Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, 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("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.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: | \(31.6926245622\) |
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: | \( x^{12} - 4 x^{11} - 22 x^{10} + 92 x^{9} + 125 x^{8} - 620 x^{7} - 94 x^{6} + 1280 x^{5} - 234 x^{4} + \cdots - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 441) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(4.12935\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.71513 | 1.91989 | 0.959944 | − | 0.280191i | \(-0.0903976\pi\) | ||||
0.959944 | + | 0.280191i | \(0.0903976\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.37195 | 2.68597 | ||||||||
\(5\) | −1.58639 | −0.709457 | −0.354728 | − | 0.934969i | \(-0.615427\pi\) | ||||
−0.354728 | + | 0.934969i | \(0.615427\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 9.15528 | 3.23688 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.30727 | −1.36208 | ||||||||
\(11\) | 1.34875 | 0.406664 | 0.203332 | − | 0.979110i | \(-0.434823\pi\) | ||||
0.203332 | + | 0.979110i | \(0.434823\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.17832 | 0.881508 | 0.440754 | − | 0.897628i | \(-0.354711\pi\) | ||||
0.440754 | + | 0.897628i | \(0.354711\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.1139 | 3.52848 | ||||||||
\(17\) | 2.80054 | 0.679230 | 0.339615 | − | 0.940565i | \(-0.389703\pi\) | ||||
0.339615 | + | 0.940565i | \(0.389703\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.625693 | −0.143544 | −0.0717719 | − | 0.997421i | \(-0.522865\pi\) | ||||
−0.0717719 | + | 0.997421i | \(0.522865\pi\) | |||||||
\(20\) | −8.52202 | −1.90558 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.66204 | 0.780750 | ||||||||
\(23\) | 0.284867 | 0.0593989 | 0.0296995 | − | 0.999559i | \(-0.490545\pi\) | ||||
0.0296995 | + | 0.999559i | \(0.490545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.48336 | −0.496671 | ||||||||
\(26\) | 8.62957 | 1.69240 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.54792 | 0.844527 | 0.422264 | − | 0.906473i | \(-0.361236\pi\) | ||||
0.422264 | + | 0.906473i | \(0.361236\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.43005 | −1.33448 | −0.667238 | − | 0.744845i | \(-0.732524\pi\) | ||||
−0.667238 | + | 0.744845i | \(0.732524\pi\) | |||||||
\(32\) | 20.0106 | 3.53741 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.60383 | 1.30405 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.02252 | 1.31889 | 0.659447 | − | 0.751751i | \(-0.270791\pi\) | ||||
0.659447 | + | 0.751751i | \(0.270791\pi\) | |||||||
\(38\) | −1.69884 | −0.275588 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −14.5239 | −2.29643 | ||||||||
\(41\) | −10.0266 | −1.56589 | −0.782944 | − | 0.622092i | \(-0.786283\pi\) | ||||
−0.782944 | + | 0.622092i | \(0.786283\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.25873 | 0.954448 | 0.477224 | − | 0.878782i | \(-0.341643\pi\) | ||||
0.477224 | + | 0.878782i | \(0.341643\pi\) | |||||||
\(44\) | 7.24542 | 1.09229 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.773452 | 0.114039 | ||||||||
\(47\) | 11.1477 | 1.62605 | 0.813026 | − | 0.582227i | \(-0.197819\pi\) | ||||
0.813026 | + | 0.582227i | \(0.197819\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.74264 | −0.953554 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 17.0738 | 2.36771 | ||||||||
\(53\) | −2.78698 | −0.382821 | −0.191410 | − | 0.981510i | \(-0.561306\pi\) | ||||
−0.191410 | + | 0.981510i | \(0.561306\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.13965 | −0.288510 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.3482 | 1.62140 | ||||||||
\(59\) | 4.57469 | 0.595574 | 0.297787 | − | 0.954632i | \(-0.403752\pi\) | ||||
0.297787 | + | 0.954632i | \(0.403752\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.385014 | 0.0492960 | 0.0246480 | − | 0.999696i | \(-0.492154\pi\) | ||||
0.0246480 | + | 0.999696i | \(0.492154\pi\) | |||||||
\(62\) | −20.1736 | −2.56205 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 26.1036 | 3.26295 | ||||||||
\(65\) | −5.04207 | −0.625392 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.53916 | −0.310208 | −0.155104 | − | 0.987898i | \(-0.549571\pi\) | ||||
−0.155104 | + | 0.987898i | \(0.549571\pi\) | |||||||
\(68\) | 15.0443 | 1.82439 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.45208 | 0.172330 | 0.0861651 | − | 0.996281i | \(-0.472539\pi\) | ||||
0.0861651 | + | 0.996281i | \(0.472539\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.468134 | 0.0547909 | 0.0273955 | − | 0.999625i | \(-0.491279\pi\) | ||||
0.0273955 | + | 0.999625i | \(0.491279\pi\) | |||||||
\(74\) | 21.7822 | 2.53213 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.36119 | −0.385555 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.7124 | −1.76778 | −0.883892 | − | 0.467691i | \(-0.845086\pi\) | ||||
−0.883892 | + | 0.467691i | \(0.845086\pi\) | |||||||
\(80\) | −22.3902 | −2.50330 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −27.2235 | −3.00633 | ||||||||
\(83\) | 13.9868 | 1.53525 | 0.767623 | − | 0.640901i | \(-0.221439\pi\) | ||||
0.767623 | + | 0.640901i | \(0.221439\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.44275 | −0.481884 | ||||||||
\(86\) | 16.9933 | 1.83243 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.3482 | 1.31632 | ||||||||
\(89\) | −2.58706 | −0.274228 | −0.137114 | − | 0.990555i | \(-0.543783\pi\) | ||||
−0.137114 | + | 0.990555i | \(0.543783\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.53029 | 0.159544 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 30.2674 | 3.12184 | ||||||||
\(95\) | 0.992595 | 0.101838 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.4592 | 1.46811 | 0.734057 | − | 0.679088i | \(-0.237624\pi\) | ||||
0.734057 | + | 0.679088i | \(0.237624\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.3405 | −1.33405 | ||||||||
\(101\) | 9.83776 | 0.978894 | 0.489447 | − | 0.872033i | \(-0.337199\pi\) | ||||
0.489447 | + | 0.872033i | \(0.337199\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.0579 | −1.08957 | −0.544786 | − | 0.838575i | \(-0.683389\pi\) | ||||
−0.544786 | + | 0.838575i | \(0.683389\pi\) | |||||||
\(104\) | 29.0984 | 2.85334 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.56701 | −0.734973 | ||||||||
\(107\) | 1.92431 | 0.186030 | 0.0930149 | − | 0.995665i | \(-0.470350\pi\) | ||||
0.0930149 | + | 0.995665i | \(0.470350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.6068 | −1.78221 | −0.891105 | − | 0.453797i | \(-0.850069\pi\) | ||||
−0.891105 | + | 0.453797i | \(0.850069\pi\) | |||||||
\(110\) | −5.80944 | −0.553908 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.18677 | 0.299786 | 0.149893 | − | 0.988702i | \(-0.452107\pi\) | ||||
0.149893 | + | 0.988702i | \(0.452107\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.451911 | −0.0421410 | ||||||||
\(116\) | 24.4312 | 2.26838 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.4209 | 1.14344 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.18087 | −0.834624 | ||||||||
\(122\) | 1.04536 | 0.0946428 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −39.9138 | −3.58437 | ||||||||
\(125\) | 11.8715 | 1.06182 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.37387 | −0.743061 | −0.371530 | − | 0.928421i | \(-0.621167\pi\) | ||||
−0.371530 | + | 0.928421i | \(0.621167\pi\) | |||||||
\(128\) | 30.8535 | 2.72709 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −13.6899 | −1.20068 | ||||||||
\(131\) | −11.9726 | −1.04605 | −0.523024 | − | 0.852318i | \(-0.675196\pi\) | ||||
−0.523024 | + | 0.852318i | \(0.675196\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.89415 | −0.595564 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 25.6397 | 2.19859 | ||||||||
\(137\) | −16.5505 | −1.41401 | −0.707003 | − | 0.707211i | \(-0.749953\pi\) | ||||
−0.707003 | + | 0.707211i | \(0.749953\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.90239 | 0.670272 | 0.335136 | − | 0.942170i | \(-0.391218\pi\) | ||||
0.335136 | + | 0.942170i | \(0.391218\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.94259 | 0.330855 | ||||||||
\(143\) | 4.28677 | 0.358478 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.21479 | −0.599156 | ||||||||
\(146\) | 1.27105 | 0.105192 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 43.0965 | 3.54251 | ||||||||
\(149\) | 13.6685 | 1.11977 | 0.559885 | − | 0.828570i | \(-0.310845\pi\) | ||||
0.559885 | + | 0.828570i | \(0.310845\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.89963 | 0.317348 | 0.158674 | − | 0.987331i | \(-0.449278\pi\) | ||||
0.158674 | + | 0.987331i | \(0.449278\pi\) | |||||||
\(152\) | −5.72839 | −0.464634 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.7870 | 0.946753 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.294352 | 0.0234919 | 0.0117459 | − | 0.999931i | \(-0.496261\pi\) | ||||
0.0117459 | + | 0.999931i | \(0.496261\pi\) | |||||||
\(158\) | −42.6613 | −3.39395 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −31.7447 | −2.50964 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7091 | 0.838802 | 0.419401 | − | 0.907801i | \(-0.362240\pi\) | ||||
0.419401 | + | 0.907801i | \(0.362240\pi\) | |||||||
\(164\) | −53.8622 | −4.20593 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 37.9759 | 2.94750 | ||||||||
\(167\) | −3.19745 | −0.247426 | −0.123713 | − | 0.992318i | \(-0.539480\pi\) | ||||
−0.123713 | + | 0.992318i | \(0.539480\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.89826 | −0.222943 | ||||||||
\(170\) | −12.0627 | −0.925164 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 33.6216 | 2.56362 | ||||||||
\(173\) | −11.4375 | −0.869577 | −0.434789 | − | 0.900533i | \(-0.643177\pi\) | ||||
−0.434789 | + | 0.900533i | \(0.643177\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 19.0362 | 1.43491 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.02421 | −0.526487 | ||||||||
\(179\) | −1.09855 | −0.0821095 | −0.0410547 | − | 0.999157i | \(-0.513072\pi\) | ||||
−0.0410547 | + | 0.999157i | \(0.513072\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.19013 | −0.237120 | −0.118560 | − | 0.992947i | \(-0.537828\pi\) | ||||
−0.118560 | + | 0.992947i | \(0.537828\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.60804 | 0.192267 | ||||||||
\(185\) | −12.7269 | −0.935698 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.77723 | 0.276218 | ||||||||
\(188\) | 59.8846 | 4.36753 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.69503 | 0.195518 | ||||||||
\(191\) | −3.86815 | −0.279889 | −0.139945 | − | 0.990159i | \(-0.544692\pi\) | ||||
−0.139945 | + | 0.990159i | \(0.544692\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.13585 | −0.297705 | −0.148853 | − | 0.988859i | \(-0.547558\pi\) | ||||
−0.148853 | + | 0.988859i | \(0.547558\pi\) | |||||||
\(194\) | 39.2588 | 2.81862 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.889267 | 0.0633576 | 0.0316788 | − | 0.999498i | \(-0.489915\pi\) | ||||
0.0316788 | + | 0.999498i | \(0.489915\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.32386 | −0.448287 | −0.224143 | − | 0.974556i | \(-0.571958\pi\) | ||||
−0.224143 | + | 0.974556i | \(0.571958\pi\) | |||||||
\(200\) | −22.7358 | −1.60767 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 26.7108 | 1.87937 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.9061 | 1.11093 | ||||||||
\(206\) | −30.0238 | −2.09186 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 44.8586 | 3.11038 | ||||||||
\(209\) | −0.843905 | −0.0583741 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.4258 | −0.786586 | −0.393293 | − | 0.919413i | \(-0.628664\pi\) | ||||
−0.393293 | + | 0.919413i | \(0.628664\pi\) | |||||||
\(212\) | −14.9715 | −1.02825 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.22475 | 0.357156 | ||||||||
\(215\) | −9.92881 | −0.677139 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −50.5200 | −3.42164 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −11.4941 | −0.774931 | ||||||||
\(221\) | 8.90101 | 0.598747 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.7191 | 1.11959 | 0.559796 | − | 0.828631i | \(-0.310880\pi\) | ||||
0.559796 | + | 0.828631i | \(0.310880\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.65250 | 0.575555 | ||||||||
\(227\) | 17.0700 | 1.13298 | 0.566489 | − | 0.824070i | \(-0.308302\pi\) | ||||
0.566489 | + | 0.824070i | \(0.308302\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.7894 | −1.30772 | −0.653861 | − | 0.756615i | \(-0.726852\pi\) | ||||
−0.653861 | + | 0.756615i | \(0.726852\pi\) | |||||||
\(230\) | −1.22700 | −0.0809059 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 41.6375 | 2.73363 | ||||||||
\(233\) | −5.93159 | −0.388591 | −0.194296 | − | 0.980943i | \(-0.562242\pi\) | ||||
−0.194296 | + | 0.980943i | \(0.562242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.6846 | −1.15361 | ||||||||
\(236\) | 24.5750 | 1.59969 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.0554 | −1.29727 | −0.648637 | − | 0.761098i | \(-0.724661\pi\) | ||||
−0.648637 | + | 0.761098i | \(0.724661\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.2887 | −1.88665 | −0.943326 | − | 0.331869i | \(-0.892321\pi\) | ||||
−0.943326 | + | 0.331869i | \(0.892321\pi\) | |||||||
\(242\) | −24.9273 | −1.60239 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.06827 | 0.132408 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.98865 | −0.126535 | ||||||||
\(248\) | −68.0242 | −4.31954 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 32.2328 | 2.03858 | ||||||||
\(251\) | −22.7856 | −1.43821 | −0.719106 | − | 0.694901i | \(-0.755448\pi\) | ||||
−0.719106 | + | 0.694901i | \(0.755448\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.384215 | 0.0241554 | ||||||||
\(254\) | −22.7362 | −1.42659 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 31.5642 | 1.97276 | ||||||||
\(257\) | −24.2889 | −1.51510 | −0.757550 | − | 0.652778i | \(-0.773604\pi\) | ||||
−0.757550 | + | 0.652778i | \(0.773604\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −27.0857 | −1.67979 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −32.5071 | −2.00830 | ||||||||
\(263\) | 8.61155 | 0.531011 | 0.265506 | − | 0.964109i | \(-0.414461\pi\) | ||||
0.265506 | + | 0.964109i | \(0.414461\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.42124 | 0.271595 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.6402 | −0.833209 | ||||||||
\(269\) | −15.2312 | −0.928664 | −0.464332 | − | 0.885661i | \(-0.653706\pi\) | ||||
−0.464332 | + | 0.885661i | \(0.653706\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.67820 | 0.284181 | 0.142090 | − | 0.989854i | \(-0.454618\pi\) | ||||
0.142090 | + | 0.989854i | \(0.454618\pi\) | |||||||
\(272\) | 39.5265 | 2.39665 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −44.9368 | −2.71473 | ||||||||
\(275\) | −3.34943 | −0.201978 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3907 | −0.984824 | −0.492412 | − | 0.870362i | \(-0.663885\pi\) | ||||
−0.492412 | + | 0.870362i | \(0.663885\pi\) | |||||||
\(278\) | 21.4560 | 1.28685 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.51404 | 0.209630 | 0.104815 | − | 0.994492i | \(-0.466575\pi\) | ||||
0.104815 | + | 0.994492i | \(0.466575\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.0708 | −1.54975 | −0.774874 | − | 0.632116i | \(-0.782187\pi\) | ||||
−0.774874 | + | 0.632116i | \(0.782187\pi\) | |||||||
\(284\) | 7.80050 | 0.462874 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.6392 | 0.688237 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.15699 | −0.538647 | ||||||||
\(290\) | −19.5891 | −1.15031 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.51479 | 0.147167 | ||||||||
\(293\) | 18.8838 | 1.10321 | 0.551603 | − | 0.834107i | \(-0.314016\pi\) | ||||
0.551603 | + | 0.834107i | \(0.314016\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.25725 | −0.422534 | ||||||||
\(296\) | 73.4484 | 4.26910 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 37.1119 | 2.14983 | ||||||||
\(299\) | 0.905400 | 0.0523606 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.5880 | 0.609272 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.83097 | −0.506491 | ||||||||
\(305\) | −0.610783 | −0.0349734 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6407 | 1.23510 | 0.617551 | − | 0.786531i | \(-0.288125\pi\) | ||||
0.617551 | + | 0.786531i | \(0.288125\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 32.0032 | 1.81766 | ||||||||
\(311\) | 4.49448 | 0.254859 | 0.127429 | − | 0.991848i | \(-0.459327\pi\) | ||||
0.127429 | + | 0.991848i | \(0.459327\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.60204 | −0.486216 | −0.243108 | − | 0.969999i | \(-0.578167\pi\) | ||||
−0.243108 | + | 0.969999i | \(0.578167\pi\) | |||||||
\(314\) | 0.799206 | 0.0451018 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84.4062 | −4.74822 | ||||||||
\(317\) | 8.06255 | 0.452838 | 0.226419 | − | 0.974030i | \(-0.427298\pi\) | ||||
0.226419 | + | 0.974030i | \(0.427298\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.13402 | 0.343439 | ||||||||
\(320\) | −41.4105 | −2.31492 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.75228 | −0.0974992 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.89291 | −0.437820 | ||||||||
\(326\) | 29.0766 | 1.61041 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −91.7961 | −5.06859 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.9026 | −1.25884 | −0.629419 | − | 0.777066i | \(-0.716707\pi\) | ||||
−0.629419 | + | 0.777066i | \(0.716707\pi\) | |||||||
\(332\) | 75.1361 | 4.12363 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.68150 | −0.475030 | ||||||||
\(335\) | 4.02810 | 0.220079 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.6378 | 0.742899 | 0.371450 | − | 0.928453i | \(-0.378861\pi\) | ||||
0.371450 | + | 0.928453i | \(0.378861\pi\) | |||||||
\(338\) | −7.86916 | −0.428026 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −23.8662 | −1.29433 | ||||||||
\(341\) | −10.0213 | −0.542683 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 57.3005 | 3.08943 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −31.0543 | −1.66949 | ||||||||
\(347\) | 2.82563 | 0.151688 | 0.0758440 | − | 0.997120i | \(-0.475835\pi\) | ||||
0.0758440 | + | 0.997120i | \(0.475835\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.62404 | −0.193990 | −0.0969951 | − | 0.995285i | \(-0.530923\pi\) | ||||
−0.0969951 | + | 0.995285i | \(0.530923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 26.9893 | 1.43854 | ||||||||
\(353\) | −2.75401 | −0.146581 | −0.0732907 | − | 0.997311i | \(-0.523350\pi\) | ||||
−0.0732907 | + | 0.997311i | \(0.523350\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.30357 | −0.122261 | ||||||||
\(356\) | −13.8975 | −0.736568 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.98271 | −0.157641 | ||||||||
\(359\) | 16.8015 | 0.886750 | 0.443375 | − | 0.896336i | \(-0.353781\pi\) | ||||
0.443375 | + | 0.896336i | \(0.353781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6085 | −0.979395 | ||||||||
\(362\) | −8.66163 | −0.455245 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.742644 | −0.0388718 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.9339 | 1.24934 | 0.624670 | − | 0.780889i | \(-0.285233\pi\) | ||||
0.624670 | + | 0.780889i | \(0.285233\pi\) | |||||||
\(368\) | 4.02059 | 0.209588 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −34.5551 | −1.79644 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.1606 | −0.992098 | −0.496049 | − | 0.868295i | \(-0.665216\pi\) | ||||
−0.496049 | + | 0.868295i | \(0.665216\pi\) | |||||||
\(374\) | 10.2557 | 0.530309 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 102.060 | 5.26334 | ||||||||
\(377\) | 14.4548 | 0.744458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0770 | 0.517622 | 0.258811 | − | 0.965928i | \(-0.416669\pi\) | ||||
0.258811 | + | 0.965928i | \(0.416669\pi\) | |||||||
\(380\) | 5.33217 | 0.273534 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.5025 | −0.537357 | ||||||||
\(383\) | −20.1435 | −1.02929 | −0.514643 | − | 0.857405i | \(-0.672075\pi\) | ||||
−0.514643 | + | 0.857405i | \(0.672075\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.2294 | −0.571561 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 77.6743 | 3.94332 | ||||||||
\(389\) | −13.3947 | −0.679139 | −0.339570 | − | 0.940581i | \(-0.610281\pi\) | ||||
−0.339570 | + | 0.940581i | \(0.610281\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.797781 | 0.0403455 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.41448 | 0.121640 | ||||||||
\(395\) | 24.9261 | 1.25417 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0133 | 0.904061 | 0.452031 | − | 0.892002i | \(-0.350700\pi\) | ||||
0.452031 | + | 0.892002i | \(0.350700\pi\) | |||||||
\(398\) | −17.1701 | −0.860661 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −35.0499 | −1.75249 | ||||||||
\(401\) | −28.8675 | −1.44157 | −0.720787 | − | 0.693157i | \(-0.756219\pi\) | ||||
−0.720787 | + | 0.693157i | \(0.756219\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.6151 | −1.17635 | ||||||||
\(404\) | 52.8479 | 2.62928 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.8204 | 0.536347 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.8587 | 0.536931 | 0.268465 | − | 0.963289i | \(-0.413484\pi\) | ||||
0.268465 | + | 0.963289i | \(0.413484\pi\) | |||||||
\(410\) | 43.1872 | 2.13286 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −59.4027 | −2.92656 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.1885 | −1.08919 | ||||||||
\(416\) | 63.6001 | 3.11825 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.29131 | −0.112072 | ||||||||
\(419\) | 0.495144 | 0.0241893 | 0.0120947 | − | 0.999927i | \(-0.496150\pi\) | ||||
0.0120947 | + | 0.999927i | \(0.496150\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0064 | −0.926315 | −0.463158 | − | 0.886276i | \(-0.653284\pi\) | ||||
−0.463158 | + | 0.886276i | \(0.653284\pi\) | |||||||
\(422\) | −31.0226 | −1.51016 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −25.5155 | −1.23914 | ||||||||
\(425\) | −6.95473 | −0.337354 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.3373 | 0.499671 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.9580 | −1.30003 | ||||||||
\(431\) | 16.9215 | 0.815078 | 0.407539 | − | 0.913188i | \(-0.366387\pi\) | ||||
0.407539 | + | 0.913188i | \(0.366387\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.4740 | 1.60866 | 0.804330 | − | 0.594183i | \(-0.202524\pi\) | ||||
0.804330 | + | 0.594183i | \(0.202524\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −99.9548 | −4.78697 | ||||||||
\(437\) | −0.178239 | −0.00852634 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.9315 | −0.999005 | −0.499502 | − | 0.866313i | \(-0.666484\pi\) | ||||
−0.499502 | + | 0.866313i | \(0.666484\pi\) | |||||||
\(440\) | −19.5891 | −0.933874 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.1674 | 1.14953 | ||||||||
\(443\) | 30.8580 | 1.46611 | 0.733054 | − | 0.680170i | \(-0.238094\pi\) | ||||
0.733054 | + | 0.680170i | \(0.238094\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.10409 | 0.194553 | ||||||||
\(446\) | 45.3945 | 2.14949 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.2789 | 1.57053 | 0.785263 | − | 0.619162i | \(-0.212528\pi\) | ||||
0.785263 | + | 0.619162i | \(0.212528\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.5234 | −0.636791 | ||||||||
\(452\) | 17.1191 | 0.805217 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 46.3474 | 2.17519 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.7904 | 1.11287 | 0.556434 | − | 0.830892i | \(-0.312169\pi\) | ||||
0.556434 | + | 0.830892i | \(0.312169\pi\) | |||||||
\(458\) | −53.7309 | −2.51068 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.42764 | −0.113189 | ||||||||
\(461\) | −17.0624 | −0.794677 | −0.397339 | − | 0.917672i | \(-0.630066\pi\) | ||||
−0.397339 | + | 0.917672i | \(0.630066\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.2485 | −1.68461 | −0.842306 | − | 0.538999i | \(-0.818803\pi\) | ||||
−0.842306 | + | 0.538999i | \(0.818803\pi\) | |||||||
\(464\) | 64.1889 | 2.97990 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.1051 | −0.746052 | ||||||||
\(467\) | −8.19160 | −0.379062 | −0.189531 | − | 0.981875i | \(-0.560697\pi\) | ||||
−0.189531 | + | 0.981875i | \(0.560697\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −48.0159 | −2.21481 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 41.8826 | 1.92780 | ||||||||
\(473\) | 8.44148 | 0.388140 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.55382 | 0.0712941 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −54.4530 | −2.49062 | ||||||||
\(479\) | −25.5549 | −1.16763 | −0.583817 | − | 0.811885i | \(-0.698441\pi\) | ||||
−0.583817 | + | 0.811885i | \(0.698441\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.4982 | 1.16262 | ||||||||
\(482\) | −79.5227 | −3.62216 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −49.3191 | −2.24178 | ||||||||
\(485\) | −22.9381 | −1.04156 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.92281 | −0.313702 | −0.156851 | − | 0.987622i | \(-0.550134\pi\) | ||||
−0.156851 | + | 0.987622i | \(0.550134\pi\) | |||||||
\(488\) | 3.52491 | 0.159565 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.4524 | 1.69021 | 0.845103 | − | 0.534604i | \(-0.179539\pi\) | ||||
0.845103 | + | 0.534604i | \(0.179539\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.7366 | 0.573628 | ||||||||
\(494\) | −5.39946 | −0.242933 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −104.867 | −4.70867 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.6250 | 1.14713 | 0.573566 | − | 0.819159i | \(-0.305560\pi\) | ||||
0.573566 | + | 0.819159i | \(0.305560\pi\) | |||||||
\(500\) | 63.7733 | 2.85203 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −61.8658 | −2.76121 | ||||||||
\(503\) | −5.79692 | −0.258472 | −0.129236 | − | 0.991614i | \(-0.541252\pi\) | ||||
−0.129236 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6066 | −0.694483 | ||||||||
\(506\) | 1.04320 | 0.0463757 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −44.9840 | −1.99584 | ||||||||
\(509\) | 25.1395 | 1.11429 | 0.557144 | − | 0.830416i | \(-0.311897\pi\) | ||||
0.557144 | + | 0.830416i | \(0.311897\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 23.9940 | 1.06039 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −65.9475 | −2.90882 | ||||||||
\(515\) | 17.5423 | 0.773004 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.0354 | 0.661257 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −46.1616 | −2.02432 | ||||||||
\(521\) | 7.29656 | 0.319668 | 0.159834 | − | 0.987144i | \(-0.448904\pi\) | ||||
0.159834 | + | 0.987144i | \(0.448904\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.7727 | −0.733421 | −0.366710 | − | 0.930335i | \(-0.619516\pi\) | ||||
−0.366710 | + | 0.930335i | \(0.619516\pi\) | |||||||
\(524\) | −64.3160 | −2.80966 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.3815 | 1.01948 | ||||||||
\(527\) | −20.8081 | −0.906416 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9189 | −0.996472 | ||||||||
\(530\) | 12.0042 | 0.521431 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31.8677 | −1.38034 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.05271 | −0.131980 | ||||||||
\(536\) | −23.2467 | −1.00411 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −41.3548 | −1.78293 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.29816 | −0.227786 | −0.113893 | − | 0.993493i | \(-0.536332\pi\) | ||||
−0.113893 | + | 0.993493i | \(0.536332\pi\) | |||||||
\(542\) | 12.7019 | 0.545595 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 56.0404 | 2.40271 | ||||||||
\(545\) | 29.5177 | 1.26440 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.8650 | −1.40521 | −0.702603 | − | 0.711582i | \(-0.747979\pi\) | ||||
−0.702603 | + | 0.711582i | \(0.747979\pi\) | |||||||
\(548\) | −88.9084 | −3.79798 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.09416 | −0.387776 | ||||||||
\(551\) | −2.84560 | −0.121227 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −44.5030 | −1.89075 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 42.4512 | 1.80033 | ||||||||
\(557\) | 18.8160 | 0.797258 | 0.398629 | − | 0.917112i | \(-0.369486\pi\) | ||||
0.398629 | + | 0.917112i | \(0.369486\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.8923 | 0.841354 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.54108 | 0.402466 | ||||||||
\(563\) | 27.6650 | 1.16594 | 0.582970 | − | 0.812494i | \(-0.301891\pi\) | ||||
0.582970 | + | 0.812494i | \(0.301891\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.05547 | −0.212685 | ||||||||
\(566\) | −70.7856 | −2.97534 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.2942 | 0.557812 | ||||||||
\(569\) | 40.1831 | 1.68456 | 0.842282 | − | 0.539037i | \(-0.181212\pi\) | ||||
0.842282 | + | 0.539037i | \(0.181212\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.81129 | −0.285044 | −0.142522 | − | 0.989792i | \(-0.545521\pi\) | ||||
−0.142522 | + | 0.989792i | \(0.545521\pi\) | |||||||
\(572\) | 23.0283 | 0.962862 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.707427 | −0.0295017 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.4222 | 1.51628 | 0.758138 | − | 0.652094i | \(-0.226109\pi\) | ||||
0.758138 | + | 0.652094i | \(0.226109\pi\) | |||||||
\(578\) | −24.8625 | −1.03414 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −38.7575 | −1.60932 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.75894 | −0.155679 | ||||||||
\(584\) | 4.28590 | 0.177352 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 51.2721 | 2.11803 | ||||||||
\(587\) | −11.1589 | −0.460575 | −0.230288 | − | 0.973123i | \(-0.573967\pi\) | ||||
−0.230288 | + | 0.973123i | \(0.573967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.64893 | 0.191556 | ||||||||
\(590\) | −19.7044 | −0.811218 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 113.229 | 4.65369 | ||||||||
\(593\) | 19.8085 | 0.813439 | 0.406720 | − | 0.913553i | \(-0.366673\pi\) | ||||
0.406720 | + | 0.913553i | \(0.366673\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 73.4266 | 3.00767 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.45828 | 0.100527 | ||||||||
\(599\) | 18.1320 | 0.740853 | 0.370427 | − | 0.928862i | \(-0.379211\pi\) | ||||
0.370427 | + | 0.928862i | \(0.379211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.6570 | −1.00578 | −0.502889 | − | 0.864351i | \(-0.667730\pi\) | ||||
−0.502889 | + | 0.864351i | \(0.667730\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.9486 | 0.852387 | ||||||||
\(605\) | 14.5645 | 0.592130 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.2775 | −0.701273 | −0.350637 | − | 0.936512i | \(-0.614035\pi\) | ||||
−0.350637 | + | 0.936512i | \(0.614035\pi\) | |||||||
\(608\) | −12.5205 | −0.507772 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.65836 | −0.0671450 | ||||||||
\(611\) | 35.4308 | 1.43338 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.5566 | 0.789882 | 0.394941 | − | 0.918707i | \(-0.370765\pi\) | ||||
0.394941 | + | 0.918707i | \(0.370765\pi\) | |||||||
\(614\) | 58.7575 | 2.37126 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.7446 | 0.875404 | 0.437702 | − | 0.899120i | \(-0.355792\pi\) | ||||
0.437702 | + | 0.899120i | \(0.355792\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.8048 | −1.35873 | −0.679366 | − | 0.733800i | \(-0.737745\pi\) | ||||
−0.679366 | + | 0.733800i | \(0.737745\pi\) | |||||||
\(620\) | 63.3190 | 2.54295 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.2031 | 0.489300 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.41615 | −0.256646 | ||||||||
\(626\) | −23.3557 | −0.933481 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.58125 | 0.0630986 | ||||||||
\(629\) | 22.4674 | 0.895832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.6410 | −0.941134 | −0.470567 | − | 0.882364i | \(-0.655951\pi\) | ||||
−0.470567 | + | 0.882364i | \(0.655951\pi\) | |||||||
\(632\) | −143.852 | −5.72211 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 21.8909 | 0.869399 | ||||||||
\(635\) | 13.2843 | 0.527169 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.6547 | 0.659365 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −48.9458 | −1.93475 | ||||||||
\(641\) | −15.9180 | −0.628724 | −0.314362 | − | 0.949303i | \(-0.601791\pi\) | ||||
−0.314362 | + | 0.949303i | \(0.601791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.5054 | −1.04527 | −0.522636 | − | 0.852556i | \(-0.675051\pi\) | ||||
−0.522636 | + | 0.852556i | \(0.675051\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.75766 | −0.187188 | ||||||||
\(647\) | 0.0160392 | 0.000630565 0 | 0.000315282 | − | 1.00000i | \(-0.499900\pi\) | ||||
0.000315282 | 1.00000i | \(0.499900\pi\) | ||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.17012 | 0.242198 | ||||||||
\(650\) | −21.4303 | −0.840566 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 57.5287 | 2.25300 | ||||||||
\(653\) | 33.2879 | 1.30266 | 0.651328 | − | 0.758796i | \(-0.274212\pi\) | ||||
0.651328 | + | 0.758796i | \(0.274212\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.9932 | 0.742126 | ||||||||
\(656\) | −141.514 | −5.52520 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.8312 | 1.51265 | 0.756324 | − | 0.654197i | \(-0.226993\pi\) | ||||
0.756324 | + | 0.654197i | \(0.226993\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.30644 | −0.206397 | −0.103198 | − | 0.994661i | \(-0.532908\pi\) | ||||
−0.103198 | + | 0.994661i | \(0.532908\pi\) | |||||||
\(662\) | −62.1835 | −2.41683 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 128.053 | 4.96941 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.29555 | 0.0501640 | ||||||||
\(668\) | −17.1765 | −0.664579 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.9368 | 0.422527 | ||||||||
\(671\) | 0.519288 | 0.0200469 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.07129 | 0.234031 | 0.117016 | − | 0.993130i | \(-0.462667\pi\) | ||||
0.117016 | + | 0.993130i | \(0.462667\pi\) | |||||||
\(674\) | 37.0285 | 1.42628 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.5693 | −0.598819 | ||||||||
\(677\) | −34.7850 | −1.33690 | −0.668449 | − | 0.743758i | \(-0.733041\pi\) | ||||
−0.668449 | + | 0.743758i | \(0.733041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −40.6746 | −1.55980 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −27.2091 | −1.04189 | ||||||||
\(683\) | −19.4241 | −0.743243 | −0.371622 | − | 0.928384i | \(-0.621198\pi\) | ||||
−0.371622 | + | 0.928384i | \(0.621198\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.2556 | 1.00318 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 88.3352 | 3.36775 | ||||||||
\(689\) | −8.85791 | −0.337459 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.63675 | 0.252474 | 0.126237 | − | 0.992000i | \(-0.459710\pi\) | ||||
0.126237 | + | 0.992000i | \(0.459710\pi\) | |||||||
\(692\) | −61.4416 | −2.33566 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.67197 | 0.291224 | ||||||||
\(695\) | −12.5363 | −0.475529 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.0798 | −1.06360 | ||||||||
\(698\) | −9.83974 | −0.372440 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.9153 | 0.525574 | 0.262787 | − | 0.964854i | \(-0.415358\pi\) | ||||
0.262787 | + | 0.964854i | \(0.415358\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.01963 | −0.189319 | ||||||||
\(704\) | 35.2072 | 1.32692 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.47751 | −0.281420 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.1556 | 1.28274 | 0.641370 | − | 0.767231i | \(-0.278366\pi\) | ||||
0.641370 | + | 0.767231i | \(0.278366\pi\) | |||||||
\(710\) | −6.25450 | −0.234727 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23.6852 | −0.887642 | ||||||||
\(713\) | −2.11658 | −0.0792664 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.80050 | −0.254324 | ||||||||
\(716\) | −5.90135 | −0.220544 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 45.6183 | 1.70246 | ||||||||
\(719\) | −44.2900 | −1.65174 | −0.825870 | − | 0.563861i | \(-0.809316\pi\) | ||||
−0.825870 | + | 0.563861i | \(0.809316\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −50.5246 | −1.88033 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.1372 | −0.636899 | ||||||||
\(725\) | −11.2941 | −0.419453 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.2494 | 1.04771 | 0.523857 | − | 0.851806i | \(-0.324493\pi\) | ||||
0.523857 | + | 0.851806i | \(0.324493\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.01638 | −0.0746295 | ||||||||
\(731\) | 17.5278 | 0.648290 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.0169 | 0.924020 | 0.462010 | − | 0.886875i | \(-0.347128\pi\) | ||||
0.462010 | + | 0.886875i | \(0.347128\pi\) | |||||||
\(734\) | 64.9838 | 2.39859 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.70036 | 0.210118 | ||||||||
\(737\) | −3.42470 | −0.126150 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.0230 | 1.17798 | 0.588992 | − | 0.808139i | \(-0.299525\pi\) | ||||
0.588992 | + | 0.808139i | \(0.299525\pi\) | |||||||
\(740\) | −68.3680 | −2.51326 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.8063 | 1.42367 | 0.711833 | − | 0.702349i | \(-0.247865\pi\) | ||||
0.711833 | + | 0.702349i | \(0.247865\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.6837 | −0.794428 | ||||||||
\(746\) | −52.0236 | −1.90472 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 20.2911 | 0.741915 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.6991 | 0.791811 | 0.395905 | − | 0.918291i | \(-0.370431\pi\) | ||||
0.395905 | + | 0.918291i | \(0.370431\pi\) | |||||||
\(752\) | 157.337 | 5.73749 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 39.2466 | 1.42928 | ||||||||
\(755\) | −6.18635 | −0.225144 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5242 | 1.21846 | 0.609229 | − | 0.792995i | \(-0.291479\pi\) | ||||
0.609229 | + | 0.792995i | \(0.291479\pi\) | |||||||
\(758\) | 27.3605 | 0.993778 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.08748 | 0.329638 | ||||||||
\(761\) | −13.3210 | −0.482884 | −0.241442 | − | 0.970415i | \(-0.577620\pi\) | ||||
−0.241442 | + | 0.970415i | \(0.577620\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −20.7795 | −0.751775 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −54.6923 | −1.97611 | ||||||||
\(767\) | 14.5398 | 0.525003 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 54.7135 | 1.97302 | 0.986510 | − | 0.163698i | \(-0.0523423\pi\) | ||||
0.986510 | + | 0.163698i | \(0.0523423\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −22.2176 | −0.799628 | ||||||||
\(773\) | 2.36042 | 0.0848983 | 0.0424491 | − | 0.999099i | \(-0.486484\pi\) | ||||
0.0424491 | + | 0.999099i | \(0.486484\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.4515 | 0.662796 | ||||||||
\(776\) | 132.378 | 4.75211 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36.3684 | −1.30387 | ||||||||
\(779\) | 6.27356 | 0.224774 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.95850 | 0.0700805 | ||||||||
\(782\) | 2.16608 | 0.0774589 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.466959 | −0.0166665 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.66794 | 0.0594557 | 0.0297278 | − | 0.999558i | \(-0.490536\pi\) | ||||
0.0297278 | + | 0.999558i | \(0.490536\pi\) | |||||||
\(788\) | 4.77709 | 0.170177 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 67.6775 | 2.40786 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.22370 | 0.0434548 | ||||||||
\(794\) | 48.9085 | 1.73570 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −33.9715 | −1.20409 | ||||||||
\(797\) | 28.6295 | 1.01411 | 0.507055 | − | 0.861914i | \(-0.330734\pi\) | ||||
0.507055 | + | 0.861914i | \(0.330734\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.2194 | 1.10446 | ||||||||
\(800\) | −49.6934 | −1.75693 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −78.3791 | −2.76766 | ||||||||
\(803\) | 0.631397 | 0.0222815 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −64.1181 | −2.25846 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 90.0675 | 3.16856 | ||||||||
\(809\) | 2.85691 | 0.100444 | 0.0502219 | − | 0.998738i | \(-0.484007\pi\) | ||||
0.0502219 | + | 0.998738i | \(0.484007\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.2917 | −0.923225 | −0.461613 | − | 0.887082i | \(-0.652729\pi\) | ||||
−0.461613 | + | 0.887082i | \(0.652729\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 29.3788 | 1.02973 | ||||||||
\(815\) | −16.9889 | −0.595094 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.91605 | −0.137005 | ||||||||
\(818\) | 29.4829 | 1.03085 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 85.4467 | 2.98393 | ||||||||
\(821\) | 2.65849 | 0.0927821 | 0.0463910 | − | 0.998923i | \(-0.485228\pi\) | ||||
0.0463910 | + | 0.998923i | \(0.485228\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2154 | −0.425801 | −0.212901 | − | 0.977074i | \(-0.568291\pi\) | ||||
−0.212901 | + | 0.977074i | \(0.568291\pi\) | |||||||
\(824\) | −101.239 | −3.52681 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.15812 | −0.318459 | −0.159230 | − | 0.987242i | \(-0.550901\pi\) | ||||
−0.159230 | + | 0.987242i | \(0.550901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.3431 | −0.637083 | −0.318541 | − | 0.947909i | \(-0.603193\pi\) | ||||
−0.318541 | + | 0.947909i | \(0.603193\pi\) | |||||||
\(830\) | −60.2447 | −2.09113 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 82.9656 | 2.87631 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.07241 | 0.175538 | ||||||||
\(836\) | −4.53341 | −0.156791 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.34438 | 0.0464409 | ||||||||
\(839\) | 18.9411 | 0.653920 | 0.326960 | − | 0.945038i | \(-0.393976\pi\) | ||||
0.326960 | + | 0.945038i | \(0.393976\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.31643 | −0.286773 | ||||||||
\(842\) | −51.6049 | −1.77842 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −61.3789 | −2.11275 | ||||||||
\(845\) | 4.59778 | 0.158168 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −39.3351 | −1.35077 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18.8830 | −0.647682 | ||||||||
\(851\) | 2.28535 | 0.0783408 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.9584 | −0.683364 | −0.341682 | − | 0.939816i | \(-0.610997\pi\) | ||||
−0.341682 | + | 0.939816i | \(0.610997\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.6176 | 0.602156 | ||||||||
\(857\) | −16.4000 | −0.560214 | −0.280107 | − | 0.959969i | \(-0.590370\pi\) | ||||
−0.280107 | + | 0.959969i | \(0.590370\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.7151 | −1.15034 | −0.575172 | − | 0.818033i | \(-0.695065\pi\) | ||||
−0.575172 | + | 0.818033i | \(0.695065\pi\) | |||||||
\(860\) | −53.3371 | −1.81878 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 45.9440 | 1.56486 | ||||||||
\(863\) | 28.6831 | 0.976383 | 0.488191 | − | 0.872737i | \(-0.337657\pi\) | ||||
0.488191 | + | 0.872737i | \(0.337657\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.1444 | 0.616927 | ||||||||
\(866\) | 90.8865 | 3.08845 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.1921 | −0.718894 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.07027 | −0.273451 | ||||||||
\(872\) | −170.351 | −5.76880 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.483944 | −0.0163696 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.5243 | −0.996964 | −0.498482 | − | 0.866900i | \(-0.666109\pi\) | ||||
−0.498482 | + | 0.866900i | \(0.666109\pi\) | |||||||
\(878\) | −56.8317 | −1.91798 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −30.1988 | −1.01800 | ||||||||
\(881\) | 57.5032 | 1.93733 | 0.968666 | − | 0.248366i | \(-0.0798934\pi\) | ||||
0.968666 | + | 0.248366i | \(0.0798934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8715 | 0.668730 | 0.334365 | − | 0.942444i | \(-0.391478\pi\) | ||||
0.334365 | + | 0.942444i | \(0.391478\pi\) | |||||||
\(884\) | 47.8158 | 1.60822 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 83.7836 | 2.81477 | ||||||||
\(887\) | 37.0951 | 1.24553 | 0.622766 | − | 0.782408i | \(-0.286009\pi\) | ||||
0.622766 | + | 0.782408i | \(0.286009\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 11.1432 | 0.373519 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 89.8139 | 3.00719 | ||||||||
\(893\) | −6.97501 | −0.233410 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.74273 | 0.0582531 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 90.3565 | 3.01524 | ||||||||
\(899\) | −33.7913 | −1.12700 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.80503 | −0.260023 | ||||||||
\(902\) | −36.7177 | −1.22257 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29.1757 | 0.970371 | ||||||||
\(905\) | 5.06080 | 0.168227 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.4088 | 0.810479 | 0.405240 | − | 0.914210i | \(-0.367188\pi\) | ||||
0.405240 | + | 0.914210i | \(0.367188\pi\) | |||||||
\(908\) | 91.6993 | 3.04315 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.0986 | −0.831553 | −0.415776 | − | 0.909467i | \(-0.636490\pi\) | ||||
−0.415776 | + | 0.909467i | \(0.636490\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.8647 | 0.624330 | ||||||||
\(914\) | 64.5941 | 2.13658 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −106.308 | −3.51250 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.5976 | −0.943348 | −0.471674 | − | 0.881773i | \(-0.656350\pi\) | ||||
−0.471674 | + | 0.881773i | \(0.656350\pi\) | |||||||
\(920\) | −4.13738 | −0.136405 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −46.3268 | −1.52569 | ||||||||
\(923\) | 4.61518 | 0.151911 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.9228 | −0.655057 | ||||||||
\(926\) | −98.4196 | −3.23427 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 91.0065 | 2.98744 | ||||||||
\(929\) | −45.4570 | −1.49140 | −0.745698 | − | 0.666284i | \(-0.767884\pi\) | ||||
−0.745698 | + | 0.666284i | \(0.767884\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −31.8642 | −1.04375 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.2413 | −0.727757 | ||||||||
\(935\) | −5.99217 | −0.195965 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.0083 | −0.882322 | −0.441161 | − | 0.897428i | \(-0.645433\pi\) | ||||
−0.441161 | + | 0.897428i | \(0.645433\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −95.0005 | −3.09857 | ||||||||
\(941\) | 12.7131 | 0.414436 | 0.207218 | − | 0.978295i | \(-0.433559\pi\) | ||||
0.207218 | + | 0.978295i | \(0.433559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.85624 | −0.0930121 | ||||||||
\(944\) | 64.5667 | 2.10147 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.9197 | 0.745185 | ||||||||
\(947\) | −47.5447 | −1.54500 | −0.772498 | − | 0.635017i | \(-0.780993\pi\) | ||||
−0.772498 | + | 0.635017i | \(0.780993\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.48788 | 0.0482987 | ||||||||
\(950\) | 4.21882 | 0.136877 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.2355 | −1.23857 | −0.619285 | − | 0.785166i | \(-0.712577\pi\) | ||||
−0.619285 | + | 0.785166i | \(0.712577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.13640 | 0.198569 | ||||||||
\(956\) | −107.736 | −3.48444 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −69.3850 | −2.24173 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.2056 | 0.780826 | ||||||||
\(962\) | 69.2309 | 2.23209 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −157.337 | −5.06749 | ||||||||
\(965\) | 6.56109 | 0.211209 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.8185 | 1.31263 | 0.656317 | − | 0.754485i | \(-0.272113\pi\) | ||||
0.656317 | + | 0.754485i | \(0.272113\pi\) | |||||||
\(968\) | −84.0534 | −2.70158 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −62.2799 | −1.99969 | ||||||||
\(971\) | 44.9471 | 1.44242 | 0.721210 | − | 0.692717i | \(-0.243586\pi\) | ||||
0.721210 | + | 0.692717i | \(0.243586\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18.7963 | −0.602274 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.43405 | 0.173940 | ||||||||
\(977\) | −53.5104 | −1.71195 | −0.855974 | − | 0.517018i | \(-0.827042\pi\) | ||||
−0.855974 | + | 0.517018i | \(0.827042\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.48930 | −0.111519 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 101.688 | 3.24501 | ||||||||
\(983\) | 11.6056 | 0.370160 | 0.185080 | − | 0.982723i | \(-0.440746\pi\) | ||||
0.185080 | + | 0.982723i | \(0.440746\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.41073 | −0.0449495 | ||||||||
\(986\) | 34.5816 | 1.10130 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.6829 | −0.339870 | ||||||||
\(989\) | 1.78291 | 0.0566932 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.0091 | 0.826208 | 0.413104 | − | 0.910684i | \(-0.364445\pi\) | ||||
0.413104 | + | 0.910684i | \(0.364445\pi\) | |||||||
\(992\) | −148.680 | −4.72058 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0321 | 0.318040 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.8998 | 1.48533 | 0.742666 | − | 0.669662i | \(-0.233561\pi\) | ||||
0.742666 | + | 0.669662i | \(0.233561\pi\) | |||||||
\(998\) | 69.5753 | 2.20237 | ||||||||
\(999\) | 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 | 3969.2.a.bi.1.11 | 12 | ||
3.2 | odd | 2 | 3969.2.a.bh.1.2 | 12 | |||
7.6 | odd | 2 | inner | 3969.2.a.bi.1.12 | 12 | ||
9.2 | odd | 6 | 441.2.f.h.148.11 | ✓ | 24 | ||
9.4 | even | 3 | 1323.2.f.h.883.1 | 24 | |||
9.5 | odd | 6 | 441.2.f.h.295.11 | yes | 24 | ||
9.7 | even | 3 | 1323.2.f.h.442.1 | 24 | |||
21.20 | even | 2 | 3969.2.a.bh.1.1 | 12 | |||
63.2 | odd | 6 | 441.2.g.h.67.12 | 24 | |||
63.4 | even | 3 | 1323.2.g.h.667.2 | 24 | |||
63.5 | even | 6 | 441.2.h.h.214.2 | 24 | |||
63.11 | odd | 6 | 441.2.h.h.373.1 | 24 | |||
63.13 | odd | 6 | 1323.2.f.h.883.2 | 24 | |||
63.16 | even | 3 | 1323.2.g.h.361.2 | 24 | |||
63.20 | even | 6 | 441.2.f.h.148.12 | yes | 24 | ||
63.23 | odd | 6 | 441.2.h.h.214.1 | 24 | |||
63.25 | even | 3 | 1323.2.h.h.226.11 | 24 | |||
63.31 | odd | 6 | 1323.2.g.h.667.1 | 24 | |||
63.32 | odd | 6 | 441.2.g.h.79.12 | 24 | |||
63.34 | odd | 6 | 1323.2.f.h.442.2 | 24 | |||
63.38 | even | 6 | 441.2.h.h.373.2 | 24 | |||
63.40 | odd | 6 | 1323.2.h.h.802.12 | 24 | |||
63.41 | even | 6 | 441.2.f.h.295.12 | yes | 24 | ||
63.47 | even | 6 | 441.2.g.h.67.11 | 24 | |||
63.52 | odd | 6 | 1323.2.h.h.226.12 | 24 | |||
63.58 | even | 3 | 1323.2.h.h.802.11 | 24 | |||
63.59 | even | 6 | 441.2.g.h.79.11 | 24 | |||
63.61 | odd | 6 | 1323.2.g.h.361.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.11 | ✓ | 24 | 9.2 | odd | 6 | ||
441.2.f.h.148.12 | yes | 24 | 63.20 | even | 6 | ||
441.2.f.h.295.11 | yes | 24 | 9.5 | odd | 6 | ||
441.2.f.h.295.12 | yes | 24 | 63.41 | even | 6 | ||
441.2.g.h.67.11 | 24 | 63.47 | even | 6 | |||
441.2.g.h.67.12 | 24 | 63.2 | odd | 6 | |||
441.2.g.h.79.11 | 24 | 63.59 | even | 6 | |||
441.2.g.h.79.12 | 24 | 63.32 | odd | 6 | |||
441.2.h.h.214.1 | 24 | 63.23 | odd | 6 | |||
441.2.h.h.214.2 | 24 | 63.5 | even | 6 | |||
441.2.h.h.373.1 | 24 | 63.11 | odd | 6 | |||
441.2.h.h.373.2 | 24 | 63.38 | even | 6 | |||
1323.2.f.h.442.1 | 24 | 9.7 | even | 3 | |||
1323.2.f.h.442.2 | 24 | 63.34 | odd | 6 | |||
1323.2.f.h.883.1 | 24 | 9.4 | even | 3 | |||
1323.2.f.h.883.2 | 24 | 63.13 | odd | 6 | |||
1323.2.g.h.361.1 | 24 | 63.61 | odd | 6 | |||
1323.2.g.h.361.2 | 24 | 63.16 | even | 3 | |||
1323.2.g.h.667.1 | 24 | 63.31 | odd | 6 | |||
1323.2.g.h.667.2 | 24 | 63.4 | even | 3 | |||
1323.2.h.h.226.11 | 24 | 63.25 | even | 3 | |||
1323.2.h.h.226.12 | 24 | 63.52 | odd | 6 | |||
1323.2.h.h.802.11 | 24 | 63.58 | even | 3 | |||
1323.2.h.h.802.12 | 24 | 63.40 | odd | 6 | |||
3969.2.a.bh.1.1 | 12 | 21.20 | even | 2 | |||
3969.2.a.bh.1.2 | 12 | 3.2 | odd | 2 | |||
3969.2.a.bi.1.11 | 12 | 1.1 | even | 1 | trivial | ||
3969.2.a.bi.1.12 | 12 | 7.6 | odd | 2 | inner |