Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, 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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 32x^{10} + 393x^{8} - 2334x^{6} + 6955x^{4} - 9591x^{2} + 4537 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.55274\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.380581 | 0.269111 | 0.134556 | − | 0.990906i | \(-0.457039\pi\) | ||||
0.134556 | + | 0.990906i | \(0.457039\pi\) | |||||||
\(3\) | 1.55274 | 0.896472 | 0.448236 | − | 0.893915i | \(-0.352052\pi\) | ||||
0.448236 | + | 0.893915i | \(0.352052\pi\) | |||||||
\(4\) | −1.85516 | −0.927579 | ||||||||
\(5\) | −3.06093 | −1.36889 | −0.684444 | − | 0.729065i | \(-0.739955\pi\) | ||||
−0.684444 | + | 0.729065i | \(0.739955\pi\) | |||||||
\(6\) | 0.590942 | 0.241251 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.46720 | −0.518734 | ||||||||
\(9\) | −0.589012 | −0.196337 | ||||||||
\(10\) | −1.16493 | −0.368384 | ||||||||
\(11\) | −3.73748 | −1.12689 | −0.563446 | − | 0.826153i | \(-0.690525\pi\) | ||||
−0.563446 | + | 0.826153i | \(0.690525\pi\) | |||||||
\(12\) | −2.88057 | −0.831549 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.75281 | −1.22717 | ||||||||
\(16\) | 3.15193 | 0.787982 | ||||||||
\(17\) | 7.73178 | 1.87523 | 0.937616 | − | 0.347674i | \(-0.113028\pi\) | ||||
0.937616 | + | 0.347674i | \(0.113028\pi\) | |||||||
\(18\) | −0.224167 | −0.0528366 | ||||||||
\(19\) | 1.81919 | 0.417350 | 0.208675 | − | 0.977985i | \(-0.433085\pi\) | ||||
0.208675 | + | 0.977985i | \(0.433085\pi\) | |||||||
\(20\) | 5.67850 | 1.26975 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.42241 | −0.303260 | ||||||||
\(23\) | 7.93036 | 1.65360 | 0.826798 | − | 0.562500i | \(-0.190160\pi\) | ||||
0.826798 | + | 0.562500i | \(0.190160\pi\) | |||||||
\(24\) | −2.27817 | −0.465030 | ||||||||
\(25\) | 4.36927 | 0.873855 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.57279 | −1.07248 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.73572 | 0.322315 | 0.161158 | − | 0.986929i | \(-0.448477\pi\) | ||||
0.161158 | + | 0.986929i | \(0.448477\pi\) | |||||||
\(30\) | −1.80883 | −0.330246 | ||||||||
\(31\) | −7.54905 | −1.35585 | −0.677925 | − | 0.735131i | \(-0.737120\pi\) | ||||
−0.677925 | + | 0.735131i | \(0.737120\pi\) | |||||||
\(32\) | 4.13396 | 0.730789 | ||||||||
\(33\) | −5.80331 | −1.01023 | ||||||||
\(34\) | 2.94257 | 0.504646 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.09271 | 0.182118 | ||||||||
\(37\) | −0.792076 | −0.130217 | −0.0651083 | − | 0.997878i | \(-0.520739\pi\) | ||||
−0.0651083 | + | 0.997878i | \(0.520739\pi\) | |||||||
\(38\) | 0.692348 | 0.112314 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.49099 | 0.710088 | ||||||||
\(41\) | −0.638943 | −0.0997862 | −0.0498931 | − | 0.998755i | \(-0.515888\pi\) | ||||
−0.0498931 | + | 0.998755i | \(0.515888\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.02523 | 0.918839 | 0.459420 | − | 0.888219i | \(-0.348057\pi\) | ||||
0.459420 | + | 0.888219i | \(0.348057\pi\) | |||||||
\(44\) | 6.93361 | 1.04528 | ||||||||
\(45\) | 1.80292 | 0.268764 | ||||||||
\(46\) | 3.01815 | 0.445001 | ||||||||
\(47\) | −4.04419 | −0.589905 | −0.294953 | − | 0.955512i | \(-0.595304\pi\) | ||||
−0.294953 | + | 0.955512i | \(0.595304\pi\) | |||||||
\(48\) | 4.89411 | 0.706404 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.66286 | 0.235164 | ||||||||
\(51\) | 12.0054 | 1.68109 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.35719 | −0.186424 | −0.0932120 | − | 0.995646i | \(-0.529713\pi\) | ||||
−0.0932120 | + | 0.995646i | \(0.529713\pi\) | |||||||
\(54\) | −2.12090 | −0.288618 | ||||||||
\(55\) | 11.4401 | 1.54259 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.82472 | 0.374143 | ||||||||
\(58\) | 0.660583 | 0.0867387 | ||||||||
\(59\) | 9.65105 | 1.25646 | 0.628230 | − | 0.778028i | \(-0.283780\pi\) | ||||
0.628230 | + | 0.778028i | \(0.283780\pi\) | |||||||
\(60\) | 8.81722 | 1.13830 | ||||||||
\(61\) | −13.1507 | −1.68378 | −0.841890 | − | 0.539649i | \(-0.818557\pi\) | ||||
−0.841890 | + | 0.539649i | \(0.818557\pi\) | |||||||
\(62\) | −2.87303 | −0.364875 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.73055 | −0.591318 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.20863 | −0.271864 | ||||||||
\(67\) | 9.49985 | 1.16059 | 0.580295 | − | 0.814406i | \(-0.302937\pi\) | ||||
0.580295 | + | 0.814406i | \(0.302937\pi\) | |||||||
\(68\) | −14.3437 | −1.73943 | ||||||||
\(69\) | 12.3138 | 1.48240 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.89385 | −0.462115 | −0.231058 | − | 0.972940i | \(-0.574219\pi\) | ||||
−0.231058 | + | 0.972940i | \(0.574219\pi\) | |||||||
\(72\) | 0.864198 | 0.101847 | ||||||||
\(73\) | 13.7495 | 1.60925 | 0.804626 | − | 0.593782i | \(-0.202366\pi\) | ||||
0.804626 | + | 0.593782i | \(0.202366\pi\) | |||||||
\(74\) | −0.301449 | −0.0350428 | ||||||||
\(75\) | 6.78433 | 0.783387 | ||||||||
\(76\) | −3.37488 | −0.387125 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3589 | −1.27797 | −0.638987 | − | 0.769217i | \(-0.720646\pi\) | ||||
−0.638987 | + | 0.769217i | \(0.720646\pi\) | |||||||
\(80\) | −9.64782 | −1.07866 | ||||||||
\(81\) | −6.88603 | −0.765115 | ||||||||
\(82\) | −0.243170 | −0.0268536 | ||||||||
\(83\) | −0.0617751 | −0.00678070 | −0.00339035 | − | 0.999994i | \(-0.501079\pi\) | ||||
−0.00339035 | + | 0.999994i | \(0.501079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.6664 | −2.56698 | ||||||||
\(86\) | 2.29309 | 0.247270 | ||||||||
\(87\) | 2.69512 | 0.288947 | ||||||||
\(88\) | 5.48363 | 0.584557 | ||||||||
\(89\) | −13.4132 | −1.42179 | −0.710896 | − | 0.703298i | \(-0.751710\pi\) | ||||
−0.710896 | + | 0.703298i | \(0.751710\pi\) | |||||||
\(90\) | 0.686158 | 0.0723274 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −14.7121 | −1.53384 | ||||||||
\(93\) | −11.7217 | −1.21548 | ||||||||
\(94\) | −1.53914 | −0.158750 | ||||||||
\(95\) | −5.56840 | −0.571306 | ||||||||
\(96\) | 6.41895 | 0.655132 | ||||||||
\(97\) | −12.0577 | −1.22428 | −0.612138 | − | 0.790751i | \(-0.709690\pi\) | ||||
−0.612138 | + | 0.790751i | \(0.709690\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.20142 | 0.221251 | ||||||||
\(100\) | −8.10570 | −0.810570 | ||||||||
\(101\) | 11.4174 | 1.13608 | 0.568039 | − | 0.823001i | \(-0.307702\pi\) | ||||
0.568039 | + | 0.823001i | \(0.307702\pi\) | |||||||
\(102\) | 4.56903 | 0.452401 | ||||||||
\(103\) | 10.8166 | 1.06579 | 0.532894 | − | 0.846182i | \(-0.321104\pi\) | ||||
0.532894 | + | 0.846182i | \(0.321104\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.516520 | −0.0501688 | ||||||||
\(107\) | −5.94982 | −0.575191 | −0.287595 | − | 0.957752i | \(-0.592856\pi\) | ||||
−0.287595 | + | 0.957752i | \(0.592856\pi\) | |||||||
\(108\) | 10.3384 | 0.994813 | ||||||||
\(109\) | 13.2566 | 1.26975 | 0.634874 | − | 0.772616i | \(-0.281052\pi\) | ||||
0.634874 | + | 0.772616i | \(0.281052\pi\) | |||||||
\(110\) | 4.35390 | 0.415128 | ||||||||
\(111\) | −1.22989 | −0.116736 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.61581 | −0.340147 | −0.170074 | − | 0.985431i | \(-0.554401\pi\) | ||||
−0.170074 | + | 0.985431i | \(0.554401\pi\) | |||||||
\(114\) | 1.07503 | 0.100686 | ||||||||
\(115\) | −24.2743 | −2.26359 | ||||||||
\(116\) | −3.22004 | −0.298973 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.67301 | 0.338128 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.97333 | 0.636575 | ||||||||
\(121\) | 2.96873 | 0.269885 | ||||||||
\(122\) | −5.00492 | −0.453125 | ||||||||
\(123\) | −0.992110 | −0.0894556 | ||||||||
\(124\) | 14.0047 | 1.25766 | ||||||||
\(125\) | 1.93060 | 0.172678 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.1895 | −1.17038 | −0.585190 | − | 0.810896i | \(-0.698980\pi\) | ||||
−0.585190 | + | 0.810896i | \(0.698980\pi\) | |||||||
\(128\) | −10.0683 | −0.889919 | ||||||||
\(129\) | 9.35559 | 0.823714 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.72057 | 0.412438 | 0.206219 | − | 0.978506i | \(-0.433884\pi\) | ||||
0.206219 | + | 0.978506i | \(0.433884\pi\) | |||||||
\(132\) | 10.7661 | 0.937066 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.61546 | 0.312328 | ||||||||
\(135\) | 17.0579 | 1.46811 | ||||||||
\(136\) | −11.3441 | −0.972746 | ||||||||
\(137\) | 18.5298 | 1.58311 | 0.791556 | − | 0.611097i | \(-0.209271\pi\) | ||||
0.791556 | + | 0.611097i | \(0.209271\pi\) | |||||||
\(138\) | 4.68638 | 0.398932 | ||||||||
\(139\) | 10.4140 | 0.883302 | 0.441651 | − | 0.897187i | \(-0.354393\pi\) | ||||
0.441651 | + | 0.897187i | \(0.354393\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.27955 | −0.528834 | ||||||||
\(142\) | −1.48193 | −0.124360 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.85652 | −0.154710 | ||||||||
\(145\) | −5.31292 | −0.441214 | ||||||||
\(146\) | 5.23278 | 0.433068 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.46943 | 0.120786 | ||||||||
\(149\) | −19.7675 | −1.61942 | −0.809708 | − | 0.586833i | \(-0.800374\pi\) | ||||
−0.809708 | + | 0.586833i | \(0.800374\pi\) | |||||||
\(150\) | 2.58199 | 0.210818 | ||||||||
\(151\) | −3.27167 | −0.266245 | −0.133122 | − | 0.991100i | \(-0.542500\pi\) | ||||
−0.133122 | + | 0.991100i | \(0.542500\pi\) | |||||||
\(152\) | −2.66911 | −0.216494 | ||||||||
\(153\) | −4.55411 | −0.368178 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.1071 | 1.85601 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.05962 | 0.563419 | 0.281709 | − | 0.959500i | \(-0.409099\pi\) | ||||
0.281709 | + | 0.959500i | \(0.409099\pi\) | |||||||
\(158\) | −4.32298 | −0.343918 | ||||||||
\(159\) | −2.10735 | −0.167124 | ||||||||
\(160\) | −12.6538 | −1.00037 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.62069 | −0.205901 | ||||||||
\(163\) | −11.5801 | −0.907020 | −0.453510 | − | 0.891251i | \(-0.649828\pi\) | ||||
−0.453510 | + | 0.891251i | \(0.649828\pi\) | |||||||
\(164\) | 1.18534 | 0.0925596 | ||||||||
\(165\) | 17.7635 | 1.38289 | ||||||||
\(166\) | −0.0235104 | −0.00182476 | ||||||||
\(167\) | 6.42722 | 0.497353 | 0.248677 | − | 0.968587i | \(-0.420004\pi\) | ||||
0.248677 | + | 0.968587i | \(0.420004\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −9.00699 | −0.690804 | ||||||||
\(171\) | −1.07152 | −0.0819413 | ||||||||
\(172\) | −11.1778 | −0.852296 | ||||||||
\(173\) | 2.00814 | 0.152676 | 0.0763381 | − | 0.997082i | \(-0.475677\pi\) | ||||
0.0763381 | + | 0.997082i | \(0.475677\pi\) | |||||||
\(174\) | 1.02571 | 0.0777589 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.7803 | −0.887970 | ||||||||
\(177\) | 14.9855 | 1.12638 | ||||||||
\(178\) | −5.10479 | −0.382620 | ||||||||
\(179\) | −16.5700 | −1.23850 | −0.619251 | − | 0.785193i | \(-0.712563\pi\) | ||||
−0.619251 | + | 0.785193i | \(0.712563\pi\) | |||||||
\(180\) | −3.34470 | −0.249300 | ||||||||
\(181\) | −16.6654 | −1.23873 | −0.619364 | − | 0.785104i | \(-0.712609\pi\) | ||||
−0.619364 | + | 0.785104i | \(0.712609\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.4196 | −1.50946 | ||||||||
\(184\) | −11.6354 | −0.857775 | ||||||||
\(185\) | 2.42449 | 0.178252 | ||||||||
\(186\) | −4.46105 | −0.327100 | ||||||||
\(187\) | −28.8973 | −2.11318 | ||||||||
\(188\) | 7.50260 | 0.547184 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.11923 | −0.153745 | ||||||||
\(191\) | −23.2729 | −1.68397 | −0.841983 | − | 0.539504i | \(-0.818612\pi\) | ||||
−0.841983 | + | 0.539504i | \(0.818612\pi\) | |||||||
\(192\) | −7.34529 | −0.530100 | ||||||||
\(193\) | −18.7077 | −1.34661 | −0.673304 | − | 0.739366i | \(-0.735125\pi\) | ||||
−0.673304 | + | 0.739366i | \(0.735125\pi\) | |||||||
\(194\) | −4.58894 | −0.329467 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.5601 | −1.74983 | −0.874916 | − | 0.484274i | \(-0.839084\pi\) | ||||
−0.874916 | + | 0.484274i | \(0.839084\pi\) | |||||||
\(198\) | 0.837818 | 0.0595411 | ||||||||
\(199\) | −13.0279 | −0.923521 | −0.461761 | − | 0.887005i | \(-0.652782\pi\) | ||||
−0.461761 | + | 0.887005i | \(0.652782\pi\) | |||||||
\(200\) | −6.41060 | −0.453298 | ||||||||
\(201\) | 14.7508 | 1.04044 | ||||||||
\(202\) | 4.34527 | 0.305732 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −22.2719 | −1.55935 | ||||||||
\(205\) | 1.95576 | 0.136596 | ||||||||
\(206\) | 4.11658 | 0.286816 | ||||||||
\(207\) | −4.67108 | −0.324662 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.79917 | −0.470308 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.3026 | 1.12232 | 0.561160 | − | 0.827708i | \(-0.310355\pi\) | ||||
0.561160 | + | 0.827708i | \(0.310355\pi\) | |||||||
\(212\) | 2.51780 | 0.172923 | ||||||||
\(213\) | −6.04612 | −0.414273 | ||||||||
\(214\) | −2.26439 | −0.154790 | ||||||||
\(215\) | −18.4428 | −1.25779 | ||||||||
\(216\) | 8.17639 | 0.556333 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.04520 | 0.341704 | ||||||||
\(219\) | 21.3493 | 1.44265 | ||||||||
\(220\) | −21.2233 | −1.43087 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.468071 | −0.0314149 | ||||||||
\(223\) | −13.1556 | −0.880962 | −0.440481 | − | 0.897762i | \(-0.645192\pi\) | ||||
−0.440481 | + | 0.897762i | \(0.645192\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.57355 | −0.171570 | ||||||||
\(226\) | −1.37611 | −0.0915375 | ||||||||
\(227\) | 19.8288 | 1.31608 | 0.658041 | − | 0.752982i | \(-0.271385\pi\) | ||||
0.658041 | + | 0.752982i | \(0.271385\pi\) | |||||||
\(228\) | −5.24029 | −0.347047 | ||||||||
\(229\) | −12.3921 | −0.818895 | −0.409447 | − | 0.912334i | \(-0.634278\pi\) | ||||
−0.409447 | + | 0.912334i | \(0.634278\pi\) | |||||||
\(230\) | −9.23833 | −0.609157 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.54665 | −0.167196 | ||||||||
\(233\) | 7.21563 | 0.472711 | 0.236356 | − | 0.971667i | \(-0.424047\pi\) | ||||
0.236356 | + | 0.971667i | \(0.424047\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.3790 | 0.807514 | ||||||||
\(236\) | −17.9042 | −1.16547 | ||||||||
\(237\) | −17.6374 | −1.14567 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.77492 | 0.179495 | 0.0897473 | − | 0.995965i | \(-0.471394\pi\) | ||||
0.0897473 | + | 0.995965i | \(0.471394\pi\) | |||||||
\(240\) | −14.9805 | −0.966988 | ||||||||
\(241\) | −25.8988 | −1.66829 | −0.834143 | − | 0.551548i | \(-0.814037\pi\) | ||||
−0.834143 | + | 0.551548i | \(0.814037\pi\) | |||||||
\(242\) | 1.12984 | 0.0726291 | ||||||||
\(243\) | 6.02617 | 0.386579 | ||||||||
\(244\) | 24.3967 | 1.56184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.377578 | −0.0240735 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 11.0760 | 0.703325 | ||||||||
\(249\) | −0.0959204 | −0.00607871 | ||||||||
\(250\) | 0.734751 | 0.0464698 | ||||||||
\(251\) | −12.7038 | −0.801859 | −0.400929 | − | 0.916109i | \(-0.631313\pi\) | ||||
−0.400929 | + | 0.916109i | \(0.631313\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.6396 | −1.86342 | ||||||||
\(254\) | −5.01968 | −0.314963 | ||||||||
\(255\) | −36.7477 | −2.30123 | ||||||||
\(256\) | 5.62929 | 0.351831 | ||||||||
\(257\) | −8.15704 | −0.508822 | −0.254411 | − | 0.967096i | \(-0.581882\pi\) | ||||
−0.254411 | + | 0.967096i | \(0.581882\pi\) | |||||||
\(258\) | 3.56056 | 0.221671 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.02236 | −0.0632825 | ||||||||
\(262\) | 1.79656 | 0.110992 | ||||||||
\(263\) | −15.3357 | −0.945637 | −0.472819 | − | 0.881160i | \(-0.656763\pi\) | ||||
−0.472819 | + | 0.881160i | \(0.656763\pi\) | |||||||
\(264\) | 8.51462 | 0.524039 | ||||||||
\(265\) | 4.15425 | 0.255194 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.8271 | −1.27460 | ||||||||
\(268\) | −17.6237 | −1.07654 | ||||||||
\(269\) | −16.8969 | −1.03022 | −0.515110 | − | 0.857124i | \(-0.672249\pi\) | ||||
−0.515110 | + | 0.857124i | \(0.672249\pi\) | |||||||
\(270\) | 6.49191 | 0.395085 | ||||||||
\(271\) | 8.83794 | 0.536866 | 0.268433 | − | 0.963298i | \(-0.413494\pi\) | ||||
0.268433 | + | 0.963298i | \(0.413494\pi\) | |||||||
\(272\) | 24.3700 | 1.47765 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.05211 | 0.426033 | ||||||||
\(275\) | −16.3301 | −0.984740 | ||||||||
\(276\) | −22.8440 | −1.37505 | ||||||||
\(277\) | 2.99750 | 0.180102 | 0.0900511 | − | 0.995937i | \(-0.471297\pi\) | ||||
0.0900511 | + | 0.995937i | \(0.471297\pi\) | |||||||
\(278\) | 3.96337 | 0.237707 | ||||||||
\(279\) | 4.44648 | 0.266204 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.22958 | −0.252316 | −0.126158 | − | 0.992010i | \(-0.540265\pi\) | ||||
−0.126158 | + | 0.992010i | \(0.540265\pi\) | |||||||
\(282\) | −2.38988 | −0.142315 | ||||||||
\(283\) | −3.94077 | −0.234255 | −0.117127 | − | 0.993117i | \(-0.537369\pi\) | ||||
−0.117127 | + | 0.993117i | \(0.537369\pi\) | |||||||
\(284\) | 7.22371 | 0.428648 | ||||||||
\(285\) | −8.64625 | −0.512160 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.43495 | −0.143481 | ||||||||
\(289\) | 42.7804 | 2.51649 | ||||||||
\(290\) | −2.02200 | −0.118736 | ||||||||
\(291\) | −18.7225 | −1.09753 | ||||||||
\(292\) | −25.5074 | −1.49271 | ||||||||
\(293\) | −17.4163 | −1.01747 | −0.508735 | − | 0.860923i | \(-0.669887\pi\) | ||||
−0.508735 | + | 0.860923i | \(0.669887\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.5412 | −1.71995 | ||||||||
\(296\) | 1.16213 | 0.0675477 | ||||||||
\(297\) | 20.8282 | 1.20857 | ||||||||
\(298\) | −7.52313 | −0.435803 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −12.5860 | −0.726653 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.24514 | −0.0716495 | ||||||||
\(303\) | 17.7283 | 1.01846 | ||||||||
\(304\) | 5.73394 | 0.328864 | ||||||||
\(305\) | 40.2535 | 2.30491 | ||||||||
\(306\) | −1.73321 | −0.0990808 | ||||||||
\(307\) | −24.2434 | −1.38365 | −0.691823 | − | 0.722067i | \(-0.743192\pi\) | ||||
−0.691823 | + | 0.722067i | \(0.743192\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.7953 | 0.955450 | ||||||||
\(310\) | 8.79412 | 0.499473 | ||||||||
\(311\) | 10.1457 | 0.575309 | 0.287655 | − | 0.957734i | \(-0.407124\pi\) | ||||
0.287655 | + | 0.957734i | \(0.407124\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.32223 | 0.413877 | 0.206938 | − | 0.978354i | \(-0.433650\pi\) | ||||
0.206938 | + | 0.978354i | \(0.433650\pi\) | |||||||
\(314\) | 2.68676 | 0.151622 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21.0725 | 1.18542 | ||||||||
\(317\) | −9.20624 | −0.517074 | −0.258537 | − | 0.966001i | \(-0.583240\pi\) | ||||
−0.258537 | + | 0.966001i | \(0.583240\pi\) | |||||||
\(318\) | −0.802019 | −0.0449750 | ||||||||
\(319\) | −6.48722 | −0.363214 | ||||||||
\(320\) | 14.4799 | 0.809449 | ||||||||
\(321\) | −9.23849 | −0.515642 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.0655 | 0.782628 | ||||||||
\(324\) | 12.7747 | 0.709704 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.40715 | −0.244090 | ||||||||
\(327\) | 20.5839 | 1.13829 | ||||||||
\(328\) | 0.937458 | 0.0517624 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.76046 | 0.372151 | ||||||||
\(331\) | −1.39303 | −0.0765677 | −0.0382839 | − | 0.999267i | \(-0.512189\pi\) | ||||
−0.0382839 | + | 0.999267i | \(0.512189\pi\) | |||||||
\(332\) | 0.114603 | 0.00628964 | ||||||||
\(333\) | 0.466542 | 0.0255663 | ||||||||
\(334\) | 2.44608 | 0.133844 | ||||||||
\(335\) | −29.0783 | −1.58872 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.7496 | 0.803463 | 0.401731 | − | 0.915758i | \(-0.368409\pi\) | ||||
0.401731 | + | 0.915758i | \(0.368409\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.61440 | −0.304933 | ||||||||
\(340\) | 43.9049 | 2.38108 | ||||||||
\(341\) | 28.2144 | 1.52790 | ||||||||
\(342\) | −0.407801 | −0.0220514 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.84022 | −0.476633 | ||||||||
\(345\) | −37.6915 | −2.02924 | ||||||||
\(346\) | 0.764261 | 0.0410869 | ||||||||
\(347\) | −1.76919 | −0.0949751 | −0.0474876 | − | 0.998872i | \(-0.515121\pi\) | ||||
−0.0474876 | + | 0.998872i | \(0.515121\pi\) | |||||||
\(348\) | −4.99987 | −0.268021 | ||||||||
\(349\) | 22.7396 | 1.21722 | 0.608611 | − | 0.793468i | \(-0.291727\pi\) | ||||
0.608611 | + | 0.793468i | \(0.291727\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −15.4506 | −0.823520 | ||||||||
\(353\) | 10.6199 | 0.565238 | 0.282619 | − | 0.959232i | \(-0.408797\pi\) | ||||
0.282619 | + | 0.959232i | \(0.408797\pi\) | |||||||
\(354\) | 5.70321 | 0.303122 | ||||||||
\(355\) | 11.9188 | 0.632584 | ||||||||
\(356\) | 24.8835 | 1.31882 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.30624 | −0.333295 | ||||||||
\(359\) | −22.5223 | −1.18868 | −0.594341 | − | 0.804213i | \(-0.702587\pi\) | ||||
−0.594341 | + | 0.804213i | \(0.702587\pi\) | |||||||
\(360\) | −2.64525 | −0.139417 | ||||||||
\(361\) | −15.6906 | −0.825819 | ||||||||
\(362\) | −6.34253 | −0.333356 | ||||||||
\(363\) | 4.60966 | 0.241944 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −42.0861 | −2.20289 | ||||||||
\(366\) | −7.77133 | −0.406214 | ||||||||
\(367\) | −4.19604 | −0.219032 | −0.109516 | − | 0.993985i | \(-0.534930\pi\) | ||||
−0.109516 | + | 0.993985i | \(0.534930\pi\) | |||||||
\(368\) | 24.9959 | 1.30300 | ||||||||
\(369\) | 0.376345 | 0.0195917 | ||||||||
\(370\) | 0.922714 | 0.0479696 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 21.7456 | 1.12746 | ||||||||
\(373\) | −23.0008 | −1.19093 | −0.595467 | − | 0.803380i | \(-0.703033\pi\) | ||||
−0.595467 | + | 0.803380i | \(0.703033\pi\) | |||||||
\(374\) | −10.9978 | −0.568682 | ||||||||
\(375\) | 2.99772 | 0.154801 | ||||||||
\(376\) | 5.93363 | 0.306004 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.1835 | −1.85862 | −0.929312 | − | 0.369296i | \(-0.879599\pi\) | ||||
−0.929312 | + | 0.369296i | \(0.879599\pi\) | |||||||
\(380\) | 10.3303 | 0.529931 | ||||||||
\(381\) | −20.4798 | −1.04921 | ||||||||
\(382\) | −8.85722 | −0.453175 | ||||||||
\(383\) | −5.13170 | −0.262218 | −0.131109 | − | 0.991368i | \(-0.541854\pi\) | ||||
−0.131109 | + | 0.991368i | \(0.541854\pi\) | |||||||
\(384\) | −15.6334 | −0.797788 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.11979 | −0.362388 | ||||||||
\(387\) | −3.54893 | −0.180402 | ||||||||
\(388\) | 22.3690 | 1.13561 | ||||||||
\(389\) | −6.14146 | −0.311385 | −0.155692 | − | 0.987806i | \(-0.549761\pi\) | ||||
−0.155692 | + | 0.987806i | \(0.549761\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 61.3158 | 3.10087 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.32979 | 0.369739 | ||||||||
\(394\) | −9.34710 | −0.470900 | ||||||||
\(395\) | 34.7687 | 1.74940 | ||||||||
\(396\) | −4.08398 | −0.205228 | ||||||||
\(397\) | 27.2224 | 1.36625 | 0.683126 | − | 0.730300i | \(-0.260620\pi\) | ||||
0.683126 | + | 0.730300i | \(0.260620\pi\) | |||||||
\(398\) | −4.95816 | −0.248530 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.7716 | 0.688582 | ||||||||
\(401\) | −19.2585 | −0.961724 | −0.480862 | − | 0.876796i | \(-0.659676\pi\) | ||||
−0.480862 | + | 0.876796i | \(0.659676\pi\) | |||||||
\(402\) | 5.61386 | 0.279994 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −21.1812 | −1.05380 | ||||||||
\(405\) | 21.0776 | 1.04736 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.96037 | 0.146740 | ||||||||
\(408\) | −17.6143 | −0.872040 | ||||||||
\(409\) | 14.3384 | 0.708988 | 0.354494 | − | 0.935058i | \(-0.384653\pi\) | ||||
0.354494 | + | 0.935058i | \(0.384653\pi\) | |||||||
\(410\) | 0.744325 | 0.0367596 | ||||||||
\(411\) | 28.7720 | 1.41922 | ||||||||
\(412\) | −20.0664 | −0.988603 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.77772 | −0.0873703 | ||||||||
\(415\) | 0.189089 | 0.00928202 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.1702 | 0.791856 | ||||||||
\(418\) | −2.58763 | −0.126565 | ||||||||
\(419\) | −29.9476 | −1.46304 | −0.731518 | − | 0.681822i | \(-0.761188\pi\) | ||||
−0.731518 | + | 0.681822i | \(0.761188\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.0011 | 1.85206 | 0.926030 | − | 0.377450i | \(-0.123199\pi\) | ||||
0.926030 | + | 0.377450i | \(0.123199\pi\) | |||||||
\(422\) | 6.20447 | 0.302029 | ||||||||
\(423\) | 2.38207 | 0.115820 | ||||||||
\(424\) | 1.99127 | 0.0967044 | ||||||||
\(425\) | 33.7823 | 1.63868 | ||||||||
\(426\) | −2.30104 | −0.111486 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.0379 | 0.533535 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.01898 | −0.338485 | ||||||||
\(431\) | −4.41887 | −0.212850 | −0.106425 | − | 0.994321i | \(-0.533940\pi\) | ||||
−0.106425 | + | 0.994321i | \(0.533940\pi\) | |||||||
\(432\) | −17.5650 | −0.845097 | ||||||||
\(433\) | 1.64351 | 0.0789819 | 0.0394910 | − | 0.999220i | \(-0.487426\pi\) | ||||
0.0394910 | + | 0.999220i | \(0.487426\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.24955 | −0.395536 | ||||||||
\(436\) | −24.5930 | −1.17779 | ||||||||
\(437\) | 14.4268 | 0.690128 | ||||||||
\(438\) | 8.12513 | 0.388234 | ||||||||
\(439\) | 22.9235 | 1.09408 | 0.547040 | − | 0.837106i | \(-0.315754\pi\) | ||||
0.547040 | + | 0.837106i | \(0.315754\pi\) | |||||||
\(440\) | −16.7850 | −0.800193 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.19065 | −0.151593 | −0.0757963 | − | 0.997123i | \(-0.524150\pi\) | ||||
−0.0757963 | + | 0.997123i | \(0.524150\pi\) | |||||||
\(444\) | 2.28163 | 0.108281 | ||||||||
\(445\) | 41.0567 | 1.94627 | ||||||||
\(446\) | −5.00676 | −0.237077 | ||||||||
\(447\) | −30.6937 | −1.45176 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.8788 | −0.749368 | −0.374684 | − | 0.927153i | \(-0.622249\pi\) | ||||
−0.374684 | + | 0.927153i | \(0.622249\pi\) | |||||||
\(450\) | −0.979446 | −0.0461715 | ||||||||
\(451\) | 2.38804 | 0.112448 | ||||||||
\(452\) | 6.70791 | 0.315513 | ||||||||
\(453\) | −5.08004 | −0.238681 | ||||||||
\(454\) | 7.54646 | 0.354173 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.14442 | −0.194080 | ||||||||
\(457\) | 7.21120 | 0.337325 | 0.168663 | − | 0.985674i | \(-0.446055\pi\) | ||||
0.168663 | + | 0.985674i | \(0.446055\pi\) | |||||||
\(458\) | −4.71621 | −0.220374 | ||||||||
\(459\) | −43.0875 | −2.01115 | ||||||||
\(460\) | 45.0326 | 2.09966 | ||||||||
\(461\) | 26.5787 | 1.23789 | 0.618946 | − | 0.785434i | \(-0.287560\pi\) | ||||
0.618946 | + | 0.785434i | \(0.287560\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.65498 | −0.262809 | −0.131405 | − | 0.991329i | \(-0.541949\pi\) | ||||
−0.131405 | + | 0.991329i | \(0.541949\pi\) | |||||||
\(464\) | 5.47087 | 0.253979 | ||||||||
\(465\) | 35.8792 | 1.66386 | ||||||||
\(466\) | 2.74613 | 0.127212 | ||||||||
\(467\) | 12.0821 | 0.559092 | 0.279546 | − | 0.960132i | \(-0.409816\pi\) | ||||
0.279546 | + | 0.960132i | \(0.409816\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.71120 | 0.217311 | ||||||||
\(471\) | 10.9617 | 0.505089 | ||||||||
\(472\) | −14.1600 | −0.651768 | ||||||||
\(473\) | −22.5192 | −1.03543 | ||||||||
\(474\) | −6.71244 | −0.308313 | ||||||||
\(475\) | 7.94853 | 0.364703 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.799399 | 0.0366020 | ||||||||
\(478\) | 1.05608 | 0.0483041 | ||||||||
\(479\) | 12.5135 | 0.571754 | 0.285877 | − | 0.958266i | \(-0.407715\pi\) | ||||
0.285877 | + | 0.958266i | \(0.407715\pi\) | |||||||
\(480\) | −19.6480 | −0.896802 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −9.85658 | −0.448955 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.50747 | −0.250340 | ||||||||
\(485\) | 36.9078 | 1.67590 | ||||||||
\(486\) | 2.29345 | 0.104033 | ||||||||
\(487\) | −17.3599 | −0.786652 | −0.393326 | − | 0.919399i | \(-0.628676\pi\) | ||||
−0.393326 | + | 0.919399i | \(0.628676\pi\) | |||||||
\(488\) | 19.2948 | 0.873433 | ||||||||
\(489\) | −17.9808 | −0.813119 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.6384 | −1.02166 | −0.510829 | − | 0.859683i | \(-0.670661\pi\) | ||||
−0.510829 | + | 0.859683i | \(0.670661\pi\) | |||||||
\(492\) | 1.84052 | 0.0829771 | ||||||||
\(493\) | 13.4202 | 0.604416 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.73838 | −0.302868 | ||||||||
\(496\) | −23.7941 | −1.06838 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.0365055 | −0.00163585 | ||||||||
\(499\) | 8.34265 | 0.373468 | 0.186734 | − | 0.982410i | \(-0.440210\pi\) | ||||
0.186734 | + | 0.982410i | \(0.440210\pi\) | |||||||
\(500\) | −3.58157 | −0.160173 | ||||||||
\(501\) | 9.97978 | 0.445864 | ||||||||
\(502\) | −4.83484 | −0.215789 | ||||||||
\(503\) | 18.2399 | 0.813275 | 0.406638 | − | 0.913590i | \(-0.366701\pi\) | ||||
0.406638 | + | 0.913590i | \(0.366701\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.9480 | −1.55516 | ||||||||
\(506\) | −11.2803 | −0.501468 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 24.4686 | 1.08562 | ||||||||
\(509\) | 41.3455 | 1.83261 | 0.916304 | − | 0.400483i | \(-0.131158\pi\) | ||||
0.916304 | + | 0.400483i | \(0.131158\pi\) | |||||||
\(510\) | −13.9855 | −0.619287 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.2790 | 0.984601 | ||||||||
\(513\) | −10.1379 | −0.447601 | ||||||||
\(514\) | −3.10442 | −0.136930 | ||||||||
\(515\) | −33.1087 | −1.45895 | ||||||||
\(516\) | −17.3561 | −0.764060 | ||||||||
\(517\) | 15.1151 | 0.664759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.11812 | 0.136870 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.5390 | −0.593155 | −0.296577 | − | 0.955009i | \(-0.595845\pi\) | ||||
−0.296577 | + | 0.955009i | \(0.595845\pi\) | |||||||
\(522\) | −0.389091 | −0.0170300 | ||||||||
\(523\) | 33.7576 | 1.47612 | 0.738058 | − | 0.674738i | \(-0.235743\pi\) | ||||
0.738058 | + | 0.674738i | \(0.235743\pi\) | |||||||
\(524\) | −8.75740 | −0.382569 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.83646 | −0.254482 | ||||||||
\(527\) | −58.3676 | −2.54253 | ||||||||
\(528\) | −18.2916 | −0.796041 | ||||||||
\(529\) | 39.8907 | 1.73438 | ||||||||
\(530\) | 1.58103 | 0.0686755 | ||||||||
\(531\) | −5.68458 | −0.246690 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −7.92639 | −0.343009 | ||||||||
\(535\) | 18.2120 | 0.787372 | ||||||||
\(536\) | −13.9382 | −0.602038 | ||||||||
\(537\) | −25.7289 | −1.11028 | ||||||||
\(538\) | −6.43063 | −0.277244 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −31.6451 | −1.36179 | ||||||||
\(541\) | 9.62332 | 0.413739 | 0.206870 | − | 0.978369i | \(-0.433672\pi\) | ||||
0.206870 | + | 0.978369i | \(0.433672\pi\) | |||||||
\(542\) | 3.36355 | 0.144477 | ||||||||
\(543\) | −25.8769 | −1.11049 | ||||||||
\(544\) | 31.9629 | 1.37040 | ||||||||
\(545\) | −40.5774 | −1.73814 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.2943 | −1.16702 | −0.583509 | − | 0.812106i | \(-0.698321\pi\) | ||||
−0.583509 | + | 0.812106i | \(0.698321\pi\) | |||||||
\(548\) | −34.3758 | −1.46846 | ||||||||
\(549\) | 7.74594 | 0.330589 | ||||||||
\(550\) | −6.21491 | −0.265005 | ||||||||
\(551\) | 3.15760 | 0.134518 | ||||||||
\(552\) | −18.0668 | −0.768972 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.14079 | 0.0484676 | ||||||||
\(555\) | 3.76459 | 0.159798 | ||||||||
\(556\) | −19.3196 | −0.819333 | ||||||||
\(557\) | 14.8829 | 0.630609 | 0.315305 | − | 0.948991i | \(-0.397893\pi\) | ||||
0.315305 | + | 0.948991i | \(0.397893\pi\) | |||||||
\(558\) | 1.69225 | 0.0716385 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −44.8699 | −1.89441 | ||||||||
\(562\) | −1.60970 | −0.0679011 | ||||||||
\(563\) | −21.2764 | −0.896692 | −0.448346 | − | 0.893860i | \(-0.647987\pi\) | ||||
−0.448346 | + | 0.893860i | \(0.647987\pi\) | |||||||
\(564\) | 11.6496 | 0.490535 | ||||||||
\(565\) | 11.0677 | 0.465623 | ||||||||
\(566\) | −1.49978 | −0.0630406 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.71306 | 0.239715 | ||||||||
\(569\) | −5.23482 | −0.219455 | −0.109728 | − | 0.993962i | \(-0.534998\pi\) | ||||
−0.109728 | + | 0.993962i | \(0.534998\pi\) | |||||||
\(570\) | −3.29060 | −0.137828 | ||||||||
\(571\) | 4.71034 | 0.197122 | 0.0985609 | − | 0.995131i | \(-0.468576\pi\) | ||||
0.0985609 | + | 0.995131i | \(0.468576\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −36.1366 | −1.50963 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.6499 | 1.44500 | ||||||||
\(576\) | 2.78635 | 0.116098 | ||||||||
\(577\) | 24.4488 | 1.01782 | 0.508908 | − | 0.860821i | \(-0.330049\pi\) | ||||
0.508908 | + | 0.860821i | \(0.330049\pi\) | |||||||
\(578\) | 16.2814 | 0.677217 | ||||||||
\(579\) | −29.0481 | −1.20720 | ||||||||
\(580\) | 9.85630 | 0.409260 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −7.12542 | −0.295358 | ||||||||
\(583\) | 5.07246 | 0.210080 | ||||||||
\(584\) | −20.1732 | −0.834773 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.62830 | −0.273813 | ||||||||
\(587\) | −15.7681 | −0.650819 | −0.325409 | − | 0.945573i | \(-0.605502\pi\) | ||||
−0.325409 | + | 0.945573i | \(0.605502\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.7331 | −0.565864 | ||||||||
\(590\) | −11.2428 | −0.462859 | ||||||||
\(591\) | −38.1353 | −1.56868 | ||||||||
\(592\) | −2.49657 | −0.102608 | ||||||||
\(593\) | −27.2990 | −1.12104 | −0.560518 | − | 0.828142i | \(-0.689398\pi\) | ||||
−0.560518 | + | 0.828142i | \(0.689398\pi\) | |||||||
\(594\) | 7.92681 | 0.325241 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 36.6718 | 1.50214 | ||||||||
\(597\) | −20.2288 | −0.827911 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.1193 | 0.413462 | 0.206731 | − | 0.978398i | \(-0.433718\pi\) | ||||
0.206731 | + | 0.978398i | \(0.433718\pi\) | |||||||
\(600\) | −9.95397 | −0.406369 | ||||||||
\(601\) | 42.8861 | 1.74936 | 0.874680 | − | 0.484701i | \(-0.161071\pi\) | ||||
0.874680 | + | 0.484701i | \(0.161071\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.59552 | −0.227867 | ||||||||
\(604\) | 6.06946 | 0.246963 | ||||||||
\(605\) | −9.08708 | −0.369442 | ||||||||
\(606\) | 6.74705 | 0.274080 | ||||||||
\(607\) | 17.5891 | 0.713920 | 0.356960 | − | 0.934120i | \(-0.383813\pi\) | ||||
0.356960 | + | 0.934120i | \(0.383813\pi\) | |||||||
\(608\) | 7.52045 | 0.304995 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.3197 | 0.620277 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 8.44859 | 0.341514 | ||||||||
\(613\) | −26.3045 | −1.06243 | −0.531214 | − | 0.847238i | \(-0.678264\pi\) | ||||
−0.531214 | + | 0.847238i | \(0.678264\pi\) | |||||||
\(614\) | −9.22660 | −0.372355 | ||||||||
\(615\) | 3.03678 | 0.122455 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.7580 | 1.19801 | 0.599007 | − | 0.800744i | \(-0.295562\pi\) | ||||
0.599007 | + | 0.800744i | \(0.295562\pi\) | |||||||
\(618\) | 6.39196 | 0.257123 | ||||||||
\(619\) | 15.4684 | 0.621727 | 0.310864 | − | 0.950455i | \(-0.399382\pi\) | ||||
0.310864 | + | 0.950455i | \(0.399382\pi\) | |||||||
\(620\) | −42.8673 | −1.72159 | ||||||||
\(621\) | −44.1942 | −1.77345 | ||||||||
\(622\) | 3.86126 | 0.154822 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.7558 | −1.11023 | ||||||||
\(626\) | 2.78670 | 0.111379 | ||||||||
\(627\) | −10.5573 | −0.421618 | ||||||||
\(628\) | −13.0967 | −0.522615 | ||||||||
\(629\) | −6.12416 | −0.244186 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.00930 | 0.239227 | 0.119613 | − | 0.992821i | \(-0.461835\pi\) | ||||
0.119613 | + | 0.992821i | \(0.461835\pi\) | |||||||
\(632\) | 16.6658 | 0.662929 | ||||||||
\(633\) | 25.3137 | 1.00613 | ||||||||
\(634\) | −3.50372 | −0.139151 | ||||||||
\(635\) | 40.3721 | 1.60212 | ||||||||
\(636\) | 3.90947 | 0.155021 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.46891 | −0.0977452 | ||||||||
\(639\) | 2.29352 | 0.0907304 | ||||||||
\(640\) | 30.8183 | 1.21820 | ||||||||
\(641\) | 22.5972 | 0.892534 | 0.446267 | − | 0.894900i | \(-0.352753\pi\) | ||||
0.446267 | + | 0.894900i | \(0.352753\pi\) | |||||||
\(642\) | −3.51600 | −0.138765 | ||||||||
\(643\) | −5.53812 | −0.218402 | −0.109201 | − | 0.994020i | \(-0.534829\pi\) | ||||
−0.109201 | + | 0.994020i | \(0.534829\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −28.6368 | −1.12757 | ||||||||
\(646\) | 5.35308 | 0.210614 | ||||||||
\(647\) | −18.2801 | −0.718666 | −0.359333 | − | 0.933209i | \(-0.616996\pi\) | ||||
−0.359333 | + | 0.933209i | \(0.616996\pi\) | |||||||
\(648\) | 10.1032 | 0.396891 | ||||||||
\(649\) | −36.0706 | −1.41589 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.4828 | 0.841333 | ||||||||
\(653\) | −23.2707 | −0.910654 | −0.455327 | − | 0.890324i | \(-0.650478\pi\) | ||||
−0.455327 | + | 0.890324i | \(0.650478\pi\) | |||||||
\(654\) | 7.83386 | 0.306328 | ||||||||
\(655\) | −14.4493 | −0.564581 | ||||||||
\(656\) | −2.01390 | −0.0786297 | ||||||||
\(657\) | −8.09859 | −0.315956 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.3408 | −0.987137 | −0.493569 | − | 0.869707i | \(-0.664308\pi\) | ||||
−0.493569 | + | 0.869707i | \(0.664308\pi\) | |||||||
\(660\) | −32.9541 | −1.28274 | ||||||||
\(661\) | −0.199005 | −0.00774041 | −0.00387020 | − | 0.999993i | \(-0.501232\pi\) | ||||
−0.00387020 | + | 0.999993i | \(0.501232\pi\) | |||||||
\(662\) | −0.530160 | −0.0206053 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.0906365 | 0.00351738 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.177557 | 0.00688020 | ||||||||
\(667\) | 13.7649 | 0.532979 | ||||||||
\(668\) | −11.9235 | −0.461335 | ||||||||
\(669\) | −20.4271 | −0.789758 | ||||||||
\(670\) | −11.0667 | −0.427543 | ||||||||
\(671\) | 49.1506 | 1.89744 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.4410 | 1.36615 | 0.683076 | − | 0.730347i | \(-0.260642\pi\) | ||||
0.683076 | + | 0.730347i | \(0.260642\pi\) | |||||||
\(674\) | 5.61342 | 0.216221 | ||||||||
\(675\) | −24.3490 | −0.937195 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.4391 | −1.01614 | −0.508069 | − | 0.861316i | \(-0.669641\pi\) | ||||
−0.508069 | + | 0.861316i | \(0.669641\pi\) | |||||||
\(678\) | −2.13674 | −0.0820608 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 34.7234 | 1.33158 | ||||||||
\(681\) | 30.7888 | 1.17983 | ||||||||
\(682\) | 10.7379 | 0.411174 | ||||||||
\(683\) | 36.6530 | 1.40249 | 0.701244 | − | 0.712921i | \(-0.252628\pi\) | ||||
0.701244 | + | 0.712921i | \(0.252628\pi\) | |||||||
\(684\) | 1.98784 | 0.0760071 | ||||||||
\(685\) | −56.7185 | −2.16710 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.2417 | −0.734117 | ||||||||
\(688\) | 18.9911 | 0.724029 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −14.3447 | −0.546093 | ||||||||
\(691\) | −28.9855 | −1.10266 | −0.551330 | − | 0.834287i | \(-0.685880\pi\) | ||||
−0.551330 | + | 0.834287i | \(0.685880\pi\) | |||||||
\(692\) | −3.72542 | −0.141619 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.673321 | −0.0255589 | ||||||||
\(695\) | −31.8764 | −1.20914 | ||||||||
\(696\) | −3.95428 | −0.149886 | ||||||||
\(697\) | −4.94017 | −0.187122 | ||||||||
\(698\) | 8.65426 | 0.327569 | ||||||||
\(699\) | 11.2040 | 0.423773 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.59251 | 0.135687 | 0.0678436 | − | 0.997696i | \(-0.478388\pi\) | ||||
0.0678436 | + | 0.997696i | \(0.478388\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.44093 | −0.0543459 | ||||||||
\(704\) | 17.6803 | 0.666352 | ||||||||
\(705\) | 19.2213 | 0.723914 | ||||||||
\(706\) | 4.04172 | 0.152112 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −27.8005 | −1.04481 | ||||||||
\(709\) | 33.8684 | 1.27196 | 0.635978 | − | 0.771707i | \(-0.280597\pi\) | ||||
0.635978 | + | 0.771707i | \(0.280597\pi\) | |||||||
\(710\) | 4.53607 | 0.170236 | ||||||||
\(711\) | 6.69052 | 0.250914 | ||||||||
\(712\) | 19.6798 | 0.737531 | ||||||||
\(713\) | −59.8667 | −2.24203 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 30.7400 | 1.14881 | ||||||||
\(717\) | 4.30872 | 0.160912 | ||||||||
\(718\) | −8.57157 | −0.319888 | ||||||||
\(719\) | 4.19141 | 0.156313 | 0.0781565 | − | 0.996941i | \(-0.475097\pi\) | ||||
0.0781565 | + | 0.996941i | \(0.475097\pi\) | |||||||
\(720\) | 5.68268 | 0.211781 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.97153 | −0.222237 | ||||||||
\(723\) | −40.2139 | −1.49557 | ||||||||
\(724\) | 30.9169 | 1.14902 | ||||||||
\(725\) | 7.58384 | 0.281657 | ||||||||
\(726\) | 1.75435 | 0.0651100 | ||||||||
\(727\) | 16.0777 | 0.596289 | 0.298145 | − | 0.954521i | \(-0.403632\pi\) | ||||
0.298145 | + | 0.954521i | \(0.403632\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30.0151 | 1.11167 | ||||||||
\(730\) | −16.0172 | −0.592822 | ||||||||
\(731\) | 46.5857 | 1.72304 | ||||||||
\(732\) | 37.8816 | 1.40015 | ||||||||
\(733\) | −5.57149 | −0.205788 | −0.102894 | − | 0.994692i | \(-0.532810\pi\) | ||||
−0.102894 | + | 0.994692i | \(0.532810\pi\) | |||||||
\(734\) | −1.59693 | −0.0589439 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 32.7838 | 1.20843 | ||||||||
\(737\) | −35.5055 | −1.30786 | ||||||||
\(738\) | 0.143230 | 0.00527236 | ||||||||
\(739\) | −5.57700 | −0.205153 | −0.102577 | − | 0.994725i | \(-0.532709\pi\) | ||||
−0.102577 | + | 0.994725i | \(0.532709\pi\) | |||||||
\(740\) | −4.49781 | −0.165343 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.49100 | −0.128073 | −0.0640363 | − | 0.997948i | \(-0.520397\pi\) | ||||
−0.0640363 | + | 0.997948i | \(0.520397\pi\) | |||||||
\(744\) | 17.1981 | 0.630511 | ||||||||
\(745\) | 60.5068 | 2.21680 | ||||||||
\(746\) | −8.75366 | −0.320494 | ||||||||
\(747\) | 0.0363863 | 0.00133130 | ||||||||
\(748\) | 53.6091 | 1.96014 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.14087 | 0.0416589 | ||||||||
\(751\) | 13.8176 | 0.504213 | 0.252106 | − | 0.967700i | \(-0.418877\pi\) | ||||
0.252106 | + | 0.967700i | \(0.418877\pi\) | |||||||
\(752\) | −12.7470 | −0.464835 | ||||||||
\(753\) | −19.7257 | −0.718844 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.0143 | 0.364459 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.70505 | 0.0983166 | 0.0491583 | − | 0.998791i | \(-0.484346\pi\) | ||||
0.0491583 | + | 0.998791i | \(0.484346\pi\) | |||||||
\(758\) | −13.7708 | −0.500177 | ||||||||
\(759\) | −46.0224 | −1.67051 | ||||||||
\(760\) | 8.16995 | 0.296355 | ||||||||
\(761\) | −11.4906 | −0.416533 | −0.208266 | − | 0.978072i | \(-0.566782\pi\) | ||||
−0.208266 | + | 0.978072i | \(0.566782\pi\) | |||||||
\(762\) | −7.79423 | −0.282355 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 43.1749 | 1.56201 | ||||||||
\(765\) | 13.9398 | 0.503994 | ||||||||
\(766\) | −1.95303 | −0.0705658 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 8.74080 | 0.315407 | ||||||||
\(769\) | 3.84729 | 0.138737 | 0.0693684 | − | 0.997591i | \(-0.477902\pi\) | ||||
0.0693684 | + | 0.997591i | \(0.477902\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.6657 | −0.456145 | ||||||||
\(772\) | 34.7057 | 1.24908 | ||||||||
\(773\) | −39.3566 | −1.41556 | −0.707779 | − | 0.706434i | \(-0.750303\pi\) | ||||
−0.707779 | + | 0.706434i | \(0.750303\pi\) | |||||||
\(774\) | −1.35066 | −0.0485483 | ||||||||
\(775\) | −32.9839 | −1.18482 | ||||||||
\(776\) | 17.6911 | 0.635073 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.33732 | −0.0837972 | ||||||||
\(779\) | −1.16236 | −0.0416458 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.5532 | 0.520754 | ||||||||
\(782\) | 23.3356 | 0.834481 | ||||||||
\(783\) | −9.67280 | −0.345678 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.6090 | −0.771257 | ||||||||
\(786\) | 2.78958 | 0.0995011 | ||||||||
\(787\) | 45.6015 | 1.62552 | 0.812759 | − | 0.582600i | \(-0.197965\pi\) | ||||
0.812759 | + | 0.582600i | \(0.197965\pi\) | |||||||
\(788\) | 45.5628 | 1.62311 | ||||||||
\(789\) | −23.8122 | −0.847738 | ||||||||
\(790\) | 13.2323 | 0.470785 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.22992 | −0.114770 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 10.3603 | 0.367674 | ||||||||
\(795\) | 6.45045 | 0.228774 | ||||||||
\(796\) | 24.1688 | 0.856639 | ||||||||
\(797\) | 43.4464 | 1.53895 | 0.769474 | − | 0.638678i | \(-0.220518\pi\) | ||||
0.769474 | + | 0.638678i | \(0.220518\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.2687 | −1.10621 | ||||||||
\(800\) | 18.0624 | 0.638603 | ||||||||
\(801\) | 7.90050 | 0.279150 | ||||||||
\(802\) | −7.32942 | −0.258811 | ||||||||
\(803\) | −51.3883 | −1.81345 | ||||||||
\(804\) | −27.3650 | −0.965088 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.2364 | −0.923564 | ||||||||
\(808\) | −16.7517 | −0.589322 | ||||||||
\(809\) | −38.8316 | −1.36525 | −0.682623 | − | 0.730771i | \(-0.739161\pi\) | ||||
−0.682623 | + | 0.730771i | \(0.739161\pi\) | |||||||
\(810\) | 8.02175 | 0.281856 | ||||||||
\(811\) | −12.0920 | −0.424608 | −0.212304 | − | 0.977204i | \(-0.568097\pi\) | ||||
−0.212304 | + | 0.977204i | \(0.568097\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.7230 | 0.481286 | ||||||||
\(814\) | 1.12666 | 0.0394894 | ||||||||
\(815\) | 35.4457 | 1.24161 | ||||||||
\(816\) | 37.8402 | 1.32467 | ||||||||
\(817\) | 10.9610 | 0.383478 | ||||||||
\(818\) | 5.45692 | 0.190797 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.62824 | −0.126704 | ||||||||
\(821\) | −17.9409 | −0.626141 | −0.313070 | − | 0.949730i | \(-0.601358\pi\) | ||||
−0.313070 | + | 0.949730i | \(0.601358\pi\) | |||||||
\(822\) | 10.9501 | 0.381927 | ||||||||
\(823\) | −24.5609 | −0.856137 | −0.428069 | − | 0.903746i | \(-0.640806\pi\) | ||||
−0.428069 | + | 0.903746i | \(0.640806\pi\) | |||||||
\(824\) | −15.8701 | −0.552860 | ||||||||
\(825\) | −25.3563 | −0.882792 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.5984 | −0.438088 | −0.219044 | − | 0.975715i | \(-0.570294\pi\) | ||||
−0.219044 | + | 0.975715i | \(0.570294\pi\) | |||||||
\(828\) | 8.66558 | 0.301150 | ||||||||
\(829\) | −39.5002 | −1.37190 | −0.685950 | − | 0.727649i | \(-0.740613\pi\) | ||||
−0.685950 | + | 0.727649i | \(0.740613\pi\) | |||||||
\(830\) | 0.0719638 | 0.00249790 | ||||||||
\(831\) | 4.65432 | 0.161457 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6.15406 | 0.213098 | ||||||||
\(835\) | −19.6733 | −0.680821 | ||||||||
\(836\) | 12.6135 | 0.436248 | ||||||||
\(837\) | 42.0692 | 1.45413 | ||||||||
\(838\) | −11.3975 | −0.393720 | ||||||||
\(839\) | −8.12030 | −0.280344 | −0.140172 | − | 0.990127i | \(-0.544766\pi\) | ||||
−0.140172 | + | 0.990127i | \(0.544766\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.9873 | −0.896113 | ||||||||
\(842\) | 14.4625 | 0.498411 | ||||||||
\(843\) | −6.56742 | −0.226194 | ||||||||
\(844\) | −30.2440 | −1.04104 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.906572 | 0.0311686 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.27776 | −0.146899 | ||||||||
\(849\) | −6.11898 | −0.210003 | ||||||||
\(850\) | 12.8569 | 0.440988 | ||||||||
\(851\) | −6.28145 | −0.215325 | ||||||||
\(852\) | 11.2165 | 0.384271 | ||||||||
\(853\) | −17.7841 | −0.608914 | −0.304457 | − | 0.952526i | \(-0.598475\pi\) | ||||
−0.304457 | + | 0.952526i | \(0.598475\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.27985 | 0.112169 | ||||||||
\(856\) | 8.72957 | 0.298371 | ||||||||
\(857\) | 6.33988 | 0.216566 | 0.108283 | − | 0.994120i | \(-0.465465\pi\) | ||||
0.108283 | + | 0.994120i | \(0.465465\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.0394 | 1.26377 | 0.631883 | − | 0.775063i | \(-0.282282\pi\) | ||||
0.631883 | + | 0.775063i | \(0.282282\pi\) | |||||||
\(860\) | 34.2143 | 1.16670 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.68174 | −0.0572803 | ||||||||
\(863\) | −29.5338 | −1.00534 | −0.502672 | − | 0.864477i | \(-0.667650\pi\) | ||||
−0.502672 | + | 0.864477i | \(0.667650\pi\) | |||||||
\(864\) | −23.0377 | −0.783759 | ||||||||
\(865\) | −6.14678 | −0.208997 | ||||||||
\(866\) | 0.625488 | 0.0212549 | ||||||||
\(867\) | 66.4266 | 2.25597 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.4536 | 1.44014 | ||||||||
\(870\) | −3.13962 | −0.106443 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −19.4500 | −0.658661 | ||||||||
\(873\) | 7.10214 | 0.240371 | ||||||||
\(874\) | 5.49057 | 0.185721 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −39.6063 | −1.33817 | ||||||||
\(877\) | −1.60539 | −0.0542101 | −0.0271050 | − | 0.999633i | \(-0.508629\pi\) | ||||
−0.0271050 | + | 0.999633i | \(0.508629\pi\) | |||||||
\(878\) | 8.72426 | 0.294430 | ||||||||
\(879\) | −27.0429 | −0.912133 | ||||||||
\(880\) | 36.0585 | 1.21553 | ||||||||
\(881\) | −24.3581 | −0.820645 | −0.410322 | − | 0.911941i | \(-0.634584\pi\) | ||||
−0.410322 | + | 0.911941i | \(0.634584\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.5955 | −0.491176 | −0.245588 | − | 0.969374i | \(-0.578981\pi\) | ||||
−0.245588 | + | 0.969374i | \(0.578981\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −45.8696 | −1.54189 | ||||||||
\(886\) | −1.21430 | −0.0407953 | ||||||||
\(887\) | −37.0966 | −1.24558 | −0.622790 | − | 0.782389i | \(-0.714001\pi\) | ||||
−0.622790 | + | 0.782389i | \(0.714001\pi\) | |||||||
\(888\) | 1.80449 | 0.0605547 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 15.6254 | 0.523764 | ||||||||
\(891\) | 25.7364 | 0.862201 | ||||||||
\(892\) | 24.4056 | 0.817161 | ||||||||
\(893\) | −7.35713 | −0.246197 | ||||||||
\(894\) | −11.6814 | −0.390686 | ||||||||
\(895\) | 50.7196 | 1.69537 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.04318 | −0.201663 | ||||||||
\(899\) | −13.1030 | −0.437011 | ||||||||
\(900\) | 4.77435 | 0.159145 | ||||||||
\(901\) | −10.4935 | −0.349588 | ||||||||
\(902\) | 0.908841 | 0.0302611 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.30512 | 0.176446 | ||||||||
\(905\) | 51.0115 | 1.69568 | ||||||||
\(906\) | −1.93337 | −0.0642318 | ||||||||
\(907\) | 18.7039 | 0.621053 | 0.310526 | − | 0.950565i | \(-0.399495\pi\) | ||||
0.310526 | + | 0.950565i | \(0.399495\pi\) | |||||||
\(908\) | −36.7855 | −1.22077 | ||||||||
\(909\) | −6.72501 | −0.223054 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.0911 | 1.22888 | 0.614442 | − | 0.788962i | \(-0.289381\pi\) | ||||
0.614442 | + | 0.788962i | \(0.289381\pi\) | |||||||
\(912\) | 8.90330 | 0.294818 | ||||||||
\(913\) | 0.230883 | 0.00764112 | ||||||||
\(914\) | 2.74444 | 0.0907782 | ||||||||
\(915\) | 62.5030 | 2.06629 | ||||||||
\(916\) | 22.9894 | 0.759590 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −16.3983 | −0.541225 | ||||||||
\(919\) | 15.8724 | 0.523581 | 0.261791 | − | 0.965125i | \(-0.415687\pi\) | ||||
0.261791 | + | 0.965125i | \(0.415687\pi\) | |||||||
\(920\) | 35.6152 | 1.17420 | ||||||||
\(921\) | −37.6437 | −1.24040 | ||||||||
\(922\) | 10.1153 | 0.333131 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.46080 | −0.113790 | ||||||||
\(926\) | −2.15218 | −0.0707250 | ||||||||
\(927\) | −6.37108 | −0.209254 | ||||||||
\(928\) | 7.17541 | 0.235544 | ||||||||
\(929\) | −18.0818 | −0.593244 | −0.296622 | − | 0.954995i | \(-0.595860\pi\) | ||||
−0.296622 | + | 0.954995i | \(0.595860\pi\) | |||||||
\(930\) | 13.6549 | 0.447763 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −13.3861 | −0.438477 | ||||||||
\(933\) | 15.7536 | 0.515749 | ||||||||
\(934\) | 4.59821 | 0.150458 | ||||||||
\(935\) | 88.4526 | 2.89271 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.07980 | −0.231287 | −0.115643 | − | 0.993291i | \(-0.536893\pi\) | ||||
−0.115643 | + | 0.993291i | \(0.536893\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.3695 | 0.371029 | ||||||||
\(940\) | −22.9649 | −0.749033 | ||||||||
\(941\) | −5.13090 | −0.167262 | −0.0836312 | − | 0.996497i | \(-0.526652\pi\) | ||||
−0.0836312 | + | 0.996497i | \(0.526652\pi\) | |||||||
\(942\) | 4.17182 | 0.135925 | ||||||||
\(943\) | −5.06705 | −0.165006 | ||||||||
\(944\) | 30.4194 | 0.990068 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.57037 | −0.278647 | ||||||||
\(947\) | −51.4951 | −1.67336 | −0.836682 | − | 0.547688i | \(-0.815508\pi\) | ||||
−0.836682 | + | 0.547688i | \(0.815508\pi\) | |||||||
\(948\) | 32.7201 | 1.06270 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.02506 | 0.0981459 | ||||||||
\(951\) | −14.2949 | −0.463543 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.2520 | 0.364487 | 0.182243 | − | 0.983253i | \(-0.441664\pi\) | ||||
0.182243 | + | 0.983253i | \(0.441664\pi\) | |||||||
\(954\) | 0.304236 | 0.00985001 | ||||||||
\(955\) | 71.2366 | 2.30516 | ||||||||
\(956\) | −5.14791 | −0.166495 | ||||||||
\(957\) | −10.0729 | −0.325612 | ||||||||
\(958\) | 4.76239 | 0.153866 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 22.4834 | 0.725648 | ||||||||
\(961\) | 25.9881 | 0.838327 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.50451 | 0.112931 | ||||||||
\(964\) | 48.0463 | 1.54747 | ||||||||
\(965\) | 57.2628 | 1.84336 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.02854 | −0.161707 | −0.0808535 | − | 0.996726i | \(-0.525765\pi\) | ||||
−0.0808535 | + | 0.996726i | \(0.525765\pi\) | |||||||
\(968\) | −4.35573 | −0.139998 | ||||||||
\(969\) | 21.8401 | 0.701604 | ||||||||
\(970\) | 14.0464 | 0.451003 | ||||||||
\(971\) | −32.9918 | −1.05876 | −0.529378 | − | 0.848386i | \(-0.677575\pi\) | ||||
−0.529378 | + | 0.848386i | \(0.677575\pi\) | |||||||
\(972\) | −11.1795 | −0.358583 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.60685 | −0.211697 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −41.4502 | −1.32679 | ||||||||
\(977\) | −45.7585 | −1.46394 | −0.731972 | − | 0.681335i | \(-0.761400\pi\) | ||||
−0.731972 | + | 0.681335i | \(0.761400\pi\) | |||||||
\(978\) | −6.84314 | −0.218820 | ||||||||
\(979\) | 50.1313 | 1.60220 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.80827 | −0.249299 | ||||||||
\(982\) | −8.61575 | −0.274940 | ||||||||
\(983\) | 37.4003 | 1.19288 | 0.596442 | − | 0.802656i | \(-0.296581\pi\) | ||||
0.596442 | + | 0.802656i | \(0.296581\pi\) | |||||||
\(984\) | 1.45562 | 0.0464036 | ||||||||
\(985\) | 75.1766 | 2.39533 | ||||||||
\(986\) | 5.10748 | 0.162655 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 47.7823 | 1.51939 | ||||||||
\(990\) | −2.56450 | −0.0815051 | ||||||||
\(991\) | 27.9614 | 0.888222 | 0.444111 | − | 0.895972i | \(-0.353520\pi\) | ||||
0.444111 | + | 0.895972i | \(0.353520\pi\) | |||||||
\(992\) | −31.2075 | −0.990839 | ||||||||
\(993\) | −2.16300 | −0.0686409 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.8774 | 1.26420 | ||||||||
\(996\) | 0.177948 | 0.00563848 | ||||||||
\(997\) | −20.0402 | −0.634678 | −0.317339 | − | 0.948312i | \(-0.602789\pi\) | ||||
−0.317339 | + | 0.948312i | \(0.602789\pi\) | |||||||
\(998\) | 3.17505 | 0.100505 | ||||||||
\(999\) | 4.41407 | 0.139655 |
(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 | 8281.2.a.cm.1.8 | yes | 12 | |
7.6 | odd | 2 | inner | 8281.2.a.cm.1.7 | ✓ | 12 | |
13.12 | even | 2 | 8281.2.a.cr.1.6 | yes | 12 | ||
91.90 | odd | 2 | 8281.2.a.cr.1.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8281.2.a.cm.1.7 | ✓ | 12 | 7.6 | odd | 2 | inner | |
8281.2.a.cm.1.8 | yes | 12 | 1.1 | even | 1 | trivial | |
8281.2.a.cr.1.5 | yes | 12 | 91.90 | odd | 2 | ||
8281.2.a.cr.1.6 | yes | 12 | 13.12 | even | 2 |