Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4096,2,Mod(1,4096)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4096, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4096.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4096 = 2^{12} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4096.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: | \(32.7067246679\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{48})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 20x^{4} - 16x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1024) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.261052\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4096.1 |
$q$-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 | ||||||||
\(3\) | −0.931852 | −0.538005 | −0.269002 | − | 0.963140i | \(-0.586694\pi\) | ||||
−0.269002 | + | 0.963140i | \(0.586694\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.956470 | −0.427747 | −0.213873 | − | 0.976861i | \(-0.568608\pi\) | ||||
−0.213873 | + | 0.976861i | \(0.568608\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.32633 | −1.25724 | −0.628618 | − | 0.777714i | \(-0.716379\pi\) | ||||
−0.628618 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.13165 | −0.710551 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.96713 | −0.593111 | −0.296556 | − | 0.955016i | \(-0.595838\pi\) | ||||
−0.296556 | + | 0.955016i | \(0.595838\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.21694 | −0.614869 | −0.307435 | − | 0.951569i | \(-0.599471\pi\) | ||||
−0.307435 | + | 0.951569i | \(0.599471\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.891289 | 0.230130 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.00997 | −1.45763 | −0.728816 | − | 0.684710i | \(-0.759929\pi\) | ||||
−0.728816 | + | 0.684710i | \(0.759929\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.04284 | −0.927491 | −0.463746 | − | 0.885968i | \(-0.653495\pi\) | ||||
−0.463746 | + | 0.885968i | \(0.653495\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.09965 | 0.676399 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.11870 | 0.858808 | 0.429404 | − | 0.903112i | \(-0.358724\pi\) | ||||
0.429404 | + | 0.903112i | \(0.358724\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.08516 | −0.817033 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.78194 | 0.920285 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.4925 | −1.94841 | −0.974207 | − | 0.225658i | \(-0.927547\pi\) | ||||
−0.974207 | + | 0.225658i | \(0.927547\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.52140 | −1.35088 | −0.675442 | − | 0.737413i | \(-0.736047\pi\) | ||||
−0.675442 | + | 0.737413i | \(0.736047\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.83307 | 0.319097 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.18154 | 0.537779 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.59915 | 0.427298 | 0.213649 | − | 0.976911i | \(-0.431465\pi\) | ||||
0.213649 | + | 0.976911i | \(0.431465\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.06586 | 0.330803 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.95011 | 0.304556 | 0.152278 | − | 0.988338i | \(-0.451339\pi\) | ||||
0.152278 | + | 0.988338i | \(0.451339\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.7603 | 1.79343 | 0.896713 | − | 0.442613i | \(-0.145948\pi\) | ||||
0.896713 | + | 0.442613i | \(0.145948\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.03886 | 0.303936 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.33173 | −0.485983 | −0.242991 | − | 0.970028i | \(-0.578129\pi\) | ||||
−0.242991 | + | 0.970028i | \(0.578129\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.06450 | 0.580643 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.60040 | 0.784213 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.69153 | −1.19387 | −0.596937 | − | 0.802288i | \(-0.703616\pi\) | ||||
−0.596937 | + | 0.802288i | \(0.703616\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.88150 | 0.253701 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.76733 | 0.498995 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.3061 | 1.60212 | 0.801062 | − | 0.598582i | \(-0.204269\pi\) | ||||
0.801062 | + | 0.598582i | \(0.204269\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.179920 | 0.0230364 | 0.0115182 | − | 0.999934i | \(-0.496334\pi\) | ||||
0.0115182 | + | 0.999934i | \(0.496334\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.09059 | 0.893330 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.12044 | 0.263008 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.08808 | −1.11029 | −0.555143 | − | 0.831755i | \(-0.687336\pi\) | ||||
−0.555143 | + | 0.831755i | \(0.687336\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.83802 | −0.462043 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.2039 | −1.32966 | −0.664829 | − | 0.746996i | \(-0.731496\pi\) | ||||
−0.664829 | + | 0.746996i | \(0.731496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.26670 | −0.967545 | −0.483772 | − | 0.875194i | \(-0.660734\pi\) | ||||
−0.483772 | + | 0.875194i | \(0.660734\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.80677 | 0.439568 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.54332 | 0.745681 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.80100 | −0.202628 | −0.101314 | − | 0.994855i | \(-0.532305\pi\) | ||||
−0.101314 | + | 0.994855i | \(0.532305\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.93890 | 0.215433 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.18519 | 0.569148 | 0.284574 | − | 0.958654i | \(-0.408148\pi\) | ||||
0.284574 | + | 0.958654i | \(0.408148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.74836 | 0.623497 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.77748 | 1.04826 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.02458 | −0.956604 | −0.478302 | − | 0.878196i | \(-0.658747\pi\) | ||||
−0.478302 | + | 0.878196i | \(0.658747\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.37429 | 0.773036 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.00883 | 0.726782 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.86686 | 0.396731 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.874915 | −0.0888342 | −0.0444171 | − | 0.999013i | \(-0.514143\pi\) | ||||
−0.0444171 | + | 0.999013i | \(0.514143\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.19323 | 0.421436 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.00183995 | 0.000183082 0 | 9.15410e−5 | − | 1.00000i | \(-0.499971\pi\) | ||||
9.15410e−5 | 1.00000i | \(0.499971\pi\) | ||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.6303 | −1.24450 | −0.622251 | − | 0.782818i | \(-0.713782\pi\) | ||||
−0.622251 | + | 0.782818i | \(0.713782\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.96472 | −0.289327 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.33145 | 0.322064 | 0.161032 | − | 0.986949i | \(-0.448518\pi\) | ||||
0.161032 | + | 0.986949i | \(0.448518\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.34751 | 0.799546 | 0.399773 | − | 0.916614i | \(-0.369089\pi\) | ||||
0.399773 | + | 0.916614i | \(0.369089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.42202 | −0.229888 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.03528 | 0.661823 | 0.330912 | − | 0.943662i | \(-0.392644\pi\) | ||||
0.330912 | + | 0.943662i | \(0.392644\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.93942 | −0.367352 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.72575 | 0.436896 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.9912 | 1.83259 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.13041 | −0.648219 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.81722 | −0.163853 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.68969 | 0.777230 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.09821 | 0.0974502 | 0.0487251 | − | 0.998812i | \(-0.484484\pi\) | ||||
0.0487251 | + | 0.998812i | \(0.484484\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.9588 | −0.964872 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.4665 | 1.61343 | 0.806713 | − | 0.590943i | \(-0.201244\pi\) | ||||
0.806713 | + | 0.590943i | \(0.201244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.4478 | 1.16608 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.57378 | −0.393649 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.24745 | 0.704627 | 0.352314 | − | 0.935882i | \(-0.385395\pi\) | ||||
0.352314 | + | 0.935882i | \(0.385395\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.4312 | 1.13922 | 0.569611 | − | 0.821914i | \(-0.307094\pi\) | ||||
0.569611 | + | 0.821914i | \(0.307094\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.10468 | 0.261461 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.36101 | 0.364686 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0358 | 0.833427 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.78751 | −0.312389 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.9879 | −1.47362 | −0.736812 | − | 0.676097i | \(-0.763670\pi\) | ||||
−0.736812 | + | 0.676097i | \(0.763670\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0898 | 0.983853 | 0.491927 | − | 0.870637i | \(-0.336293\pi\) | ||||
0.491927 | + | 0.870637i | \(0.336293\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.8112 | 1.03572 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.19400 | 0.577836 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.91874 | 0.472367 | 0.236184 | − | 0.971708i | \(-0.424103\pi\) | ||||
0.236184 | + | 0.971708i | \(0.424103\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.09922 | 0.642310 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.7002 | −1.07973 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.75298 | −0.607260 | −0.303630 | − | 0.952790i | \(-0.598199\pi\) | ||||
−0.303630 | + | 0.952790i | \(0.598199\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.75328 | −0.136493 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.6401 | −1.59718 | −0.798591 | − | 0.601874i | \(-0.794421\pi\) | ||||
−0.798591 | + | 0.601874i | \(0.794421\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.08516 | −0.621936 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.61793 | 0.659030 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.18056 | −0.545928 | −0.272964 | − | 0.962024i | \(-0.588004\pi\) | ||||
−0.272964 | + | 0.962024i | \(0.588004\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.5886 | 1.02720 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.4675 | −0.861950 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.871267 | −0.0651216 | −0.0325608 | − | 0.999470i | \(-0.510366\pi\) | ||||
−0.0325608 | + | 0.999470i | \(0.510366\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.2495 | 1.28215 | 0.641073 | − | 0.767480i | \(-0.278490\pi\) | ||||
0.641073 | + | 0.767480i | \(0.278490\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.167659 | −0.0123937 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.48601 | −0.182775 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.8224 | 0.864538 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.9063 | −1.15702 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.7629 | −1.57471 | −0.787356 | − | 0.616499i | \(-0.788551\pi\) | ||||
−0.787356 | + | 0.616499i | \(0.788551\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.640834 | 0.0461283 | 0.0230641 | − | 0.999734i | \(-0.492658\pi\) | ||||
0.0230641 | + | 0.999734i | \(0.492658\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.97594 | −0.141500 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.6906 | −1.47414 | −0.737072 | − | 0.675815i | \(-0.763792\pi\) | ||||
−0.737072 | + | 0.675815i | \(0.763792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.2579 | −0.798051 | −0.399025 | − | 0.916940i | \(-0.630651\pi\) | ||||
−0.399025 | + | 0.916940i | \(0.630651\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.46875 | 0.597339 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 34.9017 | 2.44962 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.86522 | −0.130273 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.77964 | −0.610227 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.95278 | 0.550105 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.94986 | 0.409605 | 0.204803 | − | 0.978803i | \(-0.434345\pi\) | ||||
0.204803 | + | 0.978803i | \(0.434345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.4404 | 0.715362 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.2484 | −0.767132 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.0187 | 1.69838 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.70334 | 0.520544 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.3238 | 0.896253 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.3054 | 1.02493 | 0.512464 | − | 0.858709i | \(-0.328733\pi\) | ||||
0.512464 | + | 0.858709i | \(0.328733\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.70815 | 0.580543 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.4512 | −1.15827 | −0.579137 | − | 0.815230i | \(-0.696610\pi\) | ||||
−0.579137 | + | 0.815230i | \(0.696610\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.2781 | −1.00960 | −0.504801 | − | 0.863235i | \(-0.668434\pi\) | ||||
−0.504801 | + | 0.863235i | \(0.668434\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.09741 | −0.401180 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.6189 | 0.761181 | 0.380591 | − | 0.924744i | \(-0.375721\pi\) | ||||
0.380591 | + | 0.924744i | \(0.375721\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.18670 | 0.207877 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.67826 | 0.109015 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.21394 | 0.272577 | 0.136289 | − | 0.990669i | \(-0.456483\pi\) | ||||
0.136289 | + | 0.990669i | \(0.456483\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.9382 | −1.34875 | −0.674373 | − | 0.738391i | \(-0.735586\pi\) | ||||
−0.674373 | + | 0.738391i | \(0.735586\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1526 | −1.03619 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.88757 | −0.248368 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.96275 | 0.570286 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.83183 | −0.306205 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.2424 | 1.15145 | 0.575725 | − | 0.817644i | \(-0.304720\pi\) | ||||
0.575725 | + | 0.817644i | \(0.304720\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.10201 | −0.509369 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.35662 | −0.335444 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.7839 | 0.984570 | 0.492285 | − | 0.870434i | \(-0.336162\pi\) | ||||
0.492285 | + | 0.870434i | \(0.336162\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.64564 | −0.537214 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.3664 | 1.38445 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.2230 | 1.37033 | 0.685163 | − | 0.728389i | \(-0.259731\pi\) | ||||
0.685163 | + | 0.728389i | \(0.259731\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.31319 | 0.510675 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.40957 | 0.514657 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.47367 | −0.577620 | −0.288810 | − | 0.957386i | \(-0.593260\pi\) | ||||
−0.288810 | + | 0.957386i | \(0.593260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.69345 | 0.406598 | 0.203299 | − | 0.979117i | \(-0.434834\pi\) | ||||
0.203299 | + | 0.979117i | \(0.434834\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.87175 | −0.415897 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.03604 | 0.484591 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.2893 | −1.51949 | −0.759744 | − | 0.650222i | \(-0.774676\pi\) | ||||
−0.759744 | + | 0.650222i | \(0.774676\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.0330 | 0.959871 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.3123 | −1.15208 | −0.576038 | − | 0.817423i | \(-0.695402\pi\) | ||||
−0.576038 | + | 0.817423i | \(0.695402\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.7995 | 0.820293 | 0.410147 | − | 0.912020i | \(-0.365478\pi\) | ||||
0.410147 | + | 0.912020i | \(0.365478\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.60334 | −0.213443 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.48672 | −0.382899 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.1197 | 1.12469 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.815291 | 0.0477932 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.0812 | 0.939475 | 0.469737 | − | 0.882806i | \(-0.344349\pi\) | ||||
0.469737 | + | 0.882806i | \(0.344349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.7705 | −0.685303 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.40669 | −0.545831 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.13092 | −0.528055 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −39.1186 | −2.25476 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.00171456 | −9.84990e−5 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.172088 | −0.00985375 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.93701 | −0.395916 | −0.197958 | − | 0.980210i | \(-0.563431\pi\) | ||||
−0.197958 | + | 0.980210i | \(0.563431\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.7696 | 0.669548 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.7625 | 1.74438 | 0.872192 | − | 0.489165i | \(-0.162698\pi\) | ||||
0.872192 | + | 0.489165i | \(0.162698\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.94082 | 0.222749 | 0.111374 | − | 0.993779i | \(-0.464475\pi\) | ||||
0.111374 | + | 0.993779i | \(0.464475\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.78194 | −0.382119 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.23285 | 0.237741 | 0.118870 | − | 0.992910i | \(-0.462073\pi\) | ||||
0.118870 | + | 0.992910i | \(0.462073\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.6401 | 1.15563 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.10442 | −0.173272 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.2973 | 1.35194 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.05658 | 0.502368 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.77864 | −0.430160 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.0824 | 0.610995 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.1959 | −0.890207 | −0.445104 | − | 0.895479i | \(-0.646833\pi\) | ||||
−0.445104 | + | 0.895479i | \(0.646833\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.54048 | −0.303617 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.69248 | 0.474921 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.16071 | −0.117702 | −0.0588508 | − | 0.998267i | \(-0.518744\pi\) | ||||
−0.0588508 | + | 0.998267i | \(0.518744\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.55583 | −0.356064 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.7956 | 0.801224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.76445 | 0.527231 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.67095 | 0.197637 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.79143 | −0.471948 | −0.235974 | − | 0.971759i | \(-0.575828\pi\) | ||||
−0.235974 | + | 0.971759i | \(0.575828\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0209 | 0.857581 | 0.428791 | − | 0.903404i | \(-0.358940\pi\) | ||||
0.428791 | + | 0.903404i | \(0.358940\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.6013 | −0.565855 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.59235 | 0.137977 | 0.0689885 | − | 0.997617i | \(-0.478023\pi\) | ||||
0.0689885 | + | 0.997617i | \(0.478023\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.7162 | 0.568757 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.6288 | −0.985940 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.99581 | −0.369225 | −0.184612 | − | 0.982811i | \(-0.559103\pi\) | ||||
−0.184612 | + | 0.982811i | \(0.559103\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.65545 | −0.139760 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.64448 | 0.348745 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.90686 | 0.413864 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.5663 | −1.02135 | −0.510675 | − | 0.859774i | \(-0.670605\pi\) | ||||
−0.510675 | + | 0.859774i | \(0.670605\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.15696 | −0.216403 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.9109 | 1.50098 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0445 | −1.14142 | −0.570710 | − | 0.821151i | \(-0.693332\pi\) | ||||
−0.570710 | + | 0.821151i | \(0.693332\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.09750 | −0.418153 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.2613 | 1.19802 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.20637 | 0.216067 | 0.108033 | − | 0.994147i | \(-0.465545\pi\) | ||||
0.108033 | + | 0.994147i | \(0.465545\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.02337 | −0.0524287 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.6568 | −1.05552 | −0.527758 | − | 0.849395i | \(-0.676967\pi\) | ||||
−0.527758 | + | 0.849395i | \(0.676967\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.25850 | −0.318963 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.0688 | −1.27432 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.2094 | −0.872552 | −0.436276 | − | 0.899813i | \(-0.643703\pi\) | ||||
−0.436276 | + | 0.899813i | \(0.643703\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.7533 | −1.25183 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.2080 | −0.868031 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.72260 | 0.0866733 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.2902 | −0.968148 | −0.484074 | − | 0.875027i | \(-0.660843\pi\) | ||||
−0.484074 | + | 0.875027i | \(0.660843\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.5314 | −0.627354 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.119032 | 0.00594418 | 0.00297209 | − | 0.999996i | \(-0.499054\pi\) | ||||
0.00297209 | + | 0.999996i | \(0.499054\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.6745 | 0.830617 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.85450 | −0.0921509 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.11286 | −0.253435 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.9207 | 0.737780 | 0.368890 | − | 0.929473i | \(-0.379738\pi\) | ||||
0.368890 | + | 0.929473i | \(0.379738\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.68540 | −0.379093 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −40.9344 | −2.01425 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.95948 | −0.243451 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.5159 | −0.612907 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.13973 | 0.446505 | 0.223253 | − | 0.974761i | \(-0.428333\pi\) | ||||
0.223253 | + | 0.974761i | \(0.428333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.3008 | 1.33056 | 0.665281 | − | 0.746593i | \(-0.268312\pi\) | ||||
0.665281 | + | 0.746593i | \(0.268312\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.10209 | 0.345315 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.5517 | 1.19093 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.598475 | −0.0289622 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.06381 | −0.196203 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.31726 | 0.159787 | 0.0798934 | − | 0.996803i | \(-0.474542\pi\) | ||||
0.0798934 | + | 0.996803i | \(0.474542\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.3224 | 1.07275 | 0.536374 | − | 0.843981i | \(-0.319794\pi\) | ||||
0.536374 | + | 0.843981i | \(0.319794\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.35187 | −0.448388 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.6512 | −0.796537 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.8766 | −1.42593 | −0.712967 | − | 0.701198i | \(-0.752649\pi\) | ||||
−0.712967 | + | 0.701198i | \(0.752649\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.66410 | −0.412576 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.239370 | 0.0113728 | 0.00568640 | − | 0.999984i | \(-0.498190\pi\) | ||||
0.00568640 | + | 0.999984i | \(0.498190\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.63174 | 0.409184 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.7620 | 0.792817 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.5081 | 1.01503 | 0.507515 | − | 0.861643i | \(-0.330564\pi\) | ||||
0.507515 | + | 0.861643i | \(0.330564\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.83612 | −0.180636 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.2659 | −0.529318 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.05329 | −0.330664 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.7705 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −28.7393 | −1.34144 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.5412 | 1.37587 | 0.687935 | − | 0.725772i | \(-0.258517\pi\) | ||||
0.687935 | + | 0.725772i | \(0.258517\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.6338 | −1.84194 | −0.920969 | − | 0.389635i | \(-0.872601\pi\) | ||||
−0.920969 | + | 0.389635i | \(0.872601\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.70374 | −0.310878 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.3341 | −0.987226 | −0.493613 | − | 0.869682i | \(-0.664324\pi\) | ||||
−0.493613 | + | 0.869682i | \(0.664324\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.2300 | 1.39589 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.51539 | −0.254136 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.1340 | −1.06370 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.5157 | 0.757791 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.5273 | 0.848308 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.07863 | 0.140666 | 0.0703331 | − | 0.997524i | \(-0.477594\pi\) | ||||
0.0703331 | + | 0.997524i | \(0.477594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.76217 | −0.262732 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.7665 | 0.580897 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.836831 | 0.0379985 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.7895 | 1.34989 | 0.674945 | − | 0.737868i | \(-0.264167\pi\) | ||||
0.674945 | + | 0.737868i | \(0.264167\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.22463 | 0.326709 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.4068 | 0.785559 | 0.392779 | − | 0.919633i | \(-0.371514\pi\) | ||||
0.392779 | + | 0.919633i | \(0.371514\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 63.0597 | 2.84007 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.01070 | −0.180268 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 37.2679 | 1.67169 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.1192 | 0.900660 | 0.450330 | − | 0.892862i | \(-0.351306\pi\) | ||||
0.450330 | + | 0.892862i | \(0.351306\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.2335 | 0.859292 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.6866 | −0.699430 | −0.349715 | − | 0.936856i | \(-0.613722\pi\) | ||||
−0.349715 | + | 0.936856i | \(0.613722\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.00175986 | −7.83127e−5 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.53417 | 0.334604 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.3256 | 1.61010 | 0.805051 | − | 0.593205i | \(-0.202138\pi\) | ||||
0.805051 | + | 0.593205i | \(0.202138\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.4978 | 1.21643 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.3326 | −0.853556 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.0805 | 0.532331 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.55394 | 0.288242 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.69122 | 0.293712 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.45856 | 0.326766 | 0.163383 | − | 0.986563i | \(-0.447759\pi\) | ||||
0.163383 | + | 0.986563i | \(0.447759\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.14674 | −0.268778 | −0.134389 | − | 0.990929i | \(-0.542907\pi\) | ||||
−0.134389 | + | 0.990929i | \(0.542907\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.6626 | −0.552640 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 45.2034 | 1.96909 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.03631 | −0.262448 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.2324 | −1.13839 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.32329 | −0.187262 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.18644 | −0.137762 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.811892 | 0.0350357 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.99539 | −0.344386 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.1218 | −0.908096 | −0.454048 | − | 0.890977i | \(-0.650020\pi\) | ||||
−0.454048 | + | 0.890977i | \(0.650020\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.0740 | −0.689801 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.98414 | −0.342003 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.90338 | 0.166896 | 0.0834481 | − | 0.996512i | \(-0.473407\pi\) | ||||
0.0834481 | + | 0.996512i | \(0.473407\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.383527 | −0.0163685 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.4196 | 1.80714 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.99071 | 0.254751 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.31659 | 0.0983339 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.1224 | −0.810241 | −0.405120 | − | 0.914263i | \(-0.632770\pi\) | ||||
−0.405120 | + | 0.914263i | \(0.632770\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.0719 | −1.10272 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.0167 | −0.465125 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.94285 | 0.124026 | 0.0620132 | − | 0.998075i | \(-0.480248\pi\) | ||||
0.0620132 | + | 0.998075i | \(0.480248\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.72903 | −0.283093 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.44943 | −0.270851 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.7138 | 0.616836 | 0.308418 | − | 0.951251i | \(-0.400201\pi\) | ||||
0.308418 | + | 0.951251i | \(0.400201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.9101 | −1.71203 | −0.856017 | − | 0.516947i | \(-0.827068\pi\) | ||||
−0.856017 | + | 0.516947i | \(0.827068\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.2798 | 0.847203 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.8256 | −0.701675 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.1981 | −1.25716 | −0.628582 | − | 0.777744i | \(-0.716364\pi\) | ||||
−0.628582 | + | 0.777744i | \(0.716364\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.597162 | −0.0248172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.2477 | −0.715554 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.0974 | 0.708100 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.52004 | −0.186881 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.7558 | −0.897958 | −0.448979 | − | 0.893542i | \(-0.648212\pi\) | ||||
−0.448979 | + | 0.893542i | \(0.648212\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.4078 | 1.25293 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.2806 | 0.793096 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.2715 | −1.57162 | −0.785810 | − | 0.618468i | \(-0.787754\pi\) | ||||
−0.785810 | + | 0.618468i | \(0.787754\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.1210 | −0.783883 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.4907 | 0.429355 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.90639 | −0.159611 | −0.0798053 | − | 0.996810i | \(-0.525430\pi\) | ||||
−0.0798053 | + | 0.996810i | \(0.525430\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.4101 | −1.19966 | −0.599831 | − | 0.800127i | \(-0.704766\pi\) | ||||
−0.599831 | + | 0.800127i | \(0.704766\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.3726 | 0.788915 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.82002 | 0.277273 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.7402 | −0.760642 | −0.380321 | − | 0.924855i | \(-0.624187\pi\) | ||||
−0.380321 | + | 0.924855i | \(0.624187\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −32.5232 | −1.31790 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.38625 | 0.298816 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.1882 | −0.653837 | −0.326918 | − | 0.945053i | \(-0.606010\pi\) | ||||
−0.326918 | + | 0.945053i | \(0.606010\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.73811 | 0.0700875 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.4721 | −1.46831 | −0.734156 | − | 0.678981i | \(-0.762422\pi\) | ||||
−0.734156 | + | 0.678981i | \(0.762422\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.78117 | 0.232365 | 0.116183 | − | 0.993228i | \(-0.462934\pi\) | ||||
0.116183 | + | 0.993228i | \(0.462934\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.6954 | 0.790348 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.0188 | 1.20268 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.1144 | 0.484576 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.41081 | −0.295959 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.6208 | −0.622842 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.68906 | −0.306097 | −0.153048 | − | 0.988219i | \(-0.548909\pi\) | ||||
−0.153048 | + | 0.988219i | \(0.548909\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.54439 | −0.220370 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.05040 | −0.0416840 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.01076 | −0.357019 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.8828 | 0.944789 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1732 | 0.441315 | 0.220658 | − | 0.975351i | \(-0.429180\pi\) | ||||
0.220658 | + | 0.975351i | \(0.429180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.7449 | −1.52795 | −0.763976 | − | 0.645245i | \(-0.776755\pi\) | ||||
−0.763976 | + | 0.645245i | \(0.776755\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.4818 | 0.412721 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.31385 | −0.169595 | −0.0847975 | − | 0.996398i | \(-0.527024\pi\) | ||||
−0.0847975 | + | 0.996398i | \(0.527024\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.2078 | −0.950238 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.3137 | −0.913736 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.8647 | −0.659967 | −0.329983 | − | 0.943987i | \(-0.607043\pi\) | ||||
−0.329983 | + | 0.943987i | \(0.607043\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.6627 | −0.690138 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.6217 | 0.687490 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.9416 | 1.63381 | 0.816906 | − | 0.576770i | \(-0.195687\pi\) | ||||
0.816906 | + | 0.576770i | \(0.195687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.5399 | −0.954492 | −0.477246 | − | 0.878770i | \(-0.658365\pi\) | ||||
−0.477246 | + | 0.878770i | \(0.658365\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.4158 | −0.482188 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.8625 | −0.498785 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −43.2156 | −1.67331 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.2624 | −0.551416 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.353926 | −0.0136632 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.5003 | 0.751680 | 0.375840 | − | 0.926685i | \(-0.377354\pi\) | ||||
0.375840 | + | 0.926685i | \(0.377354\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.5350 | −0.751903 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.8407 | 0.647241 | 0.323620 | − | 0.946187i | \(-0.395100\pi\) | ||||
0.323620 | + | 0.946187i | \(0.395100\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.91026 | 0.111686 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.2619 | 0.623157 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −49.0773 | −1.87789 | −0.938946 | − | 0.344064i | \(-0.888196\pi\) | ||||
−0.938946 | + | 0.344064i | \(0.888196\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.88844 | −0.301402 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.2369 | 0.543171 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.2686 | 0.734076 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.79239 | 0.334478 | 0.167239 | − | 0.985916i | \(-0.446515\pi\) | ||||
0.167239 | + | 0.985916i | \(0.446515\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.9481 | −0.529844 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.8466 | −0.487298 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.7201 | −0.443931 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.8271 | −0.409519 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.7148 | −1.04678 | −0.523388 | − | 0.852095i | \(-0.675332\pi\) | ||||
−0.523388 | + | 0.852095i | \(0.675332\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.5079 | −0.396315 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.96953 | −0.111839 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.00612030 | −0.000230177 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.2864 | −0.836982 | −0.418491 | − | 0.908221i | \(-0.637441\pi\) | ||||
−0.418491 | + | 0.908221i | \(0.637441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.83910 | 0.143977 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.9784 | −1.16015 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.17118 | −0.155993 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.92677 | −0.146648 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.6036 | 1.25320 | 0.626601 | − | 0.779340i | \(-0.284445\pi\) | ||||
0.626601 | + | 0.779340i | \(0.284445\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.0126 | 1.56463 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.5113 | 0.725632 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 42.8637 | 1.59192 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.18854 | −0.340784 | −0.170392 | − | 0.985376i | \(-0.554503\pi\) | ||||
−0.170392 | + | 0.985376i | \(0.554503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.23511 | 0.342041 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −70.6789 | −2.61415 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.5832 | 0.575579 | 0.287790 | − | 0.957694i | \(-0.407080\pi\) | ||||
0.287790 | + | 0.957694i | \(0.407080\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.62264 | 0.133623 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.8774 | 0.658523 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.94470 | −0.365822 | −0.182911 | − | 0.983129i | \(-0.558552\pi\) | ||||
−0.182911 | + | 0.983129i | \(0.558552\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.35195 | −0.306817 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.64206 | −0.170301 | −0.0851503 | − | 0.996368i | \(-0.527137\pi\) | ||||
−0.0851503 | + | 0.996368i | \(0.527137\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.2049 | 0.630338 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.0530 | −0.404409 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.0815 | −0.404910 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.40568 | −0.197256 | −0.0986280 | − | 0.995124i | \(-0.531445\pi\) | ||||
−0.0986280 | + | 0.995124i | \(0.531445\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.9992 | −0.619485 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.5635 | −0.420840 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.576865 | 0.0209665 | 0.0104833 | − | 0.999945i | \(-0.496663\pi\) | ||||
0.0104833 | + | 0.999945i | \(0.496663\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.54987 | 0.274043 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.29201 | −0.191835 | −0.0959177 | − | 0.995389i | \(-0.530579\pi\) | ||||
−0.0959177 | + | 0.995389i | \(0.530579\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.7666 | −1.00522 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.2535 | −0.443026 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.2820 | −0.985097 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.7699 | 1.57838 | 0.789192 | − | 0.614146i | \(-0.210499\pi\) | ||||
0.789192 | + | 0.614146i | \(0.210499\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.7082 | −0.529704 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.7295 | 1.71671 | 0.858355 | − | 0.513057i | \(-0.171487\pi\) | ||||
0.858355 | + | 0.513057i | \(0.171487\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.7262 | 1.10372 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.05646 | 0.289024 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.88399 | −0.282473 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.0395 | 0.788635 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −50.1746 | −1.79309 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.66110 | −0.202053 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.7247 | −1.38038 | −0.690192 | − | 0.723626i | \(-0.742474\pi\) | ||||
−0.690192 | + | 0.723626i | \(0.742474\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.7085 | −0.737242 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.4017 | −0.832068 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.398873 | −0.0141644 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.74666 | −0.274746 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.3788 | −1.00523 | −0.502614 | − | 0.864511i | \(-0.667628\pi\) | ||||
−0.502614 | + | 0.864511i | \(0.667628\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.0236 | 0.708383 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.2373 | 0.679715 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.2617 | 0.573862 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.1038 | 0.461849 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.82805 | 0.310762 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −51.1815 | −1.79945 | −0.899723 | − | 0.436462i | \(-0.856231\pi\) | ||||
−0.899723 | + | 0.436462i | \(0.856231\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.89583 | −0.171916 | −0.0859579 | − | 0.996299i | \(-0.527395\pi\) | ||||
−0.0859579 | + | 0.996299i | \(0.527395\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.23731 | −0.218752 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.41550 | 0.259754 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.5449 | −1.66339 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.7194 | −0.549281 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.6353 | 1.03428 | 0.517139 | − | 0.855901i | \(-0.326997\pi\) | ||||
0.517139 | + | 0.855901i | \(0.326997\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.8933 | −0.867727 | −0.433864 | − | 0.900979i | \(-0.642850\pi\) | ||||
−0.433864 | + | 0.900979i | \(0.642850\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.48840 | −0.260713 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.7571 | −0.826116 | −0.413058 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413058 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −49.8269 | −1.73056 | −0.865279 | − | 0.501291i | \(-0.832859\pi\) | ||||
−0.865279 | + | 0.501291i | \(0.832859\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.5659 | 0.817492 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.4275 | −0.846363 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.7417 | 0.683189 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −35.9669 | −1.24320 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.1823 | 1.59439 | 0.797196 | − | 0.603721i | \(-0.206316\pi\) | ||||
0.797196 | + | 0.603721i | \(0.206316\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 81.0931 | 2.79631 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.9962 | 0.619822 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.73322 | 0.266031 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.7181 | 0.814964 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.8591 | −0.441322 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.7051 | 0.366967 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.275353 | 0.00942791 | 0.00471395 | − | 0.999989i | \(-0.498499\pi\) | ||||
0.00471395 | + | 0.999989i | \(0.498499\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.24280 | −0.281898 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.2182 | 0.758960 | 0.379480 | − | 0.925200i | \(-0.376103\pi\) | ||||
0.379480 | + | 0.925200i | \(0.376103\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.537410 | −0.0183362 | −0.00916809 | − | 0.999958i | \(-0.502918\pi\) | ||||
−0.00916809 | + | 0.999958i | \(0.502918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.04466 | 0.206002 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.3841 | 0.387520 | 0.193760 | − | 0.981049i | \(-0.437932\pi\) | ||||
0.193760 | + | 0.981049i | \(0.437932\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.86800 | 0.233519 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.8167 | −0.605088 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.54279 | 0.120181 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.1478 | 0.682681 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.86502 | 0.0631212 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.9048 | −0.977161 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.60167 | −0.155387 | −0.0776937 | − | 0.996977i | \(-0.524756\pi\) | ||||
−0.0776937 | + | 0.996977i | \(0.524756\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.9853 | −0.505442 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.1185 | −1.38532 | −0.692658 | − | 0.721266i | \(-0.743561\pi\) | ||||
−0.692658 | + | 0.721266i | \(0.743561\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.1779 | −1.04922 | −0.524610 | − | 0.851343i | \(-0.675789\pi\) | ||||
−0.524610 | + | 0.851343i | \(0.675789\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.9683 | 0.368696 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.6870 | −0.425988 | −0.212994 | − | 0.977054i | \(-0.568321\pi\) | ||||
−0.212994 | + | 0.977054i | \(0.568321\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.65301 | −0.122518 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.81406 | −0.127776 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.4696 | 0.450745 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.833341 | 0.0278555 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.50867 | 0.284096 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 78.9185 | 2.63208 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 52.2358 | 1.74023 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36.4527 | 1.21307 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.4986 | −0.548434 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.38915 | −0.212148 | −0.106074 | − | 0.994358i | \(-0.533828\pi\) | ||||
−0.106074 | + | 0.994358i | \(0.533828\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.00392214 | −0.000130089 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.93353 | 0.0971921 | 0.0485961 | − | 0.998819i | \(-0.484525\pi\) | ||||
0.0485961 | + | 0.998819i | \(0.484525\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.1999 | −0.337568 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.160361 | 0.00530136 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −61.4258 | −2.02846 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.8980 | −1.44806 | −0.724030 | − | 0.689768i | \(-0.757712\pi\) | ||||
−0.724030 | + | 0.689768i | \(0.757712\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.46427 | 0.213005 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.8384 | 0.817566 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.6180 | −0.349116 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.9234 | 0.884282 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.7583 | 0.385776 | 0.192888 | − | 0.981221i | \(-0.438215\pi\) | ||||
0.192888 | + | 0.981221i | \(0.438215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.4321 | −0.538541 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.6661 | −0.938486 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.3078 | −0.369803 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.07498 | 0.0677867 | 0.0338934 | − | 0.999425i | \(-0.489209\pi\) | ||||
0.0338934 | + | 0.999425i | \(0.489209\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.67226 | −0.119840 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.1156 | −0.329760 | −0.164880 | − | 0.986314i | \(-0.552724\pi\) | ||||
−0.164880 | + | 0.986314i | \(0.552724\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.03193 | 0.261556 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.2139 | 0.494909 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.7585 | 1.16199 | 0.580997 | − | 0.813906i | \(-0.302663\pi\) | ||||
0.580997 | + | 0.813906i | \(0.302663\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.3268 | 0.594914 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.94439 | −0.127906 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.9438 | −0.516472 | −0.258236 | − | 0.966082i | \(-0.583141\pi\) | ||||
−0.258236 | + | 0.966082i | \(0.583141\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.8156 | 0.673578 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.2335 | −0.621732 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.4338 | −0.885883 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.5715 | 0.824886 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.10150 | −0.228843 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.612939 | −0.0197312 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.6191 | 1.14543 | 0.572717 | − | 0.819753i | \(-0.305889\pi\) | ||||
0.572717 | + | 0.819753i | \(0.305889\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.6415 | −0.727350 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.63473 | 0.245010 | 0.122505 | − | 0.992468i | \(-0.460907\pi\) | ||||
0.122505 | + | 0.992468i | \(0.460907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.6768 | −1.43227 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.43939 | −0.270277 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.0511 | 0.673484 | 0.336742 | − | 0.941597i | \(-0.390675\pi\) | ||||
0.336742 | + | 0.941597i | \(0.390675\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.7525 | 0.567372 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.7940 | −0.568118 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.4067 | −1.06551 | −0.532755 | − | 0.846270i | \(-0.678843\pi\) | ||||
−0.532755 | + | 0.846270i | \(0.678843\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.7899 | 0.630560 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.3272 | −0.328718 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.4371 | 1.54021 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.0358 | 0.858822 | 0.429411 | − | 0.903109i | \(-0.358721\pi\) | ||||
0.429411 | + | 0.903109i | \(0.358721\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.0922 | 0.478936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.7678 | 0.341364 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.0996 | −1.11162 | −0.555808 | − | 0.831311i | \(-0.687591\pi\) | ||||
−0.555808 | + | 0.831311i | \(0.687591\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.4290 | 0.393235 |
(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 | 4096.2.a.s.1.1 | 8 | ||
4.3 | odd | 2 | 4096.2.a.i.1.7 | 8 | |||
8.3 | odd | 2 | inner | 4096.2.a.s.1.2 | 8 | ||
8.5 | even | 2 | 4096.2.a.i.1.8 | 8 | |||
64.3 | odd | 16 | 1024.2.g.f.641.2 | yes | 16 | ||
64.5 | even | 16 | 1024.2.g.g.897.2 | yes | 16 | ||
64.11 | odd | 16 | 1024.2.g.a.385.3 | yes | 16 | ||
64.13 | even | 16 | 1024.2.g.g.129.2 | yes | 16 | ||
64.19 | odd | 16 | 1024.2.g.d.129.2 | yes | 16 | ||
64.21 | even | 16 | 1024.2.g.f.385.3 | yes | 16 | ||
64.27 | odd | 16 | 1024.2.g.d.897.2 | yes | 16 | ||
64.29 | even | 16 | 1024.2.g.a.641.2 | yes | 16 | ||
64.35 | odd | 16 | 1024.2.g.a.641.3 | yes | 16 | ||
64.37 | even | 16 | 1024.2.g.d.897.3 | yes | 16 | ||
64.43 | odd | 16 | 1024.2.g.f.385.2 | yes | 16 | ||
64.45 | even | 16 | 1024.2.g.d.129.3 | yes | 16 | ||
64.51 | odd | 16 | 1024.2.g.g.129.3 | yes | 16 | ||
64.53 | even | 16 | 1024.2.g.a.385.2 | ✓ | 16 | ||
64.59 | odd | 16 | 1024.2.g.g.897.3 | yes | 16 | ||
64.61 | even | 16 | 1024.2.g.f.641.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.a.385.2 | ✓ | 16 | 64.53 | even | 16 | ||
1024.2.g.a.385.3 | yes | 16 | 64.11 | odd | 16 | ||
1024.2.g.a.641.2 | yes | 16 | 64.29 | even | 16 | ||
1024.2.g.a.641.3 | yes | 16 | 64.35 | odd | 16 | ||
1024.2.g.d.129.2 | yes | 16 | 64.19 | odd | 16 | ||
1024.2.g.d.129.3 | yes | 16 | 64.45 | even | 16 | ||
1024.2.g.d.897.2 | yes | 16 | 64.27 | odd | 16 | ||
1024.2.g.d.897.3 | yes | 16 | 64.37 | even | 16 | ||
1024.2.g.f.385.2 | yes | 16 | 64.43 | odd | 16 | ||
1024.2.g.f.385.3 | yes | 16 | 64.21 | even | 16 | ||
1024.2.g.f.641.2 | yes | 16 | 64.3 | odd | 16 | ||
1024.2.g.f.641.3 | yes | 16 | 64.61 | even | 16 | ||
1024.2.g.g.129.2 | yes | 16 | 64.13 | even | 16 | ||
1024.2.g.g.129.3 | yes | 16 | 64.51 | odd | 16 | ||
1024.2.g.g.897.2 | yes | 16 | 64.5 | even | 16 | ||
1024.2.g.g.897.3 | yes | 16 | 64.59 | odd | 16 | ||
4096.2.a.i.1.7 | 8 | 4.3 | odd | 2 | |||
4096.2.a.i.1.8 | 8 | 8.5 | even | 2 | |||
4096.2.a.s.1.1 | 8 | 1.1 | even | 1 | trivial | ||
4096.2.a.s.1.2 | 8 | 8.3 | odd | 2 | inner |