Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - 6x - 3 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.523976\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.523976 | 0.302518 | 0.151259 | − | 0.988494i | \(-0.451667\pi\) | ||||
0.151259 | + | 0.988494i | \(0.451667\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.72545 | 1.21886 | 0.609429 | − | 0.792841i | \(-0.291399\pi\) | ||||
0.609429 | + | 0.792841i | \(0.291399\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.67750 | 1.76793 | 0.883964 | − | 0.467556i | \(-0.154865\pi\) | ||||
0.883964 | + | 0.467556i | \(0.154865\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.72545 | −0.908483 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.67750 | −0.742604 | −0.371302 | − | 0.928512i | \(-0.621089\pi\) | ||||
−0.371302 | + | 0.928512i | \(0.621089\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.42807 | 0.368726 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.201472 | 0.0488642 | 0.0244321 | − | 0.999701i | \(-0.492222\pi\) | ||||
0.0244321 | + | 0.999701i | \(0.492222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.45090 | 0.534830 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.79853 | 0.375019 | 0.187509 | − | 0.982263i | \(-0.439958\pi\) | ||||
0.187509 | + | 0.982263i | \(0.439958\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.42807 | 0.485614 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.00000 | −0.577350 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.92692 | −0.914906 | −0.457453 | − | 0.889234i | \(-0.651238\pi\) | ||||
−0.457453 | + | 0.889234i | \(0.651238\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.57193 | 0.461932 | 0.230966 | − | 0.972962i | \(-0.425811\pi\) | ||||
0.230966 | + | 0.972962i | \(0.425811\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.523976 | 0.0912126 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.7483 | 2.15485 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.40294 | 0.723840 | 0.361920 | − | 0.932209i | \(-0.382121\pi\) | ||||
0.361920 | + | 0.932209i | \(0.382121\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.40294 | −0.224651 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.97487 | 0.776945 | 0.388472 | − | 0.921460i | \(-0.373003\pi\) | ||||
0.388472 | + | 0.921460i | \(0.373003\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.7734 | 1.79543 | 0.897713 | − | 0.440580i | \(-0.145227\pi\) | ||||
0.897713 | + | 0.440580i | \(0.145227\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.42807 | −1.10731 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.4989 | 1.82314 | 0.911572 | − | 0.411140i | \(-0.134869\pi\) | ||||
0.911572 | + | 0.411140i | \(0.134869\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.8790 | 2.12557 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.105567 | 0.0147823 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.10557 | −0.563943 | −0.281971 | − | 0.959423i | \(-0.590988\pi\) | ||||
−0.281971 | + | 0.959423i | \(0.590988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.72545 | 0.367499 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.523976 | 0.0694024 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.24943 | 0.683417 | 0.341708 | − | 0.939806i | \(-0.388994\pi\) | ||||
0.341708 | + | 0.939806i | \(0.388994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.59706 | 0.204482 | 0.102241 | − | 0.994760i | \(-0.467399\pi\) | ||||
0.102241 | + | 0.994760i | \(0.467399\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.7483 | −1.60613 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.29738 | −0.905128 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.08044 | −1.10935 | −0.554676 | − | 0.832066i | \(-0.687158\pi\) | ||||
−0.554676 | + | 0.832066i | \(0.687158\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.942386 | 0.113450 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.8214 | −1.52161 | −0.760807 | − | 0.648978i | \(-0.775197\pi\) | ||||
−0.760807 | + | 0.648978i | \(0.775197\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.20147 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.27225 | 0.146907 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.67750 | 0.533050 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.8538 | −1.33366 | −0.666831 | − | 0.745209i | \(-0.732350\pi\) | ||||
−0.666831 | + | 0.745209i | \(0.732350\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.60442 | 0.733824 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.6775 | 1.50130 | 0.750650 | − | 0.660700i | \(-0.229740\pi\) | ||||
0.750650 | + | 0.660700i | \(0.229740\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.549103 | 0.0595585 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.58159 | −0.276776 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.45090 | −0.577794 | −0.288897 | − | 0.957360i | \(-0.593289\pi\) | ||||
−0.288897 | + | 0.957360i | \(0.593289\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.5240 | −1.31287 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.34763 | 0.139743 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.72545 | 0.279625 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.8059 | 1.70638 | 0.853190 | − | 0.521601i | \(-0.174665\pi\) | ||||
0.853190 | + | 0.521601i | \(0.174665\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.72545 | −0.273918 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.45090 | 0.741392 | 0.370696 | − | 0.928754i | \(-0.379119\pi\) | ||||
0.370696 | + | 0.928754i | \(0.379119\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.4834 | 1.42709 | 0.713545 | − | 0.700609i | \(-0.247088\pi\) | ||||
0.713545 | + | 0.700609i | \(0.247088\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.67980 | 0.651881 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.15352 | −0.111515 | −0.0557575 | − | 0.998444i | \(-0.517757\pi\) | ||||
−0.0557575 | + | 0.998444i | \(0.517757\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.55646 | −0.915343 | −0.457672 | − | 0.889121i | \(-0.651316\pi\) | ||||
−0.457672 | + | 0.889121i | \(0.651316\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.30704 | 0.218974 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.00000 | −0.752577 | −0.376288 | − | 0.926503i | \(-0.622800\pi\) | ||||
−0.376288 | + | 0.926503i | \(0.622800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.90179 | 0.457095 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.29738 | 0.674643 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.942386 | 0.0863884 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.60672 | 0.235040 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.00966 | −0.626963 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.75794 | −0.510934 | −0.255467 | − | 0.966818i | \(-0.582229\pi\) | ||||
−0.255467 | + | 0.966818i | \(0.582229\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.16898 | 0.543149 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.42807 | −0.124771 | −0.0623856 | − | 0.998052i | \(-0.519871\pi\) | ||||
−0.0623856 | + | 0.998052i | \(0.519871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.67750 | 0.405590 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.17635 | −0.703708 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.5313 | −1.24150 | −0.620748 | − | 0.784010i | \(-0.713171\pi\) | ||||
−0.620748 | + | 0.784010i | \(0.713171\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.1763 | −1.37206 | −0.686030 | − | 0.727573i | \(-0.740648\pi\) | ||||
−0.686030 | + | 0.727573i | \(0.740648\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.54910 | 0.551534 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.67750 | −0.223903 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.4281 | −1.11514 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.79623 | 0.643022 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.30704 | 0.516693 | 0.258346 | − | 0.966052i | \(-0.416822\pi\) | ||||
0.258346 | + | 0.966052i | \(0.416822\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.498850 | −0.0405959 | −0.0202979 | − | 0.999794i | \(-0.506461\pi\) | ||||
−0.0202979 | + | 0.999794i | \(0.506461\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.549103 | −0.0443923 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.00966 | 0.563030 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.6272 | −1.08757 | −0.543786 | − | 0.839224i | \(-0.683010\pi\) | ||||
−0.543786 | + | 0.839224i | \(0.683010\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.15122 | −0.170603 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.41261 | 0.663006 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.9497 | −1.24928 | −0.624640 | − | 0.780913i | \(-0.714754\pi\) | ||||
−0.624640 | + | 0.780913i | \(0.714754\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.42807 | 0.111175 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.8059 | −1.45524 | −0.727622 | − | 0.685979i | \(-0.759374\pi\) | ||||
−0.727622 | + | 0.685979i | \(0.759374\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.83102 | −0.448540 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.72545 | −0.208420 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.22430 | −0.245139 | −0.122569 | − | 0.992460i | \(-0.539113\pi\) | ||||
−0.122569 | + | 0.992460i | \(0.539113\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.3573 | 0.858531 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.75057 | 0.206746 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.3778 | −0.999905 | −0.499953 | − | 0.866053i | \(-0.666649\pi\) | ||||
−0.499953 | + | 0.866053i | \(0.666649\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.9497 | 1.18554 | 0.592768 | − | 0.805373i | \(-0.298035\pi\) | ||||
0.592768 | + | 0.805373i | \(0.298035\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.836819 | 0.0618595 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.0000 | 0.882258 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.201472 | 0.0147331 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.0325 | −1.02071 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0553 | 1.74058 | 0.870291 | − | 0.492538i | \(-0.163931\pi\) | ||||
0.870291 | + | 0.492538i | \(0.163931\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0325 | 0.938099 | 0.469050 | − | 0.883172i | \(-0.344597\pi\) | ||||
0.469050 | + | 0.883172i | \(0.344597\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.82365 | −0.273818 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.59706 | −0.398774 | −0.199387 | − | 0.979921i | \(-0.563895\pi\) | ||||
−0.199387 | + | 0.979921i | \(0.563895\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.39558 | 0.524259 | 0.262129 | − | 0.965033i | \(-0.415575\pi\) | ||||
0.262129 | + | 0.965033i | \(0.415575\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.75794 | −0.335599 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.0457 | −1.61749 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.5588 | 0.946985 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.90179 | −0.340698 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.2974 | 0.984272 | 0.492136 | − | 0.870518i | \(-0.336216\pi\) | ||||
0.492136 | + | 0.870518i | \(0.336216\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.71809 | −0.460316 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 32.0878 | 2.18837 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0302 | 0.816662 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.15352 | 0.0779476 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.539441 | −0.0362868 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.402945 | 0.0269832 | 0.0134916 | − | 0.999909i | \(-0.495705\pi\) | ||||
0.0134916 | + | 0.999909i | \(0.495705\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.61758 | −0.441172 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.0074 | 1.39431 | 0.697154 | − | 0.716922i | \(-0.254449\pi\) | ||||
0.697154 | + | 0.716922i | \(0.254449\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.3299 | −0.946944 | −0.473472 | − | 0.880809i | \(-0.657000\pi\) | ||||
−0.473472 | + | 0.880809i | \(0.657000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.45090 | 0.161257 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.4029 | −1.59869 | −0.799345 | − | 0.600872i | \(-0.794820\pi\) | ||||
−0.799345 | + | 0.600872i | \(0.794820\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 34.0650 | 2.22215 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.21113 | −0.403456 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.6849 | 0.820515 | 0.410258 | − | 0.911970i | \(-0.365439\pi\) | ||||
0.410258 | + | 0.911970i | \(0.365439\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.9343 | −1.54174 | −0.770871 | − | 0.636991i | \(-0.780179\pi\) | ||||
−0.770871 | + | 0.636991i | \(0.780179\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.4606 | 0.799345 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 40.5519 | 2.59076 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.67750 | −0.170365 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.16669 | 0.454170 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.4989 | −1.16764 | −0.583819 | − | 0.811884i | \(-0.698442\pi\) | ||||
−0.583819 | + | 0.811884i | \(0.698442\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.79853 | 0.113072 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.287717 | 0.0180175 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.7579 | 1.73149 | 0.865746 | − | 0.500483i | \(-0.166844\pi\) | ||||
0.865746 | + | 0.500483i | \(0.166844\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.5948 | 1.27970 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.4281 | 0.831177 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.2723 | −1.25004 | −0.625020 | − | 0.780608i | \(-0.714909\pi\) | ||||
−0.625020 | + | 0.780608i | \(0.714909\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.1895 | −0.687366 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.85614 | −0.174793 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.6427 | −0.953753 | −0.476876 | − | 0.878970i | \(-0.658231\pi\) | ||||
−0.476876 | + | 0.878970i | \(0.658231\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.3395 | 0.749573 | 0.374786 | − | 0.927111i | \(-0.377716\pi\) | ||||
0.374786 | + | 0.927111i | \(0.377716\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.56227 | −0.397167 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.42807 | 0.146418 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.49885 | 0.510646 | 0.255323 | − | 0.966856i | \(-0.417818\pi\) | ||||
0.255323 | + | 0.966856i | \(0.417818\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.00966 | −0.419657 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.12839 | −0.425244 | −0.212622 | − | 0.977134i | \(-0.568200\pi\) | ||||
−0.212622 | + | 0.977134i | \(0.568200\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.5240 | −0.685029 | −0.342515 | − | 0.939512i | \(-0.611279\pi\) | ||||
−0.342515 | + | 0.939512i | \(0.611279\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.42807 | 0.0845916 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.2700 | 1.37358 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9594 | −0.997612 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.80589 | 0.516210 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.6775 | 0.623786 | 0.311893 | − | 0.950117i | \(-0.399037\pi\) | ||||
0.311893 | + | 0.950117i | \(0.399037\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.3070 | 0.832988 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.00000 | −0.174078 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.81555 | −0.278490 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 55.0700 | 3.17418 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.90409 | 0.224284 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.35269 | 0.249234 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.2568 | 1.72685 | 0.863423 | − | 0.504481i | \(-0.168316\pi\) | ||||
0.863423 | + | 0.504481i | \(0.168316\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.58895 | 0.431720 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.79623 | −0.498788 | −0.249394 | − | 0.968402i | \(-0.580231\pi\) | ||||
−0.249394 | + | 0.968402i | \(0.580231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.1860 | 0.575747 | 0.287874 | − | 0.957668i | \(-0.407052\pi\) | ||||
0.287874 | + | 0.957668i | \(0.407052\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −34.7448 | −1.95765 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.0097 | −0.674530 | −0.337265 | − | 0.941410i | \(-0.609502\pi\) | ||||
−0.337265 | + | 0.941410i | \(0.609502\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.92692 | −0.275855 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.604417 | −0.0337353 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.201472 | 0.0112102 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.50115 | −0.360619 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.00736 | −0.276908 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 58.4633 | 3.22319 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.1667 | −1.43825 | −0.719126 | − | 0.694880i | \(-0.755457\pi\) | ||||
−0.719126 | + | 0.694880i | \(0.755457\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.0000 | −0.657596 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.7483 | −1.35214 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.3778 | 0.946630 | 0.473315 | − | 0.880893i | \(-0.343057\pi\) | ||||
0.473315 | + | 0.880893i | \(0.343057\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.19181 | −0.227668 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.57193 | 0.139278 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 36.8538 | 1.98992 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.56842 | 0.138279 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.4029 | 0.665825 | 0.332912 | − | 0.942958i | \(-0.391969\pi\) | ||||
0.332912 | + | 0.942958i | \(0.391969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.8036 | −1.27418 | −0.637088 | − | 0.770791i | \(-0.719861\pi\) | ||||
−0.637088 | + | 0.770791i | \(0.719861\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.03249 | 0.428742 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.2664 | −1.29157 | −0.645786 | − | 0.763518i | \(-0.723470\pi\) | ||||
−0.645786 | + | 0.763518i | \(0.723470\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −34.9439 | −1.85463 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.493788 | 0.0261340 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.3395 | −1.07348 | −0.536740 | − | 0.843748i | \(-0.680344\pi\) | ||||
−0.536740 | + | 0.843748i | \(0.680344\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.523976 | 0.0275016 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.0170 | 1.20148 | 0.600739 | − | 0.799445i | \(-0.294873\pi\) | ||||
0.600739 | + | 0.799445i | \(0.294873\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.5588 | −0.705841 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.2038 | −0.997010 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.5890 | −0.962499 | −0.481250 | − | 0.876584i | \(-0.659817\pi\) | ||||
−0.481250 | + | 0.876584i | \(0.659817\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.67290 | −0.189668 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.1918 | 0.679413 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.5816 | 0.543540 | 0.271770 | − | 0.962362i | \(-0.412391\pi\) | ||||
0.271770 | + | 0.962362i | \(0.412391\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.01702 | −0.154567 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.0878 | 1.33302 | 0.666512 | − | 0.745494i | \(-0.267786\pi\) | ||||
0.666512 | + | 0.745494i | \(0.267786\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.7483 | 0.649712 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32.0878 | −1.63111 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.46636 | −0.479964 | −0.239982 | − | 0.970777i | \(-0.577141\pi\) | ||||
−0.239982 | + | 0.970777i | \(0.577141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.362354 | 0.0183250 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.748275 | −0.0377455 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −32.3070 | −1.62554 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.1667 | −1.26308 | −0.631540 | − | 0.775343i | \(-0.717577\pi\) | ||||
−0.631540 | + | 0.775343i | \(0.717577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.45090 | 0.122698 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.0650 | −0.802247 | −0.401123 | − | 0.916024i | \(-0.631380\pi\) | ||||
−0.401123 | + | 0.916024i | \(0.631380\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.88633 | −0.343033 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000 | 0.894427 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.40294 | 0.218246 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.5313 | −0.965763 | −0.482881 | − | 0.875686i | \(-0.660410\pi\) | ||||
−0.482881 | + | 0.875686i | \(0.660410\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.61408 | −0.375575 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.5542 | 1.20823 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 37.2773 | 1.82987 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.47602 | −0.415073 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.9018 | −1.21653 | −0.608266 | − | 0.793733i | \(-0.708135\pi\) | ||||
−0.608266 | + | 0.793733i | \(0.708135\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.6044 | 1.29662 | 0.648310 | − | 0.761377i | \(-0.275476\pi\) | ||||
0.648310 | + | 0.761377i | \(0.275476\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −34.0650 | −1.65630 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.489189 | 0.0237292 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.47022 | 0.361509 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.40294 | −0.0677348 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.5948 | 1.57003 | 0.785017 | − | 0.619474i | \(-0.212654\pi\) | ||||
0.785017 | + | 0.619474i | \(0.212654\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.7386 | 0.948577 | 0.474289 | − | 0.880369i | \(-0.342705\pi\) | ||||
0.474289 | + | 0.880369i | \(0.342705\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.03599 | −0.337350 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.79853 | 0.0860352 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.4029 | 1.16469 | 0.582345 | − | 0.812942i | \(-0.302135\pi\) | ||||
0.582345 | + | 0.812942i | \(0.302135\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −40.5519 | −1.93104 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.5948 | 0.788441 | 0.394220 | − | 0.919016i | \(-0.371015\pi\) | ||||
0.394220 | + | 0.919016i | \(0.371015\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.8561 | −0.704249 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.30474 | 0.156309 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.9520 | −0.988788 | −0.494394 | − | 0.869238i | \(-0.664610\pi\) | ||||
−0.494394 | + | 0.869238i | \(0.664610\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.97487 | 0.234258 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.261386 | −0.0122810 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −34.1335 | −1.60020 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.3144 | 1.09060 | 0.545301 | − | 0.838240i | \(-0.316415\pi\) | ||||
0.545301 | + | 0.838240i | \(0.316415\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.604417 | −0.0282118 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.8059 | 0.969027 | 0.484513 | − | 0.874784i | \(-0.338997\pi\) | ||||
0.484513 | + | 0.874784i | \(0.338997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.29002 | 0.431744 | 0.215872 | − | 0.976422i | \(-0.430741\pi\) | ||||
0.215872 | + | 0.976422i | \(0.430741\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.67290 | 0.170327 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.0457 | −0.557406 | −0.278703 | − | 0.960377i | \(-0.589905\pi\) | ||||
−0.278703 | + | 0.960377i | \(0.589905\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −42.4737 | −1.96125 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.14035 | −0.329010 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.7734 | 0.541342 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.42807 | 0.111408 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.1895 | 0.512333 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.188307 | −0.00860396 | −0.00430198 | − | 0.999991i | \(-0.501369\pi\) | ||||
−0.00430198 | + | 0.999991i | \(0.501369\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.7889 | −0.537526 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.40801 | 0.200571 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 45.8036 | 2.07983 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.3852 | 1.51283 | 0.756413 | − | 0.654094i | \(-0.226950\pi\) | ||||
0.756413 | + | 0.654094i | \(0.226950\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.35729 | −0.377930 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.5217 | −0.565095 | −0.282548 | − | 0.959253i | \(-0.591180\pi\) | ||||
−0.282548 | + | 0.959253i | \(0.591180\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.992638 | −0.0447062 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.42807 | −0.333867 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −59.9718 | −2.69010 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.3070 | −0.730003 | −0.365002 | − | 0.931007i | \(-0.618932\pi\) | ||||
−0.365002 | + | 0.931007i | \(0.618932\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.85384 | −0.440237 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.9726 | 0.845945 | 0.422973 | − | 0.906142i | \(-0.360987\pi\) | ||||
0.422973 | + | 0.906142i | \(0.360987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.3070 | 0.903651 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.05531 | −0.135691 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.6907 | −1.36034 | −0.680170 | − | 0.733055i | \(-0.738094\pi\) | ||||
−0.680170 | + | 0.733055i | \(0.738094\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.2974 | 0.455529 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.00000 | −0.132453 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 39.4737 | 1.73942 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4989 | 0.549699 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.68946 | −0.0741589 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.1106 | −1.84490 | −0.922450 | − | 0.386116i | \(-0.873816\pi\) | ||||
−0.922450 | + | 0.386116i | \(0.873816\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.8133 | −1.65346 | −0.826729 | − | 0.562600i | \(-0.809801\pi\) | ||||
−0.826729 | + | 0.562600i | \(0.809801\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.95095 | 0.259721 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.518173 | 0.0225720 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7653 | −0.859361 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.3070 | −0.620873 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.3202 | −0.576962 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.14386 | −0.135921 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.00966 | −0.302489 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.8790 | 0.640883 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.5661 | 0.583253 | 0.291627 | − | 0.956532i | \(-0.405804\pi\) | ||||
0.291627 | + | 0.956532i | \(0.405804\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.35729 | 0.358646 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.0457 | −1.11567 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −46.4177 | −1.98468 | −0.992338 | − | 0.123552i | \(-0.960571\pi\) | ||||
−0.992338 | + | 0.123552i | \(0.960571\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.35269 | −0.185768 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.92692 | −0.209894 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −55.4463 | −2.35782 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.28772 | 0.266899 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.2065 | −1.61886 | −0.809431 | − | 0.587214i | \(-0.800225\pi\) | ||||
−0.809431 | + | 0.587214i | \(0.800225\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.5232 | −1.33329 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.105567 | 0.00445703 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.01702 | 0.295732 | 0.147866 | − | 0.989007i | \(-0.452760\pi\) | ||||
0.147866 | + | 0.989007i | \(0.452760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.8036 | −0.917284 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30.8921 | 1.29735 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.4235 | −1.73656 | −0.868281 | − | 0.496072i | \(-0.834775\pi\) | ||||
−0.868281 | + | 0.496072i | \(0.834775\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.1381 | −0.507962 | −0.253981 | − | 0.967209i | \(-0.581740\pi\) | ||||
−0.253981 | + | 0.967209i | \(0.581740\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.6044 | 0.526557 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.36695 | 0.182115 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.8384 | 0.534469 | 0.267234 | − | 0.963632i | \(-0.413890\pi\) | ||||
0.267234 | + | 0.963632i | \(0.413890\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.82872 | 0.283792 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 63.9764 | 2.65419 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.10557 | −0.170035 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.8886 | 0.822294 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.00000 | −0.165098 | −0.0825488 | − | 0.996587i | \(-0.526306\pi\) | ||||
−0.0825488 | + | 0.996587i | \(0.526306\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.57193 | 0.105974 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.93272 | −0.120636 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.4177 | 1.65975 | 0.829877 | − | 0.557946i | \(-0.188410\pi\) | ||||
0.829877 | + | 0.557946i | \(0.188410\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.56842 | 0.105295 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.87511 | 0.158598 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.679795 | −0.0277757 | −0.0138878 | − | 0.999904i | \(-0.504421\pi\) | ||||
−0.0138878 | + | 0.999904i | \(0.504421\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.5240 | 0.877981 | 0.438991 | − | 0.898492i | \(-0.355336\pi\) | ||||
0.438991 | + | 0.898492i | \(0.355336\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.7483 | 1.00783 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.72545 | 0.110805 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.3550 | −0.542062 | −0.271031 | − | 0.962571i | \(-0.587365\pi\) | ||||
−0.271031 | + | 0.962571i | \(0.587365\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.0754 | −0.489319 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.4656 | −1.35387 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.11293 | 0.368068 | 0.184034 | − | 0.982920i | \(-0.441084\pi\) | ||||
0.184034 | + | 0.982920i | \(0.441084\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.10447 | 0.286480 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.329866 | 0.0132799 | 0.00663995 | − | 0.999978i | \(-0.497886\pi\) | ||||
0.00663995 | + | 0.999978i | \(0.497886\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.92112 | −0.358570 | −0.179285 | − | 0.983797i | \(-0.557378\pi\) | ||||
−0.179285 | + | 0.983797i | \(0.557378\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.39558 | −0.216517 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.4966 | −1.02150 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2448 | −1.24979 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.523976 | 0.0209256 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.887072 | 0.0353699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.6597 | −1.77788 | −0.888938 | − | 0.458028i | \(-0.848556\pi\) | ||||
−0.888938 | + | 0.458028i | \(0.848556\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.49149 | 0.297760 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.6930 | −0.622756 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −39.8384 | −1.57845 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 34.9439 | 1.38236 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.93272 | −0.273826 | −0.136913 | − | 0.990583i | \(-0.543718\pi\) | ||||
−0.136913 | + | 0.990583i | \(0.543718\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.4966 | −0.926614 | −0.463307 | − | 0.886198i | \(-0.653337\pi\) | ||||
−0.463307 | + | 0.886198i | \(0.653337\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.8133 | 0.662021 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.9880 | −0.825125 | −0.412562 | − | 0.910929i | \(-0.635366\pi\) | ||||
−0.412562 | + | 0.910929i | \(0.635366\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.24943 | 0.206058 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.30353 | 0.247055 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −44.1335 | −1.72708 | −0.863538 | − | 0.504284i | \(-0.831756\pi\) | ||||
−0.863538 | + | 0.504284i | \(0.831756\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.89213 | −0.152078 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.0862 | −0.938267 | −0.469133 | − | 0.883127i | \(-0.655434\pi\) | ||||
−0.469133 | + | 0.883127i | \(0.655434\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.65237 | −0.375434 | −0.187717 | − | 0.982223i | \(-0.560109\pi\) | ||||
−0.187717 | + | 0.982223i | \(0.560109\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.282655 | −0.0109774 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.7483 | 0.494357 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.86120 | −0.343107 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.211133 | 0.00816289 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.59706 | 0.0616536 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.6176 | 0.948938 | 0.474469 | − | 0.880272i | \(-0.342640\pi\) | ||||
0.474469 | + | 0.880272i | \(0.342640\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.28421 | −0.280369 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.5719 | 0.829077 | 0.414538 | − | 0.910032i | \(-0.363943\pi\) | ||||
0.414538 | + | 0.910032i | \(0.363943\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 78.6095 | 3.01675 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.0074 | 0.421803 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.997701 | 0.0381759 | 0.0190880 | − | 0.999818i | \(-0.493924\pi\) | ||||
0.0190880 | + | 0.999818i | \(0.493924\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −39.6044 | −1.51321 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.50851 | −0.286468 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.9926 | 0.418786 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.00230 | 0.342464 | 0.171232 | − | 0.985231i | \(-0.445225\pi\) | ||||
0.171232 | + | 0.985231i | \(0.445225\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.7483 | −0.484267 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −44.0878 | −1.67235 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.00230 | 0.0379648 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.7866 | −0.483632 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.0936 | −0.570078 | −0.285039 | − | 0.958516i | \(-0.592006\pi\) | ||||
−0.285039 | + | 0.958516i | \(0.592006\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.40294 | 0.166060 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.8492 | 0.672241 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.8515 | 1.31073 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.9246 | −0.860952 | −0.430476 | − | 0.902602i | \(-0.641654\pi\) | ||||
−0.430476 | + | 0.902602i | \(0.641654\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 32.3070 | 1.21161 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.62569 | 0.173233 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.29738 | −0.272906 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.64657 | 0.248221 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.70032 | −0.249880 | −0.124940 | − | 0.992164i | \(-0.539874\pi\) | ||||
−0.124940 | + | 0.992164i | \(0.539874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 67.7460 | 2.52299 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.5410 | −0.466405 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.9629 | −0.444291 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.4583 | 0.684579 | 0.342289 | − | 0.939595i | \(-0.388798\pi\) | ||||
0.342289 | + | 0.939595i | \(0.388798\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.2842 | −0.492008 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.37201 | 0.0877321 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.8995 | 1.54759 | 0.773797 | − | 0.633434i | \(-0.218355\pi\) | ||||
0.773797 | + | 0.633434i | \(0.218355\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.2482 | 0.783752 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.08044 | −0.334482 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.8361 | 1.28147 | 0.640733 | − | 0.767764i | \(-0.278631\pi\) | ||||
0.640733 | + | 0.767764i | \(0.278631\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.40294 | −0.0515385 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.7889 | 0.946102 | 0.473051 | − | 0.881035i | \(-0.343153\pi\) | ||||
0.473051 | + | 0.881035i | \(0.343153\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.1895 | 0.629775 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −37.2773 | −1.36391 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.39558 | −0.197150 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.5011 | 1.22247 | 0.611237 | − | 0.791447i | \(-0.290672\pi\) | ||||
0.611237 | + | 0.791447i | \(0.290672\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.69296 | −0.353231 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.35959 | −0.0494806 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.53134 | 0.273731 | 0.136866 | − | 0.990590i | \(-0.456297\pi\) | ||||
0.136866 | + | 0.990590i | \(0.456297\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.942386 | 0.0342064 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.1969 | 1.38464 | 0.692318 | − | 0.721593i | \(-0.256590\pi\) | ||||
0.692318 | + | 0.721593i | \(0.256590\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −44.7003 | −1.61826 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.49655 | −0.0541079 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.0553 | −0.507508 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.6501 | 0.600417 | 0.300208 | − | 0.953874i | \(-0.402944\pi\) | ||||
0.300208 | + | 0.953874i | \(0.402944\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.5445 | 0.523808 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.6330 | −0.850022 | −0.425011 | − | 0.905188i | \(-0.639730\pi\) | ||||
−0.425011 | + | 0.905188i | \(0.639730\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.24483 | 0.224321 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.7912 | 0.387131 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.97487 | 0.178243 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.8214 | −0.458784 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.7808 | 0.528221 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −37.1404 | −1.32560 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.3933 | 0.726942 | 0.363471 | − | 0.931606i | \(-0.381592\pi\) | ||||
0.363471 | + | 0.931606i | \(0.381592\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.6222 | −0.378160 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −37.4200 | −1.33050 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.27611 | −0.151849 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.86304 | −0.207941 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.70262 | −0.343685 | −0.171842 | − | 0.985124i | \(-0.554972\pi\) | ||||
−0.171842 | + | 0.985124i | \(0.554972\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.51817 | 0.0890865 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.8561 | 0.524916 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.20147 | 0.0776883 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.9281 | 0.808110 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.19641 | −0.288527 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.0723 | −0.951813 | −0.475906 | − | 0.879496i | \(-0.657880\pi\) | ||||
−0.475906 | + | 0.879496i | \(0.657880\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.9548 | −1.82438 | −0.912190 | − | 0.409767i | \(-0.865610\pi\) | ||||
−0.912190 | + | 0.409767i | \(0.865610\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.46562 | 0.226759 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −43.4702 | −1.52270 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.7734 | 0.411899 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 34.1335 | 1.19272 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.6574 | −0.895451 | −0.447725 | − | 0.894171i | \(-0.647766\pi\) | ||||
−0.447725 | + | 0.894171i | \(0.647766\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.8635 | 1.45927 | 0.729635 | − | 0.683837i | \(-0.239690\pi\) | ||||
0.729635 | + | 0.683837i | \(0.239690\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.27225 | 0.0442941 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.15582 | −0.214059 | −0.107029 | − | 0.994256i | \(-0.534134\pi\) | ||||
−0.107029 | + | 0.994256i | \(0.534134\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.247126 | −0.00858303 | −0.00429151 | − | 0.999991i | \(-0.501366\pi\) | ||||
−0.00429151 | + | 0.999991i | \(0.501366\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.45320 | 0.154480 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.99770 | 0.103864 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −51.2545 | −1.77373 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.71579 | −0.266697 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.9320 | −0.584557 | −0.292278 | − | 0.956333i | \(-0.594413\pi\) | ||||
−0.292278 | + | 0.956333i | \(0.594413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.72545 | −0.162947 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.73511 | −0.128644 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.8921 | −0.546706 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.67750 | 0.160721 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.03829 | −0.207234 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.91882 | 0.271454 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.6930 | 0.742753 | 0.371376 | − | 0.928482i | \(-0.378886\pi\) | ||||
0.371376 | + | 0.928482i | \(0.378886\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.42807 | −0.254035 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.7328 | 1.18645 | 0.593225 | − | 0.805037i | \(-0.297854\pi\) | ||||
0.593225 | + | 0.805037i | \(0.297854\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.3047 | 0.522191 | 0.261095 | − | 0.965313i | \(-0.415916\pi\) | ||||
0.261095 | + | 0.965313i | \(0.415916\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.1929 | 0.415533 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.8457 | −1.22020 | −0.610102 | − | 0.792323i | \(-0.708871\pi\) | ||||
−0.610102 | + | 0.792323i | \(0.708871\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.78766 | −0.298789 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.88633 | −0.301796 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.8538 | −0.402114 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.3128 | 0.823809 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −45.8036 | −1.55022 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −32.7877 | −1.10843 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.4907 | −1.53611 | −0.768057 | − | 0.640382i | \(-0.778776\pi\) | ||||
−0.768057 | + | 0.640382i | \(0.778776\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.59476 | 0.188706 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.3322 | 1.05561 | 0.527804 | − | 0.849366i | \(-0.323016\pi\) | ||||
0.527804 | + | 0.849366i | \(0.323016\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.3550 | −1.18979 | −0.594895 | − | 0.803803i | \(-0.702806\pi\) | ||||
−0.594895 | + | 0.803803i | \(0.702806\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.49655 | 0.251994 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.6141 | 0.557846 | 0.278923 | − | 0.960313i | \(-0.410023\pi\) | ||||
0.278923 | + | 0.960313i | \(0.410023\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.9327 | −0.903295 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.60442 | 0.221256 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.4989 | 0.418258 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.4606 | −1.21874 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.52323 | −0.0842484 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.6717 | −0.422625 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.827158 | −0.0275566 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.8554 | 0.960248 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 43.4702 | 1.44500 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −54.8612 | −1.82164 | −0.910818 | − | 0.412808i | \(-0.864548\pi\) | ||||
−0.910818 | + | 0.412808i | \(0.864548\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.3070 | −0.673542 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.98298 | −0.0988304 | −0.0494152 | − | 0.998778i | \(-0.515736\pi\) | ||||
−0.0494152 | + | 0.998778i | \(0.515736\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.6775 | 0.452659 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.28071 | 0.0753979 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.67980 | −0.220586 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.6701 | 0.879767 | 0.439883 | − | 0.898055i | \(-0.355020\pi\) | ||||
0.439883 | + | 0.898055i | \(0.355020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.8538 | 0.522402 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.3291 | 1.12996 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.6907 | 0.351507 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −39.4737 | −1.29649 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.7595 | 1.43570 | 0.717851 | − | 0.696197i | \(-0.245126\pi\) | ||||
0.717851 | + | 0.696197i | \(0.245126\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.8790 | 0.487638 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.60902 | −0.150892 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.549103 | 0.0179576 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.7823 | 1.56098 | 0.780490 | − | 0.625168i | \(-0.214970\pi\) | ||||
0.780490 | + | 0.625168i | \(0.214970\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.33723 | 0.174174 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.2664 | 1.18225 | 0.591126 | − | 0.806579i | \(-0.298684\pi\) | ||||
0.591126 | + | 0.806579i | \(0.298684\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.94745 | 0.291369 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −38.2448 | −1.24410 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.5468 | −1.15512 | −0.577558 | − | 0.816350i | \(-0.695994\pi\) | ||||
−0.577558 | + | 0.816350i | \(0.695994\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.89443 | −0.191341 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.29278 | −0.204057 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.2088 | 0.751808 | 0.375904 | − | 0.926659i | \(-0.377332\pi\) | ||||
0.375904 | + | 0.926659i | \(0.377332\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 65.5615 | 2.12152 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.58159 | −0.0834510 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −67.9703 | −2.19487 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.3852 | −0.786619 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.14386 | 0.101309 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.5194 | 1.14341 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.09591 | 0.196031 | 0.0980156 | − | 0.995185i | \(-0.468751\pi\) | ||||
0.0980156 | + | 0.995185i | \(0.468751\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.105567 | 0.00339129 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.9822 | −1.12263 | −0.561317 | − | 0.827601i | \(-0.689705\pi\) | ||||
−0.561317 | + | 0.827601i | \(0.689705\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −75.6648 | −2.42570 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.40645 | −0.109094 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.9018 | −0.348779 | −0.174390 | − | 0.984677i | \(-0.555795\pi\) | ||||
−0.174390 | + | 0.984677i | \(0.555795\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.45090 | −0.174211 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.0457 | 0.831574 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.4281 | 0.811030 | 0.405515 | − | 0.914089i | \(-0.367092\pi\) | ||||
0.405515 | + | 0.914089i | \(0.367092\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.2545 | −0.486048 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 30.6334 | 0.975072 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.1748 | 0.673319 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.3925 | −1.56901 | −0.784503 | − | 0.620125i | \(-0.787082\pi\) | ||||
−0.784503 | + | 0.620125i | \(0.787082\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.7107 | −0.435097 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.1563 | 0.638997 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.7409 | 0.656871 | 0.328436 | − | 0.944526i | \(-0.393479\pi\) | ||||
0.328436 | + | 0.944526i | \(0.393479\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.2088 | −0.417909 |
(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 | 3344.2.a.q.1.2 | 3 | ||
4.3 | odd | 2 | 418.2.a.g.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 3762.2.a.bg.1.1 | 3 | |||
44.43 | even | 2 | 4598.2.a.bo.1.2 | 3 | |||
76.75 | even | 2 | 7942.2.a.bi.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.a.g.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
3344.2.a.q.1.2 | 3 | 1.1 | even | 1 | trivial | ||
3762.2.a.bg.1.1 | 3 | 12.11 | even | 2 | |||
4598.2.a.bo.1.2 | 3 | 44.43 | even | 2 | |||
7942.2.a.bi.1.2 | 3 | 76.75 | even | 2 |