Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4608,2,Mod(1,4608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4608, 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("4608.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4608 = 2^{9} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4608.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: | \(36.7950652514\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 512) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.517638\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4608.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.46410 | −1.54919 | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843 | 1.06904 | 0.534522 | − | 0.845154i | \(-0.320491\pi\) | ||||
0.534522 | + | 0.845154i | \(0.320491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.44949 | 0.738549 | 0.369274 | − | 0.929320i | \(-0.379606\pi\) | ||||
0.369274 | + | 0.929320i | \(0.379606\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.46410 | −0.960769 | −0.480384 | − | 0.877058i | \(-0.659503\pi\) | ||||
−0.480384 | + | 0.877058i | \(0.659503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.44949 | 0.561951 | 0.280976 | − | 0.959715i | \(-0.409342\pi\) | ||||
0.280976 | + | 0.959715i | \(0.409342\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.00000 | 1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.46410 | −0.643268 | −0.321634 | − | 0.946864i | \(-0.604232\pi\) | ||||
−0.321634 | + | 0.946864i | \(0.604232\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.79796 | −1.65616 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.46410 | −0.569495 | −0.284747 | − | 0.958603i | \(-0.591910\pi\) | ||||
−0.284747 | + | 0.958603i | \(0.591910\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.2474 | 1.86772 | 0.933859 | − | 0.357641i | \(-0.116419\pi\) | ||||
0.933859 | + | 0.357641i | \(0.116419\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.3137 | 1.65027 | 0.825137 | − | 0.564933i | \(-0.191098\pi\) | ||||
0.825137 | + | 0.564933i | \(0.191098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3923 | −1.42749 | −0.713746 | − | 0.700404i | \(-0.753003\pi\) | ||||
−0.713746 | + | 0.700404i | \(0.753003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.48528 | −1.14416 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.44949 | −0.318896 | −0.159448 | − | 0.987206i | \(-0.550971\pi\) | ||||
−0.159448 | + | 0.987206i | \(0.550971\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.46410 | −0.443533 | −0.221766 | − | 0.975100i | \(-0.571182\pi\) | ||||
−0.221766 | + | 0.975100i | \(0.571182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0000 | 1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.34847 | −0.897758 | −0.448879 | − | 0.893592i | \(-0.648177\pi\) | ||||
−0.448879 | + | 0.893592i | \(0.648177\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.82843 | 0.335673 | 0.167836 | − | 0.985815i | \(-0.446322\pi\) | ||||
0.167836 | + | 0.985815i | \(0.446322\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.00000 | 0.936329 | 0.468165 | − | 0.883641i | \(-0.344915\pi\) | ||||
0.468165 | + | 0.883641i | \(0.344915\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.92820 | 0.789542 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.65685 | 0.636446 | 0.318223 | − | 0.948016i | \(-0.396914\pi\) | ||||
0.318223 | + | 0.948016i | \(0.396914\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.34847 | −0.806599 | −0.403300 | − | 0.915068i | \(-0.632137\pi\) | ||||
−0.403300 | + | 0.915068i | \(0.632137\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.8564 | 1.50294 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.00000 | 0.847998 | 0.423999 | − | 0.905663i | \(-0.360626\pi\) | ||||
0.423999 | + | 0.905663i | \(0.360626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.79796 | −1.02711 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.48528 | −0.870572 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0000 | 1.21842 | 0.609208 | − | 0.793011i | \(-0.291488\pi\) | ||||
0.609208 | + | 0.793011i | \(0.291488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.46410 | 0.344691 | 0.172345 | − | 0.985037i | \(-0.444865\pi\) | ||||
0.172345 | + | 0.985037i | \(0.444865\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.1421 | −1.39347 | −0.696733 | − | 0.717331i | \(-0.745364\pi\) | ||||
−0.696733 | + | 0.717331i | \(0.745364\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.44949 | 0.236801 | 0.118401 | − | 0.992966i | \(-0.462223\pi\) | ||||
0.118401 | + | 0.992966i | \(0.462223\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.3923 | −0.995402 | −0.497701 | − | 0.867349i | \(-0.665822\pi\) | ||||
−0.497701 | + | 0.867349i | \(0.665822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.79796 | 0.913664 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.3137 | −1.03713 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.65685 | 0.501965 | 0.250982 | − | 0.967992i | \(-0.419246\pi\) | ||||
0.250982 | + | 0.967992i | \(0.419246\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.34847 | 0.642039 | 0.321019 | − | 0.947073i | \(-0.395975\pi\) | ||||
0.321019 | + | 0.947073i | \(0.395975\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.92820 | 0.600751 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2474 | 1.03882 | 0.519408 | − | 0.854527i | \(-0.326153\pi\) | ||||
0.519408 | + | 0.854527i | \(0.326153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.48528 | −0.709575 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0000 | 0.996546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.3923 | 0.851371 | 0.425685 | − | 0.904871i | \(-0.360033\pi\) | ||||
0.425685 | + | 0.904871i | \(0.360033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.7990 | −1.61122 | −0.805609 | − | 0.592447i | \(-0.798162\pi\) | ||||
−0.805609 | + | 0.592447i | \(0.798162\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.5959 | −1.57398 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.2487 | 1.93526 | 0.967629 | − | 0.252377i | \(-0.0812124\pi\) | ||||
0.967629 | + | 0.252377i | \(0.0812124\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | −0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.1464 | 1.34301 | 0.671506 | − | 0.740999i | \(-0.265648\pi\) | ||||
0.671506 | + | 0.740999i | \(0.265648\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.48528 | 0.656611 | 0.328305 | − | 0.944572i | \(-0.393522\pi\) | ||||
0.328305 | + | 0.944572i | \(0.393522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.3205 | 1.31685 | 0.658427 | − | 0.752645i | \(-0.271222\pi\) | ||||
0.658427 | + | 0.752645i | \(0.271222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.7990 | 1.49666 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.2474 | 0.915417 | 0.457709 | − | 0.889102i | \(-0.348670\pi\) | ||||
0.457709 | + | 0.889102i | \(0.348670\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.2487 | −1.80239 | −0.901196 | − | 0.433411i | \(-0.857310\pi\) | ||||
−0.901196 | + | 0.433411i | \(0.857310\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.0000 | 0.882258 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.79796 | −0.716498 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9706 | 1.22795 | 0.613973 | − | 0.789327i | \(-0.289570\pi\) | ||||
0.613973 | + | 0.789327i | \(0.289570\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.0000 | 0.863779 | 0.431889 | − | 0.901927i | \(-0.357847\pi\) | ||||
0.431889 | + | 0.901927i | \(0.357847\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.3923 | 0.740421 | 0.370211 | − | 0.928948i | \(-0.379286\pi\) | ||||
0.370211 | + | 0.928948i | \(0.379286\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.82843 | 0.200502 | 0.100251 | − | 0.994962i | \(-0.468035\pi\) | ||||
0.100251 | + | 0.994962i | \(0.468035\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.79796 | −0.687682 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.92820 | −0.483887 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.2474 | −0.843149 | −0.421575 | − | 0.906794i | \(-0.638522\pi\) | ||||
−0.421575 | + | 0.906794i | \(0.638522\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −42.4264 | −2.89346 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000 | 1.08615 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.8564 | 0.932083 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.65685 | −0.378811 | −0.189405 | − | 0.981899i | \(-0.560656\pi\) | ||||
−0.189405 | + | 0.981899i | \(0.560656\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.0454 | 1.46321 | 0.731603 | − | 0.681731i | \(-0.238773\pi\) | ||||
0.731603 | + | 0.681731i | \(0.238773\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.46410 | 0.228914 | 0.114457 | − | 0.993428i | \(-0.463487\pi\) | ||||
0.114457 | + | 0.993428i | \(0.463487\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.00000 | 0.524097 | 0.262049 | − | 0.965055i | \(-0.415602\pi\) | ||||
0.262049 | + | 0.965055i | \(0.415602\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −39.1918 | −2.55659 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9706 | 1.09773 | 0.548867 | − | 0.835910i | \(-0.315059\pi\) | ||||
0.548867 | + | 0.835910i | \(0.315059\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0000 | 1.28831 | 0.644157 | − | 0.764894i | \(-0.277208\pi\) | ||||
0.644157 | + | 0.764894i | \(0.277208\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.46410 | −0.221313 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.48528 | −0.539906 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.1464 | 1.08227 | 0.541136 | − | 0.840935i | \(-0.317994\pi\) | ||||
0.541136 | + | 0.840935i | \(0.317994\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.92820 | −0.435572 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.0000 | 0.623783 | 0.311891 | − | 0.950118i | \(-0.399037\pi\) | ||||
0.311891 | + | 0.950118i | \(0.399037\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.79796 | −0.608816 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.4558 | 1.56967 | 0.784837 | − | 0.619702i | \(-0.212746\pi\) | ||||
0.784837 | + | 0.619702i | \(0.212746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.0000 | 2.21146 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.46410 | −0.211210 | −0.105605 | − | 0.994408i | \(-0.533678\pi\) | ||||
−0.105605 | + | 0.994408i | \(0.533678\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.3137 | 0.687259 | 0.343629 | − | 0.939105i | \(-0.388344\pi\) | ||||
0.343629 | + | 0.939105i | \(0.388344\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.1464 | 1.03397 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.2487 | 1.45696 | 0.728482 | − | 0.685065i | \(-0.240226\pi\) | ||||
0.728482 | + | 0.685065i | \(0.240226\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.0000 | −1.90896 | −0.954480 | − | 0.298275i | \(-0.903589\pi\) | ||||
−0.954480 | + | 0.298275i | \(0.903589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.9444 | 1.60168 | 0.800839 | − | 0.598880i | \(-0.204387\pi\) | ||||
0.800839 | + | 0.598880i | \(0.204387\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.65685 | 0.333914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.3923 | 0.607125 | 0.303562 | − | 0.952812i | \(-0.401824\pi\) | ||||
0.303562 | + | 0.952812i | \(0.401824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.48528 | 0.494032 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.79796 | 0.566631 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34.6410 | 1.99667 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.0000 | 0.687118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.44949 | 0.139800 | 0.0698999 | − | 0.997554i | \(-0.477732\pi\) | ||||
0.0698999 | + | 0.997554i | \(0.477732\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.48528 | −0.481156 | −0.240578 | − | 0.970630i | \(-0.577337\pi\) | ||||
−0.240578 | + | 0.970630i | \(0.577337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.0000 | 1.69570 | 0.847850 | − | 0.530236i | \(-0.177897\pi\) | ||||
0.847850 | + | 0.530236i | \(0.177897\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.3205 | −0.972817 | −0.486408 | − | 0.873732i | \(-0.661693\pi\) | ||||
−0.486408 | + | 0.873732i | \(0.661693\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.48528 | −0.475085 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.79796 | −0.545173 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.2487 | −1.34508 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.0000 | 1.76422 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.44949 | −0.134636 | −0.0673181 | − | 0.997732i | \(-0.521444\pi\) | ||||
−0.0673181 | + | 0.997732i | \(0.521444\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.4558 | 1.39080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.8564 | 0.750366 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.1464 | 0.920468 | 0.460234 | − | 0.887798i | \(-0.347765\pi\) | ||||
0.460234 | + | 0.887798i | \(0.347765\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.3205 | 0.927146 | 0.463573 | − | 0.886059i | \(-0.346567\pi\) | ||||
0.463573 | + | 0.886059i | \(0.346567\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.0000 | −1.38384 | −0.691920 | − | 0.721974i | \(-0.743235\pi\) | ||||
−0.691920 | + | 0.721974i | \(0.743235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.79796 | −0.520022 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.82843 | 0.149279 | 0.0746393 | − | 0.997211i | \(-0.476219\pi\) | ||||
0.0746393 | + | 0.997211i | \(0.476219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0000 | −0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27.7128 | −1.45055 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.6274 | 1.18114 | 0.590571 | − | 0.806986i | \(-0.298903\pi\) | ||||
0.590571 | + | 0.806986i | \(0.298903\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.3939 | −1.52605 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.46410 | −0.179364 | −0.0896822 | − | 0.995970i | \(-0.528585\pi\) | ||||
−0.0896822 | + | 0.995970i | \(0.528585\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.44949 | 0.125822 | 0.0629109 | − | 0.998019i | \(-0.479962\pi\) | ||||
0.0629109 | + | 0.998019i | \(0.479962\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.9411 | −1.73431 | −0.867155 | − | 0.498038i | \(-0.834054\pi\) | ||||
−0.867155 | + | 0.498038i | \(0.834054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.0000 | −1.22315 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.46410 | 0.175637 | 0.0878185 | − | 0.996136i | \(-0.472010\pi\) | ||||
0.0878185 | + | 0.996136i | \(0.472010\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.3137 | 0.572159 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.5959 | −0.985978 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.2487 | −1.21701 | −0.608504 | − | 0.793551i | \(-0.708230\pi\) | ||||
−0.608504 | + | 0.793551i | \(0.708230\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.00000 | −0.199750 | −0.0998752 | − | 0.995000i | \(-0.531844\pi\) | ||||
−0.0998752 | + | 0.995000i | \(0.531844\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.5959 | −0.976142 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.48528 | −0.420600 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.0000 | −0.890043 | −0.445021 | − | 0.895520i | \(-0.646804\pi\) | ||||
−0.445021 | + | 0.895520i | \(0.646804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.92820 | −0.340915 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.4558 | 1.24958 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.8434 | −1.55565 | −0.777825 | − | 0.628481i | \(-0.783677\pi\) | ||||
−0.777825 | + | 0.628481i | \(0.783677\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.3923 | −0.506490 | −0.253245 | − | 0.967402i | \(-0.581498\pi\) | ||||
−0.253245 | + | 0.967402i | \(0.581498\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −28.0000 | −1.35820 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.79796 | −0.474156 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.65685 | 0.272481 | 0.136241 | − | 0.990676i | \(-0.456498\pi\) | ||||
0.136241 | + | 0.990676i | \(0.456498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.00000 | 0.192228 | 0.0961139 | − | 0.995370i | \(-0.469359\pi\) | ||||
0.0961139 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.92820 | −0.331421 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.82843 | −0.134993 | −0.0674967 | − | 0.997719i | \(-0.521501\pi\) | ||||
−0.0674967 | + | 0.997719i | \(0.521501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.8434 | 1.51292 | 0.756462 | − | 0.654038i | \(-0.226926\pi\) | ||||
0.756462 | + | 0.654038i | \(0.226926\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.7128 | −1.31371 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.00000 | 0.188772 | 0.0943858 | − | 0.995536i | \(-0.469911\pi\) | ||||
0.0943858 | + | 0.995536i | \(0.469911\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.89898 | 0.230684 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 33.9411 | 1.59118 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.0000 | −0.842004 | −0.421002 | − | 0.907060i | \(-0.638322\pi\) | ||||
−0.421002 | + | 0.907060i | \(0.638322\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.3205 | −0.806696 | −0.403348 | − | 0.915047i | \(-0.632154\pi\) | ||||
−0.403348 | + | 0.915047i | \(0.632154\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.65685 | −0.262896 | −0.131448 | − | 0.991323i | \(-0.541963\pi\) | ||||
−0.131448 | + | 0.991323i | \(0.541963\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.1464 | 0.793442 | 0.396721 | − | 0.917939i | \(-0.370148\pi\) | ||||
0.396721 | + | 0.917939i | \(0.370148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.7846 | −0.959744 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.0000 | 1.37940 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.1464 | 0.786732 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.65685 | −0.258468 | −0.129234 | − | 0.991614i | \(-0.541252\pi\) | ||||
−0.129234 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | 0.547153 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −41.5692 | −1.88756 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.1421 | 0.640841 | 0.320421 | − | 0.947275i | \(-0.396176\pi\) | ||||
0.320421 | + | 0.947275i | \(0.396176\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.34847 | 0.331632 | 0.165816 | − | 0.986157i | \(-0.446974\pi\) | ||||
0.165816 | + | 0.986157i | \(0.446974\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.8564 | 0.624061 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.8434 | −1.42550 | −0.712752 | − | 0.701416i | \(-0.752552\pi\) | ||||
−0.712752 | + | 0.701416i | \(0.752552\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.1421 | −0.630567 | −0.315283 | − | 0.948998i | \(-0.602100\pi\) | ||||
−0.315283 | + | 0.948998i | \(0.602100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.3923 | −0.460631 | −0.230315 | − | 0.973116i | \(-0.573976\pi\) | ||||
−0.230315 | + | 0.973116i | \(0.573976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.6274 | 1.00098 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 48.9898 | 2.15875 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.7128 | 1.21881 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.0000 | 0.613351 | 0.306676 | − | 0.951814i | \(-0.400783\pi\) | ||||
0.306676 | + | 0.951814i | \(0.400783\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.0454 | −0.963978 | −0.481989 | − | 0.876177i | \(-0.660086\pi\) | ||||
−0.481989 | + | 0.876177i | \(0.660086\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.6274 | −0.985666 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.92820 | −0.300094 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.48528 | −0.366851 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.44949 | 0.105507 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.1769 | −1.34040 | −0.670200 | − | 0.742180i | \(-0.733792\pi\) | ||||
−0.670200 | + | 0.742180i | \(0.733792\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 36.0000 | 1.54207 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.2474 | 0.523663 | 0.261832 | − | 0.965114i | \(-0.415674\pi\) | ||||
0.261832 | + | 0.965114i | \(0.415674\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.48528 | −0.361485 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000 | 0.680389 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.3205 | 0.733893 | 0.366947 | − | 0.930242i | \(-0.380403\pi\) | ||||
0.366947 | + | 0.930242i | \(0.380403\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.4264 | −1.79445 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.0454 | −0.929103 | −0.464552 | − | 0.885546i | \(-0.653784\pi\) | ||||
−0.464552 | + | 0.885546i | \(0.653784\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.6410 | −1.45736 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.00000 | −0.0838444 | −0.0419222 | − | 0.999121i | \(-0.513348\pi\) | ||||
−0.0419222 | + | 0.999121i | \(0.513348\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.34847 | 0.307524 | 0.153762 | − | 0.988108i | \(-0.450861\pi\) | ||||
0.153762 | + | 0.988108i | \(0.450861\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.7990 | −0.825675 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.0000 | 1.24892 | 0.624458 | − | 0.781058i | \(-0.285320\pi\) | ||||
0.624458 | + | 0.781058i | \(0.285320\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.7846 | −0.862291 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.4558 | −1.05427 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.0454 | 0.909911 | 0.454956 | − | 0.890514i | \(-0.349655\pi\) | ||||
0.454956 | + | 0.890514i | \(0.349655\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.8564 | 0.570943 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.0000 | −1.39621 | −0.698106 | − | 0.715994i | \(-0.745974\pi\) | ||||
−0.698106 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 39.1918 | 1.60671 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.82843 | 0.115566 | 0.0577832 | − | 0.998329i | \(-0.481597\pi\) | ||||
0.0577832 | + | 0.998329i | \(0.481597\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.0000 | −0.978980 | −0.489490 | − | 0.872009i | \(-0.662817\pi\) | ||||
−0.489490 | + | 0.872009i | \(0.662817\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.3205 | 0.704179 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.2548 | −1.83684 | −0.918419 | − | 0.395610i | \(-0.870533\pi\) | ||||
−0.918419 | + | 0.395610i | \(0.870533\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39.1918 | −1.58553 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.3923 | −0.419741 | −0.209871 | − | 0.977729i | \(-0.567304\pi\) | ||||
−0.209871 | + | 0.977729i | \(0.567304\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.0000 | −1.28827 | −0.644136 | − | 0.764911i | \(-0.722783\pi\) | ||||
−0.644136 | + | 0.764911i | \(0.722783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.1464 | 0.689173 | 0.344587 | − | 0.938755i | \(-0.388019\pi\) | ||||
0.344587 | + | 0.938755i | \(0.388019\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.6274 | 0.906548 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.8564 | 0.552491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.7990 | −0.788185 | −0.394093 | − | 0.919071i | \(-0.628941\pi\) | ||||
−0.394093 | + | 0.919071i | \(0.628941\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.5959 | −0.777640 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.46410 | −0.137253 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.00000 | 0.157991 | 0.0789953 | − | 0.996875i | \(-0.474829\pi\) | ||||
0.0789953 | + | 0.996875i | \(0.474829\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.34847 | −0.289795 | −0.144898 | − | 0.989447i | \(-0.546285\pi\) | ||||
−0.144898 | + | 0.989447i | \(0.546285\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.1421 | 0.555985 | 0.277992 | − | 0.960583i | \(-0.410331\pi\) | ||||
0.277992 | + | 0.960583i | \(0.410331\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | −0.235521 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.1769 | −1.22005 | −0.610023 | − | 0.792383i | \(-0.708840\pi\) | ||||
−0.610023 | + | 0.792383i | \(0.708840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.4558 | −0.994642 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.5403 | −1.81295 | −0.906476 | − | 0.422256i | \(-0.861238\pi\) | ||||
−0.906476 | + | 0.422256i | \(0.861238\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.1769 | 1.21264 | 0.606321 | − | 0.795220i | \(-0.292645\pi\) | ||||
0.606321 | + | 0.795220i | \(0.292645\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −24.0000 | −0.930680 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.79796 | 0.379378 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.48528 | −0.327571 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.0000 | −0.770943 | −0.385472 | − | 0.922720i | \(-0.625961\pi\) | ||||
−0.385472 | + | 0.922720i | \(0.625961\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.46410 | 0.133136 | 0.0665681 | − | 0.997782i | \(-0.478795\pi\) | ||||
0.0665681 | + | 0.997782i | \(0.478795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.9411 | 1.30254 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.2474 | −0.468636 | −0.234318 | − | 0.972160i | \(-0.575286\pi\) | ||||
−0.234318 | + | 0.972160i | \(0.575286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.92820 | 0.264713 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 36.0000 | 1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.34847 | 0.279549 | 0.139774 | − | 0.990183i | \(-0.455362\pi\) | ||||
0.139774 | + | 0.990183i | \(0.455362\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −42.4264 | −1.60933 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.00000 | −0.303022 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.0333 | 1.70089 | 0.850443 | − | 0.526068i | \(-0.176334\pi\) | ||||
0.850443 | + | 0.526068i | \(0.176334\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.48528 | −0.320028 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.79796 | 0.368490 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.3923 | 0.390291 | 0.195146 | − | 0.980774i | \(-0.437482\pi\) | ||||
0.195146 | + | 0.980774i | \(0.437482\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.0000 | −0.599205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.3939 | 1.09927 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.5980 | 1.47676 | 0.738378 | − | 0.674387i | \(-0.235592\pi\) | ||||
0.738378 | + | 0.674387i | \(0.235592\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.0000 | −1.48968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.2487 | −0.900575 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.7990 | 0.734304 | 0.367152 | − | 0.930161i | \(-0.380333\pi\) | ||||
0.367152 | + | 0.930161i | \(0.380333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.9898 | −1.81195 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.3205 | 0.639748 | 0.319874 | − | 0.947460i | \(-0.396359\pi\) | ||||
0.319874 | + | 0.947460i | \(0.396359\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.0000 | −0.663039 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.7423 | 1.35159 | 0.675795 | − | 0.737090i | \(-0.263801\pi\) | ||||
0.675795 | + | 0.737090i | \(0.263801\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.4264 | 1.55647 | 0.778237 | − | 0.627971i | \(-0.216114\pi\) | ||||
0.778237 | + | 0.627971i | \(0.216114\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36.0000 | −1.31894 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.92820 | 0.253151 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.2843 | 1.03211 | 0.516054 | − | 0.856556i | \(-0.327400\pi\) | ||||
0.516054 | + | 0.856556i | \(0.327400\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 68.5857 | 2.49609 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.0333 | 1.63676 | 0.818382 | − | 0.574675i | \(-0.194871\pi\) | ||||
0.818382 | + | 0.574675i | \(0.194871\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.0000 | −0.507500 | −0.253750 | − | 0.967270i | \(-0.581664\pi\) | ||||
−0.253750 | + | 0.967270i | \(0.581664\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.3939 | −1.06413 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.48528 | 0.306386 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.0000 | 0.432731 | 0.216366 | − | 0.976312i | \(-0.430580\pi\) | ||||
0.216366 | + | 0.976312i | \(0.430580\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 45.0333 | 1.61974 | 0.809868 | − | 0.586612i | \(-0.199539\pi\) | ||||
0.809868 | + | 0.586612i | \(0.199539\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.5980 | 1.42240 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.89898 | 0.175524 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.92820 | 0.247911 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −84.0000 | −2.99809 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.34847 | 0.261945 | 0.130972 | − | 0.991386i | \(-0.458190\pi\) | ||||
0.130972 | + | 0.991386i | \(0.458190\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.2843 | 1.00567 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0000 | 0.426132 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.0333 | 1.59516 | 0.797581 | − | 0.603212i | \(-0.206113\pi\) | ||||
0.797581 | + | 0.603212i | \(0.206113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.2548 | −1.60100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.5959 | 0.691525 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.7128 | 0.976748 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −46.0000 | −1.61727 | −0.808637 | − | 0.588308i | \(-0.799794\pi\) | ||||
−0.808637 | + | 0.588308i | \(0.799794\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.7423 | 1.29020 | 0.645099 | − | 0.764099i | \(-0.276816\pi\) | ||||
0.645099 | + | 0.764099i | \(0.276816\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −59.3970 | −2.08059 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.0000 | 1.04957 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.46410 | 0.120898 | 0.0604490 | − | 0.998171i | \(-0.480747\pi\) | ||||
0.0604490 | + | 0.998171i | \(0.480747\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.7990 | 0.690149 | 0.345075 | − | 0.938575i | \(-0.387854\pi\) | ||||
0.345075 | + | 0.938575i | \(0.387854\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.34847 | −0.255531 | −0.127766 | − | 0.991804i | \(-0.540781\pi\) | ||||
−0.127766 | + | 0.991804i | \(0.540781\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.3205 | −0.601566 | −0.300783 | − | 0.953693i | \(-0.597248\pi\) | ||||
−0.300783 | + | 0.953693i | \(0.597248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.00000 | −0.138592 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.3939 | −1.01722 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.7696 | −1.26943 | −0.634713 | − | 0.772748i | \(-0.718882\pi\) | ||||
−0.634713 | + | 0.772748i | \(0.718882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.0000 | −0.586207 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.46410 | 0.119169 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.1421 | −0.485930 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.79796 | 0.335870 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.3205 | −0.593043 | −0.296521 | − | 0.955026i | \(-0.595827\pi\) | ||||
−0.296521 | + | 0.955026i | \(0.595827\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.0000 | 0.478231 | 0.239115 | − | 0.970991i | \(-0.423143\pi\) | ||||
0.239115 | + | 0.970991i | \(0.423143\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.1464 | −0.585029 | −0.292514 | − | 0.956261i | \(-0.594492\pi\) | ||||
−0.292514 | + | 0.956261i | \(0.594492\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.9706 | −0.577685 | −0.288842 | − | 0.957377i | \(-0.593270\pi\) | ||||
−0.288842 | + | 0.957377i | \(0.593270\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −60.0000 | −2.04006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.8564 | 0.470046 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.4558 | 0.862538 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.5959 | −0.662463 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.1051 | −1.28672 | −0.643359 | − | 0.765564i | \(-0.722460\pi\) | ||||
−0.643359 | + | 0.765564i | \(0.722460\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.0000 | −0.471672 | −0.235836 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235836 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.44949 | 0.0824319 | 0.0412159 | − | 0.999150i | \(-0.486877\pi\) | ||||
0.0412159 | + | 0.999150i | \(0.486877\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.4558 | 0.854724 | 0.427362 | − | 0.904081i | \(-0.359443\pi\) | ||||
0.427362 | + | 0.904081i | \(0.359443\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000 | 0.536623 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.7128 | 0.927374 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.4264 | −1.41816 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.5959 | −0.653560 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.5692 | 1.38487 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 84.0000 | 2.79225 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.34847 | −0.244002 | −0.122001 | − | 0.992530i | \(-0.538931\pi\) | ||||
−0.122001 | + | 0.992530i | \(0.538931\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | −0.595713 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.7846 | 0.686368 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.7696 | 1.21292 | 0.606458 | − | 0.795116i | \(-0.292590\pi\) | ||||
0.606458 | + | 0.795116i | \(0.292590\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.79796 | −0.322504 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.2487 | −0.797293 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.0000 | −0.918650 | −0.459325 | − | 0.888268i | \(-0.651909\pi\) | ||||
−0.459325 | + | 0.888268i | \(0.651909\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.44949 | 0.0802788 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33.9411 | 1.10999 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.00000 | −0.261349 | −0.130674 | − | 0.991425i | \(-0.541714\pi\) | ||||
−0.130674 | + | 0.991425i | \(0.541714\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.1051 | 1.24219 | 0.621096 | − | 0.783735i | \(-0.286688\pi\) | ||||
0.621096 | + | 0.783735i | \(0.286688\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.65685 | −0.184213 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.6413 | −1.35316 | −0.676581 | − | 0.736369i | \(-0.736539\pi\) | ||||
−0.676581 | + | 0.736369i | \(0.736539\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.7128 | −0.899596 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.0000 | −1.10137 | −0.550684 | − | 0.834714i | \(-0.685633\pi\) | ||||
−0.550684 | + | 0.834714i | \(0.685633\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −58.7878 | −1.90233 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.65685 | −0.182669 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −41.5692 | −1.33816 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.1421 | 0.454780 | 0.227390 | − | 0.973804i | \(-0.426981\pi\) | ||||
0.227390 | + | 0.973804i | \(0.426981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.4393 | −1.65077 | −0.825383 | − | 0.564574i | \(-0.809041\pi\) | ||||
−0.825383 | + | 0.564574i | \(0.809041\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.6410 | 1.11054 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.0000 | 0.895799 | 0.447900 | − | 0.894084i | \(-0.352172\pi\) | ||||
0.447900 | + | 0.894084i | \(0.352172\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.5959 | 0.626288 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.4264 | −1.35319 | −0.676596 | − | 0.736354i | \(-0.736546\pi\) | ||||
−0.676596 | + | 0.736354i | \(0.736546\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0000 | −1.14706 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34.6410 | −1.10152 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.2548 | 1.43757 | 0.718784 | − | 0.695234i | \(-0.244699\pi\) | ||||
0.718784 | + | 0.695234i | \(0.244699\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.79796 | −0.310616 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.3923 | 0.329128 | 0.164564 | − | 0.986366i | \(-0.447378\pi\) | ||||
0.164564 | + | 0.986366i | \(0.447378\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 4608.2.a.w.1.2 | 4 | ||
3.2 | odd | 2 | 512.2.a.g.1.2 | yes | 4 | ||
4.3 | odd | 2 | inner | 4608.2.a.w.1.1 | 4 | ||
8.3 | odd | 2 | inner | 4608.2.a.w.1.3 | 4 | ||
8.5 | even | 2 | inner | 4608.2.a.w.1.4 | 4 | ||
12.11 | even | 2 | 512.2.a.g.1.4 | yes | 4 | ||
16.3 | odd | 4 | 4608.2.d.d.2305.4 | 4 | |||
16.5 | even | 4 | 4608.2.d.d.2305.1 | 4 | |||
16.11 | odd | 4 | 4608.2.d.d.2305.2 | 4 | |||
16.13 | even | 4 | 4608.2.d.d.2305.3 | 4 | |||
24.5 | odd | 2 | 512.2.a.g.1.3 | yes | 4 | ||
24.11 | even | 2 | 512.2.a.g.1.1 | ✓ | 4 | ||
48.5 | odd | 4 | 512.2.b.d.257.4 | 4 | |||
48.11 | even | 4 | 512.2.b.d.257.2 | 4 | |||
48.29 | odd | 4 | 512.2.b.d.257.1 | 4 | |||
48.35 | even | 4 | 512.2.b.d.257.3 | 4 | |||
96.5 | odd | 8 | 1024.2.e.p.769.4 | 8 | |||
96.11 | even | 8 | 1024.2.e.p.769.3 | 8 | |||
96.29 | odd | 8 | 1024.2.e.p.257.1 | 8 | |||
96.35 | even | 8 | 1024.2.e.p.257.3 | 8 | |||
96.53 | odd | 8 | 1024.2.e.p.769.1 | 8 | |||
96.59 | even | 8 | 1024.2.e.p.769.2 | 8 | |||
96.77 | odd | 8 | 1024.2.e.p.257.4 | 8 | |||
96.83 | even | 8 | 1024.2.e.p.257.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
512.2.a.g.1.1 | ✓ | 4 | 24.11 | even | 2 | ||
512.2.a.g.1.2 | yes | 4 | 3.2 | odd | 2 | ||
512.2.a.g.1.3 | yes | 4 | 24.5 | odd | 2 | ||
512.2.a.g.1.4 | yes | 4 | 12.11 | even | 2 | ||
512.2.b.d.257.1 | 4 | 48.29 | odd | 4 | |||
512.2.b.d.257.2 | 4 | 48.11 | even | 4 | |||
512.2.b.d.257.3 | 4 | 48.35 | even | 4 | |||
512.2.b.d.257.4 | 4 | 48.5 | odd | 4 | |||
1024.2.e.p.257.1 | 8 | 96.29 | odd | 8 | |||
1024.2.e.p.257.2 | 8 | 96.83 | even | 8 | |||
1024.2.e.p.257.3 | 8 | 96.35 | even | 8 | |||
1024.2.e.p.257.4 | 8 | 96.77 | odd | 8 | |||
1024.2.e.p.769.1 | 8 | 96.53 | odd | 8 | |||
1024.2.e.p.769.2 | 8 | 96.59 | even | 8 | |||
1024.2.e.p.769.3 | 8 | 96.11 | even | 8 | |||
1024.2.e.p.769.4 | 8 | 96.5 | odd | 8 | |||
4608.2.a.w.1.1 | 4 | 4.3 | odd | 2 | inner | ||
4608.2.a.w.1.2 | 4 | 1.1 | even | 1 | trivial | ||
4608.2.a.w.1.3 | 4 | 8.3 | odd | 2 | inner | ||
4608.2.a.w.1.4 | 4 | 8.5 | even | 2 | inner | ||
4608.2.d.d.2305.1 | 4 | 16.5 | even | 4 | |||
4608.2.d.d.2305.2 | 4 | 16.11 | odd | 4 | |||
4608.2.d.d.2305.3 | 4 | 16.13 | even | 4 | |||
4608.2.d.d.2305.4 | 4 | 16.3 | odd | 4 |