Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
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: | \( x^{12} - 3 x^{11} - 31 x^{10} + 82 x^{9} + 334 x^{8} - 684 x^{7} - 1561 x^{6} + 1551 x^{5} + 3573 x^{4} + 345 x^{3} - 1607 x^{2} - 594 x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.60206\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.60206 | 1.16368 | 0.581839 | − | 0.813304i | \(-0.302334\pi\) | ||||
0.581839 | + | 0.813304i | \(0.302334\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.35416 | −1.64572 | −0.822859 | − | 0.568245i | \(-0.807623\pi\) | ||||
−0.822859 | + | 0.568245i | \(0.807623\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.60206 | −0.822844 | ||||||||
\(11\) | 0.265163 | 0.0799497 | 0.0399749 | − | 0.999201i | \(-0.487272\pi\) | ||||
0.0399749 | + | 0.999201i | \(0.487272\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.05522 | 1.12472 | 0.562358 | − | 0.826894i | \(-0.309894\pi\) | ||||
0.562358 | + | 0.826894i | \(0.309894\pi\) | |||||||
\(14\) | 4.35416 | 1.16370 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.33216 | 1.05070 | 0.525352 | − | 0.850885i | \(-0.323934\pi\) | ||||
0.525352 | + | 0.850885i | \(0.323934\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.48387 | 1.02867 | 0.514336 | − | 0.857589i | \(-0.328039\pi\) | ||||
0.514336 | + | 0.857589i | \(0.328039\pi\) | |||||||
\(20\) | 2.60206 | 0.581839 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.265163 | −0.0565330 | ||||||||
\(23\) | −7.28167 | −1.51833 | −0.759167 | − | 0.650896i | \(-0.774393\pi\) | ||||
−0.759167 | + | 0.650896i | \(0.774393\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.77072 | 0.354144 | ||||||||
\(26\) | −4.05522 | −0.795294 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.35416 | −0.822859 | ||||||||
\(29\) | −4.41220 | −0.819326 | −0.409663 | − | 0.912237i | \(-0.634354\pi\) | ||||
−0.409663 | + | 0.912237i | \(0.634354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50928 | −0.450681 | −0.225340 | − | 0.974280i | \(-0.572349\pi\) | ||||
−0.225340 | + | 0.974280i | \(0.572349\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.33216 | −0.742959 | ||||||||
\(35\) | −11.3298 | −1.91509 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.01155 | −0.166297 | −0.0831486 | − | 0.996537i | \(-0.526498\pi\) | ||||
−0.0831486 | + | 0.996537i | \(0.526498\pi\) | |||||||
\(38\) | −4.48387 | −0.727380 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.60206 | −0.411422 | ||||||||
\(41\) | 7.56092 | 1.18082 | 0.590409 | − | 0.807104i | \(-0.298966\pi\) | ||||
0.590409 | + | 0.807104i | \(0.298966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.16581 | 1.24527 | 0.622637 | − | 0.782511i | \(-0.286061\pi\) | ||||
0.622637 | + | 0.782511i | \(0.286061\pi\) | |||||||
\(44\) | 0.265163 | 0.0399749 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.28167 | 1.07362 | ||||||||
\(47\) | −4.04984 | −0.590730 | −0.295365 | − | 0.955385i | \(-0.595441\pi\) | ||||
−0.295365 | + | 0.955385i | \(0.595441\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.9587 | 1.70839 | ||||||||
\(50\) | −1.77072 | −0.250418 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.05522 | 0.562358 | ||||||||
\(53\) | 12.0518 | 1.65544 | 0.827721 | − | 0.561140i | \(-0.189637\pi\) | ||||
0.827721 | + | 0.561140i | \(0.189637\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.689971 | 0.0930357 | ||||||||
\(56\) | 4.35416 | 0.581849 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.41220 | 0.579351 | ||||||||
\(59\) | 2.90383 | 0.378046 | 0.189023 | − | 0.981973i | \(-0.439468\pi\) | ||||
0.189023 | + | 0.981973i | \(0.439468\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.59376 | −0.588171 | −0.294086 | − | 0.955779i | \(-0.595015\pi\) | ||||
−0.294086 | + | 0.955779i | \(0.595015\pi\) | |||||||
\(62\) | 2.50928 | 0.318679 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.5519 | 1.30881 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.97293 | −0.363201 | −0.181601 | − | 0.983372i | \(-0.558128\pi\) | ||||
−0.181601 | + | 0.983372i | \(0.558128\pi\) | |||||||
\(68\) | 4.33216 | 0.525352 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.3298 | 1.35417 | ||||||||
\(71\) | 6.06746 | 0.720075 | 0.360037 | − | 0.932938i | \(-0.382764\pi\) | ||||
0.360037 | + | 0.932938i | \(0.382764\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.42989 | −0.518479 | −0.259240 | − | 0.965813i | \(-0.583472\pi\) | ||||
−0.259240 | + | 0.965813i | \(0.583472\pi\) | |||||||
\(74\) | 1.01155 | 0.117590 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.48387 | 0.514336 | ||||||||
\(77\) | −1.15456 | −0.131575 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.32897 | 0.599555 | 0.299778 | − | 0.954009i | \(-0.403087\pi\) | ||||
0.299778 | + | 0.954009i | \(0.403087\pi\) | |||||||
\(80\) | 2.60206 | 0.290919 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.56092 | −0.834964 | ||||||||
\(83\) | −14.1972 | −1.55835 | −0.779173 | − | 0.626808i | \(-0.784361\pi\) | ||||
−0.779173 | + | 0.626808i | \(0.784361\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.2725 | 1.22268 | ||||||||
\(86\) | −8.16581 | −0.880542 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.265163 | −0.0282665 | ||||||||
\(89\) | −2.33739 | −0.247763 | −0.123881 | − | 0.992297i | \(-0.539534\pi\) | ||||
−0.123881 | + | 0.992297i | \(0.539534\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.6571 | −1.85097 | ||||||||
\(92\) | −7.28167 | −0.759167 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.04984 | 0.417709 | ||||||||
\(95\) | 11.6673 | 1.19704 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.03002 | 0.206117 | 0.103058 | − | 0.994675i | \(-0.467137\pi\) | ||||
0.103058 | + | 0.994675i | \(0.467137\pi\) | |||||||
\(98\) | −11.9587 | −1.20801 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.77072 | 0.177072 | ||||||||
\(101\) | 4.87422 | 0.485003 | 0.242501 | − | 0.970151i | \(-0.422032\pi\) | ||||
0.242501 | + | 0.970151i | \(0.422032\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.98778 | 0.688527 | 0.344263 | − | 0.938873i | \(-0.388129\pi\) | ||||
0.344263 | + | 0.938873i | \(0.388129\pi\) | |||||||
\(104\) | −4.05522 | −0.397647 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0518 | −1.17057 | ||||||||
\(107\) | 0.355452 | 0.0343629 | 0.0171814 | − | 0.999852i | \(-0.494531\pi\) | ||||
0.0171814 | + | 0.999852i | \(0.494531\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.84322 | −0.559679 | −0.279839 | − | 0.960047i | \(-0.590281\pi\) | ||||
−0.279839 | + | 0.960047i | \(0.590281\pi\) | |||||||
\(110\) | −0.689971 | −0.0657862 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.35416 | −0.411430 | ||||||||
\(113\) | 19.5256 | 1.83681 | 0.918407 | − | 0.395637i | \(-0.129476\pi\) | ||||
0.918407 | + | 0.395637i | \(0.129476\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.9474 | −1.76685 | ||||||||
\(116\) | −4.41220 | −0.409663 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.90383 | −0.267319 | ||||||||
\(119\) | −18.8629 | −1.72916 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9297 | −0.993608 | ||||||||
\(122\) | 4.59376 | 0.415900 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.50928 | −0.225340 | ||||||||
\(125\) | −8.40278 | −0.751568 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.2907 | −1.44556 | −0.722782 | − | 0.691076i | \(-0.757137\pi\) | ||||
−0.722782 | + | 0.691076i | \(0.757137\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.5519 | −0.925465 | ||||||||
\(131\) | 17.6406 | 1.54127 | 0.770635 | − | 0.637277i | \(-0.219939\pi\) | ||||
0.770635 | + | 0.637277i | \(0.219939\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.5235 | −1.69290 | ||||||||
\(134\) | 2.97293 | 0.256822 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.33216 | −0.371480 | ||||||||
\(137\) | 17.1254 | 1.46312 | 0.731561 | − | 0.681776i | \(-0.238792\pi\) | ||||
0.731561 | + | 0.681776i | \(0.238792\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.15986 | 0.268016 | 0.134008 | − | 0.990980i | \(-0.457215\pi\) | ||||
0.134008 | + | 0.990980i | \(0.457215\pi\) | |||||||
\(140\) | −11.3298 | −0.957543 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.06746 | −0.509170 | ||||||||
\(143\) | 1.07530 | 0.0899207 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.4808 | −0.953431 | ||||||||
\(146\) | 4.42989 | 0.366620 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.01155 | −0.0831486 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4612 | −0.932701 | −0.466351 | − | 0.884600i | \(-0.654431\pi\) | ||||
−0.466351 | + | 0.884600i | \(0.654431\pi\) | |||||||
\(152\) | −4.48387 | −0.363690 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.15456 | 0.0930374 | ||||||||
\(155\) | −6.52931 | −0.524447 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4362 | 1.07233 | 0.536164 | − | 0.844114i | \(-0.319873\pi\) | ||||
0.536164 | + | 0.844114i | \(0.319873\pi\) | |||||||
\(158\) | −5.32897 | −0.423950 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.60206 | −0.205711 | ||||||||
\(161\) | 31.7056 | 2.49875 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.50198 | −0.195970 | −0.0979852 | − | 0.995188i | \(-0.531240\pi\) | ||||
−0.0979852 | + | 0.995188i | \(0.531240\pi\) | |||||||
\(164\) | 7.56092 | 0.590409 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.1972 | 1.10192 | ||||||||
\(167\) | 12.6702 | 0.980451 | 0.490226 | − | 0.871596i | \(-0.336914\pi\) | ||||
0.490226 | + | 0.871596i | \(0.336914\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.44481 | 0.264985 | ||||||||
\(170\) | −11.2725 | −0.864565 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.16581 | 0.622637 | ||||||||
\(173\) | −8.32877 | −0.633225 | −0.316612 | − | 0.948555i | \(-0.602545\pi\) | ||||
−0.316612 | + | 0.948555i | \(0.602545\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.71001 | −0.582822 | ||||||||
\(176\) | 0.265163 | 0.0199874 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.33739 | 0.175195 | ||||||||
\(179\) | −7.90674 | −0.590978 | −0.295489 | − | 0.955346i | \(-0.595482\pi\) | ||||
−0.295489 | + | 0.955346i | \(0.595482\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.3762 | 1.73754 | 0.868769 | − | 0.495217i | \(-0.164912\pi\) | ||||
0.868769 | + | 0.495217i | \(0.164912\pi\) | |||||||
\(182\) | 17.6571 | 1.30883 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.28167 | 0.536812 | ||||||||
\(185\) | −2.63211 | −0.193516 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.14873 | 0.0840034 | ||||||||
\(188\) | −4.04984 | −0.295365 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.6673 | −0.846436 | ||||||||
\(191\) | 14.9135 | 1.07910 | 0.539551 | − | 0.841953i | \(-0.318594\pi\) | ||||
0.539551 | + | 0.841953i | \(0.318594\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.9804 | −1.36624 | −0.683120 | − | 0.730306i | \(-0.739377\pi\) | ||||
−0.683120 | + | 0.730306i | \(0.739377\pi\) | |||||||
\(194\) | −2.03002 | −0.145747 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.9587 | 0.854195 | ||||||||
\(197\) | −7.79120 | −0.555100 | −0.277550 | − | 0.960711i | \(-0.589522\pi\) | ||||
−0.277550 | + | 0.960711i | \(0.589522\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.84292 | −0.626858 | −0.313429 | − | 0.949612i | \(-0.601478\pi\) | ||||
−0.313429 | + | 0.949612i | \(0.601478\pi\) | |||||||
\(200\) | −1.77072 | −0.125209 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.87422 | −0.342949 | ||||||||
\(203\) | 19.2115 | 1.34838 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.6740 | 1.37409 | ||||||||
\(206\) | −6.98778 | −0.486862 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.05522 | 0.281179 | ||||||||
\(209\) | 1.18896 | 0.0822420 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.6600 | 1.21576 | 0.607882 | − | 0.794028i | \(-0.292019\pi\) | ||||
0.607882 | + | 0.794028i | \(0.292019\pi\) | |||||||
\(212\) | 12.0518 | 0.827721 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.355452 | −0.0242982 | ||||||||
\(215\) | 21.2479 | 1.44910 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.9258 | 0.741694 | ||||||||
\(218\) | 5.84322 | 0.395753 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.689971 | 0.0465178 | ||||||||
\(221\) | 17.5679 | 1.18174 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3515 | −0.760154 | −0.380077 | − | 0.924955i | \(-0.624102\pi\) | ||||
−0.380077 | + | 0.924955i | \(0.624102\pi\) | |||||||
\(224\) | 4.35416 | 0.290925 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.5256 | −1.29882 | ||||||||
\(227\) | −0.921850 | −0.0611854 | −0.0305927 | − | 0.999532i | \(-0.509739\pi\) | ||||
−0.0305927 | + | 0.999532i | \(0.509739\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.88284 | −0.322667 | −0.161334 | − | 0.986900i | \(-0.551579\pi\) | ||||
−0.161334 | + | 0.986900i | \(0.551579\pi\) | |||||||
\(230\) | 18.9474 | 1.24935 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.41220 | 0.289675 | ||||||||
\(233\) | 15.2267 | 0.997532 | 0.498766 | − | 0.866737i | \(-0.333787\pi\) | ||||
0.498766 | + | 0.866737i | \(0.333787\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.5379 | −0.687418 | ||||||||
\(236\) | 2.90383 | 0.189023 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.8629 | 1.22270 | ||||||||
\(239\) | 17.2969 | 1.11884 | 0.559420 | − | 0.828884i | \(-0.311024\pi\) | ||||
0.559420 | + | 0.828884i | \(0.311024\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.4918 | 1.70649 | 0.853243 | − | 0.521514i | \(-0.174632\pi\) | ||||
0.853243 | + | 0.521514i | \(0.174632\pi\) | |||||||
\(242\) | 10.9297 | 0.702587 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.59376 | −0.294086 | ||||||||
\(245\) | 31.1174 | 1.98801 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.1831 | 1.15696 | ||||||||
\(248\) | 2.50928 | 0.159340 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.40278 | 0.531438 | ||||||||
\(251\) | 24.6534 | 1.55611 | 0.778055 | − | 0.628196i | \(-0.216206\pi\) | ||||
0.778055 | + | 0.628196i | \(0.216206\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.93083 | −0.121390 | ||||||||
\(254\) | 16.2907 | 1.02217 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.11123 | −0.131695 | −0.0658474 | − | 0.997830i | \(-0.520975\pi\) | ||||
−0.0658474 | + | 0.997830i | \(0.520975\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.40444 | 0.273679 | ||||||||
\(260\) | 10.5519 | 0.654403 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.6406 | −1.08984 | ||||||||
\(263\) | −3.80370 | −0.234546 | −0.117273 | − | 0.993100i | \(-0.537415\pi\) | ||||
−0.117273 | + | 0.993100i | \(0.537415\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 31.3595 | 1.92640 | ||||||||
\(266\) | 19.5235 | 1.19706 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.97293 | −0.181601 | ||||||||
\(269\) | 13.7256 | 0.836863 | 0.418432 | − | 0.908248i | \(-0.362580\pi\) | ||||
0.418432 | + | 0.908248i | \(0.362580\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.0605 | −1.03635 | −0.518175 | − | 0.855275i | \(-0.673388\pi\) | ||||
−0.518175 | + | 0.855275i | \(0.673388\pi\) | |||||||
\(272\) | 4.33216 | 0.262676 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.1254 | −1.03458 | ||||||||
\(275\) | 0.469530 | 0.0283137 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.2140 | −0.613702 | −0.306851 | − | 0.951758i | \(-0.599275\pi\) | ||||
−0.306851 | + | 0.951758i | \(0.599275\pi\) | |||||||
\(278\) | −3.15986 | −0.189516 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.3298 | 0.677085 | ||||||||
\(281\) | −17.2972 | −1.03186 | −0.515931 | − | 0.856630i | \(-0.672554\pi\) | ||||
−0.515931 | + | 0.856630i | \(0.672554\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.3288 | −0.851758 | −0.425879 | − | 0.904780i | \(-0.640035\pi\) | ||||
−0.425879 | + | 0.904780i | \(0.640035\pi\) | |||||||
\(284\) | 6.06746 | 0.360037 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.07530 | −0.0635836 | ||||||||
\(287\) | −32.9215 | −1.94329 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.76761 | 0.103977 | ||||||||
\(290\) | 11.4808 | 0.674177 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.42989 | −0.259240 | ||||||||
\(293\) | 15.1302 | 0.883914 | 0.441957 | − | 0.897036i | \(-0.354284\pi\) | ||||
0.441957 | + | 0.897036i | \(0.354284\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.55593 | 0.439923 | ||||||||
\(296\) | 1.01155 | 0.0587950 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | −29.5288 | −1.70769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −35.5553 | −2.04937 | ||||||||
\(302\) | 11.4612 | 0.659519 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.48387 | 0.257168 | ||||||||
\(305\) | −11.9533 | −0.684441 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.43123 | −0.481196 | −0.240598 | − | 0.970625i | \(-0.577344\pi\) | ||||
−0.240598 | + | 0.970625i | \(0.577344\pi\) | |||||||
\(308\) | −1.15456 | −0.0657874 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.52931 | 0.370840 | ||||||||
\(311\) | 15.3131 | 0.868325 | 0.434162 | − | 0.900835i | \(-0.357044\pi\) | ||||
0.434162 | + | 0.900835i | \(0.357044\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.41309 | −0.532059 | −0.266030 | − | 0.963965i | \(-0.585712\pi\) | ||||
−0.266030 | + | 0.963965i | \(0.585712\pi\) | |||||||
\(314\) | −13.4362 | −0.758250 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.32897 | 0.299778 | ||||||||
\(317\) | 4.77010 | 0.267916 | 0.133958 | − | 0.990987i | \(-0.457231\pi\) | ||||
0.133958 | + | 0.990987i | \(0.457231\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.16995 | −0.0655049 | ||||||||
\(320\) | 2.60206 | 0.145460 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −31.7056 | −1.76688 | ||||||||
\(323\) | 19.4249 | 1.08083 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.18066 | 0.398312 | ||||||||
\(326\) | 2.50198 | 0.138572 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.56092 | −0.417482 | ||||||||
\(329\) | 17.6337 | 0.972175 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.1235 | 1.21601 | 0.608007 | − | 0.793931i | \(-0.291969\pi\) | ||||
0.608007 | + | 0.793931i | \(0.291969\pi\) | |||||||
\(332\) | −14.1972 | −0.779173 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.6702 | −0.693284 | ||||||||
\(335\) | −7.73574 | −0.422649 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.4043 | 1.81965 | 0.909824 | − | 0.414995i | \(-0.136217\pi\) | ||||
0.909824 | + | 0.414995i | \(0.136217\pi\) | |||||||
\(338\) | −3.44481 | −0.187373 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.2725 | 0.611340 | ||||||||
\(341\) | −0.665370 | −0.0360318 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −21.5911 | −1.16581 | ||||||||
\(344\) | −8.16581 | −0.440271 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.32877 | 0.447758 | ||||||||
\(347\) | 35.4242 | 1.90167 | 0.950835 | − | 0.309697i | \(-0.100228\pi\) | ||||
0.950835 | + | 0.309697i | \(0.100228\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.3976 | 1.46656 | 0.733280 | − | 0.679926i | \(-0.237988\pi\) | ||||
0.733280 | + | 0.679926i | \(0.237988\pi\) | |||||||
\(350\) | 7.71001 | 0.412117 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.265163 | −0.0141333 | ||||||||
\(353\) | −14.5285 | −0.773273 | −0.386637 | − | 0.922232i | \(-0.626363\pi\) | ||||
−0.386637 | + | 0.922232i | \(0.626363\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.7879 | 0.837934 | ||||||||
\(356\) | −2.33739 | −0.123881 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.90674 | 0.417884 | ||||||||
\(359\) | −1.18115 | −0.0623385 | −0.0311693 | − | 0.999514i | \(-0.509923\pi\) | ||||
−0.0311693 | + | 0.999514i | \(0.509923\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.10512 | 0.0581642 | ||||||||
\(362\) | −23.3762 | −1.22863 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.6571 | −0.925483 | ||||||||
\(365\) | −11.5268 | −0.603342 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0480 | −0.576701 | −0.288351 | − | 0.957525i | \(-0.593107\pi\) | ||||
−0.288351 | + | 0.957525i | \(0.593107\pi\) | |||||||
\(368\) | −7.28167 | −0.379583 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.63211 | 0.136837 | ||||||||
\(371\) | −52.4755 | −2.72439 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −38.1150 | −1.97352 | −0.986761 | − | 0.162181i | \(-0.948147\pi\) | ||||
−0.986761 | + | 0.162181i | \(0.948147\pi\) | |||||||
\(374\) | −1.14873 | −0.0593994 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.04984 | 0.208854 | ||||||||
\(377\) | −17.8925 | −0.921509 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.13216 | −0.160888 | −0.0804440 | − | 0.996759i | \(-0.525634\pi\) | ||||
−0.0804440 | + | 0.996759i | \(0.525634\pi\) | |||||||
\(380\) | 11.6673 | 0.598520 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.9135 | −0.763040 | ||||||||
\(383\) | −12.2063 | −0.623713 | −0.311857 | − | 0.950129i | \(-0.600951\pi\) | ||||
−0.311857 | + | 0.950129i | \(0.600951\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.00425 | −0.153111 | ||||||||
\(386\) | 18.9804 | 0.966078 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.03002 | 0.103058 | ||||||||
\(389\) | −2.22633 | −0.112880 | −0.0564398 | − | 0.998406i | \(-0.517975\pi\) | ||||
−0.0564398 | + | 0.998406i | \(0.517975\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.5454 | −1.59532 | ||||||||
\(392\) | −11.9587 | −0.604007 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.79120 | 0.392515 | ||||||||
\(395\) | 13.8663 | 0.697689 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.6782 | 1.58988 | 0.794941 | − | 0.606687i | \(-0.207502\pi\) | ||||
0.794941 | + | 0.606687i | \(0.207502\pi\) | |||||||
\(398\) | 8.84292 | 0.443255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.77072 | 0.0885361 | ||||||||
\(401\) | 18.3003 | 0.913876 | 0.456938 | − | 0.889499i | \(-0.348946\pi\) | ||||
0.456938 | + | 0.889499i | \(0.348946\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.1757 | −0.506888 | ||||||||
\(404\) | 4.87422 | 0.242501 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −19.2115 | −0.953449 | ||||||||
\(407\) | −0.268225 | −0.0132954 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.20178 | −0.257212 | −0.128606 | − | 0.991696i | \(-0.541050\pi\) | ||||
−0.128606 | + | 0.991696i | \(0.541050\pi\) | |||||||
\(410\) | −19.6740 | −0.971629 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.98778 | 0.344263 | ||||||||
\(413\) | −12.6437 | −0.622157 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −36.9420 | −1.81341 | ||||||||
\(416\) | −4.05522 | −0.198824 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.18896 | −0.0581539 | ||||||||
\(419\) | 6.23531 | 0.304615 | 0.152307 | − | 0.988333i | \(-0.451330\pi\) | ||||
0.152307 | + | 0.988333i | \(0.451330\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.25873 | −0.110084 | −0.0550420 | − | 0.998484i | \(-0.517529\pi\) | ||||
−0.0550420 | + | 0.998484i | \(0.517529\pi\) | |||||||
\(422\) | −17.6600 | −0.859675 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.0518 | −0.585287 | ||||||||
\(425\) | 7.67105 | 0.372100 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0020 | 0.967964 | ||||||||
\(428\) | 0.355452 | 0.0171814 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21.2479 | −1.02467 | ||||||||
\(431\) | 3.93223 | 0.189409 | 0.0947043 | − | 0.995505i | \(-0.469809\pi\) | ||||
0.0947043 | + | 0.995505i | \(0.469809\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.5191 | 1.85111 | 0.925555 | − | 0.378613i | \(-0.123599\pi\) | ||||
0.925555 | + | 0.378613i | \(0.123599\pi\) | |||||||
\(434\) | −10.9258 | −0.524457 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.84322 | −0.279839 | ||||||||
\(437\) | −32.6501 | −1.56187 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.87337 | −0.471230 | −0.235615 | − | 0.971846i | \(-0.575710\pi\) | ||||
−0.235615 | + | 0.971846i | \(0.575710\pi\) | |||||||
\(440\) | −0.689971 | −0.0328931 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.5679 | −0.835618 | ||||||||
\(443\) | 32.2395 | 1.53174 | 0.765872 | − | 0.642993i | \(-0.222308\pi\) | ||||
0.765872 | + | 0.642993i | \(0.222308\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.08203 | −0.288316 | ||||||||
\(446\) | 11.3515 | 0.537510 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.35416 | −0.205715 | ||||||||
\(449\) | −17.5915 | −0.830193 | −0.415097 | − | 0.909777i | \(-0.636252\pi\) | ||||
−0.415097 | + | 0.909777i | \(0.636252\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.00488 | 0.0944061 | ||||||||
\(452\) | 19.5256 | 0.918407 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.921850 | 0.0432646 | ||||||||
\(455\) | −45.9448 | −2.15393 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.5964 | 1.52480 | 0.762398 | − | 0.647109i | \(-0.224022\pi\) | ||||
0.762398 | + | 0.647109i | \(0.224022\pi\) | |||||||
\(458\) | 4.88284 | 0.228160 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −18.9474 | −0.883425 | ||||||||
\(461\) | −2.92979 | −0.136454 | −0.0682269 | − | 0.997670i | \(-0.521734\pi\) | ||||
−0.0682269 | + | 0.997670i | \(0.521734\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.4152 | −1.55294 | −0.776468 | − | 0.630157i | \(-0.782991\pi\) | ||||
−0.776468 | + | 0.630157i | \(0.782991\pi\) | |||||||
\(464\) | −4.41220 | −0.204831 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.2267 | −0.705362 | ||||||||
\(467\) | 5.39495 | 0.249649 | 0.124824 | − | 0.992179i | \(-0.460163\pi\) | ||||
0.124824 | + | 0.992179i | \(0.460163\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9446 | 0.597727 | ||||||||
\(470\) | 10.5379 | 0.486078 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.90383 | −0.133659 | ||||||||
\(473\) | 2.16527 | 0.0995593 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.93969 | 0.364298 | ||||||||
\(476\) | −18.8629 | −0.864581 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.2969 | −0.791140 | ||||||||
\(479\) | 37.6688 | 1.72113 | 0.860565 | − | 0.509340i | \(-0.170111\pi\) | ||||
0.860565 | + | 0.509340i | \(0.170111\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.10204 | −0.187037 | ||||||||
\(482\) | −26.4918 | −1.20667 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9297 | −0.496804 | ||||||||
\(485\) | 5.28223 | 0.239854 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.1912 | −0.733693 | −0.366846 | − | 0.930282i | \(-0.619562\pi\) | ||||
−0.366846 | + | 0.930282i | \(0.619562\pi\) | |||||||
\(488\) | 4.59376 | 0.207950 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −31.1174 | −1.40574 | ||||||||
\(491\) | 27.8221 | 1.25559 | 0.627797 | − | 0.778377i | \(-0.283957\pi\) | ||||
0.627797 | + | 0.778377i | \(0.283957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.1144 | −0.860868 | ||||||||
\(494\) | −18.1831 | −0.818096 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.50928 | −0.112670 | ||||||||
\(497\) | −26.4187 | −1.18504 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.8407 | 0.932957 | 0.466479 | − | 0.884532i | \(-0.345522\pi\) | ||||
0.466479 | + | 0.884532i | \(0.345522\pi\) | |||||||
\(500\) | −8.40278 | −0.375784 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24.6534 | −1.10034 | ||||||||
\(503\) | 27.9083 | 1.24437 | 0.622185 | − | 0.782870i | \(-0.286245\pi\) | ||||
0.622185 | + | 0.782870i | \(0.286245\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.6830 | 0.564387 | ||||||||
\(506\) | 1.93083 | 0.0858360 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.2907 | −0.722782 | ||||||||
\(509\) | 15.4793 | 0.686107 | 0.343054 | − | 0.939316i | \(-0.388539\pi\) | ||||
0.343054 | + | 0.939316i | \(0.388539\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.2885 | 0.853271 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.11123 | 0.0931222 | ||||||||
\(515\) | 18.1826 | 0.801223 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.07387 | −0.0472287 | ||||||||
\(518\) | −4.40444 | −0.193520 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.5519 | −0.462733 | ||||||||
\(521\) | 2.30576 | 0.101017 | 0.0505085 | − | 0.998724i | \(-0.483916\pi\) | ||||
0.0505085 | + | 0.998724i | \(0.483916\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.0468 | 0.526768 | 0.263384 | − | 0.964691i | \(-0.415161\pi\) | ||||
0.263384 | + | 0.964691i | \(0.415161\pi\) | |||||||
\(524\) | 17.6406 | 0.770635 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.80370 | 0.165849 | ||||||||
\(527\) | −10.8706 | −0.473532 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.0227 | 1.30534 | ||||||||
\(530\) | −31.3595 | −1.36217 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −19.5235 | −0.846452 | ||||||||
\(533\) | 30.6612 | 1.32808 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.924909 | 0.0399873 | ||||||||
\(536\) | 2.97293 | 0.128411 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13.7256 | −0.591752 | ||||||||
\(539\) | 3.17102 | 0.136585 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.8801 | 0.983691 | 0.491846 | − | 0.870682i | \(-0.336322\pi\) | ||||
0.491846 | + | 0.870682i | \(0.336322\pi\) | |||||||
\(542\) | 17.0605 | 0.732810 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.33216 | −0.185740 | ||||||||
\(545\) | −15.2044 | −0.651285 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.43374 | 0.104059 | 0.0520297 | − | 0.998646i | \(-0.483431\pi\) | ||||
0.0520297 | + | 0.998646i | \(0.483431\pi\) | |||||||
\(548\) | 17.1254 | 0.731561 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.469530 | −0.0200208 | ||||||||
\(551\) | −19.7838 | −0.842817 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.2032 | −0.986700 | ||||||||
\(554\) | 10.2140 | 0.433953 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.15986 | 0.134008 | ||||||||
\(557\) | 5.06592 | 0.214650 | 0.107325 | − | 0.994224i | \(-0.465771\pi\) | ||||
0.107325 | + | 0.994224i | \(0.465771\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.1142 | 1.40058 | ||||||||
\(560\) | −11.3298 | −0.478771 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.2972 | 0.729637 | ||||||||
\(563\) | −45.2633 | −1.90762 | −0.953810 | − | 0.300411i | \(-0.902876\pi\) | ||||
−0.953810 | + | 0.300411i | \(0.902876\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 50.8068 | 2.13746 | ||||||||
\(566\) | 14.3288 | 0.602284 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.06746 | −0.254585 | ||||||||
\(569\) | 28.5576 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.04764 | 0.336783 | 0.168392 | − | 0.985720i | \(-0.446143\pi\) | ||||
0.168392 | + | 0.985720i | \(0.446143\pi\) | |||||||
\(572\) | 1.07530 | 0.0449604 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 32.9215 | 1.37412 | ||||||||
\(575\) | −12.8938 | −0.537709 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.983491 | 0.0409432 | 0.0204716 | − | 0.999790i | \(-0.493483\pi\) | ||||
0.0204716 | + | 0.999790i | \(0.493483\pi\) | |||||||
\(578\) | −1.76761 | −0.0735229 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.4808 | −0.476715 | ||||||||
\(581\) | 61.8170 | 2.56460 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.19569 | 0.132352 | ||||||||
\(584\) | 4.42989 | 0.183310 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.1302 | −0.625022 | ||||||||
\(587\) | −35.2018 | −1.45294 | −0.726468 | − | 0.687201i | \(-0.758839\pi\) | ||||
−0.726468 | + | 0.687201i | \(0.758839\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.2513 | −0.463602 | ||||||||
\(590\) | −7.55593 | −0.311073 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.01155 | −0.0415743 | ||||||||
\(593\) | −30.4208 | −1.24923 | −0.624617 | − | 0.780931i | \(-0.714745\pi\) | ||||
−0.624617 | + | 0.780931i | \(0.714745\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −49.0825 | −2.01219 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 29.5288 | 1.20752 | ||||||||
\(599\) | −18.6711 | −0.762880 | −0.381440 | − | 0.924394i | \(-0.624572\pi\) | ||||
−0.381440 | + | 0.924394i | \(0.624572\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.9550 | 0.732398 | 0.366199 | − | 0.930537i | \(-0.380659\pi\) | ||||
0.366199 | + | 0.930537i | \(0.380659\pi\) | |||||||
\(602\) | 35.5553 | 1.44912 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.4612 | −0.466351 | ||||||||
\(605\) | −28.4397 | −1.15624 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.4843 | −1.31850 | −0.659249 | − | 0.751924i | \(-0.729126\pi\) | ||||
−0.659249 | + | 0.751924i | \(0.729126\pi\) | |||||||
\(608\) | −4.48387 | −0.181845 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.9533 | 0.483973 | ||||||||
\(611\) | −16.4230 | −0.664403 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.1250 | 1.29752 | 0.648758 | − | 0.760995i | \(-0.275289\pi\) | ||||
0.648758 | + | 0.760995i | \(0.275289\pi\) | |||||||
\(614\) | 8.43123 | 0.340257 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.15456 | 0.0465187 | ||||||||
\(617\) | −24.3370 | −0.979770 | −0.489885 | − | 0.871787i | \(-0.662961\pi\) | ||||
−0.489885 | + | 0.871787i | \(0.662961\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 45.5842 | 1.83218 | 0.916091 | − | 0.400969i | \(-0.131327\pi\) | ||||
0.916091 | + | 0.400969i | \(0.131327\pi\) | |||||||
\(620\) | −6.52931 | −0.262223 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.3131 | −0.613998 | ||||||||
\(623\) | 10.1774 | 0.407748 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7182 | −1.22873 | ||||||||
\(626\) | 9.41309 | 0.376223 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.4362 | 0.536164 | ||||||||
\(629\) | −4.38218 | −0.174729 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.936949 | 0.0372993 | 0.0186497 | − | 0.999826i | \(-0.494063\pi\) | ||||
0.0186497 | + | 0.999826i | \(0.494063\pi\) | |||||||
\(632\) | −5.32897 | −0.211975 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.77010 | −0.189445 | ||||||||
\(635\) | −42.3893 | −1.68217 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 48.4953 | 1.92145 | ||||||||
\(638\) | 1.16995 | 0.0463190 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.60206 | −0.102855 | ||||||||
\(641\) | 11.5960 | 0.458013 | 0.229007 | − | 0.973425i | \(-0.426452\pi\) | ||||
0.229007 | + | 0.973425i | \(0.426452\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.8312 | 1.49192 | 0.745958 | − | 0.665993i | \(-0.231992\pi\) | ||||
0.745958 | + | 0.665993i | \(0.231992\pi\) | |||||||
\(644\) | 31.7056 | 1.24938 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19.4249 | −0.764261 | ||||||||
\(647\) | 31.6105 | 1.24274 | 0.621368 | − | 0.783519i | \(-0.286577\pi\) | ||||
0.621368 | + | 0.783519i | \(0.286577\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.769988 | 0.0302247 | ||||||||
\(650\) | −7.18066 | −0.281649 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.50198 | −0.0979852 | ||||||||
\(653\) | −15.1514 | −0.592922 | −0.296461 | − | 0.955045i | \(-0.595806\pi\) | ||||
−0.296461 | + | 0.955045i | \(0.595806\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 45.9020 | 1.79354 | ||||||||
\(656\) | 7.56092 | 0.295205 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −17.6337 | −0.687431 | ||||||||
\(659\) | −7.23718 | −0.281920 | −0.140960 | − | 0.990015i | \(-0.545019\pi\) | ||||
−0.140960 | + | 0.990015i | \(0.545019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.1606 | −1.25090 | −0.625452 | − | 0.780263i | \(-0.715085\pi\) | ||||
−0.625452 | + | 0.780263i | \(0.715085\pi\) | |||||||
\(662\) | −22.1235 | −0.859852 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.1972 | 0.550959 | ||||||||
\(665\) | −50.8014 | −1.96999 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.1282 | 1.24401 | ||||||||
\(668\) | 12.6702 | 0.490226 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.73574 | 0.298858 | ||||||||
\(671\) | −1.21810 | −0.0470241 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.41204 | −0.208619 | −0.104309 | − | 0.994545i | \(-0.533263\pi\) | ||||
−0.104309 | + | 0.994545i | \(0.533263\pi\) | |||||||
\(674\) | −33.4043 | −1.28669 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.44481 | 0.132493 | ||||||||
\(677\) | 17.8399 | 0.685641 | 0.342821 | − | 0.939401i | \(-0.388618\pi\) | ||||
0.342821 | + | 0.939401i | \(0.388618\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.83902 | −0.339211 | ||||||||
\(680\) | −11.2725 | −0.432282 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.665370 | 0.0254783 | ||||||||
\(683\) | −1.65392 | −0.0632856 | −0.0316428 | − | 0.999499i | \(-0.510074\pi\) | ||||
−0.0316428 | + | 0.999499i | \(0.510074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44.5613 | 1.70260 | ||||||||
\(686\) | 21.5911 | 0.824353 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.16581 | 0.311319 | ||||||||
\(689\) | 48.8727 | 1.86190 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.75941 | 0.143015 | 0.0715073 | − | 0.997440i | \(-0.477219\pi\) | ||||
0.0715073 | + | 0.997440i | \(0.477219\pi\) | |||||||
\(692\) | −8.32877 | −0.316612 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −35.4242 | −1.34468 | ||||||||
\(695\) | 8.22215 | 0.311884 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.7551 | 1.24069 | ||||||||
\(698\) | −27.3976 | −1.03701 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.71001 | −0.291411 | ||||||||
\(701\) | −21.4942 | −0.811824 | −0.405912 | − | 0.913912i | \(-0.633046\pi\) | ||||
−0.405912 | + | 0.913912i | \(0.633046\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.53565 | −0.171065 | ||||||||
\(704\) | 0.265163 | 0.00999372 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.5285 | 0.546787 | ||||||||
\(707\) | −21.2231 | −0.798178 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.9742 | −0.675037 | −0.337519 | − | 0.941319i | \(-0.609588\pi\) | ||||
−0.337519 | + | 0.941319i | \(0.609588\pi\) | |||||||
\(710\) | −15.7879 | −0.592509 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.33739 | 0.0875974 | ||||||||
\(713\) | 18.2718 | 0.684284 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.79798 | 0.104639 | ||||||||
\(716\) | −7.90674 | −0.295489 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.18115 | 0.0440800 | ||||||||
\(719\) | −23.9192 | −0.892035 | −0.446017 | − | 0.895024i | \(-0.647158\pi\) | ||||
−0.446017 | + | 0.895024i | \(0.647158\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.4259 | −1.13312 | ||||||||
\(722\) | −1.10512 | −0.0411283 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23.3762 | 0.868769 | ||||||||
\(725\) | −7.81278 | −0.290160 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.8898 | −1.36817 | −0.684083 | − | 0.729404i | \(-0.739798\pi\) | ||||
−0.684083 | + | 0.729404i | \(0.739798\pi\) | |||||||
\(728\) | 17.6571 | 0.654415 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.5268 | 0.426627 | ||||||||
\(731\) | 35.3756 | 1.30841 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.0334 | −0.444463 | −0.222231 | − | 0.974994i | \(-0.571334\pi\) | ||||
−0.222231 | + | 0.974994i | \(0.571334\pi\) | |||||||
\(734\) | 11.0480 | 0.407789 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.28167 | 0.268406 | ||||||||
\(737\) | −0.788312 | −0.0290378 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.356220 | 0.0131038 | 0.00655189 | − | 0.999979i | \(-0.497914\pi\) | ||||
0.00655189 | + | 0.999979i | \(0.497914\pi\) | |||||||
\(740\) | −2.63211 | −0.0967582 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 52.4755 | 1.92644 | ||||||||
\(743\) | 10.8681 | 0.398710 | 0.199355 | − | 0.979927i | \(-0.436115\pi\) | ||||
0.199355 | + | 0.979927i | \(0.436115\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.60206 | −0.0953321 | ||||||||
\(746\) | 38.1150 | 1.39549 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.14873 | 0.0420017 | ||||||||
\(749\) | −1.54770 | −0.0565516 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.1809 | −1.24728 | −0.623640 | − | 0.781712i | \(-0.714347\pi\) | ||||
−0.623640 | + | 0.781712i | \(0.714347\pi\) | |||||||
\(752\) | −4.04984 | −0.147682 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.8925 | 0.651605 | ||||||||
\(755\) | −29.8228 | −1.08536 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.4945 | 1.68987 | 0.844936 | − | 0.534868i | \(-0.179639\pi\) | ||||
0.844936 | + | 0.534868i | \(0.179639\pi\) | |||||||
\(758\) | 3.13216 | 0.113765 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.6673 | −0.423218 | ||||||||
\(761\) | 4.48038 | 0.162413 | 0.0812067 | − | 0.996697i | \(-0.474123\pi\) | ||||
0.0812067 | + | 0.996697i | \(0.474123\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.4423 | 0.921074 | ||||||||
\(764\) | 14.9135 | 0.539551 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.2063 | 0.441032 | ||||||||
\(767\) | 11.7757 | 0.425194 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.6664 | 1.10586 | 0.552929 | − | 0.833229i | \(-0.313510\pi\) | ||||
0.552929 | + | 0.833229i | \(0.313510\pi\) | |||||||
\(770\) | 3.00425 | 0.108266 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18.9804 | −0.683120 | ||||||||
\(773\) | −9.53310 | −0.342882 | −0.171441 | − | 0.985194i | \(-0.554842\pi\) | ||||
−0.171441 | + | 0.985194i | \(0.554842\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.44324 | −0.159606 | ||||||||
\(776\) | −2.03002 | −0.0728734 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.22633 | 0.0798179 | ||||||||
\(779\) | 33.9022 | 1.21467 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.60887 | 0.0575698 | ||||||||
\(782\) | 31.5454 | 1.12806 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.9587 | 0.427098 | ||||||||
\(785\) | 34.9619 | 1.24784 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.0080 | 0.641916 | 0.320958 | − | 0.947093i | \(-0.395995\pi\) | ||||
0.320958 | + | 0.947093i | \(0.395995\pi\) | |||||||
\(788\) | −7.79120 | −0.277550 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.8663 | −0.493341 | ||||||||
\(791\) | −85.0177 | −3.02288 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.6287 | −0.661525 | ||||||||
\(794\) | −31.6782 | −1.12422 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.84292 | −0.313429 | ||||||||
\(797\) | 1.60934 | 0.0570057 | 0.0285029 | − | 0.999594i | \(-0.490926\pi\) | ||||
0.0285029 | + | 0.999594i | \(0.490926\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.5445 | −0.620681 | ||||||||
\(800\) | −1.77072 | −0.0626044 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.3003 | −0.646208 | ||||||||
\(803\) | −1.17464 | −0.0414523 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 82.4999 | 2.90774 | ||||||||
\(806\) | 10.1757 | 0.358424 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.87422 | −0.171474 | ||||||||
\(809\) | 29.1199 | 1.02380 | 0.511900 | − | 0.859045i | \(-0.328942\pi\) | ||||
0.511900 | + | 0.859045i | \(0.328942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.9566 | 1.96490 | 0.982451 | − | 0.186520i | \(-0.0597208\pi\) | ||||
0.982451 | + | 0.186520i | \(0.0597208\pi\) | |||||||
\(812\) | 19.2115 | 0.674190 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.268225 | 0.00940128 | ||||||||
\(815\) | −6.51031 | −0.228046 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.6145 | 1.28098 | ||||||||
\(818\) | 5.20178 | 0.181876 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.6740 | 0.687045 | ||||||||
\(821\) | 41.8838 | 1.46175 | 0.730877 | − | 0.682509i | \(-0.239111\pi\) | ||||
0.730877 | + | 0.682509i | \(0.239111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.09408 | −0.317000 | −0.158500 | − | 0.987359i | \(-0.550666\pi\) | ||||
−0.158500 | + | 0.987359i | \(0.550666\pi\) | |||||||
\(824\) | −6.98778 | −0.243431 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.6437 | 0.439932 | ||||||||
\(827\) | 32.6643 | 1.13585 | 0.567924 | − | 0.823081i | \(-0.307747\pi\) | ||||
0.567924 | + | 0.823081i | \(0.307747\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.7027 | −1.06635 | −0.533174 | − | 0.846006i | \(-0.679001\pi\) | ||||
−0.533174 | + | 0.846006i | \(0.679001\pi\) | |||||||
\(830\) | 36.9420 | 1.28228 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.05522 | 0.140589 | ||||||||
\(833\) | 51.8072 | 1.79501 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.9687 | 1.14093 | ||||||||
\(836\) | 1.18896 | 0.0411210 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.23531 | −0.215395 | ||||||||
\(839\) | −35.8451 | −1.23751 | −0.618755 | − | 0.785584i | \(-0.712363\pi\) | ||||
−0.618755 | + | 0.785584i | \(0.712363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.53245 | −0.328705 | ||||||||
\(842\) | 2.25873 | 0.0778411 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.6600 | 0.607882 | ||||||||
\(845\) | 8.96360 | 0.308357 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 47.5896 | 1.63520 | ||||||||
\(848\) | 12.0518 | 0.413860 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.67105 | −0.263115 | ||||||||
\(851\) | 7.36575 | 0.252495 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.0443 | 1.78196 | 0.890982 | − | 0.454039i | \(-0.150017\pi\) | ||||
0.890982 | + | 0.454039i | \(0.150017\pi\) | |||||||
\(854\) | −20.0020 | −0.684454 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.355452 | −0.0121491 | ||||||||
\(857\) | −15.0154 | −0.512918 | −0.256459 | − | 0.966555i | \(-0.582556\pi\) | ||||
−0.256459 | + | 0.966555i | \(0.582556\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.4136 | −0.662383 | −0.331192 | − | 0.943564i | \(-0.607451\pi\) | ||||
−0.331192 | + | 0.943564i | \(0.607451\pi\) | |||||||
\(860\) | 21.2479 | 0.724548 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.93223 | −0.133932 | ||||||||
\(863\) | −24.8730 | −0.846687 | −0.423343 | − | 0.905969i | \(-0.639144\pi\) | ||||
−0.423343 | + | 0.905969i | \(0.639144\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.6720 | −0.736869 | ||||||||
\(866\) | −38.5191 | −1.30893 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.9258 | 0.370847 | ||||||||
\(869\) | 1.41305 | 0.0479343 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0559 | −0.408498 | ||||||||
\(872\) | 5.84322 | 0.197876 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32.6501 | 1.10441 | ||||||||
\(875\) | 36.5871 | 1.23687 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.5738 | −1.03240 | −0.516202 | − | 0.856467i | \(-0.672655\pi\) | ||||
−0.516202 | + | 0.856467i | \(0.672655\pi\) | |||||||
\(878\) | 9.87337 | 0.333210 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.689971 | 0.0232589 | ||||||||
\(881\) | 35.1220 | 1.18329 | 0.591644 | − | 0.806199i | \(-0.298479\pi\) | ||||
0.591644 | + | 0.806199i | \(0.298479\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.3339 | −0.886205 | −0.443103 | − | 0.896471i | \(-0.646122\pi\) | ||||
−0.443103 | + | 0.896471i | \(0.646122\pi\) | |||||||
\(884\) | 17.5679 | 0.590871 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.2395 | −1.08311 | ||||||||
\(887\) | 49.0364 | 1.64648 | 0.823241 | − | 0.567692i | \(-0.192163\pi\) | ||||
0.823241 | + | 0.567692i | \(0.192163\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 70.9323 | 2.37899 | ||||||||
\(890\) | 6.08203 | 0.203870 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.3515 | −0.380077 | ||||||||
\(893\) | −18.1590 | −0.607666 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.5738 | −0.687707 | ||||||||
\(896\) | 4.35416 | 0.145462 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.5915 | 0.587035 | ||||||||
\(899\) | 11.0715 | 0.369254 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 52.2103 | 1.73938 | ||||||||
\(902\) | −2.00488 | −0.0667552 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.5256 | −0.649412 | ||||||||
\(905\) | 60.8263 | 2.02193 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0934 | −0.534372 | −0.267186 | − | 0.963645i | \(-0.586094\pi\) | ||||
−0.267186 | + | 0.963645i | \(0.586094\pi\) | |||||||
\(908\) | −0.921850 | −0.0305927 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 45.9448 | 1.52306 | ||||||||
\(911\) | 0.00281244 | 9.31803e−5 0 | 4.65902e−5 | − | 1.00000i | \(-0.499985\pi\) | ||||
4.65902e−5 | 1.00000i | \(0.499985\pi\) | ||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.76458 | −0.124589 | ||||||||
\(914\) | −32.5964 | −1.07819 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.88284 | −0.161334 | ||||||||
\(917\) | −76.8102 | −2.53650 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.5632 | 0.810266 | 0.405133 | − | 0.914258i | \(-0.367225\pi\) | ||||
0.405133 | + | 0.914258i | \(0.367225\pi\) | |||||||
\(920\) | 18.9474 | 0.624676 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.92979 | 0.0964874 | ||||||||
\(923\) | 24.6049 | 0.809879 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.79117 | −0.0588932 | ||||||||
\(926\) | 33.4152 | 1.09809 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.41220 | 0.144838 | ||||||||
\(929\) | −35.7462 | −1.17279 | −0.586397 | − | 0.810024i | \(-0.699454\pi\) | ||||
−0.586397 | + | 0.810024i | \(0.699454\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 53.6215 | 1.75737 | ||||||||
\(932\) | 15.2267 | 0.498766 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.39495 | −0.176528 | ||||||||
\(935\) | 2.98907 | 0.0977529 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.5134 | −1.06217 | −0.531083 | − | 0.847320i | \(-0.678215\pi\) | ||||
−0.531083 | + | 0.847320i | \(0.678215\pi\) | |||||||
\(938\) | −12.9446 | −0.422657 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.5379 | −0.343709 | ||||||||
\(941\) | −8.80935 | −0.287176 | −0.143588 | − | 0.989638i | \(-0.545864\pi\) | ||||
−0.143588 | + | 0.989638i | \(0.545864\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −55.0562 | −1.79288 | ||||||||
\(944\) | 2.90383 | 0.0945115 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.16527 | −0.0703991 | ||||||||
\(947\) | 11.0349 | 0.358585 | 0.179292 | − | 0.983796i | \(-0.442619\pi\) | ||||
0.179292 | + | 0.983796i | \(0.442619\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.9642 | −0.583142 | ||||||||
\(950\) | −7.93969 | −0.257598 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 18.8629 | 0.611351 | ||||||||
\(953\) | −25.3792 | −0.822112 | −0.411056 | − | 0.911610i | \(-0.634840\pi\) | ||||
−0.411056 | + | 0.911610i | \(0.634840\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.8058 | 1.25573 | ||||||||
\(956\) | 17.2969 | 0.559420 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37.6688 | −1.21702 | ||||||||
\(959\) | −74.5668 | −2.40789 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.7035 | −0.796887 | ||||||||
\(962\) | 4.10204 | 0.132255 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.4918 | 0.853243 | ||||||||
\(965\) | −49.3882 | −1.58986 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.02425 | −0.290200 | −0.145100 | − | 0.989417i | \(-0.546350\pi\) | ||||
−0.145100 | + | 0.989417i | \(0.546350\pi\) | |||||||
\(968\) | 10.9297 | 0.351293 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.28223 | −0.169602 | ||||||||
\(971\) | 43.0296 | 1.38089 | 0.690443 | − | 0.723387i | \(-0.257415\pi\) | ||||
0.690443 | + | 0.723387i | \(0.257415\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.7585 | −0.441079 | ||||||||
\(974\) | 16.1912 | 0.518799 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.59376 | −0.147043 | ||||||||
\(977\) | −32.8446 | −1.05079 | −0.525396 | − | 0.850858i | \(-0.676083\pi\) | ||||
−0.525396 | + | 0.850858i | \(0.676083\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.619790 | −0.0198086 | ||||||||
\(980\) | 31.1174 | 0.994007 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −27.8221 | −0.887839 | ||||||||
\(983\) | −36.3307 | −1.15877 | −0.579385 | − | 0.815054i | \(-0.696707\pi\) | ||||
−0.579385 | + | 0.815054i | \(0.696707\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.2732 | −0.645957 | ||||||||
\(986\) | 19.1144 | 0.608726 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.1831 | 0.578481 | ||||||||
\(989\) | −59.4607 | −1.89074 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.1719 | −1.18080 | −0.590402 | − | 0.807109i | \(-0.701031\pi\) | ||||
−0.590402 | + | 0.807109i | \(0.701031\pi\) | |||||||
\(992\) | 2.50928 | 0.0796699 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 26.4187 | 0.837950 | ||||||||
\(995\) | −23.0098 | −0.729460 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.67330 | 0.0529938 | 0.0264969 | − | 0.999649i | \(-0.491565\pi\) | ||||
0.0264969 | + | 0.999649i | \(0.491565\pi\) | |||||||
\(998\) | −20.8407 | −0.659700 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8046.2.a.k.1.9 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.n.1.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.k.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.n.1.4 | yes | 12 | 3.2 | odd | 2 |