Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-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 | ||||||||
\(3\) | −1.58435 | −0.914723 | −0.457362 | − | 0.889281i | \(-0.651205\pi\) | ||||
−0.457362 | + | 0.889281i | \(0.651205\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.56834 | 1.14860 | 0.574299 | − | 0.818646i | \(-0.305275\pi\) | ||||
0.574299 | + | 0.818646i | \(0.305275\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.40444 | 1.28676 | 0.643379 | − | 0.765547i | \(-0.277532\pi\) | ||||
0.643379 | + | 0.765547i | \(0.277532\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.489844 | −0.163281 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.40161 | 0.724111 | 0.362056 | − | 0.932156i | \(-0.382075\pi\) | ||||
0.362056 | + | 0.932156i | \(0.382075\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00961 | 0.557366 | 0.278683 | − | 0.960383i | \(-0.410102\pi\) | ||||
0.278683 | + | 0.960383i | \(0.410102\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.06915 | −1.05065 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.89035 | 0.892509 | 0.446254 | − | 0.894906i | \(-0.352758\pi\) | ||||
0.446254 | + | 0.894906i | \(0.352758\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.39382 | −1.17703 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.11645 | −0.649824 | −0.324912 | − | 0.945744i | \(-0.605335\pi\) | ||||
−0.324912 | + | 0.945744i | \(0.605335\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.59639 | 0.319278 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.52912 | 1.06408 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.87609 | 1.09116 | 0.545581 | − | 0.838058i | \(-0.316309\pi\) | ||||
0.545581 | + | 0.838058i | \(0.316309\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.36059 | 0.603579 | 0.301790 | − | 0.953375i | \(-0.402416\pi\) | ||||
0.301790 | + | 0.953375i | \(0.402416\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.80498 | −0.662361 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.74378 | 1.47797 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.17469 | 0.686315 | 0.343158 | − | 0.939278i | \(-0.388504\pi\) | ||||
0.343158 | + | 0.939278i | \(0.388504\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.18392 | −0.509836 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.04299 | −0.319061 | −0.159531 | − | 0.987193i | \(-0.550998\pi\) | ||||
−0.159531 | + | 0.987193i | \(0.550998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.64231 | −0.707946 | −0.353973 | − | 0.935256i | \(-0.615169\pi\) | ||||
−0.353973 | + | 0.935256i | \(0.615169\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.25809 | −0.187545 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.53066 | −0.660865 | −0.330432 | − | 0.943830i | \(-0.607195\pi\) | ||||
−0.330432 | + | 0.943830i | \(0.607195\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.59024 | 0.655749 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.58435 | −0.221853 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.71284 | 0.647359 | 0.323679 | − | 0.946167i | \(-0.395080\pi\) | ||||
0.323679 | + | 0.946167i | \(0.395080\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.16815 | 0.831713 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.16367 | −0.816398 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.32381 | −0.809681 | −0.404840 | − | 0.914387i | \(-0.632673\pi\) | ||||
−0.404840 | + | 0.914387i | \(0.632673\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.66765 | −0.210104 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.16138 | 0.640190 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.35564 | 1.14297 | 0.571487 | − | 0.820611i | \(-0.306367\pi\) | ||||
0.571487 | + | 0.820611i | \(0.306367\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.93753 | 0.594409 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.403000 | −0.0478273 | −0.0239136 | − | 0.999714i | \(-0.507613\pi\) | ||||
−0.0239136 | + | 0.999714i | \(0.507613\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.0127794 | −0.00149572 | −0.000747860 | − | 1.00000i | \(-0.500238\pi\) | ||||
−0.000747860 | 1.00000i | \(0.500238\pi\) | ||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.52924 | −0.292051 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.17613 | 0.931757 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.39913 | −0.269923 | −0.134961 | − | 0.990851i | \(-0.543091\pi\) | ||||
−0.134961 | + | 0.990851i | \(0.543091\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.29052 | −0.810058 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.2601 | 1.12619 | 0.563097 | − | 0.826391i | \(-0.309610\pi\) | ||||
0.563097 | + | 0.826391i | \(0.309610\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.56834 | 0.278576 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.30977 | −0.998112 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.1627 | 1.39524 | 0.697622 | − | 0.716466i | \(-0.254242\pi\) | ||||
0.697622 | + | 0.716466i | \(0.254242\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.84161 | 0.717196 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.32433 | −0.552108 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.99177 | 1.02513 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.2364 | −1.85163 | −0.925815 | − | 0.377977i | \(-0.876620\pi\) | ||||
−0.925815 | + | 0.377977i | \(0.876620\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.17641 | −0.118234 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.28016 | −0.624899 | −0.312450 | − | 0.949934i | \(-0.601150\pi\) | ||||
−0.312450 | + | 0.949934i | \(0.601150\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.85117 | −0.280934 | −0.140467 | − | 0.990085i | \(-0.544860\pi\) | ||||
−0.140467 | + | 0.990085i | \(0.544860\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.8532 | −1.35193 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.09649 | 0.396022 | 0.198011 | − | 0.980200i | \(-0.436552\pi\) | ||||
0.198011 | + | 0.980200i | \(0.436552\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.9504 | −1.62355 | −0.811775 | − | 0.583971i | \(-0.801498\pi\) | ||||
−0.811775 | + | 0.583971i | \(0.801498\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.61416 | −0.627788 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.25142 | 0.776228 | 0.388114 | − | 0.921611i | \(-0.373127\pi\) | ||||
0.388114 | + | 0.921611i | \(0.373127\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.00411 | −0.746387 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.984397 | −0.0910075 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.40444 | 0.312085 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.23229 | −0.475663 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.23680 | 0.291853 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.74164 | −0.781876 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.5059 | −1.55340 | −0.776699 | − | 0.629871i | \(-0.783108\pi\) | ||||
−0.776699 | + | 0.629871i | \(0.783108\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.35503 | 0.647574 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.9296 | −0.954921 | −0.477460 | − | 0.878653i | \(-0.658443\pi\) | ||||
−0.477460 | + | 0.878653i | \(0.658443\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.2445 | 1.14844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.2007 | 1.22220 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.8932 | −1.35784 | −0.678922 | − | 0.734210i | \(-0.737553\pi\) | ||||
−0.678922 | + | 0.734210i | \(0.737553\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.02838 | 0.256863 | 0.128432 | − | 0.991718i | \(-0.459006\pi\) | ||||
0.128432 | + | 0.991718i | \(0.459006\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.17814 | 0.604508 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.82630 | 0.403595 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.0918 | 1.25331 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.27253 | −0.599829 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.61304 | −0.705608 | −0.352804 | − | 0.935697i | \(-0.614772\pi\) | ||||
−0.352804 | + | 0.935697i | \(0.614772\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.90735 | 0.724869 | 0.362435 | − | 0.932009i | \(-0.381946\pi\) | ||||
0.362435 | + | 0.932009i | \(0.381946\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.489844 | −0.0396015 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.63114 | 0.693270 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7149 | 0.855144 | 0.427572 | − | 0.903981i | \(-0.359369\pi\) | ||||
0.427572 | + | 0.903981i | \(0.359369\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.46678 | −0.592154 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.6098 | −0.836167 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.5447 | 1.92249 | 0.961244 | − | 0.275698i | \(-0.0889091\pi\) | ||||
0.961244 | + | 0.275698i | \(0.0889091\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.77249 | −0.760787 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.34988 | 0.181840 | 0.0909198 | − | 0.995858i | \(-0.471019\pi\) | ||||
0.0909198 | + | 0.995858i | \(0.471019\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.96146 | −0.689343 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.90567 | −0.145730 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.19331 | −0.318812 | −0.159406 | − | 0.987213i | \(-0.550958\pi\) | ||||
−0.159406 | + | 0.987213i | \(0.550958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.43482 | 0.410834 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.58435 | −0.119087 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.81077 | 0.284831 | 0.142415 | − | 0.989807i | \(-0.454513\pi\) | ||||
0.142415 | + | 0.989807i | \(0.454513\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.6218 | −1.08683 | −0.543414 | − | 0.839465i | \(-0.682869\pi\) | ||||
−0.543414 | + | 0.839465i | \(0.682869\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.0191 | 0.740634 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.7220 | 0.788300 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.40161 | 0.175623 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.8236 | 1.36922 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.5203 | 1.55715 | 0.778576 | − | 0.627550i | \(-0.215942\pi\) | ||||
0.778576 | + | 0.627550i | \(0.215942\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.06466 | −0.292580 | −0.146290 | − | 0.989242i | \(-0.546733\pi\) | ||||
−0.146290 | + | 0.989242i | \(0.546733\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.17741 | −0.585597 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.46476 | −0.175607 | −0.0878035 | − | 0.996138i | \(-0.527985\pi\) | ||||
−0.0878035 | + | 0.996138i | \(0.527985\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.5614 | 1.67022 | 0.835110 | − | 0.550083i | \(-0.185404\pi\) | ||||
0.835110 | + | 0.550083i | \(0.185404\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.8226 | −1.04550 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.0048 | 1.40406 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.24710 | −0.366473 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.52657 | 0.106104 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.34310 | 0.646276 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.3754 | 1.05849 | 0.529244 | − | 0.848470i | \(-0.322476\pi\) | ||||
0.529244 | + | 0.848470i | \(0.322476\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.638491 | 0.0437487 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.9231 | −0.813145 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.4409 | 0.776661 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0202471 | 0.00136817 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00961 | 0.135181 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.2116 | 1.55437 | 0.777183 | − | 0.629275i | \(-0.216648\pi\) | ||||
0.777183 | + | 0.629275i | \(0.216648\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.781982 | −0.0521322 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.58029 | −0.503122 | −0.251561 | − | 0.967841i | \(-0.580944\pi\) | ||||
−0.251561 | + | 0.967841i | \(0.580944\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.1259 | 1.46212 | 0.731062 | − | 0.682311i | \(-0.239025\pi\) | ||||
0.731062 | + | 0.682311i | \(0.239025\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.9538 | −0.852299 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.66227 | 0.305436 | 0.152718 | − | 0.988270i | \(-0.451197\pi\) | ||||
0.152718 | + | 0.988270i | \(0.451197\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.6363 | −0.759068 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.80105 | 0.246905 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.0323 | 0.648934 | 0.324467 | − | 0.945897i | \(-0.394815\pi\) | ||||
0.324467 | + | 0.945897i | \(0.394815\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.49399 | 0.482731 | 0.241365 | − | 0.970434i | \(-0.422405\pi\) | ||||
0.241365 | + | 0.970434i | \(0.422405\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.03666 | −0.323102 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.7893 | 0.753192 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.81811 | 0.497454 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.2556 | −1.03016 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.3707 | −0.780833 | −0.390416 | − | 0.920638i | \(-0.627669\pi\) | ||||
−0.390416 | + | 0.920638i | \(0.627669\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.48447 | −0.470545 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.06915 | −0.254820 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.5081 | 1.09213 | 0.546064 | − | 0.837744i | \(-0.316126\pi\) | ||||
0.546064 | + | 0.837744i | \(0.316126\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.2125 | 0.883122 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.87837 | −0.178166 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.94371 | −0.119855 | −0.0599273 | − | 0.998203i | \(-0.519087\pi\) | ||||
−0.0599273 | + | 0.998203i | \(0.519087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1042 | 0.743555 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.8543 | −1.27626 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.14731 | 0.313837 | 0.156919 | − | 0.987612i | \(-0.449844\pi\) | ||||
0.156919 | + | 0.987612i | \(0.449844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.9856 | −0.849566 | −0.424783 | − | 0.905295i | \(-0.639650\pi\) | ||||
−0.424783 | + | 0.905295i | \(0.639650\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.8395 | −0.656036 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.83390 | 0.231193 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.9058 | −1.13594 | −0.567969 | − | 0.823050i | \(-0.692271\pi\) | ||||
−0.567969 | + | 0.823050i | \(0.692271\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.64616 | −0.0985532 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.8762 | 1.36468 | 0.682341 | − | 0.731034i | \(-0.260962\pi\) | ||||
0.682341 | + | 0.731034i | \(0.260962\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.9870 | 1.78254 | 0.891271 | − | 0.453471i | \(-0.149815\pi\) | ||||
0.891271 | + | 0.453471i | \(0.149815\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.8304 | −0.937714 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.95524 | −0.410555 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.8928 | 1.69373 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.1458 | 0.651142 | 0.325571 | − | 0.945518i | \(-0.394444\pi\) | ||||
0.325571 | + | 0.945518i | \(0.394444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.56834 | 0.149535 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.2788 | 0.770513 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.26285 | −0.362190 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.8045 | −0.910956 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.94995 | 0.571610 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.2417 | −0.929998 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0152 | −0.571598 | −0.285799 | − | 0.958290i | \(-0.592259\pi\) | ||||
−0.285799 | + | 0.958290i | \(0.592259\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.51725 | 0.256977 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.84863 | −0.104826 | −0.0524131 | − | 0.998625i | \(-0.516691\pi\) | ||||
−0.0524131 | + | 0.998625i | \(0.516691\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.3405 | −1.37581 | −0.687903 | − | 0.725803i | \(-0.741469\pi\) | ||||
−0.687903 | + | 0.725803i | \(0.741469\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.28309 | −0.241325 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.5395 | 0.816618 | 0.408309 | − | 0.912844i | \(-0.366119\pi\) | ||||
0.408309 | + | 0.912844i | \(0.366119\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.1120 | 0.790123 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.49026 | −0.362251 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.89035 | 0.216465 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.20813 | 0.177955 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.8552 | 1.48510 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.4244 | −0.850374 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.8651 | 1.80643 | 0.903215 | − | 0.429188i | \(-0.141200\pi\) | ||||
0.903215 | + | 0.429188i | \(0.141200\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.04495 | −0.112062 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.0285 | 1.31282 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00139 | 0.435864 | 0.217932 | − | 0.975964i | \(-0.430069\pi\) | ||||
0.217932 | + | 0.975964i | \(0.430069\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.0731 | −0.710034 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.07080 | 0.437058 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.20389 | −0.442969 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.6813 | 0.682737 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.18570 | 0.278383 | 0.139191 | − | 0.990265i | \(-0.455550\pi\) | ||||
0.139191 | + | 0.990265i | \(0.455550\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.66895 | −0.356981 | −0.178490 | − | 0.983942i | \(-0.557121\pi\) | ||||
−0.178490 | + | 0.983942i | \(0.557121\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.1114 | 0.593082 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.0198 | −0.639750 | −0.319875 | − | 0.947460i | \(-0.603641\pi\) | ||||
−0.319875 | + | 0.947460i | \(0.603641\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.03504 | −0.0549343 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.39382 | −0.285471 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.1915 | 1.32956 | 0.664780 | − | 0.747040i | \(-0.268525\pi\) | ||||
0.664780 | + | 0.747040i | \(0.268525\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.86514 | −0.203428 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.28977 | 0.435100 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.0328220 | −0.00171798 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.5663 | −1.49115 | −0.745576 | − | 0.666421i | \(-0.767825\pi\) | ||||
−0.745576 | + | 0.666421i | \(0.767825\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.00075 | 0.0520967 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.0446 | 0.832994 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.63027 | −0.446859 | −0.223429 | − | 0.974720i | \(-0.571725\pi\) | ||||
−0.223429 | + | 0.974720i | \(0.571725\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.8498 | 0.715200 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.8087 | 0.608177 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.3382 | −0.531039 | −0.265519 | − | 0.964106i | \(-0.585543\pi\) | ||||
−0.265519 | + | 0.964106i | \(0.585543\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.7354 | 1.42093 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.0322 | 1.58567 | 0.792837 | − | 0.609434i | \(-0.208603\pi\) | ||||
0.792837 | + | 0.609434i | \(0.208603\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.9991 | 1.07021 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.27401 | 0.115594 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.2059 | 0.770970 | 0.385485 | − | 0.922714i | \(-0.374034\pi\) | ||||
0.385485 | + | 0.922714i | \(0.374034\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.11645 | −0.157605 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.3162 | 0.873488 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.16179 | −0.310033 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.9656 | −0.700913 | −0.350457 | − | 0.936579i | \(-0.613974\pi\) | ||||
−0.350457 | + | 0.936579i | \(0.613974\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.9839 | −1.05051 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.37465 | −0.218459 | −0.109230 | − | 0.994017i | \(-0.534838\pi\) | ||||
−0.109230 | + | 0.994017i | \(0.534838\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.75347 | 0.336415 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.7246 | −0.930431 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0260 | 0.496968 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −38.3304 | −1.89532 | −0.947658 | − | 0.319287i | \(-0.896557\pi\) | ||||
−0.947658 | + | 0.319287i | \(0.896557\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.1803 | 1.24205 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.40444 | 0.167522 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.3515 | 1.29355 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.79800 | −0.234959 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.43916 | 0.265720 | 0.132860 | − | 0.991135i | \(-0.457584\pi\) | ||||
0.132860 | + | 0.991135i | \(0.457584\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.49826 | −0.365443 | −0.182721 | − | 0.983165i | \(-0.558491\pi\) | ||||
−0.182721 | + | 0.983165i | \(0.558491\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.21932 | 0.107907 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.59639 | 0.0774363 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.5291 | −1.04186 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.64653 | −0.369178 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.92380 | −0.237171 | −0.118586 | − | 0.992944i | \(-0.537836\pi\) | ||||
−0.118586 | + | 0.992944i | \(0.537836\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.1257 | 0.871066 | 0.435533 | − | 0.900173i | \(-0.356560\pi\) | ||||
0.435533 | + | 0.900173i | \(0.356560\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23.9107 | −1.14643 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.1241 | −0.579974 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.03914 | −0.431414 | −0.215707 | − | 0.976458i | \(-0.569206\pi\) | ||||
−0.215707 | + | 0.976458i | \(0.569206\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.24850 | −0.107072 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.7692 | −1.55691 | −0.778456 | − | 0.627699i | \(-0.783997\pi\) | ||||
−0.778456 | + | 0.627699i | \(0.783997\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.8063 | 1.60257 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.6461 | 0.645436 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.1349 | 0.619874 | 0.309937 | − | 0.950757i | \(-0.399692\pi\) | ||||
0.309937 | + | 0.950757i | \(0.399692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.90645 | −0.231036 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.1123 | −0.663055 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.5716 | 0.823770 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.8721 | 0.742467 | 0.371233 | − | 0.928540i | \(-0.378935\pi\) | ||||
0.371233 | + | 0.928540i | \(0.378935\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.52912 | 0.258077 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.28169 | 0.0596942 | 0.0298471 | − | 0.999554i | \(-0.490498\pi\) | ||||
0.0298471 | + | 0.999554i | \(0.490498\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.1278 | 0.703048 | 0.351524 | − | 0.936179i | \(-0.385664\pi\) | ||||
0.351524 | + | 0.936179i | \(0.385664\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.6747 | −0.634150 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.8136 | −0.500396 | −0.250198 | − | 0.968195i | \(-0.580496\pi\) | ||||
−0.250198 | + | 0.968195i | \(0.580496\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.8508 | 1.47073 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.9762 | −0.782220 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.1490 | −0.512631 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.21053 | 0.284958 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.30856 | −0.105702 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.6620 | 0.715617 | 0.357808 | − | 0.933795i | \(-0.383524\pi\) | ||||
0.357808 | + | 0.933795i | \(0.383524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.38951 | 0.382529 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.8096 | 0.764861 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −46.8374 | −2.12678 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.25701 | −0.0569605 | −0.0284802 | − | 0.999594i | \(-0.509067\pi\) | ||||
−0.0284802 | + | 0.999594i | \(0.509067\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −38.8873 | −1.75854 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.47839 | −0.247236 | −0.123618 | − | 0.992330i | \(-0.539450\pi\) | ||||
−0.123618 | + | 0.992330i | \(0.539450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.87609 | 0.264646 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.02143 | −0.135803 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.37199 | −0.0615422 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0957 | −0.631008 | −0.315504 | − | 0.948924i | \(-0.602174\pi\) | ||||
−0.315504 | + | 0.948924i | \(0.602174\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.72303 | −0.166333 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.90002 | −0.307657 | −0.153828 | − | 0.988098i | \(-0.549160\pi\) | ||||
−0.153828 | + | 0.988098i | \(0.549160\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.1296 | −0.717758 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.1981 | 0.630558 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −44.2392 | −1.96087 | −0.980435 | − | 0.196843i | \(-0.936931\pi\) | ||||
−0.980435 | + | 0.196843i | \(0.936931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0435069 | −0.00192463 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.5103 | 0.949701 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.32279 | −0.322681 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.8809 | −0.478540 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.64366 | 0.291624 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.1948 | −1.19142 | −0.595712 | − | 0.803198i | \(-0.703130\pi\) | ||||
−0.595712 | + | 0.803198i | \(0.703130\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5632 | −0.680530 | −0.340265 | − | 0.940330i | \(-0.610517\pi\) | ||||
−0.340265 | + | 0.940330i | \(0.610517\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.61065 | −0.375799 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.36059 | 0.146389 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.2878 | −0.577729 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.489844 | −0.0212574 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.10562 | −0.177834 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.5212 | 0.454871 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.03759 | −0.260541 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.0239 | 0.474835 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.0833 | 0.562495 | 0.281247 | − | 0.959635i | \(-0.409252\pi\) | ||||
0.281247 | + | 0.959635i | \(0.409252\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.1660 | 0.994147 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −43.5343 | −1.86481 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.6539 | −1.26791 | −0.633954 | − | 0.773370i | \(-0.718569\pi\) | ||||
−0.633954 | + | 0.773370i | \(0.718569\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.09768 | 0.132206 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.8601 | 0.973872 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.16770 | −0.347326 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.9874 | −0.721077 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.1689 | 0.896957 | 0.448478 | − | 0.893794i | \(-0.351966\pi\) | ||||
0.448478 | + | 0.893794i | \(0.351966\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.32925 | −0.394585 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.80498 | −0.160646 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.4916 | −0.484315 | −0.242158 | − | 0.970237i | \(-0.577855\pi\) | ||||
−0.242158 | + | 0.970237i | \(0.577855\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.1925 | 0.891574 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −24.8202 | −1.04235 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.321730 | −0.0134876 | −0.00674381 | − | 0.999977i | \(-0.502147\pi\) | ||||
−0.00674381 | + | 0.999977i | \(0.502147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.79349 | −0.326148 | −0.163074 | − | 0.986614i | \(-0.552141\pi\) | ||||
−0.163074 | + | 0.986614i | \(0.552141\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −34.0956 | −1.42436 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.97507 | −0.207475 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.37064 | −0.0986910 | −0.0493455 | − | 0.998782i | \(-0.515714\pi\) | ||||
−0.0493455 | + | 0.998782i | \(0.515714\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.43983 | 0.267630 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34.9300 | 1.44914 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.3184 | 0.468760 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.52827 | −0.104531 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.8757 | −0.861633 | −0.430817 | − | 0.902440i | \(-0.641774\pi\) | ||||
−0.430817 | + | 0.902440i | \(0.641774\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.0739 | 0.538699 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.90504 | 0.160632 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.80793 | −0.238503 | −0.119252 | − | 0.992864i | \(-0.538049\pi\) | ||||
−0.119252 | + | 0.992864i | \(0.538049\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.74378 | 0.358460 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −37.3294 | −1.52779 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.2881 | 0.420359 | 0.210180 | − | 0.977663i | \(-0.432595\pi\) | ||||
0.210180 | + | 0.977663i | \(0.432595\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.1095 | −0.738702 | −0.369351 | − | 0.929290i | \(-0.620420\pi\) | ||||
−0.369351 | + | 0.929290i | \(0.620420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.58280 | −0.186626 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.4383 | −0.546346 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.2725 | 1.87814 | 0.939071 | − | 0.343723i | \(-0.111688\pi\) | ||||
0.939071 | + | 0.343723i | \(0.111688\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −31.6946 | −1.28433 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.10487 | −0.368344 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.41794 | −0.138049 | −0.0690246 | − | 0.997615i | \(-0.521989\pi\) | ||||
−0.0690246 | + | 0.997615i | \(0.521989\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.31323 | 0.335222 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.9031 | 1.32463 | 0.662315 | − | 0.749225i | \(-0.269574\pi\) | ||||
0.662315 | + | 0.749225i | \(0.269574\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.6187 | 1.39144 | 0.695721 | − | 0.718312i | \(-0.255085\pi\) | ||||
0.695721 | + | 0.718312i | \(0.255085\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.2312 | −0.691465 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 44.8117 | 1.79534 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.4335 | −1.21734 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.8027 | −0.591163 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.17469 | 0.166456 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.5945 | 0.859663 | 0.429832 | − | 0.902909i | \(-0.358573\pi\) | ||||
0.429832 | + | 0.902909i | \(0.358573\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.3600 | −0.968223 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −44.9612 | −1.78423 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.22460 | 0.365492 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.197407 | 0.00780930 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.2341 | −1.47066 | −0.735329 | − | 0.677710i | \(-0.762972\pi\) | ||||
−0.735329 | + | 0.677710i | \(0.762972\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.3056 | 1.15570 | 0.577851 | − | 0.816143i | \(-0.303892\pi\) | ||||
0.577851 | + | 0.816143i | \(0.303892\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.8903 | 0.743803 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.82457 | 0.346930 | 0.173465 | − | 0.984840i | \(-0.444504\pi\) | ||||
0.173465 | + | 0.984840i | \(0.444504\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.40161 | 0.0942713 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.1264 | −0.710430 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.86857 | −0.347054 | −0.173527 | − | 0.984829i | \(-0.555516\pi\) | ||||
−0.173527 | + | 0.984829i | \(0.555516\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.0709 | −1.09682 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.00625993 | 0.000244223 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.571452 | −0.0222606 | −0.0111303 | − | 0.999938i | \(-0.503543\pi\) | ||||
−0.0111303 | + | 0.999938i | \(0.503543\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.4476 | −0.756423 | −0.378211 | − | 0.925719i | \(-0.623461\pi\) | ||||
−0.378211 | + | 0.925719i | \(0.623461\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.18392 | −0.123653 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 34.0164 | 1.31910 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.3125 | −0.709064 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −36.7753 | −1.42181 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.1873 | −0.586299 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.70899 | 0.104424 | 0.0522119 | − | 0.998636i | \(-0.483373\pi\) | ||||
0.0522119 | + | 0.998636i | \(0.483373\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.82664 | 0.339738 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.4927 | −0.672301 | −0.336150 | − | 0.941808i | \(-0.609125\pi\) | ||||
−0.336150 | + | 0.941808i | \(0.609125\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −62.0849 | −2.38260 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0098 | 0.460217 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.4587 | −0.859358 | −0.429679 | − | 0.902982i | \(-0.641373\pi\) | ||||
−0.429679 | + | 0.902982i | \(0.641373\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −40.8191 | −1.55962 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −35.0552 | −1.33744 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.47098 | 0.360816 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.8796 | −0.413879 | −0.206940 | − | 0.978354i | \(-0.566350\pi\) | ||||
−0.206940 | + | 0.978354i | \(0.566350\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.00503 | −0.152138 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.77791 | 0.295033 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.04299 | −0.0773837 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.38666 | −0.279389 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.11500 | 0.230960 | 0.115480 | − | 0.993310i | \(-0.463159\pi\) | ||||
0.115480 | + | 0.993310i | \(0.463159\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.2410 | 0.612542 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.4359 | 0.694337 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.3805 | −0.804095 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.4801 | 0.919371 | 0.459685 | − | 0.888082i | \(-0.347962\pi\) | ||||
0.459685 | + | 0.888082i | \(0.347962\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.17520 | 0.0440734 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.4731 | −0.392220 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.3956 | 0.463569 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.8946 | −0.593595 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.2546 | −0.606193 | −0.303096 | − | 0.952960i | \(-0.598020\pi\) | ||||
−0.303096 | + | 0.952960i | \(0.598020\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.70666 | −0.361495 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.8731 | −0.441565 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.38053 | 0.348384 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.147626 | −0.00547514 | −0.00273757 | − | 0.999996i | \(-0.500871\pi\) | ||||
−0.00273757 | + | 0.999996i | \(0.500871\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.8514 | 1.10561 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.64231 | −0.171702 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.1477 | −1.03966 | −0.519829 | − | 0.854270i | \(-0.674005\pi\) | ||||
−0.519829 | + | 0.854270i | \(0.674005\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.6784 | −0.688962 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.4686 | 0.827640 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.0872 | −0.702134 | −0.351067 | − | 0.936350i | \(-0.614181\pi\) | ||||
−0.351067 | + | 0.936350i | \(0.614181\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.3866 | −0.455033 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.8807 | −0.582608 | −0.291304 | − | 0.956631i | \(-0.594089\pi\) | ||||
−0.291304 | + | 0.956631i | \(0.594089\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.1213 | −0.810460 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.02586 | −0.183887 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.9463 | 0.509585 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.9315 | −0.581348 | −0.290674 | − | 0.956822i | \(-0.593880\pi\) | ||||
−0.290674 | + | 0.956822i | \(0.593880\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.5995 | 0.714246 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.8771 | 0.832584 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.90616 | −0.105626 | −0.0528131 | − | 0.998604i | \(-0.516819\pi\) | ||||
−0.0528131 | + | 0.998604i | \(0.516819\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.8580 | 0.430418 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.6016 | −0.964306 | −0.482153 | − | 0.876087i | \(-0.660145\pi\) | ||||
−0.482153 | + | 0.876087i | \(0.660145\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −57.7065 | −2.08912 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.25809 | −0.0454863 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.00961 | 0.0725629 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.2361 | −0.513367 | −0.256684 | − | 0.966496i | \(-0.582630\pi\) | ||||
−0.256684 | + | 0.966496i | \(0.582630\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.7390 | −0.998995 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.2010 | 0.870451 | 0.435226 | − | 0.900321i | \(-0.356669\pi\) | ||||
0.435226 | + | 0.900321i | \(0.356669\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.36481 | 0.192710 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.5175 | −0.807812 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.94795 | −0.284765 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.967846 | −0.0346323 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.4896 | 1.16108 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.5196 | 0.982217 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.9610 | −0.426362 | −0.213181 | − | 0.977013i | \(-0.568382\pi\) | ||||
−0.213181 | + | 0.977013i | \(0.568382\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.07952 | 0.109634 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.0915 | 0.998818 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.7084 | −0.451289 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.1773 | −0.680147 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.7814 | 0.842379 | 0.421189 | − | 0.906973i | \(-0.361613\pi\) | ||||
0.421189 | + | 0.906973i | \(0.361613\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.53066 | −0.160283 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.44767 | −0.227817 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.0306912 | −0.00108307 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.2495 | −0.960420 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.15513 | −0.287074 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.8493 | 1.26039 | 0.630197 | − | 0.776435i | \(-0.282974\pi\) | ||||
0.630197 | + | 0.776435i | \(0.282974\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.2838 | −0.396228 | −0.198114 | − | 0.980179i | \(-0.563482\pi\) | ||||
−0.198114 | + | 0.980179i | \(0.563482\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.1581 | 0.777118 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 63.0392 | 2.20817 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.0602 | −0.631848 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.35132 | −0.117105 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.6727 | 1.55909 | 0.779545 | − | 0.626347i | \(-0.215451\pi\) | ||||
0.779545 | + | 0.626347i | \(0.215451\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.50943 | 0.192047 | 0.0960233 | − | 0.995379i | \(-0.469388\pi\) | ||||
0.0960233 | + | 0.995379i | \(0.469388\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.07423 | −0.211478 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.0548 | −1.56671 | −0.783355 | − | 0.621575i | \(-0.786493\pi\) | ||||
−0.783355 | + | 0.621575i | \(0.786493\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.79544 | 0.305478 | 0.152739 | − | 0.988267i | \(-0.451191\pi\) | ||||
0.152739 | + | 0.988267i | \(0.451191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.9533 | 1.03907 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.59024 | 0.159042 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.03531 | 0.208861 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.5811 | 0.642257 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.0845 | −1.24578 | −0.622888 | − | 0.782311i | \(-0.714041\pi\) | ||||
−0.622888 | + | 0.782311i | \(0.714041\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.52843 | 0.190635 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −36.2439 | −1.24831 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.0161 | −0.791778 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.8130 | −0.612064 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −47.5098 | −1.63053 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.0102 | −0.445984 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.4019 | 1.75997 | 0.879984 | − | 0.475003i | \(-0.157553\pi\) | ||||
0.879984 | + | 0.475003i | \(0.157553\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.89441 | −0.167385 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.1662 | 1.03046 | 0.515229 | − | 0.857052i | \(-0.327707\pi\) | ||||
0.515229 | + | 0.857052i | \(0.327707\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.7376 | −1.83350 | −0.916752 | − | 0.399456i | \(-0.869199\pi\) | ||||
−0.916752 | + | 0.399456i | \(0.869199\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.0195 | 0.375544 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −52.3451 | −1.78185 | −0.890924 | − | 0.454152i | \(-0.849942\pi\) | ||||
−0.890924 | + | 0.454152i | \(0.849942\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.7699 | −0.366187 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.58435 | −0.0538073 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.76176 | −0.195454 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.8012 | 0.637055 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.93301 | 0.302337 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.7604 | −1.00609 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −55.9527 | −1.88939 | −0.944694 | − | 0.327952i | \(-0.893642\pi\) | ||||
−0.944694 | + | 0.327952i | \(0.893642\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.6587 | −0.595615 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.22755 | 0.310884 | 0.155442 | − | 0.987845i | \(-0.450320\pi\) | ||||
0.155442 | + | 0.987845i | \(0.450320\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.84405 | 0.0957100 | 0.0478550 | − | 0.998854i | \(-0.484761\pi\) | ||||
0.0478550 | + | 0.998854i | \(0.484761\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.06915 | −0.136783 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.9105 | −0.668529 | −0.334265 | − | 0.942479i | \(-0.608488\pi\) | ||||
−0.334265 | + | 0.942479i | \(0.608488\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −59.5979 | −1.99885 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.5090 | −0.586572 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.6259 | −0.589827 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.78738 | 0.327156 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.92253 | 0.331304 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.7471 | 0.658603 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.71284 | 0.157008 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.0398 | 0.833272 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −37.5538 | −1.24833 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.1675 | −0.702856 | −0.351428 | − | 0.936215i | \(-0.614304\pi\) | ||||
−0.351428 | + | 0.936215i | \(0.614304\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.07630 | 0.102034 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.2961 | 1.13628 | 0.568141 | − | 0.822932i | \(-0.307663\pi\) | ||||
0.568141 | + | 0.822932i | \(0.307663\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.6408 | 0.815490 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25.7325 | 0.850691 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.2091 | −1.22875 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.8275 | −1.21483 | −0.607414 | − | 0.794385i | \(-0.707793\pi\) | ||||
−0.607414 | + | 0.794385i | \(0.707793\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.8676 | 0.522854 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.809873 | −0.0266573 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.66444 | 0.219125 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.39663 | 0.0458713 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.4432 | −0.572292 | −0.286146 | − | 0.958186i | \(-0.592374\pi\) | ||||
−0.286146 | + | 0.958186i | \(0.592374\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.8577 | 0.585261 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.92887 | 0.0958869 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.16815 | 0.201720 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.1147 | −1.14715 | −0.573574 | − | 0.819154i | \(-0.694444\pi\) | ||||
−0.573574 | + | 0.819154i | \(0.694444\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.5638 | 1.25848 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −61.2631 | −1.99712 | −0.998560 | − | 0.0536430i | \(-0.982917\pi\) | ||||
−0.998560 | + | 0.0536430i | \(0.982917\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.36687 | 0.207334 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 48.3455 | 1.57268 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.78619 | −0.285513 | −0.142756 | − | 0.989758i | \(-0.545597\pi\) | ||||
−0.142756 | + | 0.989758i | \(0.545597\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0256817 | −0.000833664 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.0356 | −0.746980 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.3483 | 1.53376 | 0.766880 | − | 0.641790i | \(-0.221808\pi\) | ||||
0.766880 | + | 0.641790i | \(0.221808\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 55.2715 | 1.78854 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22.3584 | −0.722744 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −54.1074 | −1.74722 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.7065 | −0.635692 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.00664 | −0.0646631 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.4394 | −0.336057 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.4753 | 0.819229 | 0.409615 | − | 0.912259i | \(-0.365663\pi\) | ||||
0.409615 | + | 0.912259i | \(0.365663\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.16367 | −0.198006 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.9071 | −1.15231 | −0.576157 | − | 0.817339i | \(-0.695448\pi\) | ||||
−0.576157 | + | 0.817339i | \(0.695448\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.3099 | 0.330521 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.08279 | −0.162779 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.56433 | 0.210012 | 0.105006 | − | 0.994472i | \(-0.466514\pi\) | ||||
0.105006 | + | 0.994472i | \(0.466514\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.6116 | 1.01031 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.30303 | 0.265095 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.05582 | 0.225046 | 0.112523 | − | 0.993649i | \(-0.464107\pi\) | ||||
0.112523 | + | 0.993649i | \(0.464107\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.33035 | −0.201702 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.4376 | 0.777857 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.4675 | 0.460040 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.2437 | −0.801894 | −0.400947 | − | 0.916101i | \(-0.631319\pi\) | ||||
−0.400947 | + | 0.916101i | \(0.631319\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −52.0698 | −1.65238 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 60.5137 | 1.91841 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.9829 | 1.39295 | 0.696477 | − | 0.717580i | \(-0.254750\pi\) | ||||
0.696477 | + | 0.717580i | \(0.254750\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23.0824 | 0.730294 |
(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 | 4012.2.a.j.1.6 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.j.1.6 | ✓ | 21 | 1.1 | even | 1 | trivial |