Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 966) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.37228 | 0.613703 | 0.306851 | − | 0.951757i | \(-0.400725\pi\) | ||||
0.306851 | + | 0.951757i | \(0.400725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.37228 | 0.380602 | 0.190301 | − | 0.981726i | \(-0.439054\pi\) | ||||
0.190301 | + | 0.981726i | \(0.439054\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.37228 | 0.354322 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.74456 | −1.15073 | −0.575363 | − | 0.817898i | \(-0.695139\pi\) | ||||
−0.575363 | + | 0.817898i | \(0.695139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.11684 | −0.623369 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.37228 | 1.74039 | 0.870194 | − | 0.492708i | \(-0.163993\pi\) | ||||
0.870194 | + | 0.492708i | \(0.163993\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.74456 | −1.21136 | −0.605680 | − | 0.795709i | \(-0.707099\pi\) | ||||
−0.605680 | + | 0.795709i | \(0.707099\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.37228 | 0.231958 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.62772 | 0.431994 | 0.215997 | − | 0.976394i | \(-0.430700\pi\) | ||||
0.215997 | + | 0.976394i | \(0.430700\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.37228 | 0.219741 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.11684 | −1.26764 | −0.633819 | − | 0.773481i | \(-0.718514\pi\) | ||||
−0.633819 | + | 0.773481i | \(0.718514\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.11684 | −0.932810 | −0.466405 | − | 0.884571i | \(-0.654451\pi\) | ||||
−0.466405 | + | 0.884571i | \(0.654451\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.37228 | 0.204568 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.62772 | −0.675022 | −0.337511 | − | 0.941322i | \(-0.609585\pi\) | ||||
−0.337511 | + | 0.941322i | \(0.609585\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.74456 | −0.664372 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.74456 | 0.651716 | 0.325858 | − | 0.945419i | \(-0.394347\pi\) | ||||
0.325858 | + | 0.945419i | \(0.394347\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.48913 | −0.740154 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.74456 | 0.357312 | 0.178656 | − | 0.983912i | \(-0.442825\pi\) | ||||
0.178656 | + | 0.983912i | \(0.442825\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.88316 | 0.233577 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.7446 | −1.74986 | −0.874929 | − | 0.484252i | \(-0.839092\pi\) | ||||
−0.874929 | + | 0.484252i | \(0.839092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.7446 | −1.49164 | −0.745819 | − | 0.666149i | \(-0.767942\pi\) | ||||
−0.745819 | + | 0.666149i | \(0.767942\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.11684 | −0.359902 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.00000 | −0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4891 | 1.51765 | 0.758823 | − | 0.651297i | \(-0.225775\pi\) | ||||
0.758823 | + | 0.651297i | \(0.225775\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.51087 | −0.706204 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.37228 | 1.00481 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.48913 | 0.793846 | 0.396923 | − | 0.917852i | \(-0.370078\pi\) | ||||
0.396923 | + | 0.917852i | \(0.370078\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.37228 | 0.143854 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.74456 | −0.699379 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.48913 | −0.563172 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.37228 | −0.951611 | −0.475805 | − | 0.879551i | \(-0.657843\pi\) | ||||
−0.475805 | + | 0.879551i | \(0.657843\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.4891 | −1.54123 | −0.770613 | − | 0.637304i | \(-0.780050\pi\) | ||||
−0.770613 | + | 0.637304i | \(0.780050\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.1168 | 0.996842 | 0.498421 | − | 0.866935i | \(-0.333913\pi\) | ||||
0.498421 | + | 0.866935i | \(0.333913\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.37228 | 0.133921 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.11684 | 0.777453 | 0.388726 | − | 0.921353i | \(-0.372915\pi\) | ||||
0.388726 | + | 0.921353i | \(0.372915\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.62772 | 0.249412 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.1168 | −1.51615 | −0.758073 | − | 0.652170i | \(-0.773859\pi\) | ||||
−0.758073 | + | 0.652170i | \(0.773859\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.37228 | 0.127966 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.37228 | 0.126867 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.74456 | −0.434933 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.11684 | −0.731871 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1386 | −0.996266 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.3723 | 1.00913 | 0.504563 | − | 0.863375i | \(-0.331653\pi\) | ||||
0.504563 | + | 0.863375i | \(0.331653\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.11684 | −0.538558 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.7446 | −1.63772 | −0.818860 | − | 0.573993i | \(-0.805394\pi\) | ||||
−0.818860 | + | 0.573993i | \(0.805394\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | −0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.37228 | 0.118107 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.11684 | −0.693469 | −0.346734 | − | 0.937963i | \(-0.612709\pi\) | ||||
−0.346734 | + | 0.937963i | \(0.612709\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.62772 | −0.731794 | −0.365897 | − | 0.930655i | \(-0.619238\pi\) | ||||
−0.365897 | + | 0.930655i | \(0.619238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.62772 | −0.389724 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.48913 | −0.459024 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.8614 | 1.06808 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.2337 | 1.49376 | 0.746881 | − | 0.664958i | \(-0.231550\pi\) | ||||
0.746881 | + | 0.664958i | \(0.231550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.37228 | 0.274432 | 0.137216 | − | 0.990541i | \(-0.456184\pi\) | ||||
0.137216 | + | 0.990541i | \(0.456184\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.74456 | −0.383575 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.25544 | −0.743415 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.2554 | −0.898282 | −0.449141 | − | 0.893461i | \(-0.648270\pi\) | ||||
−0.449141 | + | 0.893461i | \(0.648270\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.74456 | 0.376268 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.48913 | −0.427328 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.48913 | 0.424761 | 0.212381 | − | 0.977187i | \(-0.431878\pi\) | ||||
0.212381 | + | 0.977187i | \(0.431878\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1168 | −0.855142 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.48913 | −0.569388 | −0.284694 | − | 0.958618i | \(-0.591892\pi\) | ||||
−0.284694 | + | 0.958618i | \(0.591892\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.11684 | −0.235611 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.74456 | 0.206294 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.8614 | 1.55925 | 0.779627 | − | 0.626244i | \(-0.215408\pi\) | ||||
0.779627 | + | 0.626244i | \(0.215408\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.9783 | −1.55930 | −0.779651 | − | 0.626215i | \(-0.784603\pi\) | ||||
−0.779651 | + | 0.626215i | \(0.784603\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.60597 | 0.265116 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.9783 | 1.38783 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.51087 | −0.181681 | −0.0908403 | − | 0.995865i | \(-0.528955\pi\) | ||||
−0.0908403 | + | 0.995865i | \(0.528955\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.116844 | −0.00841061 | −0.00420531 | − | 0.999991i | \(-0.501339\pi\) | ||||
−0.00420531 | + | 0.999991i | \(0.501339\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.88316 | 0.134856 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.3723 | −1.52271 | −0.761356 | − | 0.648334i | \(-0.775466\pi\) | ||||
−0.761356 | + | 0.648334i | \(0.775466\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.8614 | 1.19527 | 0.597637 | − | 0.801767i | \(-0.296107\pi\) | ||||
0.597637 | + | 0.801767i | \(0.296107\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.37228 | 0.657805 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.1386 | −0.777953 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.7446 | −1.01028 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.39403 | −0.572468 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.74456 | −0.457851 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.7446 | −0.861198 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.51087 | −0.437969 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.25544 | 0.619790 | 0.309895 | − | 0.950771i | \(-0.399706\pi\) | ||||
0.309895 | + | 0.950771i | \(0.399706\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.11684 | −0.207790 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.11684 | −0.405989 | −0.202995 | − | 0.979180i | \(-0.565067\pi\) | ||||
−0.202995 | + | 0.979180i | \(0.565067\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.744563 | −0.0492021 | −0.0246010 | − | 0.999697i | \(-0.507832\pi\) | ||||
−0.0246010 | + | 0.999697i | \(0.507832\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.00000 | −0.263181 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.4891 | 1.53882 | 0.769412 | − | 0.638753i | \(-0.220549\pi\) | ||||
0.769412 | + | 0.638753i | \(0.220549\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.35053 | −0.414263 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.4891 | 0.876213 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.4891 | −0.872539 | −0.436269 | − | 0.899816i | \(-0.643701\pi\) | ||||
−0.436269 | + | 0.899816i | \(0.643701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.62772 | −0.169266 | −0.0846331 | − | 0.996412i | \(-0.526972\pi\) | ||||
−0.0846331 | + | 0.996412i | \(0.526972\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.37228 | 0.0876718 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.48913 | −0.349265 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.88316 | 0.118864 | 0.0594319 | − | 0.998232i | \(-0.481071\pi\) | ||||
0.0594319 | + | 0.998232i | \(0.481071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.51087 | −0.407727 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.9783 | 1.80761 | 0.903807 | − | 0.427941i | \(-0.140761\pi\) | ||||
0.903807 | + | 0.427941i | \(0.140761\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.62772 | 0.163278 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.37228 | 0.580130 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.1168 | −0.623831 | −0.311916 | − | 0.950110i | \(-0.600971\pi\) | ||||
−0.311916 | + | 0.950110i | \(0.600971\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.51087 | 0.399960 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.48913 | 0.458327 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.9783 | −1.27907 | −0.639533 | − | 0.768763i | \(-0.720872\pi\) | ||||
−0.639533 | + | 0.768763i | \(0.720872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.9783 | 1.63881 | 0.819406 | − | 0.573214i | \(-0.194303\pi\) | ||||
0.819406 | + | 0.573214i | \(0.194303\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.37228 | 0.0830542 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.4674 | 0.751811 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.7446 | 1.72709 | 0.863547 | − | 0.504269i | \(-0.168238\pi\) | ||||
0.863547 | + | 0.504269i | \(0.168238\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.74456 | −0.403786 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.3723 | −1.03634 | −0.518172 | − | 0.855277i | \(-0.673387\pi\) | ||||
−0.518172 | + | 0.855277i | \(0.673387\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.2554 | 0.787954 | 0.393977 | − | 0.919120i | \(-0.371099\pi\) | ||||
0.393977 | + | 0.919120i | \(0.371099\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.48913 | −0.325148 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.11684 | −0.479122 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.51087 | 0.324169 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.37228 | −0.549413 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.0000 | −0.584206 | −0.292103 | − | 0.956387i | \(-0.594355\pi\) | ||||
−0.292103 | + | 0.956387i | \(0.594355\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.76631 | 0.219283 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.00000 | −0.232104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.37228 | 0.0793611 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.11684 | −0.352569 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.4891 | −0.889827 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.74456 | −0.157153 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.37228 | −0.420758 | −0.210379 | − | 0.977620i | \(-0.567470\pi\) | ||||
−0.210379 | + | 0.977620i | \(0.567470\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.1168 | 0.575527 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.48913 | −0.311260 | −0.155630 | − | 0.987815i | \(-0.549741\pi\) | ||||
−0.155630 | + | 0.987815i | \(0.549741\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.37228 | 0.0773193 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.1168 | 0.905212 | 0.452606 | − | 0.891711i | \(-0.350494\pi\) | ||||
0.452606 | + | 0.891711i | \(0.350494\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.4891 | −2.09899 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.9783 | 1.05598 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.27719 | −0.237256 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.11684 | 0.448862 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.62772 | −0.255134 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.48913 | −0.521569 | −0.260785 | − | 0.965397i | \(-0.583981\pi\) | ||||
−0.260785 | + | 0.965397i | \(0.583981\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.62772 | 0.143998 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.48913 | 0.299903 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.2337 | 1.21115 | 0.605573 | − | 0.795790i | \(-0.292944\pi\) | ||||
0.605573 | + | 0.795790i | \(0.292944\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.1168 | −0.875347 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.9783 | 1.46095 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.37228 | 0.0738811 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.6277 | −0.892623 | −0.446311 | − | 0.894878i | \(-0.647263\pi\) | ||||
−0.446311 | + | 0.894878i | \(0.647263\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.4891 | 1.89969 | 0.949845 | − | 0.312722i | \(-0.101241\pi\) | ||||
0.949845 | + | 0.312722i | \(0.101241\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.37228 | 0.0732470 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 36.1168 | 1.92231 | 0.961153 | − | 0.276017i | \(-0.0890145\pi\) | ||||
0.961153 | + | 0.276017i | \(0.0890145\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.2337 | −1.07389 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.74456 | −0.251109 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.3723 | −1.02243 | −0.511215 | − | 0.859453i | \(-0.670804\pi\) | ||||
−0.511215 | + | 0.859453i | \(0.670804\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.4891 | −0.915423 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.3723 | 0.593628 | 0.296814 | − | 0.954935i | \(-0.404076\pi\) | ||||
0.296814 | + | 0.954935i | \(0.404076\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.11684 | −0.422546 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.74456 | 0.246325 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.4891 | −1.63045 | −0.815223 | − | 0.579148i | \(-0.803385\pi\) | ||||
−0.815223 | + | 0.579148i | \(0.803385\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.1386 | −0.575194 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.8614 | 0.662396 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.3723 | −0.789621 | −0.394811 | − | 0.918763i | \(-0.629190\pi\) | ||||
−0.394811 | + | 0.918763i | \(0.629190\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.3723 | 0.582620 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.0000 | −0.817562 | −0.408781 | − | 0.912633i | \(-0.634046\pi\) | ||||
−0.408781 | + | 0.912633i | \(0.634046\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.48913 | −0.279752 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.11684 | −0.310937 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.4891 | 0.582522 | 0.291261 | − | 0.956644i | \(-0.405925\pi\) | ||||
0.291261 | + | 0.956644i | \(0.405925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.74456 | −0.239943 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.7446 | −0.945538 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.5109 | 0.931383 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.0000 | −0.501886 | −0.250943 | − | 0.968002i | \(-0.580741\pi\) | ||||
−0.250943 | + | 0.968002i | \(0.580741\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.00000 | −0.200250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.9783 | −1.24735 | −0.623677 | − | 0.781682i | \(-0.714362\pi\) | ||||
−0.623677 | + | 0.781682i | \(0.714362\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.25544 | −0.461046 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.37228 | 0.0681892 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.5109 | −0.521005 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.744563 | 0.0368163 | 0.0184081 | − | 0.999831i | \(-0.494140\pi\) | ||||
0.0184081 | + | 0.999831i | \(0.494140\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.11684 | −0.400374 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.74456 | 0.135051 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.48913 | −0.269451 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.62772 | −0.422501 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.00000 | −0.195413 | −0.0977064 | − | 0.995215i | \(-0.531151\pi\) | ||||
−0.0977064 | + | 0.995215i | \(0.531151\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.8614 | −1.30914 | −0.654572 | − | 0.755999i | \(-0.727151\pi\) | ||||
−0.654572 | + | 0.755999i | \(0.727151\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.62772 | −0.225007 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.7881 | 0.717326 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.48913 | −0.265017 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.86141 | 0.426839 | 0.213419 | − | 0.976961i | \(-0.431540\pi\) | ||||
0.213419 | + | 0.976961i | \(0.431540\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.8614 | 0.521966 | 0.260983 | − | 0.965343i | \(-0.415953\pi\) | ||||
0.260983 | + | 0.965343i | \(0.415953\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.8614 | 0.616657 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.00000 | −0.191346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.7446 | −1.46736 | −0.733679 | − | 0.679496i | \(-0.762198\pi\) | ||||
−0.733679 | + | 0.679496i | \(0.762198\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.62772 | 0.409915 | 0.204958 | − | 0.978771i | \(-0.434294\pi\) | ||||
0.204958 | + | 0.978771i | \(0.434294\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.2772 | 0.487185 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.2337 | 0.862424 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.9783 | 1.36757 | 0.683784 | − | 0.729684i | \(-0.260333\pi\) | ||||
0.683784 | + | 0.729684i | \(0.260333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.4674 | 1.52883 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.37228 | 0.158444 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.88316 | 0.0882837 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.2337 | −0.478712 | −0.239356 | − | 0.970932i | \(-0.576936\pi\) | ||||
−0.239356 | + | 0.970932i | \(0.576936\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.74456 | −0.221457 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.5109 | −0.582690 | −0.291345 | − | 0.956618i | \(-0.594103\pi\) | ||||
−0.291345 | + | 0.956618i | \(0.594103\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.11684 | 0.0983781 | 0.0491890 | − | 0.998789i | \(-0.484336\pi\) | ||||
0.0491890 | + | 0.998789i | \(0.484336\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.25544 | −0.429211 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.8614 | −1.33555 | −0.667773 | − | 0.744365i | \(-0.732752\pi\) | ||||
−0.667773 | + | 0.744365i | \(0.732752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.2554 | −0.518623 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.4674 | 1.12501 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.4674 | 0.572042 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.74456 | 0.217239 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.74456 | 0.308167 | 0.154083 | − | 0.988058i | \(-0.450758\pi\) | ||||
0.154083 | + | 0.988058i | \(0.450758\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.60597 | 0.164418 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.8614 | −0.584006 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.88316 | −0.266591 | −0.133296 | − | 0.991076i | \(-0.542556\pi\) | ||||
−0.133296 | + | 0.991076i | \(0.542556\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.9783 | 1.39803 | 0.699014 | − | 0.715108i | \(-0.253622\pi\) | ||||
0.699014 | + | 0.715108i | \(0.253622\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.4674 | −2.00271 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.48913 | −0.246718 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.7446 | −0.661384 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.7228 | −0.972447 | −0.486223 | − | 0.873835i | \(-0.661626\pi\) | ||||
−0.486223 | + | 0.873835i | \(0.661626\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.48913 | 0.245236 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.25544 | 0.0559772 | 0.0279886 | − | 0.999608i | \(-0.491090\pi\) | ||||
0.0279886 | + | 0.999608i | \(0.491090\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.2554 | −0.945855 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.1168 | −0.493716 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.2337 | 1.16279 | 0.581394 | − | 0.813622i | \(-0.302508\pi\) | ||||
0.581394 | + | 0.813622i | \(0.302508\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.7446 | −0.563786 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.00000 | −0.176604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.8832 | 0.611765 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.5109 | 0.814107 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.48913 | −0.328736 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.0000 | −0.963837 | −0.481919 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481919 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.2337 | 1.75930 | 0.879648 | − | 0.475625i | \(-0.157778\pi\) | ||||
0.879648 | + | 0.475625i | \(0.157778\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.11684 | −0.136030 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.0000 | 1.39394 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.74456 | 0.119104 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.1386 | −0.482466 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.48913 | −0.237316 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.8614 | 0.900236 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.00000 | −0.172292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.2337 | 0.783927 | 0.391964 | − | 0.919981i | \(-0.371796\pi\) | ||||
0.391964 | + | 0.919981i | \(0.371796\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.9783 | −0.900263 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.1386 | 0.477125 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.2554 | 0.908817 | 0.454408 | − | 0.890793i | \(-0.349851\pi\) | ||||
0.454408 | + | 0.890793i | \(0.349851\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −37.4891 | −1.59709 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.4891 | 0.573616 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.60597 | 0.153065 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.2337 | −0.603101 | −0.301550 | − | 0.953450i | \(-0.597504\pi\) | ||||
−0.301550 | + | 0.953450i | \(0.597504\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.39403 | −0.355030 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.9783 | 0.801262 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.6277 | −1.03793 | −0.518967 | − | 0.854794i | \(-0.673683\pi\) | ||||
−0.518967 | + | 0.854794i | \(0.673683\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.1168 | −0.930463 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.8832 | −0.833545 | −0.416773 | − | 0.909011i | \(-0.636839\pi\) | ||||
−0.416773 | + | 0.909011i | \(0.636839\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.9783 | 0.961610 | 0.480805 | − | 0.876828i | \(-0.340345\pi\) | ||||
0.480805 | + | 0.876828i | \(0.340345\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.51087 | −0.104893 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.11684 | −0.129981 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.4674 | 1.76794 | 0.883970 | − | 0.467544i | \(-0.154861\pi\) | ||||
0.883970 | + | 0.467544i | \(0.154861\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.116844 | −0.00485587 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.00000 | −0.165948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.9783 | −0.785999 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.88316 | 0.0778589 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.51087 | −0.268733 | −0.134366 | − | 0.990932i | \(-0.542900\pi\) | ||||
−0.134366 | + | 0.990932i | \(0.542900\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.9783 | 1.11162 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.3723 | −0.879138 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.62772 | −0.107907 | −0.0539537 | − | 0.998543i | \(-0.517182\pi\) | ||||
−0.0539537 | + | 0.998543i | \(0.517182\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.51087 | −0.266920 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.8614 | 0.690091 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 48.4674 | 1.98032 | 0.990162 | − | 0.139928i | \(-0.0446872\pi\) | ||||
0.990162 | + | 0.139928i | \(0.0446872\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.2337 | 1.23326 | 0.616629 | − | 0.787254i | \(-0.288498\pi\) | ||||
0.616629 | + | 0.787254i | \(0.288498\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000 | 0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.86141 | 0.278956 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.7446 | −0.923173 | −0.461587 | − | 0.887095i | \(-0.652720\pi\) | ||||
−0.461587 | + | 0.887095i | \(0.652720\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.37228 | 0.379784 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.35053 | −0.256915 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.8832 | 1.12619 | 0.563095 | − | 0.826392i | \(-0.309610\pi\) | ||||
0.563095 | + | 0.826392i | \(0.309610\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.1386 | −0.449151 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.4891 | −1.42874 | −0.714369 | − | 0.699769i | \(-0.753286\pi\) | ||||
−0.714369 | + | 0.699769i | \(0.753286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.7446 | −1.39650 | −0.698251 | − | 0.715853i | \(-0.746038\pi\) | ||||
−0.698251 | + | 0.715853i | \(0.746038\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.48913 | 0.300045 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.298936 | 0.0119574 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.0000 | 0.638978 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.4674 | −0.497107 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.9783 | 1.39246 | 0.696231 | − | 0.717818i | \(-0.254859\pi\) | ||||
0.696231 | + | 0.717818i | \(0.254859\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.0000 | 0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.6060 | 0.619304 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.37228 | 0.0543718 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.7446 | −0.583286 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.3505 | −0.803798 | −0.401899 | − | 0.915684i | \(-0.631650\pi\) | ||||
−0.401899 | + | 0.915684i | \(0.631650\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.76631 | 0.306273 | 0.153137 | − | 0.988205i | \(-0.451063\pi\) | ||||
0.153137 | + | 0.988205i | \(0.451063\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.39403 | −0.330515 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.00000 | 0.314512 | 0.157256 | − | 0.987558i | \(-0.449735\pi\) | ||||
0.157256 | + | 0.987558i | \(0.449735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.9783 | −0.430934 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.74456 | −0.264340 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.0951 | −1.21685 | −0.608423 | − | 0.793613i | \(-0.708197\pi\) | ||||
−0.608423 | + | 0.793613i | \(0.708197\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.7228 | −1.00507 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.7446 | −0.497213 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.9783 | −0.895106 | −0.447553 | − | 0.894258i | \(-0.647704\pi\) | ||||
−0.447553 | + | 0.894258i | \(0.647704\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.48913 | 0.135711 | 0.0678556 | − | 0.997695i | \(-0.478384\pi\) | ||||
0.0678556 | + | 0.997695i | \(0.478384\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.51087 | −0.252861 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.48913 | −0.212859 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.37228 | 0.362896 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.25544 | 0.357836 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.00000 | 0.308837 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.6060 | −0.524472 | −0.262236 | − | 0.965004i | \(-0.584460\pi\) | ||||
−0.262236 | + | 0.965004i | \(0.584460\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.11684 | −0.119967 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.9783 | 1.26746 | 0.633729 | − | 0.773555i | \(-0.281524\pi\) | ||||
0.633729 | + | 0.773555i | \(0.281524\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.37228 | −0.359675 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.11684 | −0.234398 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.1386 | −0.425584 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.744563 | −0.0284068 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.51087 | 0.248045 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.8397 | −1.21124 | −0.605619 | − | 0.795755i | \(-0.707074\pi\) | ||||
−0.605619 | + | 0.795755i | \(0.707074\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.00000 | −0.151947 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.8397 | −0.449104 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.5109 | 1.45870 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.4891 | 0.888440 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.76631 | −0.217791 | −0.108895 | − | 0.994053i | \(-0.534731\pi\) | ||||
−0.108895 | + | 0.994053i | \(0.534731\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.5109 | −0.396425 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.35053 | −0.239175 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.4891 | −0.582529 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.51087 | −0.169409 | −0.0847047 | − | 0.996406i | \(-0.526995\pi\) | ||||
−0.0847047 | + | 0.996406i | \(0.526995\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.4891 | 0.505882 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.74456 | −0.252586 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.53262 | −0.281704 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.4891 | −0.503761 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.3723 | 0.424115 | 0.212057 | − | 0.977257i | \(-0.431984\pi\) | ||||
0.212057 | + | 0.977257i | \(0.431984\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.1168 | 0.376771 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.62772 | −0.0977259 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −29.2119 | −1.08490 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.5109 | −0.389827 | −0.194913 | − | 0.980820i | \(-0.562443\pi\) | ||||
−0.194913 | + | 0.980820i | \(0.562443\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.0217 | 1.07341 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.2337 | 0.673477 | 0.336738 | − | 0.941598i | \(-0.390676\pi\) | ||||
0.336738 | + | 0.941598i | \(0.390676\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.37228 | 0.0506174 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0000 | −0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.25544 | 0.193324 | 0.0966622 | − | 0.995317i | \(-0.469183\pi\) | ||||
0.0966622 | + | 0.995317i | \(0.469183\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.48913 | −0.201648 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.9565 | −1.68598 | −0.842990 | − | 0.537929i | \(-0.819207\pi\) | ||||
−0.842990 | + | 0.537929i | \(0.819207\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.0217 | 0.916726 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.00000 | −0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.4891 | −0.492225 | −0.246113 | − | 0.969241i | \(-0.579153\pi\) | ||||
−0.246113 | + | 0.969241i | \(0.579153\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.88316 | 0.0686260 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.62772 | 0.168420 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −50.0000 | −1.81728 | −0.908640 | − | 0.417579i | \(-0.862879\pi\) | ||||
−0.908640 | + | 0.417579i | \(0.862879\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.00000 | −0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.97825 | 0.180461 | 0.0902307 | − | 0.995921i | \(-0.471240\pi\) | ||||
0.0902307 | + | 0.995921i | \(0.471240\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.11684 | 0.293849 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.51087 | −0.235401 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.76631 | 0.135994 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.8832 | −1.00549 | −0.502746 | − | 0.864434i | \(-0.667677\pi\) | ||||
−0.502746 | + | 0.864434i | \(0.667677\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.9783 | 1.04363 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −41.6060 | −1.49646 | −0.748231 | − | 0.663438i | \(-0.769097\pi\) | ||||
−0.748231 | + | 0.663438i | \(0.769097\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.0217 | 0.755124 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.62772 | 0.0942689 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.4674 | 1.16326 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 58.9783 | 2.11041 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.37228 | 0.334938 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.4456 | −0.551278 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.51087 | −0.232088 | −0.116044 | − | 0.993244i | \(-0.537021\pi\) | ||||
−0.116044 | + | 0.993244i | \(0.537021\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.1168 | −0.360169 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.1168 | −0.573049 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.74456 | −0.0974623 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.51087 | 0.230917 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.86141 | 0.243043 | 0.121522 | − | 0.992589i | \(-0.461223\pi\) | ||||
0.121522 | + | 0.992589i | \(0.461223\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.9565 | 0.776765 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.48913 | 0.264615 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 50.9783 | 1.79898 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.37228 | 0.0483666 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.9783 | −0.738469 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.7446 | −0.448075 | −0.224037 | − | 0.974581i | \(-0.571924\pi\) | ||||
−0.224037 | + | 0.974581i | \(0.571924\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.6060 | −0.688459 | −0.344229 | − | 0.938886i | \(-0.611860\pi\) | ||||
−0.344229 | + | 0.938886i | \(0.611860\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.9783 | 0.946169 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.48913 | −0.192276 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.4674 | 0.856005 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.37228 | 0.0479514 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.4891 | −0.819776 | −0.409888 | − | 0.912136i | \(-0.634432\pi\) | ||||
−0.409888 | + | 0.912136i | \(0.634432\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.3505 | 1.61568 | 0.807839 | − | 0.589403i | \(-0.200637\pi\) | ||||
0.807839 | + | 0.589403i | \(0.200637\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.4674 | 0.434058 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.2337 | 0.564501 | 0.282250 | − | 0.959341i | \(-0.408919\pi\) | ||||
0.282250 | + | 0.959341i | \(0.408919\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.5109 | 0.851298 | 0.425649 | − | 0.904888i | \(-0.360046\pi\) | ||||
0.425649 | + | 0.904888i | \(0.360046\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.7446 | 0.997138 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.74456 | −0.164389 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.53262 | 0.260677 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.74456 | −0.233126 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.2554 | −1.14811 | −0.574053 | − | 0.818818i | \(-0.694630\pi\) | ||||
−0.574053 | + | 0.818818i | \(0.694630\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.8397 | 2.02895 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.3723 | −0.598333 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.2554 | −0.524803 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.00000 | 0.171802 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.2554 | 0.454925 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.62772 | 0.0900770 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.5842 | 1.38958 | 0.694789 | − | 0.719214i | \(-0.255498\pi\) | ||||
0.694789 | + | 0.719214i | \(0.255498\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.48913 | −0.187724 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.1168 | −0.823816 | −0.411908 | − | 0.911226i | \(-0.635137\pi\) | ||||
−0.411908 | + | 0.911226i | \(0.635137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.1168 | −0.754617 | −0.377308 | − | 0.926088i | \(-0.623150\pi\) | ||||
−0.377308 | + | 0.926088i | \(0.623150\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.11684 | −0.276621 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.4891 | −0.459175 | −0.229588 | − | 0.973288i | \(-0.573738\pi\) | ||||
−0.229588 | + | 0.973288i | \(0.573738\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.2772 | −0.349435 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.51087 | 0.187159 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −53.9565 | −1.83035 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.48913 | 0.185992 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.37228 | −0.317204 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.1386 | −0.376553 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.2337 | −0.750778 | −0.375389 | − | 0.926867i | \(-0.622491\pi\) | ||||
−0.375389 | + | 0.926867i | \(0.622491\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.0000 | −0.337292 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.9783 | −1.38059 | −0.690296 | − | 0.723527i | \(-0.742520\pi\) | ||||
−0.690296 | + | 0.723527i | \(0.742520\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.2554 | 0.715302 | 0.357651 | − | 0.933855i | \(-0.383578\pi\) | ||||
0.357651 | + | 0.933855i | \(0.383578\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.76631 | 0.126603 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.00000 | 0.268614 | 0.134307 | − | 0.990940i | \(-0.457119\pi\) | ||||
0.134307 | + | 0.990940i | \(0.457119\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.3723 | 0.381414 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.00000 | −0.134005 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.5109 | 0.619443 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.6277 | 0.956919 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.37228 | 0.0458191 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −63.2119 | −2.10824 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.5109 | −0.749946 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.11684 | −0.203556 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.7881 | −0.956948 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.0951 | 1.36454 | 0.682270 | − | 0.731100i | \(-0.260993\pi\) | ||||
0.682270 | + | 0.731100i | \(0.260993\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.4891 | −0.513742 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.3288 | −1.63434 | −0.817168 | − | 0.576400i | \(-0.804457\pi\) | ||||
−0.817168 | + | 0.576400i | \(0.804457\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.0000 | 0.529523 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.74456 | −0.0907324 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.7446 | −0.619000 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.9565 | 1.51597 | 0.757983 | − | 0.652275i | \(-0.226185\pi\) | ||||
0.757983 | + | 0.652275i | \(0.226185\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.37228 | −0.242925 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.2337 | −0.666000 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.19019 | −0.269292 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.1168 | 0.332281 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.8832 | 0.521109 | 0.260555 | − | 0.965459i | \(-0.416095\pi\) | ||||
0.260555 | + | 0.965459i | \(0.416095\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00000 | −0.131095 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.48913 | −0.179706 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.0435 | 0.851713 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.3723 | −1.09022 | −0.545112 | − | 0.838363i | \(-0.683513\pi\) | ||||
−0.545112 | + | 0.838363i | \(0.683513\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.00000 | −0.195803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −54.6277 | −1.78081 | −0.890406 | − | 0.455166i | \(-0.849580\pi\) | ||||
−0.890406 | + | 0.455166i | \(0.849580\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.11684 | −0.264321 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.37228 | 0.0446403 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.64947 | 0.183583 | 0.0917915 | − | 0.995778i | \(-0.470741\pi\) | ||||
0.0917915 | + | 0.995778i | \(0.470741\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.4891 | −0.567721 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.1168 | 0.522624 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.4891 | 0.760887 | 0.380444 | − | 0.924804i | \(-0.375771\pi\) | ||||
0.380444 | + | 0.924804i | \(0.375771\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.44563 | −0.111498 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −37.4891 | −1.21185 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.11684 | −0.262107 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.4891 | 0.467391 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.00000 | −0.128898 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.160343 | −0.00516162 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.4891 | 1.72009 | 0.860047 | − | 0.510215i | \(-0.170434\pi\) | ||||
0.860047 | + | 0.510215i | \(0.170434\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.9783 | 0.609669 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.4674 | 0.913562 | 0.456781 | − | 0.889579i | \(-0.349002\pi\) | ||||
0.456781 | + | 0.889579i | \(0.349002\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.62772 | −0.276592 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.27719 | −0.136980 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.35053 | 0.267157 | 0.133579 | − | 0.991038i | \(-0.457353\pi\) | ||||
0.133579 | + | 0.991038i | \(0.457353\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.9565 | −0.957414 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.11684 | 0.259151 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.76631 | 0.120127 | 0.0600633 | − | 0.998195i | \(-0.480870\pi\) | ||||
0.0600633 | + | 0.998195i | \(0.480870\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.3288 | −0.934493 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.62772 | −0.147302 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.11684 | −0.194504 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.4891 | 0.428496 | 0.214248 | − | 0.976779i | \(-0.431270\pi\) | ||||
0.214248 | + | 0.976779i | \(0.431270\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.48913 | −0.301128 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.1386 | 0.733543 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.0000 | −1.58352 | −0.791758 | − | 0.610835i | \(-0.790834\pi\) | ||||
−0.791758 | + | 0.610835i | \(0.790834\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.62772 | 0.0831373 |
(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 | 7728.2.a.bh.1.2 | 2 | ||
4.3 | odd | 2 | 966.2.a.o.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 2898.2.a.x.1.1 | 2 | |||
28.27 | even | 2 | 6762.2.a.cd.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.a.o.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
2898.2.a.x.1.1 | 2 | 12.11 | even | 2 | |||
6762.2.a.cd.1.1 | 2 | 28.27 | even | 2 | |||
7728.2.a.bh.1.2 | 2 | 1.1 | even | 1 | trivial |