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: | \(1\) |
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: | \( x^{12} - 3 x^{11} - 31 x^{10} + 82 x^{9} + 334 x^{8} - 684 x^{7} - 1561 x^{6} + 1551 x^{5} + 3573 x^{4} + \cdots - 3 \) |
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 | 1.4 | ||
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 | \(-0.697666\pi\) | ||||
−0.581839 | + | 0.813304i | \(0.697666\pi\) | |||||||
\(6\) | 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 | \(-0.512728\pi\) | ||||
−0.0399749 | + | 0.999201i | \(0.512728\pi\) | |||||||
\(12\) | 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 | \(-0.676066\pi\) | ||||
−0.525352 | + | 0.850885i | \(0.676066\pi\) | |||||||
\(18\) | 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 | \(-0.225607\pi\) | ||||
0.759167 | + | 0.650896i | \(0.225607\pi\) | |||||||
\(24\) | 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 | \(-0.365646\pi\) | ||||
0.409663 | + | 0.912237i | \(0.365646\pi\) | |||||||
\(30\) | 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 | \(-0.701034\pi\) | ||||
−0.590409 | + | 0.807104i | \(0.701034\pi\) | |||||||
\(42\) | 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 | \(-0.404559\pi\) | ||||
0.295365 | + | 0.955385i | \(0.404559\pi\) | |||||||
\(48\) | 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 | \(-0.810363\pi\) | ||||
−0.827721 | + | 0.561140i | \(0.810363\pi\) | |||||||
\(54\) | 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 | \(-0.560532\pi\) | ||||
−0.189023 | + | 0.981973i | \(0.560532\pi\) | |||||||
\(60\) | 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 | \(-0.617236\pi\) | ||||
−0.360037 | + | 0.932938i | \(0.617236\pi\) | |||||||
\(72\) | 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 | \(-0.215639\pi\) | ||||
0.779173 | + | 0.626808i | \(0.215639\pi\) | |||||||
\(84\) | 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 | \(-0.460466\pi\) | ||||
0.123881 | + | 0.992297i | \(0.460466\pi\) | |||||||
\(90\) | 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 | \(-0.577968\pi\) | ||||
−0.242501 | + | 0.970151i | \(0.577968\pi\) | |||||||
\(102\) | 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 | \(-0.505469\pi\) | ||||
−0.0171814 | + | 0.999852i | \(0.505469\pi\) | |||||||
\(108\) | 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 | \(-0.870524\pi\) | ||||
−0.918407 | + | 0.395637i | \(0.870524\pi\) | |||||||
\(114\) | 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 | \(-0.780061\pi\) | ||||
−0.770635 | + | 0.637277i | \(0.780061\pi\) | |||||||
\(132\) | 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 | \(-0.761208\pi\) | ||||
−0.731561 | + | 0.681776i | \(0.761208\pi\) | |||||||
\(138\) | 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 | \(-0.663086\pi\) | ||||
−0.490226 | + | 0.871596i | \(0.663086\pi\) | |||||||
\(168\) | 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 | \(-0.397455\pi\) | ||||
0.316612 | + | 0.948555i | \(0.397455\pi\) | |||||||
\(174\) | 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 | \(-0.404518\pi\) | ||||
0.295489 | + | 0.955346i | \(0.404518\pi\) | |||||||
\(180\) | 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 | \(-0.681406\pi\) | ||||
−0.539551 | + | 0.841953i | \(0.681406\pi\) | |||||||
\(192\) | 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 | \(-0.410478\pi\) | ||||
0.277550 | + | 0.960711i | \(0.410478\pi\) | |||||||
\(198\) | 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 | \(-0.490261\pi\) | ||||
0.0305927 | + | 0.999532i | \(0.490261\pi\) | |||||||
\(228\) | 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 | \(-0.666213\pi\) | ||||
−0.498766 | + | 0.866737i | \(0.666213\pi\) | |||||||
\(234\) | 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 | \(-0.688976\pi\) | ||||
−0.559420 | + | 0.828884i | \(0.688976\pi\) | |||||||
\(240\) | 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 | \(-0.783794\pi\) | ||||
−0.778055 | + | 0.628196i | \(0.783794\pi\) | |||||||
\(252\) | 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 | \(-0.479025\pi\) | ||||
0.0658474 | + | 0.997830i | \(0.479025\pi\) | |||||||
\(258\) | 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 | \(-0.462585\pi\) | ||||
0.117273 | + | 0.993100i | \(0.462585\pi\) | |||||||
\(264\) | 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 | \(-0.637420\pi\) | ||||
−0.418432 | + | 0.908248i | \(0.637420\pi\) | |||||||
\(270\) | 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 | \(-0.327446\pi\) | ||||
0.515931 | + | 0.856630i | \(0.327446\pi\) | |||||||
\(282\) | 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 | \(-0.645716\pi\) | ||||
−0.441957 | + | 0.897036i | \(0.645716\pi\) | |||||||
\(294\) | 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 | \(-0.642956\pi\) | ||||
−0.434162 | + | 0.900835i | \(0.642956\pi\) | |||||||
\(312\) | 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 | \(-0.542769\pi\) | ||||
−0.133958 | + | 0.990987i | \(0.542769\pi\) | |||||||
\(318\) | 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 | \(-0.899772\pi\) | ||||
−0.950835 | + | 0.309697i | \(0.899772\pi\) | |||||||
\(348\) | 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 | \(-0.373637\pi\) | ||||
0.386637 | + | 0.922232i | \(0.373637\pi\) | |||||||
\(354\) | 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 | \(-0.490077\pi\) | ||||
0.0311693 | + | 0.999514i | \(0.490077\pi\) | |||||||
\(360\) | 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 | \(-0.399049\pi\) | ||||
0.311857 | + | 0.950129i | \(0.399049\pi\) | |||||||
\(384\) | 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 | \(-0.482025\pi\) | ||||
0.0564398 | + | 0.998406i | \(0.482025\pi\) | |||||||
\(390\) | 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 | \(-0.651054\pi\) | ||||
−0.456938 | + | 0.889499i | \(0.651054\pi\) | |||||||
\(402\) | 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 | \(-0.548670\pi\) | ||||
−0.152307 | + | 0.988333i | \(0.548670\pi\) | |||||||
\(420\) | 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 | \(-0.530191\pi\) | ||||
−0.0947043 | + | 0.995505i | \(0.530191\pi\) | |||||||
\(432\) | 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 | \(-0.777692\pi\) | ||||
−0.765872 | + | 0.642993i | \(0.777692\pi\) | |||||||
\(444\) | 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 | \(-0.363748\pi\) | ||||
0.415097 | + | 0.909777i | \(0.363748\pi\) | |||||||
\(450\) | 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 | \(-0.478266\pi\) | ||||
0.0682269 | + | 0.997670i | \(0.478266\pi\) | |||||||
\(462\) | 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 | \(-0.539837\pi\) | ||||
−0.124824 | + | 0.992179i | \(0.539837\pi\) | |||||||
\(468\) | 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 | \(-0.829889\pi\) | ||||
−0.860565 | + | 0.509340i | \(0.829889\pi\) | |||||||
\(480\) | 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 | \(-0.716043\pi\) | ||||
−0.627797 | + | 0.778377i | \(0.716043\pi\) | |||||||
\(492\) | 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 | \(-0.713755\pi\) | ||||
−0.622185 | + | 0.782870i | \(0.713755\pi\) | |||||||
\(504\) | 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 | \(-0.611461\pi\) | ||||
−0.343054 | + | 0.939316i | \(0.611461\pi\) | |||||||
\(510\) | 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 | \(-0.516084\pi\) | ||||
−0.0505085 | + | 0.998724i | \(0.516084\pi\) | |||||||
\(522\) | 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 | \(-0.534229\pi\) | ||||
−0.107325 | + | 0.994224i | \(0.534229\pi\) | |||||||
\(558\) | 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 | \(-0.0971239\pi\) | ||||
0.953810 | + | 0.300411i | \(0.0971239\pi\) | |||||||
\(564\) | 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 | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(570\) | 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 | \(-0.241161\pi\) | ||||
0.726468 | + | 0.687201i | \(0.241161\pi\) | |||||||
\(588\) | 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 | \(-0.285255\pi\) | ||||
0.624617 | + | 0.780931i | \(0.285255\pi\) | |||||||
\(594\) | 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 | \(-0.375428\pi\) | ||||
0.381440 | + | 0.924394i | \(0.375428\pi\) | |||||||
\(600\) | 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 | \(-0.337039\pi\) | ||||
0.489885 | + | 0.871787i | \(0.337039\pi\) | |||||||
\(618\) | 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 | \(-0.573548\pi\) | ||||
−0.229007 | + | 0.973425i | \(0.573548\pi\) | |||||||
\(642\) | 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 | \(-0.713423\pi\) | ||||
−0.621368 | + | 0.783519i | \(0.713423\pi\) | |||||||
\(648\) | 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 | \(-0.404194\pi\) | ||||
0.296461 | + | 0.955045i | \(0.404194\pi\) | |||||||
\(654\) | 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 | \(-0.454981\pi\) | ||||
0.140960 | + | 0.990015i | \(0.454981\pi\) | |||||||
\(660\) | 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 | \(-0.611382\pi\) | ||||
−0.342821 | + | 0.939401i | \(0.611382\pi\) | |||||||
\(678\) | 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 | \(-0.489926\pi\) | ||||
0.0316428 | + | 0.999499i | \(0.489926\pi\) | |||||||
\(684\) | 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 | \(-0.366954\pi\) | ||||
0.405912 | + | 0.913912i | \(0.366954\pi\) | |||||||
\(702\) | 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 | \(-0.352842\pi\) | ||||
0.446017 | + | 0.895024i | \(0.352842\pi\) | |||||||
\(720\) | 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 | \(-0.563885\pi\) | ||||
−0.199355 | + | 0.979927i | \(0.563885\pi\) | |||||||
\(744\) | 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 | \(-0.525877\pi\) | ||||
−0.0812067 | + | 0.996697i | \(0.525877\pi\) | |||||||
\(762\) | 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 | \(-0.445158\pi\) | ||||
0.171441 | + | 0.985194i | \(0.445158\pi\) | |||||||
\(774\) | 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 | \(-0.509074\pi\) | ||||
−0.0285029 | + | 0.999594i | \(0.509074\pi\) | |||||||
\(798\) | 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 | \(-0.671058\pi\) | ||||
−0.511900 | + | 0.859045i | \(0.671058\pi\) | |||||||
\(810\) | 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 | \(-0.760889\pi\) | ||||
−0.730877 | + | 0.682509i | \(0.760889\pi\) | |||||||
\(822\) | 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 | \(-0.692253\pi\) | ||||
−0.567924 | + | 0.823081i | \(0.692253\pi\) | |||||||
\(828\) | 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 | \(-0.287637\pi\) | ||||
0.618755 | + | 0.785584i | \(0.287637\pi\) | |||||||
\(840\) | 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 | \(-0.417444\pi\) | ||||
0.256459 | + | 0.966555i | \(0.417444\pi\) | |||||||
\(858\) | 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 | \(-0.360856\pi\) | ||||
0.423343 | + | 0.905969i | \(0.360856\pi\) | |||||||
\(864\) | 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 | \(-0.701521\pi\) | ||||
−0.591644 | + | 0.806199i | \(0.701521\pi\) | |||||||
\(882\) | 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 | \(-0.807837\pi\) | ||||
−0.823241 | + | 0.567692i | \(0.807837\pi\) | |||||||
\(888\) | 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 | \(-0.500015\pi\) | ||||
−4.65902e−5 | 1.00000i | \(0.500015\pi\) | ||||||||
\(912\) | 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 | \(-0.300546\pi\) | ||||
0.586397 | + | 0.810024i | \(0.300546\pi\) | |||||||
\(930\) | 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 | \(-0.454136\pi\) | ||||
0.143588 | + | 0.989638i | \(0.454136\pi\) | |||||||
\(942\) | 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 | \(-0.557381\pi\) | ||||
−0.179292 | + | 0.983796i | \(0.557381\pi\) | |||||||
\(948\) | 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 | \(-0.365160\pi\) | ||||
0.411056 | + | 0.911610i | \(0.365160\pi\) | |||||||
\(954\) | 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 | \(-0.742585\pi\) | ||||
−0.690443 | + | 0.723387i | \(0.742585\pi\) | |||||||
\(972\) | 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 | \(-0.323917\pi\) | ||||
0.525396 | + | 0.850858i | \(0.323917\pi\) | |||||||
\(978\) | 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 | \(-0.303293\pi\) | ||||
0.579385 | + | 0.815054i | \(0.303293\pi\) | |||||||
\(984\) | 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.n.1.4 | yes | 12 | |
3.2 | odd | 2 | 8046.2.a.k.1.9 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.k.1.9 | ✓ | 12 | 3.2 | odd | 2 | ||
8046.2.a.n.1.4 | yes | 12 | 1.1 | even | 1 | trivial |