −1.73228 | −0.866140 | − | 0.499801i | \(-0.833406\pi\) | ||||
−0.866140 | + | 0.499801i | \(0.833406\pi\) | |||||||
\(602\) | −11.1168 | −0.453089 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19.1168 | 0.777853 | ||||||||
\(605\) | 12.7446 | 0.518140 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.1168 | 0.775929 | 0.387964 | − | 0.921674i | \(-0.373178\pi\) | ||||
0.387964 | + | 0.921674i | \(0.373178\pi\) | |||||||
\(608\) | 1.62772 | 0.0660127 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.1386 | −0.491477 | ||||||||
\(611\) | −1.25544 | −0.0507896 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.13859 | −0.247935 | −0.123968 | − | 0.992286i | \(-0.539562\pi\) | ||||
−0.123968 | + | 0.992286i | \(0.539562\pi\) | |||||||
\(614\) | 20.0000 | 0.807134 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.37228 | −0.0955819 | ||||||||
\(617\) | 9.39403 | 0.378189 | 0.189095 | − | 0.981959i | \(-0.439445\pi\) | ||||
0.189095 | + | 0.981959i | \(0.439445\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1168 | 0.446824 | 0.223412 | − | 0.974724i | \(-0.428281\pi\) | ||||
0.223412 | + | 0.974724i | \(0.428281\pi\) | |||||||
\(620\) | 11.2554 | 0.452029 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.4891 | 0.701250 | ||||||||
\(623\) | 3.25544 | 0.130426 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.7446 | −1.10978 | ||||||||
\(626\) | 12.9783 | 0.518715 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.3723 | −0.812943 | ||||||||
\(629\) | −19.1168 | −0.762238 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.6060 | 0.661073 | 0.330537 | − | 0.943793i | \(-0.392770\pi\) | ||||
0.330537 | + | 0.943793i | \(0.392770\pi\) | |||||||
\(632\) | 4.74456 | 0.188729 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.9783 | −1.15087 | ||||||||
\(635\) | 18.9783 | 0.753129 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 15.1168 | 0.598482 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.37228 | −0.0937727 | ||||||||
\(641\) | 18.2337 | 0.720187 | 0.360094 | − | 0.932916i | \(-0.382745\pi\) | ||||
0.360094 | + | 0.932916i | \(0.382745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.138593 | −0.00546559 | −0.00273279 | − | 0.999996i | \(-0.500870\pi\) | ||||
−0.00273279 | + | 0.999996i | \(0.500870\pi\) | |||||||
\(644\) | −3.62772 | −0.142952 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.11684 | 0.280008 | ||||||||
\(647\) | 21.4891 | 0.844825 | 0.422412 | − | 0.906404i | \(-0.361183\pi\) | ||||
0.422412 | + | 0.906404i | \(0.361183\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.74456 | 0.186240 | ||||||||
\(650\) | −0.627719 | −0.0246212 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.2337 | −0.714086 | ||||||||
\(653\) | 8.13859 | 0.318488 | 0.159244 | − | 0.987239i | \(-0.449094\pi\) | ||||
0.159244 | + | 0.987239i | \(0.449094\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.3723 | 1.03045 | ||||||||
\(656\) | 8.74456 | 0.341418 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.25544 | −0.0489420 | ||||||||
\(659\) | 9.25544 | 0.360541 | 0.180270 | − | 0.983617i | \(-0.442303\pi\) | ||||
0.180270 | + | 0.983617i | \(0.442303\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.7446 | 0.417915 | 0.208958 | − | 0.977925i | \(-0.432993\pi\) | ||||
0.208958 | + | 0.977925i | \(0.432993\pi\) | |||||||
\(662\) | 16.7446 | 0.650796 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 3.86141 | 0.149739 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.1168 | 0.895088 | ||||||||
\(668\) | 13.1168 | 0.507506 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −22.5109 | −0.869671 | ||||||||
\(671\) | 12.1386 | 0.468605 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0951 | 0.620420 | 0.310210 | − | 0.950668i | \(-0.399601\pi\) | ||||
0.310210 | + | 0.950668i | \(0.399601\pi\) | |||||||
\(674\) | −1.86141 | −0.0716987 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 35.4891 | 1.36396 | 0.681979 | − | 0.731372i | \(-0.261120\pi\) | ||||
0.681979 | + | 0.731372i | \(0.261120\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.48913 | −0.287406 | ||||||||
\(680\) | −10.3723 | −0.397759 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.2554 | −0.430993 | ||||||||
\(683\) | 11.1168 | 0.425374 | 0.212687 | − | 0.977120i | \(-0.431778\pi\) | ||||
0.212687 | + | 0.977120i | \(0.431778\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.64947 | −0.101231 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.1168 | 0.423826 | ||||||||
\(689\) | −8.74456 | −0.333141 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.4891 | 1.73049 | 0.865244 | − | 0.501351i | \(-0.167163\pi\) | ||||
0.865244 | + | 0.501351i | \(0.167163\pi\) | |||||||
\(692\) | −10.0000 | −0.380143 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.7228 | 0.976425 | ||||||||
\(695\) | −1.76631 | −0.0670000 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.2337 | 1.44820 | ||||||||
\(698\) | −22.7446 | −0.860894 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.627719 | −0.0237255 | ||||||||
\(701\) | 31.7228 | 1.19815 | 0.599077 | − | 0.800691i | \(-0.295534\pi\) | ||||
0.599077 | + | 0.800691i | \(0.295534\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.11684 | −0.268417 | ||||||||
\(704\) | 2.37228 | 0.0894087 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.74456 | −0.178564 | ||||||||
\(707\) | 2.00000 | 0.0752177 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.5109 | −1.07075 | −0.535374 | − | 0.844615i | \(-0.679829\pi\) | ||||
−0.535374 | + | 0.844615i | \(0.679829\pi\) | |||||||
\(710\) | 11.2554 | 0.422409 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.25544 | −0.122003 | ||||||||
\(713\) | −17.2119 | −0.644592 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.62772 | 0.210465 | ||||||||
\(716\) | −2.74456 | −0.102569 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.25544 | −0.121492 | ||||||||
\(719\) | −45.4891 | −1.69646 | −0.848229 | − | 0.529630i | \(-0.822331\pi\) | ||||
−0.848229 | + | 0.529630i | \(0.822331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.8614 | 0.441742 | ||||||||
\(722\) | −16.3505 | −0.608504 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23.4891 | −0.872966 | ||||||||
\(725\) | 4.00000 | 0.148556 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.0951 | 1.70957 | 0.854786 | − | 0.518980i | \(-0.173688\pi\) | ||||
0.854786 | + | 0.518980i | \(0.173688\pi\) | |||||||
\(728\) | 1.00000 | 0.0370625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 19.8614 | 0.735104 | ||||||||
\(731\) | 48.6060 | 1.79776 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.7446 | −1.13558 | −0.567788 | − | 0.823175i | \(-0.692201\pi\) | ||||
−0.567788 | + | 0.823175i | \(0.692201\pi\) | |||||||
\(734\) | 2.51087 | 0.0926781 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.62772 | 0.133719 | ||||||||
\(737\) | 22.5109 | 0.829199 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.7228 | 1.16694 | 0.583471 | − | 0.812134i | \(-0.301694\pi\) | ||||
0.583471 | + | 0.812134i | \(0.301694\pi\) | |||||||
\(740\) | 10.3723 | 0.381293 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.74456 | −0.321023 | ||||||||
\(743\) | 44.4674 | 1.63135 | 0.815675 | − | 0.578511i | \(-0.196366\pi\) | ||||
0.815675 | + | 0.578511i | \(0.196366\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.0000 | 1.75858 | ||||||||
\(746\) | −15.4891 | −0.567097 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.3723 | 0.379248 | ||||||||
\(749\) | −2.00000 | −0.0730784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.9783 | −0.400602 | −0.200301 | − | 0.979734i | \(-0.564192\pi\) | ||||
−0.200301 | + | 0.979734i | \(0.564192\pi\) | |||||||
\(752\) | 1.25544 | 0.0457811 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.37228 | −0.232065 | ||||||||
\(755\) | −45.3505 | −1.65047 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.2119 | −1.57056 | −0.785282 | − | 0.619138i | \(-0.787482\pi\) | ||||
−0.785282 | + | 0.619138i | \(0.787482\pi\) | |||||||
\(758\) | −28.7446 | −1.04405 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.86141 | −0.140068 | ||||||||
\(761\) | −46.9783 | −1.70296 | −0.851480 | − | 0.524387i | \(-0.824295\pi\) | ||||
−0.851480 | + | 0.524387i | \(0.824295\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.62772 | 0.131332 | ||||||||
\(764\) | 5.11684 | 0.185121 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.60597 | 0.238683 | ||||||||
\(767\) | −2.00000 | −0.0722158 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.6277 | −0.707794 | −0.353897 | − | 0.935284i | \(-0.615144\pi\) | ||||
−0.353897 | + | 0.935284i | \(0.615144\pi\) | |||||||
\(770\) | 5.62772 | 0.202809 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.00000 | 0.0719816 | ||||||||
\(773\) | −34.0951 | −1.22632 | −0.613158 | − | 0.789961i | \(-0.710101\pi\) | ||||
−0.613158 | + | 0.789961i | \(0.710101\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.97825 | −0.106982 | ||||||||
\(776\) | 7.48913 | 0.268844 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.25544 | 0.116713 | ||||||||
\(779\) | 14.2337 | 0.509975 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.2554 | −0.402751 | ||||||||
\(782\) | 15.8614 | 0.567203 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 48.3288 | 1.72493 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.1168 | 0.966611 | 0.483306 | − | 0.875452i | \(-0.339436\pi\) | ||||
0.483306 | + | 0.875452i | \(0.339436\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −11.2554 | −0.400450 | ||||||||
\(791\) | −20.0000 | −0.711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.11684 | −0.181704 | ||||||||
\(794\) | 5.25544 | 0.186508 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.8614 | 0.420416 | ||||||||
\(797\) | 49.7228 | 1.76127 | 0.880636 | − | 0.473793i | \(-0.157116\pi\) | ||||
0.880636 | + | 0.473793i | \(0.157116\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.48913 | 0.194191 | ||||||||
\(800\) | 0.627719 | 0.0221932 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −35.4891 | −1.25316 | ||||||||
\(803\) | −19.8614 | −0.700894 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.60597 | 0.303321 | ||||||||
\(806\) | 4.74456 | 0.167120 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.00000 | −0.0703598 | ||||||||
\(809\) | 32.7446 | 1.15124 | 0.575619 | − | 0.817718i | \(-0.304761\pi\) | ||||
0.575619 | + | 0.817718i | \(0.304761\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.11684 | 0.109447 | 0.0547236 | − | 0.998502i | \(-0.482572\pi\) | ||||
0.0547236 | + | 0.998502i | \(0.482572\pi\) | |||||||
\(812\) | −6.37228 | −0.223623 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.3723 | −0.363548 | ||||||||
\(815\) | 43.2554 | 1.51517 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.0951 | 0.633067 | ||||||||
\(818\) | 25.8614 | 0.904223 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.7446 | −0.724432 | ||||||||
\(821\) | −53.7228 | −1.87494 | −0.937470 | − | 0.348067i | \(-0.886838\pi\) | ||||
−0.937470 | + | 0.348067i | \(0.886838\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.7228 | −1.10579 | −0.552894 | − | 0.833252i | \(-0.686477\pi\) | ||||
−0.552894 | + | 0.833252i | \(0.686477\pi\) | |||||||
\(824\) | −11.8614 | −0.413212 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.00000 | −0.0695889 | ||||||||
\(827\) | 34.3723 | 1.19524 | 0.597621 | − | 0.801779i | \(-0.296113\pi\) | ||||
0.597621 | + | 0.801779i | \(0.296113\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.3723 | −0.846484 | −0.423242 | − | 0.906017i | \(-0.639108\pi\) | ||||
−0.423242 | + | 0.906017i | \(0.639108\pi\) | |||||||
\(830\) | 14.2337 | 0.494059 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 4.37228 | 0.151491 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.1168 | −1.07684 | ||||||||
\(836\) | 3.86141 | 0.133550 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.86141 | −0.133390 | ||||||||
\(839\) | −1.25544 | −0.0433425 | −0.0216713 | − | 0.999765i | \(-0.506899\pi\) | ||||
−0.0216713 | + | 0.999765i | \(0.506899\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.6060 | 0.400206 | ||||||||
\(842\) | −7.48913 | −0.258092 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.6277 | −0.606771 | ||||||||
\(845\) | −2.37228 | −0.0816090 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.37228 | 0.184594 | ||||||||
\(848\) | 8.74456 | 0.300290 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.74456 | 0.0941377 | ||||||||
\(851\) | −15.8614 | −0.543722 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.2119 | −1.34259 | −0.671296 | − | 0.741190i | \(-0.734262\pi\) | ||||
−0.671296 | + | 0.741190i | \(0.734262\pi\) | |||||||
\(854\) | −5.11684 | −0.175095 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.00000 | 0.0683586 | ||||||||
\(857\) | −0.978251 | −0.0334164 | −0.0167082 | − | 0.999860i | \(-0.505319\pi\) | ||||
−0.0167082 | + | 0.999860i | \(0.505319\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.744563 | −0.0254041 | −0.0127021 | − | 0.999919i | \(-0.504043\pi\) | ||||
−0.0127021 | + | 0.999919i | \(0.504043\pi\) | |||||||
\(860\) | −26.3723 | −0.899287 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32.7446 | −1.11528 | ||||||||
\(863\) | −18.9783 | −0.646027 | −0.323014 | − | 0.946394i | \(-0.604696\pi\) | ||||
−0.323014 | + | 0.946394i | \(0.604696\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.7228 | 0.806600 | ||||||||
\(866\) | 10.0000 | 0.339814 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.74456 | 0.161041 | ||||||||
\(869\) | 11.2554 | 0.381815 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.48913 | −0.321527 | ||||||||
\(872\) | −3.62772 | −0.122850 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.90491 | 0.199736 | ||||||||
\(875\) | −10.3723 | −0.350647 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −52.9783 | −1.78895 | −0.894474 | − | 0.447120i | \(-0.852450\pi\) | ||||
−0.894474 | + | 0.447120i | \(0.852450\pi\) | |||||||
\(878\) | 9.62772 | 0.324920 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.62772 | −0.189710 | ||||||||
\(881\) | −14.1386 | −0.476341 | −0.238171 | − | 0.971223i | \(-0.576548\pi\) | ||||
−0.238171 | + | 0.971223i | \(0.576548\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.3723 | −1.02211 | −0.511054 | − | 0.859548i | \(-0.670745\pi\) | ||||
−0.511054 | + | 0.859548i | \(0.670745\pi\) | |||||||
\(884\) | −4.37228 | −0.147056 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.9783 | 0.570395 | ||||||||
\(887\) | 53.2119 | 1.78668 | 0.893341 | − | 0.449379i | \(-0.148355\pi\) | ||||
0.893341 | + | 0.449379i | \(0.148355\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | 0.268311 | ||||||||
\(890\) | 7.72281 | 0.258869 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17.4891 | −0.585579 | ||||||||
\(893\) | 2.04350 | 0.0683831 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.51087 | 0.217635 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.372281 | −0.0124232 | ||||||||
\(899\) | −30.2337 | −1.00835 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.2337 | 1.27375 | ||||||||
\(902\) | 20.7446 | 0.690718 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.0000 | 0.665190 | ||||||||
\(905\) | 55.7228 | 1.85229 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −57.9565 | −1.92441 | −0.962207 | − | 0.272319i | \(-0.912209\pi\) | ||||
−0.962207 | + | 0.272319i | \(0.912209\pi\) | |||||||
\(908\) | 11.4891 | 0.381280 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.37228 | −0.0786404 | ||||||||
\(911\) | 22.8832 | 0.758153 | 0.379076 | − | 0.925365i | \(-0.376242\pi\) | ||||
0.379076 | + | 0.925365i | \(0.376242\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.2337 | −0.471066 | ||||||||
\(914\) | 12.2337 | 0.404654 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.00000 | 0.198246 | ||||||||
\(917\) | 11.1168 | 0.367111 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.2119 | −1.62335 | −0.811676 | − | 0.584108i | \(-0.801444\pi\) | ||||
−0.811676 | + | 0.584108i | \(0.801444\pi\) | |||||||
\(920\) | −8.60597 | −0.283730 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −36.6060 | −1.20555 | ||||||||
\(923\) | 4.74456 | 0.156169 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.74456 | −0.0902407 | ||||||||
\(926\) | −17.3505 | −0.570174 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.37228 | 0.209180 | ||||||||
\(929\) | 15.2554 | 0.500515 | 0.250257 | − | 0.968179i | \(-0.419485\pi\) | ||||
0.250257 | + | 0.968179i | \(0.419485\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.62772 | 0.0533463 | ||||||||
\(932\) | −1.48913 | −0.0487779 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34.0951 | −1.11563 | ||||||||
\(935\) | −24.6060 | −0.804701 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.5109 | 0.800735 | 0.400368 | − | 0.916355i | \(-0.368882\pi\) | ||||
0.400368 | + | 0.916355i | \(0.368882\pi\) | |||||||
\(938\) | −9.48913 | −0.309831 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.97825 | −0.0971398 | ||||||||
\(941\) | 24.7446 | 0.806650 | 0.403325 | − | 0.915057i | \(-0.367854\pi\) | ||||
0.403325 | + | 0.915057i | \(0.367854\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.7228 | 1.03304 | ||||||||
\(944\) | 2.00000 | 0.0650945 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26.3723 | 0.857437 | ||||||||
\(947\) | −8.13859 | −0.264469 | −0.132234 | − | 0.991218i | \(-0.542215\pi\) | ||||
−0.132234 | + | 0.991218i | \(0.542215\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.37228 | 0.271776 | ||||||||
\(950\) | 1.02175 | 0.0331499 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.37228 | −0.141706 | ||||||||
\(953\) | −45.4891 | −1.47354 | −0.736769 | − | 0.676145i | \(-0.763649\pi\) | ||||
−0.736769 | + | 0.676145i | \(0.763649\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.1386 | −0.392796 | ||||||||
\(956\) | −5.48913 | −0.177531 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 39.3505 | 1.27136 | ||||||||
\(959\) | −1.11684 | −0.0360648 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.48913 | −0.273843 | ||||||||
\(962\) | 4.37228 | 0.140968 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.00000 | −0.193247 | ||||||||
\(965\) | −4.74456 | −0.152733 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.8832 | 0.800188 | 0.400094 | − | 0.916474i | \(-0.368977\pi\) | ||||
0.400094 | + | 0.916474i | \(0.368977\pi\) | |||||||
\(968\) | −5.37228 | −0.172672 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17.7663 | −0.570442 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.744563 | −0.0238696 | ||||||||
\(974\) | −32.4674 | −1.04032 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.11684 | 0.163786 | ||||||||
\(977\) | −25.1168 | −0.803559 | −0.401780 | − | 0.915736i | \(-0.631608\pi\) | ||||
−0.401780 | + | 0.915736i | \(0.631608\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.72281 | −0.246822 | ||||||||
\(980\) | −2.37228 | −0.0757797 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 25.2554 | 0.805933 | ||||||||
\(983\) | 35.3505 | 1.12751 | 0.563753 | − | 0.825943i | \(-0.309357\pi\) | ||||
0.563753 | + | 0.825943i | \(0.309357\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.2337 | −0.453523 | ||||||||
\(986\) | 27.8614 | 0.887288 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.62772 | −0.0517846 | ||||||||
\(989\) | 40.3288 | 1.28238 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.2337 | 0.452148 | 0.226074 | − | 0.974110i | \(-0.427411\pi\) | ||||
0.226074 | + | 0.974110i | \(0.427411\pi\) | |||||||
\(992\) | −4.74456 | −0.150640 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.74456 | 0.150488 | ||||||||
\(995\) | −28.1386 | −0.892053 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.5109 | 0.649586 | 0.324793 | − | 0.945785i | \(-0.394705\pi\) | ||||
0.324793 | + | 0.945785i | \(0.394705\pi\) | |||||||
\(998\) | −20.0000 | −0.633089 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1638.2.a.x.1.1 | yes | 2 | |
3.2 | odd | 2 | 1638.2.a.v.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1638.2.a.v.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
1638.2.a.x.1.1 | yes | 2 | 1.1 | even | 1 | trivial |