Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9450,2,Mod(1,9450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9450, 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("9450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9450.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: | \(75.4586299101\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1890) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.73205 | 0.522233 | 0.261116 | − | 0.965307i | \(-0.415909\pi\) | ||||
0.261116 | + | 0.965307i | \(0.415909\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.46410 | −0.406069 | −0.203034 | − | 0.979172i | \(-0.565080\pi\) | ||||
−0.203034 | + | 0.979172i | \(0.565080\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.26795 | 0.520303 | 0.260152 | − | 0.965568i | \(-0.416227\pi\) | ||||
0.260152 | + | 0.965568i | \(0.416227\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.73205 | −0.369274 | ||||||||
\(23\) | 4.46410 | 0.930830 | 0.465415 | − | 0.885093i | \(-0.345905\pi\) | ||||
0.465415 | + | 0.885093i | \(0.345905\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.46410 | 0.287134 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 5.46410 | 1.01466 | 0.507329 | − | 0.861752i | \(-0.330633\pi\) | ||||
0.507329 | + | 0.861752i | \(0.330633\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.73205 | −0.670296 | −0.335148 | − | 0.942165i | \(-0.608786\pi\) | ||||
−0.335148 | + | 0.942165i | \(0.608786\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.19615 | 1.18304 | 0.591520 | − | 0.806290i | \(-0.298528\pi\) | ||||
0.591520 | + | 0.806290i | \(0.298528\pi\) | |||||||
\(38\) | −2.26795 | −0.367910 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.92820 | −1.55052 | −0.775262 | − | 0.631639i | \(-0.782382\pi\) | ||||
−0.775262 | + | 0.631639i | \(0.782382\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.4641 | −1.74826 | −0.874130 | − | 0.485693i | \(-0.838567\pi\) | ||||
−0.874130 | + | 0.485693i | \(0.838567\pi\) | |||||||
\(44\) | 1.73205 | 0.261116 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.46410 | −0.658196 | ||||||||
\(47\) | −4.53590 | −0.661629 | −0.330814 | − | 0.943696i | \(-0.607323\pi\) | ||||
−0.330814 | + | 0.943696i | \(0.607323\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.46410 | −0.203034 | ||||||||
\(53\) | −13.8564 | −1.90332 | −0.951662 | − | 0.307148i | \(-0.900625\pi\) | ||||
−0.951662 | + | 0.307148i | \(0.900625\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.46410 | −0.717472 | ||||||||
\(59\) | 8.92820 | 1.16235 | 0.581177 | − | 0.813778i | \(-0.302593\pi\) | ||||
0.581177 | + | 0.813778i | \(0.302593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.8564 | 1.77413 | 0.887066 | − | 0.461644i | \(-0.152740\pi\) | ||||
0.887066 | + | 0.461644i | \(0.152740\pi\) | |||||||
\(62\) | 3.73205 | 0.473971 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.39230 | 1.02528 | 0.512642 | − | 0.858603i | \(-0.328667\pi\) | ||||
0.512642 | + | 0.858603i | \(0.328667\pi\) | |||||||
\(68\) | −4.00000 | −0.485071 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.73205 | −0.917626 | −0.458813 | − | 0.888533i | \(-0.651725\pi\) | ||||
−0.458813 | + | 0.888533i | \(0.651725\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.07180 | 0.359527 | 0.179763 | − | 0.983710i | \(-0.442467\pi\) | ||||
0.179763 | + | 0.983710i | \(0.442467\pi\) | |||||||
\(74\) | −7.19615 | −0.836536 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.26795 | 0.260152 | ||||||||
\(77\) | −1.73205 | −0.197386 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.92820 | −0.554466 | −0.277233 | − | 0.960803i | \(-0.589417\pi\) | ||||
−0.277233 | + | 0.960803i | \(0.589417\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.92820 | 1.09639 | ||||||||
\(83\) | −2.53590 | −0.278351 | −0.139176 | − | 0.990268i | \(-0.544445\pi\) | ||||
−0.139176 | + | 0.990268i | \(0.544445\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.4641 | 1.23621 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.73205 | −0.184637 | ||||||||
\(89\) | −1.00000 | −0.106000 | −0.0529999 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0529999 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.46410 | 0.153480 | ||||||||
\(92\) | 4.46410 | 0.465415 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.53590 | 0.467842 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.92820 | 0.703452 | 0.351726 | − | 0.936103i | \(-0.385595\pi\) | ||||
0.351726 | + | 0.936103i | \(0.385595\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.928203 | −0.0923597 | −0.0461798 | − | 0.998933i | \(-0.514705\pi\) | ||||
−0.0461798 | + | 0.998933i | \(0.514705\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.53590 | −0.348402 | −0.174201 | − | 0.984710i | \(-0.555734\pi\) | ||||
−0.174201 | + | 0.984710i | \(0.555734\pi\) | |||||||
\(104\) | 1.46410 | 0.143567 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.8564 | 1.34585 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4641 | 1.38541 | 0.692705 | − | 0.721221i | \(-0.256419\pi\) | ||||
0.692705 | + | 0.721221i | \(0.256419\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −11.4641 | −1.07845 | −0.539226 | − | 0.842161i | \(-0.681283\pi\) | ||||
−0.539226 | + | 0.842161i | \(0.681283\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.46410 | 0.507329 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.92820 | −0.821908 | ||||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | −0.727273 | ||||||||
\(122\) | −13.8564 | −1.25450 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.73205 | −0.335148 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.46410 | −0.129918 | −0.0649590 | − | 0.997888i | \(-0.520692\pi\) | ||||
−0.0649590 | + | 0.997888i | \(0.520692\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.07180 | 0.617866 | 0.308933 | − | 0.951084i | \(-0.400028\pi\) | ||||
0.308933 | + | 0.951084i | \(0.400028\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.26795 | −0.196656 | ||||||||
\(134\) | −8.39230 | −0.724985 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | −6.53590 | −0.558399 | −0.279200 | − | 0.960233i | \(-0.590069\pi\) | ||||
−0.279200 | + | 0.960233i | \(0.590069\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.46410 | 0.633097 | 0.316548 | − | 0.948576i | \(-0.397476\pi\) | ||||
0.316548 | + | 0.948576i | \(0.397476\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.73205 | 0.648859 | ||||||||
\(143\) | −2.53590 | −0.212062 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.07180 | −0.254224 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.19615 | 0.591520 | ||||||||
\(149\) | −0.928203 | −0.0760414 | −0.0380207 | − | 0.999277i | \(-0.512105\pi\) | ||||
−0.0380207 | + | 0.999277i | \(0.512105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3205 | −1.40952 | −0.704761 | − | 0.709444i | \(-0.748946\pi\) | ||||
−0.704761 | + | 0.709444i | \(0.748946\pi\) | |||||||
\(152\) | −2.26795 | −0.183955 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.73205 | 0.139573 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.46410 | 0.755318 | 0.377659 | − | 0.925945i | \(-0.376729\pi\) | ||||
0.377659 | + | 0.925945i | \(0.376729\pi\) | |||||||
\(158\) | 4.92820 | 0.392067 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.46410 | −0.351820 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.46410 | 0.741286 | 0.370643 | − | 0.928775i | \(-0.379137\pi\) | ||||
0.370643 | + | 0.928775i | \(0.379137\pi\) | |||||||
\(164\) | −9.92820 | −0.775262 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.53590 | 0.196824 | ||||||||
\(167\) | 0.928203 | 0.0718265 | 0.0359133 | − | 0.999355i | \(-0.488566\pi\) | ||||
0.0359133 | + | 0.999355i | \(0.488566\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8564 | −0.835108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.4641 | −0.874130 | ||||||||
\(173\) | 6.12436 | 0.465626 | 0.232813 | − | 0.972522i | \(-0.425207\pi\) | ||||
0.232813 | + | 0.972522i | \(0.425207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.73205 | 0.130558 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.00000 | 0.0749532 | ||||||||
\(179\) | −11.4641 | −0.856867 | −0.428434 | − | 0.903573i | \(-0.640934\pi\) | ||||
−0.428434 | + | 0.903573i | \(0.640934\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.8564 | −1.77323 | −0.886616 | − | 0.462506i | \(-0.846951\pi\) | ||||
−0.886616 | + | 0.462506i | \(0.846951\pi\) | |||||||
\(182\) | −1.46410 | −0.108526 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.46410 | −0.329098 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.92820 | −0.506640 | ||||||||
\(188\) | −4.53590 | −0.330814 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.1962 | −1.38898 | −0.694492 | − | 0.719500i | \(-0.744371\pi\) | ||||
−0.694492 | + | 0.719500i | \(0.744371\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.85641 | −0.709480 | −0.354740 | − | 0.934965i | \(-0.615431\pi\) | ||||
−0.354740 | + | 0.934965i | \(0.615431\pi\) | |||||||
\(194\) | −6.92820 | −0.497416 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −12.5359 | −0.893146 | −0.446573 | − | 0.894747i | \(-0.647356\pi\) | ||||
−0.446573 | + | 0.894747i | \(0.647356\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.0526 | 1.77593 | 0.887964 | − | 0.459912i | \(-0.152119\pi\) | ||||
0.887964 | + | 0.459912i | \(0.152119\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.928203 | 0.0653082 | ||||||||
\(203\) | −5.46410 | −0.383505 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.53590 | 0.246358 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.46410 | −0.101517 | ||||||||
\(209\) | 3.92820 | 0.271719 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3923 | 0.715436 | 0.357718 | − | 0.933830i | \(-0.383555\pi\) | ||||
0.357718 | + | 0.933830i | \(0.383555\pi\) | |||||||
\(212\) | −13.8564 | −0.951662 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.00000 | −0.273434 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.73205 | 0.253348 | ||||||||
\(218\) | −14.4641 | −0.979633 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.85641 | 0.393945 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.39230 | 0.227166 | 0.113583 | − | 0.993529i | \(-0.463767\pi\) | ||||
0.113583 | + | 0.993529i | \(0.463767\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.4641 | 0.762581 | ||||||||
\(227\) | −14.7846 | −0.981289 | −0.490645 | − | 0.871360i | \(-0.663239\pi\) | ||||
−0.490645 | + | 0.871360i | \(0.663239\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.92820 | −0.193501 | −0.0967506 | − | 0.995309i | \(-0.530845\pi\) | ||||
−0.0967506 | + | 0.995309i | \(0.530845\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.46410 | −0.358736 | ||||||||
\(233\) | −19.4641 | −1.27514 | −0.637568 | − | 0.770394i | \(-0.720059\pi\) | ||||
−0.637568 | + | 0.770394i | \(0.720059\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.92820 | 0.581177 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.00000 | −0.259281 | ||||||||
\(239\) | 4.53590 | 0.293403 | 0.146701 | − | 0.989181i | \(-0.453134\pi\) | ||||
0.146701 | + | 0.989181i | \(0.453134\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3923 | 0.669427 | 0.334714 | − | 0.942320i | \(-0.391360\pi\) | ||||
0.334714 | + | 0.942320i | \(0.391360\pi\) | |||||||
\(242\) | 8.00000 | 0.514259 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.8564 | 0.887066 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.32051 | −0.211279 | ||||||||
\(248\) | 3.73205 | 0.236985 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.8564 | 1.37956 | 0.689782 | − | 0.724017i | \(-0.257706\pi\) | ||||
0.689782 | + | 0.724017i | \(0.257706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.73205 | 0.486110 | ||||||||
\(254\) | 1.46410 | 0.0918659 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.58846 | 0.223842 | 0.111921 | − | 0.993717i | \(-0.464300\pi\) | ||||
0.111921 | + | 0.993717i | \(0.464300\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.19615 | −0.447147 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.07180 | −0.436897 | ||||||||
\(263\) | −24.4641 | −1.50852 | −0.754261 | − | 0.656575i | \(-0.772004\pi\) | ||||
−0.754261 | + | 0.656575i | \(0.772004\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.26795 | 0.139057 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.39230 | 0.512642 | ||||||||
\(269\) | 16.3205 | 0.995079 | 0.497539 | − | 0.867441i | \(-0.334237\pi\) | ||||
0.497539 | + | 0.867441i | \(0.334237\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.3923 | −0.631288 | −0.315644 | − | 0.948878i | \(-0.602220\pi\) | ||||
−0.315644 | + | 0.948878i | \(0.602220\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.53590 | 0.394848 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.0526 | −1.74560 | −0.872800 | − | 0.488079i | \(-0.837698\pi\) | ||||
−0.872800 | + | 0.488079i | \(0.837698\pi\) | |||||||
\(278\) | −7.46410 | −0.447667 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.3923 | −0.619953 | −0.309976 | − | 0.950744i | \(-0.600321\pi\) | ||||
−0.309976 | + | 0.950744i | \(0.600321\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.9282 | 1.36294 | 0.681470 | − | 0.731846i | \(-0.261341\pi\) | ||||
0.681470 | + | 0.731846i | \(0.261341\pi\) | |||||||
\(284\) | −7.73205 | −0.458813 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.53590 | 0.149951 | ||||||||
\(287\) | 9.92820 | 0.586043 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.07180 | 0.179763 | ||||||||
\(293\) | −18.9282 | −1.10580 | −0.552899 | − | 0.833248i | \(-0.686478\pi\) | ||||
−0.552899 | + | 0.833248i | \(0.686478\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.19615 | −0.418268 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.928203 | 0.0537694 | ||||||||
\(299\) | −6.53590 | −0.377981 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.4641 | 0.660780 | ||||||||
\(302\) | 17.3205 | 0.996683 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.26795 | 0.130076 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0718 | −0.574828 | −0.287414 | − | 0.957806i | \(-0.592796\pi\) | ||||
−0.287414 | + | 0.957806i | \(0.592796\pi\) | |||||||
\(308\) | −1.73205 | −0.0986928 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.3923 | 0.929522 | 0.464761 | − | 0.885436i | \(-0.346140\pi\) | ||||
0.464761 | + | 0.885436i | \(0.346140\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.32051 | 0.187686 | 0.0938431 | − | 0.995587i | \(-0.470085\pi\) | ||||
0.0938431 | + | 0.995587i | \(0.470085\pi\) | |||||||
\(314\) | −9.46410 | −0.534090 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.92820 | −0.277233 | ||||||||
\(317\) | −28.9282 | −1.62477 | −0.812385 | − | 0.583122i | \(-0.801831\pi\) | ||||
−0.812385 | + | 0.583122i | \(0.801831\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.46410 | 0.529888 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.46410 | 0.248775 | ||||||||
\(323\) | −9.07180 | −0.504768 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.46410 | −0.524168 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.92820 | 0.548193 | ||||||||
\(329\) | 4.53590 | 0.250072 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.7846 | 1.58215 | 0.791073 | − | 0.611722i | \(-0.209523\pi\) | ||||
0.791073 | + | 0.611722i | \(0.209523\pi\) | |||||||
\(332\) | −2.53590 | −0.139176 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.928203 | −0.0507890 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.2679 | 0.995119 | 0.497559 | − | 0.867430i | \(-0.334230\pi\) | ||||
0.497559 | + | 0.867430i | \(0.334230\pi\) | |||||||
\(338\) | 10.8564 | 0.590511 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.46410 | −0.350051 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 11.4641 | 0.618103 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.12436 | −0.329247 | ||||||||
\(347\) | 8.07180 | 0.433317 | 0.216658 | − | 0.976247i | \(-0.430484\pi\) | ||||
0.216658 | + | 0.976247i | \(0.430484\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.8564 | 1.70523 | 0.852617 | − | 0.522536i | \(-0.175014\pi\) | ||||
0.852617 | + | 0.522536i | \(0.175014\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.73205 | −0.0923186 | ||||||||
\(353\) | 8.66025 | 0.460939 | 0.230469 | − | 0.973080i | \(-0.425974\pi\) | ||||
0.230469 | + | 0.973080i | \(0.425974\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.00000 | −0.0529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.4641 | 0.605897 | ||||||||
\(359\) | −35.4641 | −1.87172 | −0.935862 | − | 0.352367i | \(-0.885377\pi\) | ||||
−0.935862 | + | 0.352367i | \(0.885377\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.8564 | −0.729285 | ||||||||
\(362\) | 23.8564 | 1.25386 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.46410 | 0.0767398 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.60770 | −0.136121 | −0.0680603 | − | 0.997681i | \(-0.521681\pi\) | ||||
−0.0680603 | + | 0.997681i | \(0.521681\pi\) | |||||||
\(368\) | 4.46410 | 0.232707 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.8564 | 0.719389 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.19615 | 0.165490 | 0.0827452 | − | 0.996571i | \(-0.473631\pi\) | ||||
0.0827452 | + | 0.996571i | \(0.473631\pi\) | |||||||
\(374\) | 6.92820 | 0.358249 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.53590 | 0.233921 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.0000 | −0.719132 | −0.359566 | − | 0.933120i | \(-0.617075\pi\) | ||||
−0.359566 | + | 0.933120i | \(0.617075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 19.1962 | 0.982161 | ||||||||
\(383\) | −24.9282 | −1.27377 | −0.636886 | − | 0.770958i | \(-0.719778\pi\) | ||||
−0.636886 | + | 0.770958i | \(0.719778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.85641 | 0.501678 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.92820 | 0.351726 | ||||||||
\(389\) | 6.92820 | 0.351274 | 0.175637 | − | 0.984455i | \(-0.443802\pi\) | ||||
0.175637 | + | 0.984455i | \(0.443802\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.8564 | −0.903037 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.5359 | 0.631549 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.3923 | −1.32459 | −0.662296 | − | 0.749242i | \(-0.730418\pi\) | ||||
−0.662296 | + | 0.749242i | \(0.730418\pi\) | |||||||
\(398\) | −25.0526 | −1.25577 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.3923 | −1.41784 | −0.708922 | − | 0.705287i | \(-0.750818\pi\) | ||||
−0.708922 | + | 0.705287i | \(0.750818\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.46410 | 0.272186 | ||||||||
\(404\) | −0.928203 | −0.0461798 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.46410 | 0.271179 | ||||||||
\(407\) | 12.4641 | 0.617823 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.67949 | −0.132492 | −0.0662462 | − | 0.997803i | \(-0.521102\pi\) | ||||
−0.0662462 | + | 0.997803i | \(0.521102\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.53590 | −0.174201 | ||||||||
\(413\) | −8.92820 | −0.439328 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.46410 | 0.0717835 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.92820 | −0.192135 | ||||||||
\(419\) | 16.5359 | 0.807831 | 0.403916 | − | 0.914796i | \(-0.367649\pi\) | ||||
0.403916 | + | 0.914796i | \(0.367649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.46410 | −0.120093 | −0.0600465 | − | 0.998196i | \(-0.519125\pi\) | ||||
−0.0600465 | + | 0.998196i | \(0.519125\pi\) | |||||||
\(422\) | −10.3923 | −0.505889 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.8564 | 0.672927 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.8564 | −0.670559 | ||||||||
\(428\) | 4.00000 | 0.193347 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.5167 | −0.988253 | −0.494126 | − | 0.869390i | \(-0.664512\pi\) | ||||
−0.494126 | + | 0.869390i | \(0.664512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.2487 | −0.492522 | −0.246261 | − | 0.969204i | \(-0.579202\pi\) | ||||
−0.246261 | + | 0.969204i | \(0.579202\pi\) | |||||||
\(434\) | −3.73205 | −0.179144 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.4641 | 0.692705 | ||||||||
\(437\) | 10.1244 | 0.484314 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.3923 | −1.83236 | −0.916182 | − | 0.400762i | \(-0.868746\pi\) | ||||
−0.916182 | + | 0.400762i | \(0.868746\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.85641 | −0.278561 | ||||||||
\(443\) | −16.8564 | −0.800872 | −0.400436 | − | 0.916325i | \(-0.631141\pi\) | ||||
−0.400436 | + | 0.916325i | \(0.631141\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.39230 | −0.160630 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.1962 | −0.809735 | ||||||||
\(452\) | −11.4641 | −0.539226 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.7846 | 0.693876 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.5167 | −1.42751 | −0.713755 | − | 0.700396i | \(-0.753007\pi\) | ||||
−0.713755 | + | 0.700396i | \(0.753007\pi\) | |||||||
\(458\) | 2.92820 | 0.136826 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.3923 | −0.716891 | −0.358446 | − | 0.933551i | \(-0.616693\pi\) | ||||
−0.358446 | + | 0.933551i | \(0.616693\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.8564 | 1.29460 | 0.647298 | − | 0.762237i | \(-0.275899\pi\) | ||||
0.647298 | + | 0.762237i | \(0.275899\pi\) | |||||||
\(464\) | 5.46410 | 0.253665 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.4641 | 0.901657 | ||||||||
\(467\) | −28.2487 | −1.30719 | −0.653597 | − | 0.756843i | \(-0.726741\pi\) | ||||
−0.653597 | + | 0.756843i | \(0.726741\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.39230 | −0.387521 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.92820 | −0.410954 | ||||||||
\(473\) | −19.8564 | −0.912999 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.53590 | −0.207467 | ||||||||
\(479\) | −20.7846 | −0.949673 | −0.474837 | − | 0.880074i | \(-0.657493\pi\) | ||||
−0.474837 | + | 0.880074i | \(0.657493\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5359 | −0.480396 | ||||||||
\(482\) | −10.3923 | −0.473357 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.00000 | −0.363636 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.60770 | −0.254109 | −0.127054 | − | 0.991896i | \(-0.540552\pi\) | ||||
−0.127054 | + | 0.991896i | \(0.540552\pi\) | |||||||
\(488\) | −13.8564 | −0.627250 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.4449 | 0.787276 | 0.393638 | − | 0.919266i | \(-0.371216\pi\) | ||||
0.393638 | + | 0.919266i | \(0.371216\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.8564 | −0.984363 | ||||||||
\(494\) | 3.32051 | 0.149397 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.73205 | −0.167574 | ||||||||
\(497\) | 7.73205 | 0.346830 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.9282 | −0.936875 | −0.468438 | − | 0.883497i | \(-0.655183\pi\) | ||||
−0.468438 | + | 0.883497i | \(0.655183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21.8564 | −0.975499 | ||||||||
\(503\) | 12.3923 | 0.552546 | 0.276273 | − | 0.961079i | \(-0.410901\pi\) | ||||
0.276273 | + | 0.961079i | \(0.410901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.73205 | −0.343732 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.46410 | −0.0649590 | ||||||||
\(509\) | 41.7128 | 1.84889 | 0.924444 | − | 0.381318i | \(-0.124530\pi\) | ||||
0.924444 | + | 0.381318i | \(0.124530\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.07180 | −0.135888 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.58846 | −0.158280 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.85641 | −0.345524 | ||||||||
\(518\) | 7.19615 | 0.316181 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.215390 | 0.00943642 | 0.00471821 | − | 0.999989i | \(-0.498498\pi\) | ||||
0.00471821 | + | 0.999989i | \(0.498498\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.9282 | −1.39612 | −0.698061 | − | 0.716038i | \(-0.745954\pi\) | ||||
−0.698061 | + | 0.716038i | \(0.745954\pi\) | |||||||
\(524\) | 7.07180 | 0.308933 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.4641 | 1.06669 | ||||||||
\(527\) | 14.9282 | 0.650283 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.07180 | −0.133556 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.26795 | −0.0983281 | ||||||||
\(533\) | 14.5359 | 0.629620 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.39230 | −0.362492 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.3205 | −0.703627 | ||||||||
\(539\) | 1.73205 | 0.0746047 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.46410 | 0.105940 | 0.0529700 | − | 0.998596i | \(-0.483131\pi\) | ||||
0.0529700 | + | 0.998596i | \(0.483131\pi\) | |||||||
\(542\) | 10.3923 | 0.446388 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.00000 | 0.171499 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | −6.53590 | −0.279200 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.3923 | 0.527930 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.92820 | 0.209569 | ||||||||
\(554\) | 29.0526 | 1.23432 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.46410 | 0.316548 | ||||||||
\(557\) | 26.3923 | 1.11828 | 0.559139 | − | 0.829074i | \(-0.311132\pi\) | ||||
0.559139 | + | 0.829074i | \(0.311132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.7846 | 0.709913 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.3923 | 0.438373 | ||||||||
\(563\) | −3.60770 | −0.152046 | −0.0760231 | − | 0.997106i | \(-0.524222\pi\) | ||||
−0.0760231 | + | 0.997106i | \(0.524222\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −22.9282 | −0.963744 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.73205 | 0.324430 | ||||||||
\(569\) | 21.7128 | 0.910248 | 0.455124 | − | 0.890428i | \(-0.349595\pi\) | ||||
0.455124 | + | 0.890428i | \(0.349595\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.5359 | −1.02680 | −0.513398 | − | 0.858151i | \(-0.671613\pi\) | ||||
−0.513398 | + | 0.858151i | \(0.671613\pi\) | |||||||
\(572\) | −2.53590 | −0.106031 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.92820 | −0.414395 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.32051 | −0.0549735 | −0.0274867 | − | 0.999622i | \(-0.508750\pi\) | ||||
−0.0274867 | + | 0.999622i | \(0.508750\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.53590 | 0.105207 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.0000 | −0.993978 | ||||||||
\(584\) | −3.07180 | −0.127112 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.9282 | 0.781917 | ||||||||
\(587\) | 8.92820 | 0.368506 | 0.184253 | − | 0.982879i | \(-0.441013\pi\) | ||||
0.184253 | + | 0.982879i | \(0.441013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.46410 | −0.348757 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.19615 | 0.295760 | ||||||||
\(593\) | 43.3013 | 1.77817 | 0.889085 | − | 0.457742i | \(-0.151342\pi\) | ||||
0.889085 | + | 0.457742i | \(0.151342\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.928203 | −0.0380207 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.53590 | 0.267273 | ||||||||
\(599\) | 17.8756 | 0.730379 | 0.365190 | − | 0.930933i | \(-0.381004\pi\) | ||||
0.365190 | + | 0.930933i | \(0.381004\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.3923 | −0.831819 | −0.415910 | − | 0.909406i | \(-0.636537\pi\) | ||||
−0.415910 | + | 0.909406i | \(0.636537\pi\) | |||||||
\(602\) | −11.4641 | −0.467242 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.3205 | −0.704761 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.7846 | 0.518911 | 0.259456 | − | 0.965755i | \(-0.416457\pi\) | ||||
0.259456 | + | 0.965755i | \(0.416457\pi\) | |||||||
\(608\) | −2.26795 | −0.0919775 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.64102 | 0.268667 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 49.0526 | 1.98121 | 0.990607 | − | 0.136739i | \(-0.0436622\pi\) | ||||
0.990607 | + | 0.136739i | \(0.0436622\pi\) | |||||||
\(614\) | 10.0718 | 0.406465 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.73205 | 0.0697863 | ||||||||
\(617\) | −8.92820 | −0.359436 | −0.179718 | − | 0.983718i | \(-0.557519\pi\) | ||||
−0.179718 | + | 0.983718i | \(0.557519\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.6603 | −1.15195 | −0.575976 | − | 0.817466i | \(-0.695378\pi\) | ||||
−0.575976 | + | 0.817466i | \(0.695378\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16.3923 | −0.657272 | ||||||||
\(623\) | 1.00000 | 0.0400642 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.32051 | −0.132714 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.46410 | 0.377659 | ||||||||
\(629\) | −28.7846 | −1.14772 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.8564 | 0.790471 | 0.395236 | − | 0.918580i | \(-0.370663\pi\) | ||||
0.395236 | + | 0.918580i | \(0.370663\pi\) | |||||||
\(632\) | 4.92820 | 0.196033 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28.9282 | 1.14889 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.46410 | −0.0580098 | ||||||||
\(638\) | −9.46410 | −0.374687 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.9282 | 0.668624 | 0.334312 | − | 0.942462i | \(-0.391496\pi\) | ||||
0.334312 | + | 0.942462i | \(0.391496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.9282 | 1.18025 | 0.590127 | − | 0.807311i | \(-0.299078\pi\) | ||||
0.590127 | + | 0.807311i | \(0.299078\pi\) | |||||||
\(644\) | −4.46410 | −0.175910 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.07180 | 0.356925 | ||||||||
\(647\) | −27.4641 | −1.07973 | −0.539863 | − | 0.841753i | \(-0.681524\pi\) | ||||
−0.539863 | + | 0.841753i | \(0.681524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.4641 | 0.607019 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.46410 | 0.370643 | ||||||||
\(653\) | −19.8564 | −0.777041 | −0.388521 | − | 0.921440i | \(-0.627014\pi\) | ||||
−0.388521 | + | 0.921440i | \(0.627014\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.92820 | −0.387631 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.53590 | −0.176828 | ||||||||
\(659\) | −22.5167 | −0.877125 | −0.438562 | − | 0.898701i | \(-0.644512\pi\) | ||||
−0.438562 | + | 0.898701i | \(0.644512\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.2487 | −1.02096 | −0.510478 | − | 0.859891i | \(-0.670532\pi\) | ||||
−0.510478 | + | 0.859891i | \(0.670532\pi\) | |||||||
\(662\) | −28.7846 | −1.11875 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.53590 | 0.0984119 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.3923 | 0.944474 | ||||||||
\(668\) | 0.928203 | 0.0359133 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.8564 | 0.688314 | 0.344157 | − | 0.938912i | \(-0.388165\pi\) | ||||
0.344157 | + | 0.938912i | \(0.388165\pi\) | |||||||
\(674\) | −18.2679 | −0.703655 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.8564 | −0.417554 | ||||||||
\(677\) | −18.9090 | −0.726731 | −0.363365 | − | 0.931647i | \(-0.618372\pi\) | ||||
−0.363365 | + | 0.931647i | \(0.618372\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.92820 | −0.265880 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.46410 | 0.247523 | ||||||||
\(683\) | 6.85641 | 0.262353 | 0.131177 | − | 0.991359i | \(-0.458125\pi\) | ||||
0.131177 | + | 0.991359i | \(0.458125\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11.4641 | −0.437065 | ||||||||
\(689\) | 20.2872 | 0.772880 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.2487 | −1.22680 | −0.613399 | − | 0.789773i | \(-0.710198\pi\) | ||||
−0.613399 | + | 0.789773i | \(0.710198\pi\) | |||||||
\(692\) | 6.12436 | 0.232813 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.07180 | −0.306401 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.7128 | 1.50423 | ||||||||
\(698\) | −31.8564 | −1.20578 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.39230 | −0.316973 | −0.158486 | − | 0.987361i | \(-0.550661\pi\) | ||||
−0.158486 | + | 0.987361i | \(0.550661\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.3205 | 0.615540 | ||||||||
\(704\) | 1.73205 | 0.0652791 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.66025 | −0.325933 | ||||||||
\(707\) | 0.928203 | 0.0349087 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.4641 | −0.468099 | −0.234050 | − | 0.972225i | \(-0.575198\pi\) | ||||
−0.234050 | + | 0.972225i | \(0.575198\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.00000 | 0.0374766 | ||||||||
\(713\) | −16.6603 | −0.623931 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.4641 | −0.428434 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 35.4641 | 1.32351 | ||||||||
\(719\) | −20.1436 | −0.751229 | −0.375615 | − | 0.926776i | \(-0.622568\pi\) | ||||
−0.375615 | + | 0.926776i | \(0.622568\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.53590 | 0.131684 | ||||||||
\(722\) | 13.8564 | 0.515682 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23.8564 | −0.886616 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.21539 | −0.267604 | −0.133802 | − | 0.991008i | \(-0.542719\pi\) | ||||
−0.133802 | + | 0.991008i | \(0.542719\pi\) | |||||||
\(728\) | −1.46410 | −0.0542632 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.8564 | 1.69606 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.143594 | −0.00530375 | −0.00265187 | − | 0.999996i | \(-0.500844\pi\) | ||||
−0.00265187 | + | 0.999996i | \(0.500844\pi\) | |||||||
\(734\) | 2.60770 | 0.0962518 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.46410 | −0.164549 | ||||||||
\(737\) | 14.5359 | 0.535437 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.4641 | −1.74600 | −0.872998 | − | 0.487725i | \(-0.837827\pi\) | ||||
−0.872998 | + | 0.487725i | \(0.837827\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.8564 | −0.508685 | ||||||||
\(743\) | −43.3923 | −1.59191 | −0.795955 | − | 0.605356i | \(-0.793031\pi\) | ||||
−0.795955 | + | 0.605356i | \(0.793031\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.19615 | −0.117019 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.92820 | −0.253320 | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.8564 | 0.432646 | 0.216323 | − | 0.976322i | \(-0.430594\pi\) | ||||
0.216323 | + | 0.976322i | \(0.430594\pi\) | |||||||
\(752\) | −4.53590 | −0.165407 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.8564 | 0.503620 | 0.251810 | − | 0.967777i | \(-0.418974\pi\) | ||||
0.251810 | + | 0.967777i | \(0.418974\pi\) | |||||||
\(758\) | 14.0000 | 0.508503 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.71281 | −0.207089 | −0.103545 | − | 0.994625i | \(-0.533018\pi\) | ||||
−0.103545 | + | 0.994625i | \(0.533018\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.4641 | −0.523636 | ||||||||
\(764\) | −19.1962 | −0.694492 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.9282 | 0.900693 | ||||||||
\(767\) | −13.0718 | −0.471995 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.9615 | 1.80166 | 0.900829 | − | 0.434173i | \(-0.142959\pi\) | ||||
0.900829 | + | 0.434173i | \(0.142959\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.85641 | −0.354740 | ||||||||
\(773\) | −42.3731 | −1.52405 | −0.762027 | − | 0.647546i | \(-0.775795\pi\) | ||||
−0.762027 | + | 0.647546i | \(0.775795\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.92820 | −0.248708 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.92820 | −0.248388 | ||||||||
\(779\) | −22.5167 | −0.806743 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.3923 | −0.479214 | ||||||||
\(782\) | 17.8564 | 0.638544 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.8564 | −0.493928 | −0.246964 | − | 0.969025i | \(-0.579433\pi\) | ||||
−0.246964 | + | 0.969025i | \(0.579433\pi\) | |||||||
\(788\) | −12.5359 | −0.446573 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.4641 | 0.407617 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.2872 | −0.720419 | ||||||||
\(794\) | 26.3923 | 0.936628 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25.0526 | 0.887964 | ||||||||
\(797\) | 24.5167 | 0.868425 | 0.434212 | − | 0.900811i | \(-0.357027\pi\) | ||||
0.434212 | + | 0.900811i | \(0.357027\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.1436 | 0.641874 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.3923 | 1.00257 | ||||||||
\(803\) | 5.32051 | 0.187757 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.46410 | −0.192465 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.928203 | 0.0326541 | ||||||||
\(809\) | −22.5359 | −0.792320 | −0.396160 | − | 0.918181i | \(-0.629657\pi\) | ||||
−0.396160 | + | 0.918181i | \(0.629657\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.7321 | −1.32495 | −0.662476 | − | 0.749083i | \(-0.730494\pi\) | ||||
−0.662476 | + | 0.749083i | \(0.730494\pi\) | |||||||
\(812\) | −5.46410 | −0.191752 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12.4641 | −0.436867 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.0000 | −0.909625 | ||||||||
\(818\) | 2.67949 | 0.0936862 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −53.3205 | −1.86090 | −0.930449 | − | 0.366421i | \(-0.880583\pi\) | ||||
−0.930449 | + | 0.366421i | \(0.880583\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −54.4974 | −1.89966 | −0.949830 | − | 0.312766i | \(-0.898745\pi\) | ||||
−0.949830 | + | 0.312766i | \(0.898745\pi\) | |||||||
\(824\) | 3.53590 | 0.123179 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.92820 | 0.310652 | ||||||||
\(827\) | −6.85641 | −0.238421 | −0.119210 | − | 0.992869i | \(-0.538036\pi\) | ||||
−0.119210 | + | 0.992869i | \(0.538036\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.5359 | 1.26894 | 0.634472 | − | 0.772946i | \(-0.281218\pi\) | ||||
0.634472 | + | 0.772946i | \(0.281218\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.46410 | −0.0507586 | ||||||||
\(833\) | −4.00000 | −0.138592 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.92820 | 0.135860 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.5359 | −0.571223 | ||||||||
\(839\) | 17.4641 | 0.602928 | 0.301464 | − | 0.953478i | \(-0.402525\pi\) | ||||
0.301464 | + | 0.953478i | \(0.402525\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.856406 | 0.0295313 | ||||||||
\(842\) | 2.46410 | 0.0849185 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.3923 | 0.357718 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.00000 | 0.274883 | ||||||||
\(848\) | −13.8564 | −0.475831 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.1244 | 1.10121 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −56.4974 | −1.93443 | −0.967217 | − | 0.253950i | \(-0.918270\pi\) | ||||
−0.967217 | + | 0.253950i | \(0.918270\pi\) | |||||||
\(854\) | 13.8564 | 0.474156 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | 2.26795 | 0.0774717 | 0.0387358 | − | 0.999249i | \(-0.487667\pi\) | ||||
0.0387358 | + | 0.999249i | \(0.487667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.1244 | −0.823112 | −0.411556 | − | 0.911384i | \(-0.635015\pi\) | ||||
−0.411556 | + | 0.911384i | \(0.635015\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.5167 | 0.698800 | ||||||||
\(863\) | −7.21539 | −0.245615 | −0.122807 | − | 0.992431i | \(-0.539190\pi\) | ||||
−0.122807 | + | 0.992431i | \(0.539190\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.2487 | 0.348265 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.73205 | 0.126674 | ||||||||
\(869\) | −8.53590 | −0.289561 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.2872 | −0.416335 | ||||||||
\(872\) | −14.4641 | −0.489816 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.1244 | −0.342461 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.7846 | 1.37720 | 0.688599 | − | 0.725142i | \(-0.258226\pi\) | ||||
0.688599 | + | 0.725142i | \(0.258226\pi\) | |||||||
\(878\) | 38.3923 | 1.29568 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.1436 | −0.847109 | −0.423555 | − | 0.905871i | \(-0.639218\pi\) | ||||
−0.423555 | + | 0.905871i | \(0.639218\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.0718 | 1.24757 | 0.623783 | − | 0.781598i | \(-0.285595\pi\) | ||||
0.623783 | + | 0.781598i | \(0.285595\pi\) | |||||||
\(884\) | 5.85641 | 0.196972 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.8564 | 0.566302 | ||||||||
\(887\) | −37.1769 | −1.24828 | −0.624139 | − | 0.781313i | \(-0.714550\pi\) | ||||
−0.624139 | + | 0.781313i | \(0.714550\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.46410 | 0.0491044 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.39230 | 0.113583 | ||||||||
\(893\) | −10.2872 | −0.344248 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.0000 | 0.333704 | ||||||||
\(899\) | −20.3923 | −0.680121 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 55.4256 | 1.84650 | ||||||||
\(902\) | 17.1962 | 0.572569 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.4641 | 0.381290 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.9282 | −1.49182 | −0.745908 | − | 0.666049i | \(-0.767984\pi\) | ||||
−0.745908 | + | 0.666049i | \(0.767984\pi\) | |||||||
\(908\) | −14.7846 | −0.490645 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.2487 | −0.538344 | −0.269172 | − | 0.963092i | \(-0.586750\pi\) | ||||
−0.269172 | + | 0.963092i | \(0.586750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.39230 | −0.145364 | ||||||||
\(914\) | 30.5167 | 1.00940 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.92820 | −0.0967506 | ||||||||
\(917\) | −7.07180 | −0.233531 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.8564 | −1.38072 | −0.690358 | − | 0.723468i | \(-0.742547\pi\) | ||||
−0.690358 | + | 0.723468i | \(0.742547\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.3923 | 0.506919 | ||||||||
\(923\) | 11.3205 | 0.372619 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −27.8564 | −0.915418 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.46410 | −0.179368 | ||||||||
\(929\) | −43.8564 | −1.43888 | −0.719441 | − | 0.694554i | \(-0.755602\pi\) | ||||
−0.719441 | + | 0.694554i | \(0.755602\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.26795 | 0.0743290 | ||||||||
\(932\) | −19.4641 | −0.637568 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.2487 | 0.924326 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.6410 | 1.39302 | 0.696511 | − | 0.717546i | \(-0.254735\pi\) | ||||
0.696511 | + | 0.717546i | \(0.254735\pi\) | |||||||
\(938\) | 8.39230 | 0.274018 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55.1051 | 1.79638 | 0.898188 | − | 0.439612i | \(-0.144884\pi\) | ||||
0.898188 | + | 0.439612i | \(0.144884\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44.3205 | −1.44327 | ||||||||
\(944\) | 8.92820 | 0.290588 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.8564 | 0.645587 | ||||||||
\(947\) | 50.5692 | 1.64328 | 0.821639 | − | 0.570008i | \(-0.193060\pi\) | ||||
0.821639 | + | 0.570008i | \(0.193060\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.49742 | −0.145993 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.00000 | −0.129641 | ||||||||
\(953\) | 9.46410 | 0.306572 | 0.153286 | − | 0.988182i | \(-0.451014\pi\) | ||||
0.153286 | + | 0.988182i | \(0.451014\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.53590 | 0.146701 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.7846 | 0.671520 | ||||||||
\(959\) | 6.53590 | 0.211055 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.0718 | −0.550703 | ||||||||
\(962\) | 10.5359 | 0.339691 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.3923 | 0.334714 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.14359 | 0.261880 | 0.130940 | − | 0.991390i | \(-0.458200\pi\) | ||||
0.130940 | + | 0.991390i | \(0.458200\pi\) | |||||||
\(968\) | 8.00000 | 0.257130 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.3205 | 1.13349 | 0.566745 | − | 0.823894i | \(-0.308203\pi\) | ||||
0.566745 | + | 0.823894i | \(0.308203\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.46410 | −0.239288 | ||||||||
\(974\) | 5.60770 | 0.179682 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.8564 | 0.443533 | ||||||||
\(977\) | 41.5692 | 1.32992 | 0.664959 | − | 0.746880i | \(-0.268449\pi\) | ||||
0.664959 | + | 0.746880i | \(0.268449\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.73205 | −0.0553566 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.4449 | −0.556688 | ||||||||
\(983\) | −38.3923 | −1.22452 | −0.612262 | − | 0.790655i | \(-0.709740\pi\) | ||||
−0.612262 | + | 0.790655i | \(0.709740\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 21.8564 | 0.696050 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.32051 | −0.105639 | ||||||||
\(989\) | −51.1769 | −1.62733 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.6077 | −0.495795 | −0.247897 | − | 0.968786i | \(-0.579740\pi\) | ||||
−0.247897 | + | 0.968786i | \(0.579740\pi\) | |||||||
\(992\) | 3.73205 | 0.118493 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.73205 | −0.245246 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.9615 | 1.51896 | 0.759478 | − | 0.650533i | \(-0.225454\pi\) | ||||
0.759478 | + | 0.650533i | \(0.225454\pi\) | |||||||
\(998\) | 20.9282 | 0.662471 | ||||||||
\(999\) | 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 | 9450.2.a.eb.1.2 | 2 | ||
3.2 | odd | 2 | 9450.2.a.er.1.1 | 2 | |||
5.2 | odd | 4 | 1890.2.g.n.379.1 | ✓ | 4 | ||
5.3 | odd | 4 | 1890.2.g.n.379.3 | yes | 4 | ||
5.4 | even | 2 | 9450.2.a.eu.1.2 | 2 | |||
15.2 | even | 4 | 1890.2.g.q.379.4 | yes | 4 | ||
15.8 | even | 4 | 1890.2.g.q.379.2 | yes | 4 | ||
15.14 | odd | 2 | 9450.2.a.ei.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1890.2.g.n.379.1 | ✓ | 4 | 5.2 | odd | 4 | ||
1890.2.g.n.379.3 | yes | 4 | 5.3 | odd | 4 | ||
1890.2.g.q.379.2 | yes | 4 | 15.8 | even | 4 | ||
1890.2.g.q.379.4 | yes | 4 | 15.2 | even | 4 | ||
9450.2.a.eb.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9450.2.a.ei.1.1 | 2 | 15.14 | odd | 2 | |||
9450.2.a.er.1.1 | 2 | 3.2 | odd | 2 | |||
9450.2.a.eu.1.2 | 2 | 5.4 | even | 2 |