Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(609,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.c (of order \(2\), degree \(1\), 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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 609.1 | ||
Root | \(1.26217 - 1.18614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.609 |
Dual form | 1216.2.c.h.609.8 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 3.37228i | − 1.94699i | −0.228714 | − | 0.973494i | \(-0.573452\pi\) | ||||
0.228714 | − | 0.973494i | \(-0.426548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.52434i | − 1.12892i | −0.825461 | − | 0.564459i | \(-0.809085\pi\) | ||||
0.825461 | − | 0.564459i | \(-0.190915\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.31662 | −1.25357 | −0.626783 | − | 0.779194i | \(-0.715629\pi\) | ||||
−0.626783 | + | 0.779194i | \(0.715629\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.37228 | −2.79076 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.37228i | 0.715270i | 0.933862 | + | 0.357635i | \(0.116417\pi\) | ||||
−0.933862 | + | 0.357635i | \(0.883583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.84096i | − 1.61999i | −0.586436 | − | 0.809996i | \(-0.699469\pi\) | ||||
0.586436 | − | 0.809996i | \(-0.300531\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.51278 | −2.19799 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.00000 | 1.21268 | 0.606339 | − | 0.795206i | \(-0.292637\pi\) | ||||
0.606339 | + | 0.795206i | \(0.292637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.1846i | 2.44068i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.792287 | −0.165203 | −0.0826016 | − | 0.996583i | \(-0.526323\pi\) | ||||
−0.0826016 | + | 0.996583i | \(0.526323\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.37228 | −0.274456 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 18.1168i | 3.48659i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.67181i | 0.496144i | 0.968742 | + | 0.248072i | \(0.0797969\pi\) | ||||
−0.968742 | + | 0.248072i | \(0.920203\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.46410 | −0.622171 | −0.311086 | − | 0.950382i | \(-0.600693\pi\) | ||||
−0.311086 | + | 0.950382i | \(0.600693\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.00000 | 1.39262 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.37228i | 1.41517i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 10.0974i | − 1.65999i | −0.557768 | − | 0.829997i | \(-0.688342\pi\) | ||||
0.557768 | − | 0.829997i | \(-0.311658\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −19.6974 | −3.15410 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.62772i | − 0.553222i | −0.960982 | − | 0.276611i | \(-0.910789\pi\) | ||||
0.960982 | − | 0.276611i | \(-0.0892113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 21.1345i | 3.15054i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.644810 | 0.0940552 | 0.0470276 | − | 0.998894i | \(-0.485025\pi\) | ||||
0.0470276 | + | 0.998894i | \(0.485025\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.00000 | 0.571429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 16.8614i | − 2.36107i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 6.13592i | − 0.842833i | −0.906867 | − | 0.421416i | \(-0.861533\pi\) | ||||
0.906867 | − | 0.421416i | \(-0.138467\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.98844 | 0.807481 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.37228 | 0.446670 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.37228i | 0.178656i | 0.996002 | + | 0.0893279i | \(0.0284719\pi\) | ||||
−0.996002 | + | 0.0893279i | \(0.971528\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.5012i | 1.85669i | 0.371719 | + | 0.928345i | \(0.378768\pi\) | ||||
−0.371719 | + | 0.928345i | \(0.621232\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 27.7677 | 3.49840 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.7446 | −1.82884 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.62772i | 0.321027i | 0.987034 | + | 0.160513i | \(0.0513150\pi\) | ||||
−0.987034 | + | 0.160513i | \(0.948685\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.67181i | 0.321649i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.63325 | 0.787222 | 0.393611 | − | 0.919277i | \(-0.371226\pi\) | ||||
0.393611 | + | 0.919277i | \(0.371226\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.48913 | 0.993577 | 0.496788 | − | 0.867872i | \(-0.334512\pi\) | ||||
0.496788 | + | 0.867872i | \(0.334512\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.62772i | 0.534363i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 7.86797i | − 0.896638i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.294954 | 0.0331849 | 0.0165924 | − | 0.999862i | \(-0.494718\pi\) | ||||
0.0165924 | + | 0.999862i | \(0.494718\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 35.9783 | 3.99758 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 8.00000i | − 0.878114i | −0.898459 | − | 0.439057i | \(-0.855313\pi\) | ||||
0.898459 | − | 0.439057i | \(-0.144687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 12.6217i | − 1.36901i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.01011 | 0.965985 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.4891 | −1.64184 | −0.820922 | − | 0.571040i | \(-0.806540\pi\) | ||||
−0.820922 | + | 0.571040i | \(0.806540\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.3723i | 2.03077i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.6819i | 1.21136i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.52434 | 0.258992 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.74456 | −0.278668 | −0.139334 | − | 0.990245i | \(-0.544496\pi\) | ||||
−0.139334 | + | 0.990245i | \(0.544496\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 19.8614i | − 1.99615i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8564i | 1.37876i | 0.724398 | + | 0.689382i | \(0.242118\pi\) | ||||
−0.724398 | + | 0.689382i | \(0.757882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.9769 | −1.18012 | −0.590058 | − | 0.807361i | \(-0.700895\pi\) | ||||
−0.590058 | + | 0.807361i | \(0.700895\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 28.2337 | 2.75533 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 13.3723i | − 1.29275i | −0.763021 | − | 0.646374i | \(-0.776285\pi\) | ||||
0.763021 | − | 0.646374i | \(-0.223715\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 3.96143i | − 0.379437i | −0.981839 | − | 0.189718i | \(-0.939243\pi\) | ||||
0.981839 | − | 0.189718i | \(-0.0607575\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −34.0511 | −3.23199 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.7446 | −1.38705 | −0.693526 | − | 0.720432i | \(-0.743944\pi\) | ||||
−0.693526 | + | 0.720432i | \(0.743944\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00000i | 0.186501i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 48.9022i | 4.52101i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.5831 | −1.52017 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.37228 | 0.488389 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 9.15759i | − 0.819080i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.2718 | −1.08895 | −0.544475 | − | 0.838777i | \(-0.683271\pi\) | ||||
−0.544475 | + | 0.838777i | \(0.683271\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.2337 | −1.07712 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 4.37228i | − 0.382008i | −0.981589 | − | 0.191004i | \(-0.938826\pi\) | ||||
0.981589 | − | 0.191004i | \(-0.0611743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.31662i | − 0.287588i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 45.7330 | 3.93607 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.00000 | 0.427179 | 0.213589 | − | 0.976924i | \(-0.431485\pi\) | ||||
0.213589 | + | 0.976924i | \(0.431485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 3.62772i | − 0.307699i | −0.988094 | − | 0.153850i | \(-0.950833\pi\) | ||||
0.988094 | − | 0.153850i | \(-0.0491671\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.17448i | − 0.183124i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.8564 | 1.15873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.74456 | 0.560105 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 13.4891i | − 1.11256i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 4.69882i | − 0.384942i | −0.981303 | − | 0.192471i | \(-0.938350\pi\) | ||||
0.981303 | − | 0.192471i | \(-0.0616502\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.7359 | −1.28057 | −0.640286 | − | 0.768137i | \(-0.721184\pi\) | ||||
−0.640286 | + | 0.768137i | \(0.721184\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −41.8614 | −3.38429 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.74456i | 0.702380i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.6101i | 1.48525i | 0.669708 | + | 0.742625i | \(0.266419\pi\) | ||||
−0.669708 | + | 0.742625i | \(0.733581\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.6920 | −1.64099 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.62772 | 0.207093 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7446i | 0.841579i | 0.907158 | + | 0.420790i | \(0.138247\pi\) | ||||
−0.907158 | + | 0.420790i | \(0.861753\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 20.1947i | − 1.57216i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.33830 | −0.490472 | −0.245236 | − | 0.969463i | \(-0.578865\pi\) | ||||
−0.245236 | + | 0.969463i | \(0.578865\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21.1168 | −1.62437 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 8.37228i | − 0.640244i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 15.1460i | − 1.15153i | −0.817615 | − | 0.575766i | \(-0.804704\pi\) | ||||
0.817615 | − | 0.575766i | \(-0.195296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.55134 | 0.344049 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.62772 | 0.347841 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9783i | 1.71748i | 0.512416 | + | 0.858738i | \(0.328751\pi\) | ||||
−0.512416 | + | 0.858738i | \(0.671249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 8.21782i | − 0.610826i | −0.952220 | − | 0.305413i | \(-0.901205\pi\) | ||||
0.952220 | − | 0.305413i | \(-0.0987945\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 48.9022 | 3.61495 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −25.4891 | −1.87400 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.8614i | 0.867392i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 60.0868i | − 4.37067i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.07568 | 0.511978 | 0.255989 | − | 0.966680i | \(-0.417599\pi\) | ||||
0.255989 | + | 0.966680i | \(0.417599\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.25544 | 0.234332 | 0.117166 | − | 0.993112i | \(-0.462619\pi\) | ||||
0.117166 | + | 0.993112i | \(0.462619\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 49.7228i | 3.56072i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.33830i | 0.451585i | 0.974175 | + | 0.225792i | \(0.0724971\pi\) | ||||
−0.974175 | + | 0.225792i | \(0.927503\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.147477 | 0.0104544 | 0.00522718 | − | 0.999986i | \(-0.498336\pi\) | ||||
0.00522718 | + | 0.999986i | \(0.498336\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.86141 | 0.625035 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 8.86141i | − 0.621949i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.63325 | 0.461043 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.37228 | −0.164094 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2.62772i | − 0.180900i | −0.995901 | − | 0.0904498i | \(-0.971170\pi\) | ||||
0.995901 | − | 0.0904498i | \(-0.0288305\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 22.3692i | − 1.53271i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.15759 | −0.624542 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.4891 | 0.779933 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 28.6277i | − 1.93448i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 29.2048i | − 1.96453i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.92820 | 0.463947 | 0.231973 | − | 0.972722i | \(-0.425482\pi\) | ||||
0.231973 | + | 0.972722i | \(0.425482\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.4891 | 0.765942 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 14.1168i | − 0.936968i | −0.883472 | − | 0.468484i | \(-0.844800\pi\) | ||||
0.883472 | − | 0.468484i | \(-0.155200\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 12.6217i | − 0.834065i | −0.908892 | − | 0.417032i | \(-0.863070\pi\) | ||||
0.908892 | − | 0.417032i | \(-0.136930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −26.5330 | −1.74574 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.8832 | −0.712979 | −0.356490 | − | 0.934299i | \(-0.616026\pi\) | ||||
−0.356490 | + | 0.934299i | \(0.616026\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1.62772i | − 0.106181i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 0.994667i | − 0.0646105i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.4680 | 1.12991 | 0.564955 | − | 0.825122i | \(-0.308894\pi\) | ||||
0.564955 | + | 0.825122i | \(0.308894\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00000 | 0.515325 | 0.257663 | − | 0.966235i | \(-0.417048\pi\) | ||||
0.257663 | + | 0.966235i | \(0.417048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 66.9783i | − 4.29666i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 10.0974i | − 0.645096i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.84096 | 0.371652 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −26.9783 | −1.70968 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 17.8614i | − 1.12740i | −0.825979 | − | 0.563701i | \(-0.809377\pi\) | ||||
0.825979 | − | 0.563701i | \(-0.190623\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.87953i | − 0.118165i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −42.5639 | −2.66545 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.2337 | −1.01263 | −0.506315 | − | 0.862349i | \(-0.668993\pi\) | ||||
−0.506315 | + | 0.862349i | \(0.668993\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 33.4891i | 2.08091i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 22.3692i | − 1.38462i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.9600 | −1.16912 | −0.584561 | − | 0.811349i | \(-0.698733\pi\) | ||||
−0.584561 | + | 0.811349i | \(0.698733\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.4891 | −0.951489 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 52.2337i | 3.19665i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1.87953i | − 0.114597i | −0.998357 | − | 0.0572984i | \(-0.981751\pi\) | ||||
0.998357 | − | 0.0572984i | \(-0.0182486\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.37686 | −0.144384 | −0.0721920 | − | 0.997391i | \(-0.522999\pi\) | ||||
−0.0721920 | + | 0.997391i | \(0.522999\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 65.3288 | 3.95388 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 3.25544i | − 0.196310i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.3807i | 0.984224i | 0.870532 | + | 0.492112i | \(0.163775\pi\) | ||||
−0.870532 | + | 0.492112i | \(0.836225\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 29.0024 | 1.73633 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.23369 | 0.371871 | 0.185935 | − | 0.982562i | \(-0.440469\pi\) | ||||
0.185935 | + | 0.982562i | \(0.440469\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.6277i | 1.04786i | 0.851762 | + | 0.523930i | \(0.175534\pi\) | ||||
−0.851762 | + | 0.523930i | \(0.824466\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 8.51278i | − 0.504253i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.25544i | 0.542563i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 4.84630i | − 0.283124i | −0.989929 | − | 0.141562i | \(-0.954788\pi\) | ||||
0.989929 | − | 0.141562i | \(-0.0452124\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.46410 | 0.201688 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −42.9783 | −2.49385 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.62772i | 0.267628i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0318i | 0.693500i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 46.7277 | 2.68444 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.6060 | 2.09605 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 15.2554i | − 0.870674i | −0.900268 | − | 0.435337i | \(-0.856629\pi\) | ||||
0.900268 | − | 0.435337i | \(-0.143371\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 40.3894i | 2.29767i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.2164 | −1.31648 | −0.658240 | − | 0.752808i | \(-0.728699\pi\) | ||||
−0.658240 | + | 0.752808i | \(0.728699\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.88316 | 0.219489 | 0.109744 | − | 0.993960i | \(-0.464997\pi\) | ||||
0.109744 | + | 0.993960i | \(0.464997\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 70.0951i | − 3.94941i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 21.5769i | − 1.21188i | −0.795511 | − | 0.605940i | \(-0.792797\pi\) | ||||
0.795511 | − | 0.605940i | \(-0.207203\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.33830 | −0.354876 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −45.0951 | −2.51696 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.00000i | 0.278207i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.01544i | 0.444617i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.3591 | −0.738758 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.13859 | −0.117904 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 10.8614i | − 0.596997i | −0.954410 | − | 0.298498i | \(-0.903514\pi\) | ||||
0.954410 | − | 0.298498i | \(-0.0964858\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 84.5379i | 4.63265i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.63325 | 0.362413 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.2554 | −0.722070 | −0.361035 | − | 0.932552i | \(-0.617576\pi\) | ||||
−0.361035 | + | 0.932552i | \(0.617576\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 49.7228i | 2.70057i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 8.21782i | − 0.445020i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.94987 | 0.537243 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.74456 | 0.363115 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 37.1168i | − 1.99254i | −0.0863104 | − | 0.996268i | \(-0.527508\pi\) | ||||
0.0863104 | − | 0.996268i | \(-0.472492\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 13.2116i | − 0.707201i | −0.935397 | − | 0.353600i | \(-0.884957\pi\) | ||||
0.935397 | − | 0.353600i | \(-0.115043\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 105.820 | 5.64824 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.88316 | 0.206680 | 0.103340 | − | 0.994646i | \(-0.467047\pi\) | ||||
0.103340 | + | 0.994646i | \(0.467047\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 16.7446i | − 0.888709i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 55.9230i | 2.95976i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.5831 | 0.875224 | 0.437612 | − | 0.899164i | \(-0.355824\pi\) | ||||
0.437612 | + | 0.899164i | \(0.355824\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 18.1168i | − 0.950888i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 21.4294i | − 1.12167i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.05401 | −0.211618 | −0.105809 | − | 0.994386i | \(-0.533743\pi\) | ||||
−0.105809 | + | 0.994386i | \(0.533743\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.3505i | 1.05655i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 14.9436i | − 0.773753i | −0.922132 | − | 0.386876i | \(-0.873554\pi\) | ||||
0.922132 | − | 0.386876i | \(-0.126446\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −30.8820 | −1.59474 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.6060 | 0.803748 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 36.3505i | − 1.86720i | −0.358315 | − | 0.933601i | \(-0.616649\pi\) | ||||
0.358315 | − | 0.933601i | \(-0.383351\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 41.3841i | 2.12017i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.2434 | 1.28988 | 0.644938 | − | 0.764235i | \(-0.276883\pi\) | ||||
0.644938 | + | 0.764235i | \(0.276883\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.8614 | −1.01223 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 30.3723i | 1.54391i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 24.3036i | − 1.23224i | −0.787651 | − | 0.616121i | \(-0.788703\pi\) | ||||
0.787651 | − | 0.616121i | \(-0.211297\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.96143 | −0.200338 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.7446 | −0.743765 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 0.744563i | − 0.0374630i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 0.644810i | − 0.0323621i | −0.999869 | − | 0.0161810i | \(-0.994849\pi\) | ||||
0.999869 | − | 0.0161810i | \(-0.00515081\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.1846 | −0.559930 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.7228 | 1.78391 | 0.891956 | − | 0.452122i | \(-0.149333\pi\) | ||||
0.891956 | + | 0.452122i | \(0.149333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.2337i | 1.00791i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 90.8213i | − 4.51294i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.9538 | 1.18734 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00000 | −0.296681 | −0.148340 | − | 0.988936i | \(-0.547393\pi\) | ||||
−0.148340 | + | 0.988936i | \(0.547393\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 16.8614i | − 0.831712i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.55134i | − 0.223957i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.1947 | −0.991319 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.2337 | −0.599086 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.233688i | 0.0114164i | 0.999984 | + | 0.00570820i | \(0.00181699\pi\) | ||||
−0.999984 | + | 0.00570820i | \(0.998183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.3971i | 0.994093i | 0.867724 | + | 0.497046i | \(0.165582\pi\) | ||||
−0.867724 | + | 0.497046i | \(0.834418\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.39853 | −0.262486 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.86141 | −0.332827 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 48.0951i | − 2.32748i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 46.7277i | − 2.25603i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.7793 | 1.04907 | 0.524535 | − | 0.851389i | \(-0.324239\pi\) | ||||
0.524535 | + | 0.851389i | \(0.324239\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.48913 | −0.0715628 | −0.0357814 | − | 0.999360i | \(-0.511392\pi\) | ||||
−0.0357814 | + | 0.999360i | \(0.511392\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 22.7446i | − 1.09052i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 0.792287i | − 0.0379002i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.92820 | 0.330665 | 0.165333 | − | 0.986238i | \(-0.447130\pi\) | ||||
0.165333 | + | 0.986238i | \(0.447130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −33.4891 | −1.59472 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 41.3505i | − 1.96462i | −0.187254 | − | 0.982312i | \(-0.559959\pi\) | ||||
0.187254 | − | 0.982312i | \(-0.440041\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39.0998i | 1.85351i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.8457 | −0.749478 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.4891 | 1.76922 | 0.884611 | − | 0.466330i | \(-0.154424\pi\) | ||||
0.884611 | + | 0.466330i | \(0.154424\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 53.0660i | 2.49326i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 48.9022 | 2.29257 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.0000 | 1.45012 | 0.725059 | − | 0.688686i | \(-0.241812\pi\) | ||||
0.725059 | + | 0.688686i | \(0.241812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 90.5842i | 4.22811i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 7.86797i | − 0.366448i | −0.983071 | − | 0.183224i | \(-0.941347\pi\) | ||||
0.983071 | − | 0.183224i | \(-0.0586533\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.5268 | −1.46517 | −0.732587 | − | 0.680674i | \(-0.761687\pi\) | ||||
−0.732587 | + | 0.680674i | \(0.761687\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 29.4891 | 1.36753 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.8832i | 0.503612i | 0.967778 | + | 0.251806i | \(0.0810246\pi\) | ||||
−0.967778 | + | 0.251806i | \(0.918975\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 8.71516i | − 0.402429i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 62.7586 | 2.89176 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.60597 | 0.395703 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.37228i | − 0.0629646i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 51.3716i | 2.35214i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.4179 | −1.25275 | −0.626377 | − | 0.779520i | \(-0.715463\pi\) | ||||
−0.626377 | + | 0.779520i | \(0.715463\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −58.9783 | −2.68918 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 8.86141i | − 0.403208i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.92820i | 0.314594i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.6641 | −1.02701 | −0.513505 | − | 0.858087i | \(-0.671653\pi\) | ||||
−0.513505 | + | 0.858087i | \(0.671653\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.2337 | 1.63854 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 30.9783i | − 1.39803i | −0.715108 | − | 0.699014i | \(-0.753622\pi\) | ||||
0.715108 | − | 0.699014i | \(-0.246378\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.3591i | 0.601662i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −50.1369 | −2.25349 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.0000 | −0.986835 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 4.37228i | − 0.195730i | −0.995200 | − | 0.0978651i | \(-0.968799\pi\) | ||||
0.995200 | − | 0.0978651i | \(-0.0312014\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.3745i | 0.954943i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.4795 | 0.511848 | 0.255924 | − | 0.966697i | \(-0.417620\pi\) | ||||
0.255924 | + | 0.966697i | \(0.417620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.9783 | 1.55651 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 71.2119i | 3.16263i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.8102i | 1.67591i | 0.545742 | + | 0.837953i | \(0.316248\pi\) | ||||
−0.545742 | + | 0.837953i | \(0.683752\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.1552 | −1.24551 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.1168 | −0.799878 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.2337i | 1.33226i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.52967i | 0.0672749i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −51.0767 | −2.24202 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.76631 | −0.252627 | −0.126313 | − | 0.991990i | \(-0.540314\pi\) | ||||
−0.126313 | + | 0.991990i | \(0.540314\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.3723i | 1.10945i | 0.832033 | + | 0.554726i | \(0.187177\pi\) | ||||
−0.832033 | + | 0.554726i | \(0.812823\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 15.3484i | − 0.669859i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.3205 | −0.754493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3723 | −0.972708 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 11.4891i | − 0.498586i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.7562 | −1.45941 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 77.4891 | 3.34390 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.48913i | 0.408726i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.6039i | 1.01481i | 0.861707 | + | 0.507405i | \(0.169395\pi\) | ||||
−0.861707 | + | 0.507405i | \(0.830605\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −27.7128 | −1.18927 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 2.51087i | − 0.107357i | −0.998558 | − | 0.0536786i | \(-0.982905\pi\) | ||||
0.998558 | − | 0.0536786i | \(-0.0170947\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 121.408i | − 5.18158i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.67181 | −0.113823 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.978251 | −0.0415994 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 85.9565i | 3.64865i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 25.1885i | − 1.06727i | −0.845715 | − | 0.533635i | \(-0.820826\pi\) | ||||
0.845715 | − | 0.533635i | \(-0.179174\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.1894 | −0.896215 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.0000 | 1.68880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 13.4891i | − 0.568499i | −0.958750 | − | 0.284249i | \(-0.908256\pi\) | ||||
0.958750 | − | 0.284249i | \(-0.0917444\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.2203i | 1.56587i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −119.326 | −5.01124 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.9783 | −1.13099 | −0.565494 | − | 0.824753i | \(-0.691314\pi\) | ||||
−0.565494 | + | 0.824753i | \(0.691314\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 42.9783i | − 1.79858i | −0.437349 | − | 0.899292i | \(-0.644083\pi\) | ||||
0.437349 | − | 0.899292i | \(-0.355917\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 23.8612i | − 0.996815i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.08724 | 0.0453411 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.4674 | 1.39327 | 0.696633 | − | 0.717428i | \(-0.254681\pi\) | ||||
0.696633 | + | 0.717428i | \(0.254681\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 10.9783i | − 0.456241i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.5330i | 1.10077i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.5561 | 0.602853 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 123.446 | 5.10385 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.8614i | 1.31506i | 0.753428 | + | 0.657530i | \(0.228399\pi\) | ||||
−0.753428 | + | 0.657530i | \(0.771601\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 3.46410i | − 0.142736i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.3745 | 0.879230 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.97825 | 0.204432 | 0.102216 | − | 0.994762i | \(-0.467407\pi\) | ||||
0.102216 | + | 0.994762i | \(0.467407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 41.8614i | 1.71615i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 0.497333i | − 0.0203545i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.6897 | 1.62168 | 0.810838 | − | 0.585270i | \(-0.199012\pi\) | ||||
0.810838 | + | 0.585270i | \(0.199012\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.4674 | −0.916463 | −0.458232 | − | 0.888833i | \(-0.651517\pi\) | ||||
−0.458232 | + | 0.888833i | \(0.651517\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 22.0000i | − 0.895909i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 13.5615i | − 0.551351i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.8048 | 1.57504 | 0.787520 | − | 0.616289i | \(-0.211365\pi\) | ||||
0.787520 | + | 0.616289i | \(0.211365\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −29.8832 | −1.21093 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 3.76631i | − 0.152369i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.5552i | 0.749439i | 0.927138 | + | 0.374719i | \(0.122261\pi\) | ||||
−0.927138 | + | 0.374719i | \(0.877739\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.8397 | −1.64414 | −0.822071 | − | 0.569384i | \(-0.807182\pi\) | ||||
−0.822071 | + | 0.569384i | \(0.807182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.2337i | 0.652487i | 0.945286 | + | 0.326244i | \(0.105783\pi\) | ||||
−0.945286 | + | 0.326244i | \(0.894217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 14.3537i | − 0.575996i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 51.3716 | 2.05816 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.9783 | −1.19913 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.00000i | 0.319489i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 50.4868i | − 2.01304i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.8651 | 1.50738 | 0.753692 | − | 0.657227i | \(-0.228271\pi\) | ||||
0.753692 | + | 0.657227i | \(0.228271\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.86141 | −0.352209 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 30.9783i | 1.22933i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 23.3639i | − 0.925709i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −55.5354 | −2.19695 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.9783 | −0.433615 | −0.216807 | − | 0.976214i | \(-0.569564\pi\) | ||||
−0.216807 | + | 0.976214i | \(0.569564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.3723i | 1.43438i | 0.696876 | + | 0.717191i | \(0.254573\pi\) | ||||
−0.696876 | + | 0.717191i | \(0.745427\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 30.8820i | 1.21598i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.5831 | 0.651950 | 0.325975 | − | 0.945378i | \(-0.394307\pi\) | ||||
0.325975 | + | 0.945378i | \(0.394307\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.25544 | −0.127787 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 38.7446i | − 1.51852i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.3956i | 1.38514i | 0.721352 | + | 0.692569i | \(0.243521\pi\) | ||||
−0.721352 | + | 0.692569i | \(0.756479\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.0371 | −0.431256 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −71.0733 | −2.77284 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 46.8614i | − 1.82546i | −0.408562 | − | 0.912731i | \(-0.633970\pi\) | ||||
0.408562 | − | 0.912731i | \(-0.366030\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 10.5947i | − 0.412085i | −0.978543 | − | 0.206043i | \(-0.933941\pi\) | ||||
0.978543 | − | 0.206043i | \(-0.0660586\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −98.4868 | −3.82491 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.37228 | −0.324663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.11684i | − 0.0819645i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 23.3639i | − 0.903299i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.4010 | −1.32803 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.7446 | 0.645455 | 0.322728 | − | 0.946492i | \(-0.395400\pi\) | ||||
0.322728 | + | 0.946492i | \(0.395400\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 24.8614i | − 0.956916i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.84096i | 0.224486i | 0.993681 | + | 0.112243i | \(0.0358036\pi\) | ||||
−0.993681 | + | 0.112243i | \(0.964196\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.10268 | 0.349329 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −47.6060 | −1.82426 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000i | 0.459167i | 0.973289 | + | 0.229584i | \(0.0737364\pi\) | ||||
−0.973289 | + | 0.229584i | \(0.926264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 12.6217i | − 0.482250i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −42.5639 | −1.62391 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35.8397 | −1.36538 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.8614i | 0.679480i | 0.940519 | + | 0.339740i | \(0.110339\pi\) | ||||
−0.940519 | + | 0.339740i | \(0.889661\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 65.8728i | 2.50230i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.15759 | −0.347367 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 36.7011i | 1.38816i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 27.7128i | − 1.04670i | −0.852118 | − | 0.523349i | \(-0.824682\pi\) | ||||
0.852118 | − | 0.523349i | \(-0.175318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0974 | 0.380829 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.48913 | −0.206732 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 45.9565i | − 1.72837i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.7330i | 1.71754i | 0.512361 | + | 0.858770i | \(0.328771\pi\) | ||||
−0.512361 | + | 0.858770i | \(0.671229\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.46943 | −0.0926110 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.74456 | 0.102785 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 34.9783i | − 1.30811i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 58.9070i | − 2.19992i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.5369 | 1.51177 | 0.755885 | − | 0.654704i | \(-0.227207\pi\) | ||||
0.755885 | + | 0.654704i | \(0.227207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 39.7228 | 1.47935 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 26.9783i | − 1.00333i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3.66648i | − 0.136170i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0039 | 0.519375 | 0.259688 | − | 0.965693i | \(-0.416380\pi\) | ||||
0.259688 | + | 0.965693i | \(0.416380\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −117.935 | −4.36795 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 18.1386i | − 0.670880i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.1894i | 0.782647i | 0.920253 | + | 0.391324i | \(0.127983\pi\) | ||||
−0.920253 | + | 0.391324i | \(0.872017\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −34.0511 | −1.25599 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.23369 | −0.229621 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 12.6060i | − 0.463718i | −0.972749 | − | 0.231859i | \(-0.925519\pi\) | ||||
0.972749 | − | 0.231859i | \(-0.0744808\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 19.6974i | − 0.723601i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.63325 | 0.243350 | 0.121675 | − | 0.992570i | \(-0.461173\pi\) | ||||
0.121675 | + | 0.992570i | \(0.461173\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.8614 | −0.434568 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 66.9783i | 2.45061i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 44.3508i | 1.62054i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.50744 | 0.346932 | 0.173466 | − | 0.984840i | \(-0.444503\pi\) | ||||
0.173466 | + | 0.984840i | \(0.444503\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −60.2337 | −2.19504 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.7228i | 1.44566i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 18.8502i | − 0.685121i | −0.939496 | − | 0.342561i | \(-0.888706\pi\) | ||||
0.939496 | − | 0.342561i | \(-0.111294\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.33830 | −0.230066 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.0000 | −0.398750 | −0.199375 | − | 0.979923i | \(-0.563891\pi\) | ||||
−0.199375 | + | 0.979923i | \(0.563891\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.1386i | 0.475649i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 105.672i | 3.82059i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.01544 | 0.289421 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.4674 | 1.35111 | 0.675554 | − | 0.737310i | \(-0.263904\pi\) | ||||
0.675554 | + | 0.737310i | \(0.263904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54.7446i | 1.97158i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.1561i | 0.868836i | 0.900711 | + | 0.434418i | \(0.143046\pi\) | ||||
−0.900711 | + | 0.434418i | \(0.856954\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.75372 | 0.170759 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 112.935 | 4.05151 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.7359i | 0.563076i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −48.4048 | −1.72985 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.9783 | 1.67673 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 19.6060i | − 0.698877i | −0.936959 | − | 0.349439i | \(-0.886372\pi\) | ||||
0.936959 | − | 0.349439i | \(-0.113628\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 63.9384i | 2.27627i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.9022 | 1.73876 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 84.7011 | 3.00782 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 52.2337i | 1.85254i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.6487i | 0.518883i | 0.965759 | + | 0.259442i | \(0.0835385\pi\) | ||||
−0.965759 | + | 0.259442i | \(0.916461\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.22405 | 0.114059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 129.679 | 4.58199 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.1386i | 0.710676i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 6.63325i | − 0.233791i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.33830 | −0.223119 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.9783 | −1.33524 | −0.667622 | − | 0.744500i | \(-0.732688\pi\) | ||||
−0.667622 | + | 0.744500i | \(0.732688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 28.8614i | − 1.01346i | −0.862105 | − | 0.506731i | \(-0.830854\pi\) | ||||
0.862105 | − | 0.506731i | \(-0.169146\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.01544i | 0.281114i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.1229 | 0.950074 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.62772 | 0.126918 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 162.190i | − 5.66738i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 27.0680i | − 0.944680i | −0.881416 | − | 0.472340i | \(-0.843409\pi\) | ||||
0.881416 | − | 0.472340i | \(-0.156591\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.37063 | −0.256924 | −0.128462 | − | 0.991714i | \(-0.541004\pi\) | ||||
−0.128462 | + | 0.991714i | \(0.541004\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.9783 | −0.382214 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 40.3505i | − 1.40313i | −0.712608 | − | 0.701563i | \(-0.752486\pi\) | ||||
0.712608 | − | 0.701563i | \(-0.247514\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 3.26172i | − 0.113284i | −0.998395 | − | 0.0566421i | \(-0.981961\pi\) | ||||
0.998395 | − | 0.0566421i | \(-0.0180394\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 55.2405 | 1.91627 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.0000 | 0.692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0000i | 0.553703i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 62.7586i | − 2.16925i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.80240 | 0.338416 | 0.169208 | − | 0.985580i | \(-0.445879\pi\) | ||||
0.169208 | + | 0.985580i | \(0.445879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.8614 | 0.753842 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 21.0217i | − 0.724028i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 53.3060i | 1.83378i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.8178 | −0.612228 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 59.4456 | 2.04017 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.00000i | 0.274236i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.3894i | 1.38291i | 0.722421 | + | 0.691453i | \(0.243029\pi\) | ||||
−0.722421 | + | 0.691453i | \(0.756971\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.1345 | −0.722783 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.2337 | 0.759488 | 0.379744 | − | 0.925092i | \(-0.376012\pi\) | ||||
0.379744 | + | 0.925092i | \(0.376012\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.60597i | 0.293632i | 0.989164 | + | 0.146816i | \(0.0469025\pi\) | ||||
−0.989164 | + | 0.146816i | \(0.953097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.76439 | −0.0941009 | −0.0470504 | − | 0.998893i | \(-0.514982\pi\) | ||||
−0.0470504 | + | 0.998893i | \(0.514982\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.2337 | −1.29998 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 26.9783i | − 0.916229i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.699713i | 0.0237361i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.3484 | 0.520061 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.9783 | 0.777696 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30.3723i | 1.02677i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.38219i | 0.0466734i | 0.999728 | + | 0.0233367i | \(0.00742897\pi\) | ||||
−0.999728 | + | 0.0233367i | \(0.992571\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.3431 | −0.551238 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.37228 | −0.147306 | −0.0736530 | − | 0.997284i | \(-0.523466\pi\) | ||||
−0.0736530 | + | 0.997284i | \(0.523466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 18.8832i | − 0.635469i | −0.948180 | − | 0.317734i | \(-0.897078\pi\) | ||||
0.948180 | − | 0.317734i | \(-0.102922\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 11.6819i | − 0.392684i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.0333 | −1.51207 | −0.756035 | − | 0.654531i | \(-0.772866\pi\) | ||||
−0.756035 | + | 0.654531i | \(0.772866\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40.7011 | 1.36507 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 85.3505i | 2.85935i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.644810i | 0.0215777i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 58.0049 | 1.93889 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.6060 | 0.521068 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 9.25544i | − 0.308686i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 30.6796i | − 1.02209i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 40.5746 | 1.35024 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.7446 | −0.689573 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.8614i | 1.55601i | 0.628260 | + | 0.778004i | \(0.283768\pi\) | ||||
−0.628260 | + | 0.778004i | \(0.716232\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 116.010i | − 3.84780i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.6126 | −1.57747 | −0.788737 | − | 0.614730i | \(-0.789265\pi\) | ||||
−0.788737 | + | 0.614730i | \(0.789265\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.9783 | 0.628088 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 123.446i | − 4.08099i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.5012i | 0.478872i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.71516 | 0.287486 | 0.143743 | − | 0.989615i | \(-0.454086\pi\) | ||||
0.143743 | + | 0.989615i | \(0.454086\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −51.4456 | −1.69519 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 38.7446i | − 1.27529i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.8564i | 0.455596i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 100.274 | 3.29342 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.8832 | −0.914817 | −0.457408 | − | 0.889257i | \(-0.651222\pi\) | ||||
−0.457408 | + | 0.889257i | \(0.651222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000i | 0.131095i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 78.2921i | 2.56317i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.9422 | 0.979215 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.9783 | −0.717998 | −0.358999 | − | 0.933338i | \(-0.616882\pi\) | ||||
−0.358999 | + | 0.933338i | \(0.616882\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 13.0951i | − 0.427342i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 10.8896i | − 0.354992i | −0.984122 | − | 0.177496i | \(-0.943200\pi\) | ||||
0.984122 | − | 0.177496i | \(-0.0567997\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −151.679 | −4.93413 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 43.2119i | − 1.40420i | −0.712079 | − | 0.702100i | \(-0.752246\pi\) | ||||
0.712079 | − | 0.702100i | \(-0.247754\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 49.5847i | − 1.60959i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −72.7634 | −2.35951 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.2337 | 0.849793 | 0.424896 | − | 0.905242i | \(-0.360311\pi\) | ||||
0.424896 | + | 0.905242i | \(0.360311\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 17.8614i | − 0.577982i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.3745i | 0.690940i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.5831 | −0.535497 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0000 | −0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 111.957i | 3.60775i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 8.21782i | − 0.264541i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.1307 | 1.77288 | 0.886441 | − | 0.462841i | \(-0.153170\pi\) | ||||
0.886441 | + | 0.462841i | \(0.153170\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.8614 | 0.541666 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 4.00000i | − 0.128366i | −0.997938 | − | 0.0641831i | \(-0.979556\pi\) | ||||
0.997938 | − | 0.0641831i | \(-0.0204442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0318i | 0.385721i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27.0303 | 0.865663 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.4891 | 0.879455 | 0.439728 | − | 0.898131i | \(-0.355075\pi\) | ||||
0.439728 | + | 0.898131i | \(0.355075\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 36.7446i | − 1.17436i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.1662i | 1.05892i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52.6612 | 1.67963 | 0.839816 | − | 0.542871i | \(-0.182663\pi\) | ||||
0.839816 | + | 0.542871i | \(0.182663\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | 0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.21194i | 0.229559i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.87419i | 0.0913941i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.92287 | −0.251678 | −0.125839 | − | 0.992051i | \(-0.540162\pi\) | ||||
−0.125839 | + | 0.992051i | \(0.540162\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −36.6277 | −1.16235 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 0.372281i | − 0.0118021i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.8164i | 1.03931i | 0.854378 | + | 0.519653i | \(0.173939\pi\) | ||||
−0.854378 | + | 0.519653i | \(0.826061\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 182.932 | 5.78772 |
(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 | 1216.2.c.h.609.1 | ✓ | 8 | |
4.3 | odd | 2 | inner | 1216.2.c.h.609.7 | yes | 8 | |
8.3 | odd | 2 | inner | 1216.2.c.h.609.2 | yes | 8 | |
8.5 | even | 2 | inner | 1216.2.c.h.609.8 | yes | 8 | |
16.3 | odd | 4 | 4864.2.a.bi.1.1 | 4 | |||
16.5 | even | 4 | 4864.2.a.bi.1.2 | 4 | |||
16.11 | odd | 4 | 4864.2.a.bl.1.4 | 4 | |||
16.13 | even | 4 | 4864.2.a.bl.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.c.h.609.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1216.2.c.h.609.2 | yes | 8 | 8.3 | odd | 2 | inner | |
1216.2.c.h.609.7 | yes | 8 | 4.3 | odd | 2 | inner | |
1216.2.c.h.609.8 | yes | 8 | 8.5 | even | 2 | inner | |
4864.2.a.bi.1.1 | 4 | 16.3 | odd | 4 | |||
4864.2.a.bi.1.2 | 4 | 16.5 | even | 4 | |||
4864.2.a.bl.1.3 | 4 | 16.13 | even | 4 | |||
4864.2.a.bl.1.4 | 4 | 16.11 | odd | 4 |