Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(1,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1368.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.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: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.892.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 8x + 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.31955\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1368.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.319551 | 0.142907 | 0.0714537 | − | 0.997444i | \(-0.477236\pi\) | ||||
0.0714537 | + | 0.997444i | \(0.477236\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.61968 | −0.990148 | −0.495074 | − | 0.868851i | \(-0.664859\pi\) | ||||
−0.495074 | + | 0.868851i | \(0.664859\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.31955 | 1.30239 | 0.651197 | − | 0.758909i | \(-0.274267\pi\) | ||||
0.651197 | + | 0.758909i | \(0.274267\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.51757 | 1.80765 | 0.903825 | − | 0.427903i | \(-0.140748\pi\) | ||||
0.903825 | + | 0.427903i | \(0.140748\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.19802 | −1.01817 | −0.509085 | − | 0.860716i | \(-0.670016\pi\) | ||||
−0.509085 | + | 0.860716i | \(0.670016\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.639102 | −0.133262 | −0.0666309 | − | 0.997778i | \(-0.521225\pi\) | ||||
−0.0666309 | + | 0.997778i | \(0.521225\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.89789 | −0.979577 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.87847 | 1.46300 | 0.731498 | − | 0.681844i | \(-0.238822\pi\) | ||||
0.731498 | + | 0.681844i | \(0.238822\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.837122 | −0.141499 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.5176 | 1.95492 | 0.977458 | − | 0.211129i | \(-0.0677142\pi\) | ||||
0.977458 | + | 0.211129i | \(0.0677142\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.38032 | −0.210496 | −0.105248 | − | 0.994446i | \(-0.533564\pi\) | ||||
−0.105248 | + | 0.994446i | \(0.533564\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.55892 | 1.10258 | 0.551291 | − | 0.834313i | \(-0.314135\pi\) | ||||
0.551291 | + | 0.834313i | \(0.314135\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.137255 | −0.0196079 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.1567 | 1.80721 | 0.903604 | − | 0.428369i | \(-0.140912\pi\) | ||||
0.903604 | + | 0.428369i | \(0.140912\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.38032 | 0.186122 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.0351 | 1.69703 | 0.848516 | − | 0.529171i | \(-0.177497\pi\) | ||||
0.848516 | + | 0.529171i | \(0.177497\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.89789 | −0.755147 | −0.377574 | − | 0.925980i | \(-0.623241\pi\) | ||||
−0.377574 | + | 0.925980i | \(0.623241\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.08270 | 0.258327 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.7569 | 1.43634 | 0.718169 | − | 0.695868i | \(-0.244980\pi\) | ||||
0.718169 | + | 0.695868i | \(0.244980\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.7569 | −1.39529 | −0.697646 | − | 0.716443i | \(-0.745769\pi\) | ||||
−0.697646 | + | 0.716443i | \(0.745769\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.1373 | 1.77168 | 0.885841 | − | 0.463989i | \(-0.153582\pi\) | ||||
0.885841 | + | 0.463989i | \(0.153582\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.3159 | −1.28956 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.517571 | 0.0582313 | 0.0291157 | − | 0.999576i | \(-0.490731\pi\) | ||||
0.0291157 | + | 0.999576i | \(0.490731\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.8785 | 1.30383 | 0.651916 | − | 0.758291i | \(-0.273966\pi\) | ||||
0.651916 | + | 0.758291i | \(0.273966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.34148 | −0.145504 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.87847 | −0.411117 | −0.205558 | − | 0.978645i | \(-0.565901\pi\) | ||||
−0.205558 | + | 0.978645i | \(0.565901\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.0740 | −1.78984 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.319551 | −0.0327852 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.2782 | 1.14513 | 0.572564 | − | 0.819860i | \(-0.305949\pi\) | ||||
0.572564 | + | 0.819860i | \(0.305949\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.51757 | −0.449515 | −0.224758 | − | 0.974415i | \(-0.572159\pi\) | ||||
−0.224758 | + | 0.974415i | \(0.572159\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.0351 | −1.87559 | −0.937794 | − | 0.347192i | \(-0.887135\pi\) | ||||
−0.937794 | + | 0.347192i | \(0.887135\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.11784 | −0.688107 | −0.344054 | − | 0.938950i | \(-0.611800\pi\) | ||||
−0.344054 | + | 0.938950i | \(0.611800\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.27820 | −0.505560 | −0.252780 | − | 0.967524i | \(-0.581345\pi\) | ||||
−0.252780 | + | 0.967524i | \(0.581345\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.39973 | −0.131676 | −0.0658379 | − | 0.997830i | \(-0.520972\pi\) | ||||
−0.0658379 | + | 0.997830i | \(0.520972\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.204225 | −0.0190441 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.9975 | 1.00814 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.65852 | 0.696229 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.16288 | −0.282896 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.75694 | −0.865788 | −0.432894 | − | 0.901445i | \(-0.642508\pi\) | ||||
−0.432894 | + | 0.901445i | \(0.642508\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.4374 | −1.69825 | −0.849126 | − | 0.528190i | \(-0.822871\pi\) | ||||
−0.849126 | + | 0.528190i | \(0.822871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.61968 | 0.227155 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.9198 | 0.932943 | 0.466471 | − | 0.884536i | \(-0.345525\pi\) | ||||
0.466471 | + | 0.884536i | \(0.345525\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.61968 | −0.561474 | −0.280737 | − | 0.959785i | \(-0.590579\pi\) | ||||
−0.280737 | + | 0.959785i | \(0.590579\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 28.1530 | 2.35427 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.51757 | 0.209073 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.958652 | −0.0785359 | −0.0392679 | − | 0.999229i | \(-0.512503\pi\) | ||||
−0.0392679 | + | 0.999229i | \(0.512503\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.517571 | 0.0421194 | 0.0210597 | − | 0.999778i | \(-0.493296\pi\) | ||||
0.0210597 | + | 0.999778i | \(0.493296\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.91730 | −0.154002 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.67424 | 0.131949 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0351 | 1.33430 | 0.667148 | − | 0.744925i | \(-0.267515\pi\) | ||||
0.667148 | + | 0.744925i | \(0.267515\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.6391 | −0.978043 | −0.489022 | − | 0.872272i | \(-0.662646\pi\) | ||||
−0.489022 | + | 0.872272i | \(0.662646\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.4787 | 2.26760 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.60027 | 0.197695 | 0.0988473 | − | 0.995103i | \(-0.468484\pi\) | ||||
0.0988473 | + | 0.995103i | \(0.468484\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.8309 | 0.969926 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.1178 | 1.42893 | 0.714467 | − | 0.699669i | \(-0.246669\pi\) | ||||
0.714467 | + | 0.699669i | \(0.246669\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.2745 | −1.65565 | −0.827826 | − | 0.560985i | \(-0.810422\pi\) | ||||
−0.827826 | + | 0.560985i | \(0.810422\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.27820 | 0.0939754 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.1336 | −1.32606 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.55892 | −0.546944 | −0.273472 | − | 0.961880i | \(-0.588172\pi\) | ||||
−0.273472 | + | 0.961880i | \(0.588172\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.517571 | −0.0372556 | −0.0186278 | − | 0.999826i | \(-0.505930\pi\) | ||||
−0.0186278 | + | 0.999826i | \(0.505930\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.4824 | 0.818089 | 0.409045 | − | 0.912514i | \(-0.365862\pi\) | ||||
0.409045 | + | 0.912514i | \(0.365862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.38032 | −0.0978480 | −0.0489240 | − | 0.998803i | \(-0.515579\pi\) | ||||
−0.0489240 | + | 0.998803i | \(0.515579\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.6391 | −1.44858 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | 0.279372 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.31955 | −0.298790 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.72180 | 0.187376 | 0.0936881 | − | 0.995602i | \(-0.470134\pi\) | ||||
0.0936881 | + | 0.995602i | \(0.470134\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.441081 | −0.0300815 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.7181 | 1.06701 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −27.3609 | −1.84049 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.79577 | −0.655974 | −0.327987 | − | 0.944682i | \(-0.606370\pi\) | ||||
−0.327987 | + | 0.944682i | \(0.606370\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.6391 | −0.838887 | −0.419443 | − | 0.907782i | \(-0.637775\pi\) | ||||
−0.419443 | + | 0.907782i | \(0.637775\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.1373 | −0.735971 | −0.367985 | − | 0.929832i | \(-0.619952\pi\) | ||||
−0.367985 | + | 0.929832i | \(0.619952\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.8723 | −1.43290 | −0.716450 | − | 0.697639i | \(-0.754234\pi\) | ||||
−0.716450 | + | 0.697639i | \(0.754234\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.41546 | 0.157567 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.8723 | −1.67354 | −0.836769 | − | 0.547556i | \(-0.815558\pi\) | ||||
−0.836769 | + | 0.547556i | \(0.815558\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.79577 | 0.631001 | 0.315501 | − | 0.948925i | \(-0.397828\pi\) | ||||
0.315501 | + | 0.948925i | \(0.397828\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.0438601 | −0.00280212 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.51757 | −0.414703 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.28441 | −0.207310 | −0.103655 | − | 0.994613i | \(-0.533054\pi\) | ||||
−0.103655 | + | 0.994613i | \(0.533054\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.76063 | −0.173559 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.5176 | −0.780825 | −0.390412 | − | 0.920640i | \(-0.627668\pi\) | ||||
−0.390412 | + | 0.920640i | \(0.627668\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.4787 | −0.651117 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.1980 | 1.49211 | 0.746057 | − | 0.665882i | \(-0.231945\pi\) | ||||
0.746057 | + | 0.665882i | \(0.231945\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.20423 | 0.258264 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.8785 | 0.724243 | 0.362122 | − | 0.932131i | \(-0.382053\pi\) | ||||
0.362122 | + | 0.932131i | \(0.382053\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.55641 | −0.398273 | −0.199137 | − | 0.979972i | \(-0.563814\pi\) | ||||
−0.199137 | + | 0.979972i | \(0.563814\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.1567 | −1.27580 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.6585 | −1.00091 | −0.500457 | − | 0.865762i | \(-0.666835\pi\) | ||||
−0.500457 | + | 0.865762i | \(0.666835\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.3572 | −0.617859 | −0.308930 | − | 0.951085i | \(-0.599971\pi\) | ||||
−0.308930 | + | 0.951085i | \(0.599971\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.4155 | −1.80801 | −0.904006 | − | 0.427520i | \(-0.859387\pi\) | ||||
−0.904006 | + | 0.427520i | \(0.859387\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −32.7921 | −1.93566 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.623376 | 0.0366692 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.2745 | 0.717085 | 0.358542 | − | 0.933513i | \(-0.383274\pi\) | ||||
0.358542 | + | 0.933513i | \(0.383274\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.16539 | 0.242518 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.16539 | −0.240891 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.61599 | 0.208422 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.88467 | −0.107916 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.72180 | 0.155341 | 0.0776706 | − | 0.996979i | \(-0.475252\pi\) | ||||
0.0776706 | + | 0.996979i | \(0.475252\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.837122 | 0.0474688 | 0.0237344 | − | 0.999718i | \(-0.492444\pi\) | ||||
0.0237344 | + | 0.999718i | \(0.492444\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.5564 | 0.709730 | 0.354865 | − | 0.934918i | \(-0.384527\pi\) | ||||
0.354865 | + | 0.934918i | \(0.384527\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.517571 | 0.0290697 | 0.0145349 | − | 0.999894i | \(-0.495373\pi\) | ||||
0.0145349 | + | 0.999894i | \(0.495373\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.0315 | 1.90540 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.19802 | 0.233584 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −31.9223 | −1.77073 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.8020 | −1.09172 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.3133 | 1.00659 | 0.503296 | − | 0.864114i | \(-0.332120\pi\) | ||||
0.503296 | + | 0.864114i | \(0.332120\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.75694 | 0.205264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.27820 | −0.178575 | −0.0892876 | − | 0.996006i | \(-0.528459\pi\) | ||||
−0.0892876 | + | 0.996006i | \(0.528459\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.9173 | −1.40350 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.6974 | 1.00956 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.5978 | 0.729966 | 0.364983 | − | 0.931014i | \(-0.381075\pi\) | ||||
0.364983 | + | 0.931014i | \(0.381075\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.1724 | 0.865689 | 0.432844 | − | 0.901469i | \(-0.357510\pi\) | ||||
0.432844 | + | 0.901469i | \(0.357510\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.47874 | −0.344828 | −0.172414 | − | 0.985025i | \(-0.555157\pi\) | ||||
−0.172414 | + | 0.985025i | \(0.555157\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.75694 | −0.199398 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.67676 | 0.352386 | 0.176193 | − | 0.984356i | \(-0.443622\pi\) | ||||
0.176193 | + | 0.984356i | \(0.443622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.83712 | 0.253187 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.0351 | 1.30682 | 0.653412 | − | 0.757003i | \(-0.273337\pi\) | ||||
0.653412 | + | 0.757003i | \(0.273337\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −34.4663 | −1.78940 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.5564 | 0.753702 | 0.376851 | − | 0.926274i | \(-0.377007\pi\) | ||||
0.376851 | + | 0.926274i | \(0.377007\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 51.3485 | 2.64458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.23937 | −0.0636621 | −0.0318310 | − | 0.999493i | \(-0.510134\pi\) | ||||
−0.0318310 | + | 0.999493i | \(0.510134\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.67424 | −0.0855499 | −0.0427749 | − | 0.999085i | \(-0.513620\pi\) | ||||
−0.0427749 | + | 0.999085i | \(0.513620\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.61599 | −0.184288 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.6329 | −1.35034 | −0.675171 | − | 0.737661i | \(-0.735930\pi\) | ||||
−0.675171 | + | 0.737661i | \(0.735930\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.68296 | 0.135683 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.165390 | 0.00832169 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.8979 | −0.898269 | −0.449135 | − | 0.893464i | \(-0.648268\pi\) | ||||
−0.449135 | + | 0.893464i | \(0.648268\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.7958 | −1.68768 | −0.843840 | − | 0.536595i | \(-0.819710\pi\) | ||||
−0.843840 | + | 0.536595i | \(0.819710\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −39.1054 | −1.94798 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.2782 | 0.856449 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.5139 | −1.06379 | −0.531896 | − | 0.846809i | \(-0.678520\pi\) | ||||
−0.531896 | + | 0.846809i | \(0.678520\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −34.1480 | −1.68031 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.79577 | 0.186327 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.6003 | 0.517857 | 0.258928 | − | 0.965897i | \(-0.416631\pi\) | ||||
0.258928 | + | 0.965897i | \(0.416631\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.7181 | −1.15595 | −0.577975 | − | 0.816055i | \(-0.696157\pi\) | ||||
−0.577975 | + | 0.816055i | \(0.696157\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.5614 | 0.997376 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.4506 | 0.747707 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.3609 | −0.932582 | −0.466291 | − | 0.884631i | \(-0.654410\pi\) | ||||
−0.466291 | + | 0.884631i | \(0.654410\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.7569 | −0.661116 | −0.330558 | − | 0.943786i | \(-0.607237\pi\) | ||||
−0.330558 | + | 0.943786i | \(0.607237\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.639102 | 0.0305724 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.2357 | 0.965796 | 0.482898 | − | 0.875677i | \(-0.339584\pi\) | ||||
0.482898 | + | 0.875677i | \(0.339584\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.87596 | 0.326687 | 0.163343 | − | 0.986569i | \(-0.447772\pi\) | ||||
0.163343 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.23937 | −0.0587517 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.76063 | 0.224668 | 0.112334 | − | 0.993670i | \(-0.464167\pi\) | ||||
0.112334 | + | 0.993670i | \(0.464167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 54.0703 | 2.54607 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.45600 | −0.255781 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.82022 | 0.272258 | 0.136129 | − | 0.990691i | \(-0.456534\pi\) | ||||
0.136129 | + | 0.990691i | \(0.456534\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0413 | 0.700545 | 0.350273 | − | 0.936648i | \(-0.386089\pi\) | ||||
0.350273 | + | 0.936648i | \(0.386089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.6548 | −1.28523 | −0.642614 | − | 0.766190i | \(-0.722150\pi\) | ||||
−0.642614 | + | 0.766190i | \(0.722150\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.9513 | 1.61735 | 0.808676 | − | 0.588254i | \(-0.200185\pi\) | ||||
0.808676 | + | 0.588254i | \(0.200185\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.7995 | −1.42219 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.96234 | −0.274149 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.89789 | 0.224730 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.67424 | −0.442028 | −0.221014 | − | 0.975271i | \(-0.570937\pi\) | ||||
−0.221014 | + | 0.975271i | \(0.570937\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.0703 | 1.18870 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.60396 | 0.163647 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.5176 | 0.929740 | 0.464870 | − | 0.885379i | \(-0.346101\pi\) | ||||
0.464870 | + | 0.885379i | \(0.346101\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.9136 | 1.66589 | 0.832944 | − | 0.553357i | \(-0.186654\pi\) | ||||
0.832944 | + | 0.553357i | \(0.186654\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.0740 | −1.48958 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.7995 | 1.38154 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.17609 | 0.410778 | 0.205389 | − | 0.978680i | \(-0.434154\pi\) | ||||
0.205389 | + | 0.978680i | \(0.434154\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.1530 | −1.43363 | −0.716815 | − | 0.697263i | \(-0.754401\pi\) | ||||
−0.716815 | + | 0.697263i | \(0.754401\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.44359 | −0.0642391 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.9136 | −0.749683 | −0.374841 | − | 0.927089i | \(-0.622303\pi\) | ||||
−0.374841 | + | 0.927089i | \(0.622303\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.6548 | −1.75423 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.08270 | −0.268036 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.6511 | 1.43600 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0388 | 0.439809 | 0.219905 | − | 0.975521i | \(-0.429425\pi\) | ||||
0.219905 | + | 0.975521i | \(0.429425\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.2745 | 1.49872 | 0.749360 | − | 0.662163i | \(-0.230361\pi\) | ||||
0.749360 | + | 0.662163i | \(0.230361\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.1881 | 1.09721 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5915 | −0.982241 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 81.5842 | 3.53380 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.27451 | −0.0983357 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.592882 | −0.0255372 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.1724 | −1.21123 | −0.605613 | − | 0.795759i | \(-0.707072\pi\) | ||||
−0.605613 | + | 0.795759i | \(0.707072\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.68665 | −0.0722483 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.55271 | −0.322931 | −0.161465 | − | 0.986878i | \(-0.551622\pi\) | ||||
−0.161465 | + | 0.986878i | \(0.551622\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.87847 | −0.335634 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.35587 | −0.0576576 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.4374 | 0.993074 | 0.496537 | − | 0.868016i | \(-0.334605\pi\) | ||||
0.496537 | + | 0.868016i | \(0.334605\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.99631 | −0.380503 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.3133 | −1.44614 | −0.723068 | − | 0.690777i | \(-0.757268\pi\) | ||||
−0.723068 | + | 0.690777i | \(0.757268\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.447286 | −0.0188175 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.8785 | −1.00104 | −0.500519 | − | 0.865726i | \(-0.666857\pi\) | ||||
−0.500519 | + | 0.865726i | \(0.666857\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.03514 | −0.378109 | −0.189054 | − | 0.981967i | \(-0.560542\pi\) | ||||
−0.189054 | + | 0.981967i | \(0.560542\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.13025 | 0.130540 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.8554 | −0.784959 | −0.392479 | − | 0.919761i | \(-0.628383\pi\) | ||||
−0.392479 | + | 0.919761i | \(0.628383\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.1178 | −1.29099 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 56.8309 | 2.35370 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.68045 | 0.151908 | 0.0759542 | − | 0.997111i | \(-0.475800\pi\) | ||||
0.0759542 | + | 0.997111i | \(0.475800\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00000 | 0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.5139 | −0.965599 | −0.482800 | − | 0.875731i | \(-0.660380\pi\) | ||||
−0.482800 | + | 0.875731i | \(0.660380\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.51426 | 0.144070 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.31335 | −0.257956 | −0.128978 | − | 0.991647i | \(-0.541170\pi\) | ||||
−0.128978 | + | 0.991647i | \(0.541170\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.4824 | 0.794705 | 0.397352 | − | 0.917666i | \(-0.369929\pi\) | ||||
0.397352 | + | 0.917666i | \(0.369929\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.44729 | 0.0994963 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.7569 | −1.53251 | −0.766253 | − | 0.642538i | \(-0.777881\pi\) | ||||
−0.766253 | + | 0.642538i | \(0.777881\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 49.2658 | 1.99308 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.65852 | −0.188156 | −0.0940779 | − | 0.995565i | \(-0.529990\pi\) | ||||
−0.0940779 | + | 0.995565i | \(0.529990\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.3510 | −1.46344 | −0.731718 | − | 0.681607i | \(-0.761281\pi\) | ||||
−0.731718 | + | 0.681607i | \(0.761281\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.0000 | −1.12542 | −0.562708 | − | 0.826656i | \(-0.690240\pi\) | ||||
−0.562708 | + | 0.826656i | \(0.690240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.1604 | 0.407066 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.4787 | 0.939149 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.7921 | −0.669544 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.4506 | 1.41127 | 0.705633 | − | 0.708577i | \(-0.250663\pi\) | ||||
0.705633 | + | 0.708577i | \(0.250663\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.11784 | −0.123728 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.894572 | −0.0354442 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.8785 | 0.943143 | 0.471571 | − | 0.881828i | \(-0.343687\pi\) | ||||
0.471571 | + | 0.881828i | \(0.343687\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.93672 | −0.155249 | −0.0776246 | − | 0.996983i | \(-0.524734\pi\) | ||||
−0.0776246 | + | 0.996983i | \(0.524734\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.8020 | 0.621240 | 0.310620 | − | 0.950534i | \(-0.399463\pi\) | ||||
0.310620 | + | 0.950534i | \(0.399463\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 56.3060 | 2.21020 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.2720 | 1.69336 | 0.846682 | − | 0.532099i | \(-0.178597\pi\) | ||||
0.846682 | + | 0.532099i | \(0.178597\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.21123 | −0.242693 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.8396 | 0.850751 | 0.425376 | − | 0.905017i | \(-0.360142\pi\) | ||||
0.425376 | + | 0.905017i | \(0.360142\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.03514 | −0.351426 | −0.175713 | − | 0.984441i | \(-0.556223\pi\) | ||||
−0.175713 | + | 0.984441i | \(0.556223\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.837122 | 0.0324622 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.03514 | −0.194962 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.4762 | −0.983499 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.96116 | 0.383975 | 0.191987 | − | 0.981397i | \(-0.438507\pi\) | ||||
0.191987 | + | 0.981397i | \(0.438507\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.35721 | 0.244327 | 0.122164 | − | 0.992510i | \(-0.461017\pi\) | ||||
0.122164 | + | 0.992510i | \(0.461017\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.5453 | −1.13385 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.1881 | −1.42296 | −0.711482 | − | 0.702704i | \(-0.751976\pi\) | ||||
−0.711482 | + | 0.702704i | \(0.751976\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.48944 | 0.133325 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 85.7496 | 3.26680 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.8942 | 1.25135 | 0.625677 | − | 0.780082i | \(-0.284823\pi\) | ||||
0.625677 | + | 0.780082i | \(0.284823\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.11533 | −0.0802389 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −52.5490 | −1.99044 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.4399 | 0.620926 | 0.310463 | − | 0.950585i | \(-0.399516\pi\) | ||||
0.310463 | + | 0.950585i | \(0.399516\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.00000 | −0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.8346 | 0.445086 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.5139 | −1.55909 | −0.779543 | − | 0.626348i | \(-0.784549\pi\) | ||||
−0.779543 | + | 0.626348i | \(0.784549\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.83461 | 0.143607 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.99631 | 0.336443 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.8371 | 1.22462 | 0.612309 | − | 0.790619i | \(-0.290241\pi\) | ||||
0.612309 | + | 0.790619i | \(0.290241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.8661 | 1.85711 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −38.5879 | −1.43312 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.89419 | 0.181516 | 0.0907578 | − | 0.995873i | \(-0.471071\pi\) | ||||
0.0907578 | + | 0.995873i | \(0.471071\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.79459 | 0.214321 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.00000 | −0.221615 | −0.110808 | − | 0.993842i | \(-0.535344\pi\) | ||||
−0.110808 | + | 0.993842i | \(0.535344\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 50.7847 | 1.87068 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.4506 | 0.715502 | 0.357751 | − | 0.933817i | \(-0.383544\pi\) | ||||
0.357751 | + | 0.933817i | \(0.383544\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.5915 | 0.865490 | 0.432745 | − | 0.901516i | \(-0.357545\pi\) | ||||
0.432745 | + | 0.901516i | \(0.357545\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.306338 | −0.0112234 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.6465 | 0.681328 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.76063 | 0.173718 | 0.0868590 | − | 0.996221i | \(-0.472317\pi\) | ||||
0.0868590 | + | 0.996221i | \(0.472317\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.165390 | 0.00601917 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.9330 | −1.70581 | −0.852905 | − | 0.522066i | \(-0.825161\pi\) | ||||
−0.852905 | + | 0.522066i | \(0.825161\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.3108 | −1.20752 | −0.603758 | − | 0.797167i | \(-0.706331\pi\) | ||||
−0.603758 | + | 0.797167i | \(0.706331\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.8272 | 0.500579 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 84.9575 | 3.06764 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.9330 | −0.538499 | −0.269249 | − | 0.963070i | \(-0.586776\pi\) | ||||
−0.269249 | + | 0.963070i | \(0.586776\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.5176 | −1.16958 | −0.584788 | − | 0.811186i | \(-0.698822\pi\) | ||||
−0.584788 | + | 0.811186i | \(0.698822\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.3873 | 1.05562 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.5176 | −0.448489 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −50.7847 | −1.81722 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.639102 | 0.0228105 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.5564 | 0.518880 | 0.259440 | − | 0.965759i | \(-0.416462\pi\) | ||||
0.259440 | + | 0.965759i | \(0.416462\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.66686 | 0.130379 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.4399 | −1.36504 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.2394 | −0.823181 | −0.411590 | − | 0.911369i | \(-0.635027\pi\) | ||||
−0.411590 | + | 0.911369i | \(0.635027\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.7325 | −1.12262 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 65.3861 | 2.30743 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.535006 | 0.0188565 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.7896 | 1.39893 | 0.699463 | − | 0.714668i | \(-0.253422\pi\) | ||||
0.699463 | + | 0.714668i | \(0.253422\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.4750 | 1.38616 | 0.693078 | − | 0.720862i | \(-0.256254\pi\) | ||||
0.693078 | + | 0.720862i | \(0.256254\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.44359 | 0.190681 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.38032 | 0.0482911 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.3196 | −0.569556 | −0.284778 | − | 0.958593i | \(-0.591920\pi\) | ||||
−0.284778 | + | 0.958593i | \(0.591920\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.9719 | 0.591602 | 0.295801 | − | 0.955250i | \(-0.404413\pi\) | ||||
0.295801 | + | 0.955250i | \(0.404413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.1128 | 0.873258 | 0.436629 | − | 0.899642i | \(-0.356172\pi\) | ||||
0.436629 | + | 0.899642i | \(0.356172\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.5915 | −1.23615 | −0.618073 | − | 0.786121i | \(-0.712086\pi\) | ||||
−0.618073 | + | 0.786121i | \(0.712086\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.576201 | 0.0199642 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.03884 | −0.139770 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.8396 | 1.03018 | 0.515089 | − | 0.857137i | \(-0.327759\pi\) | ||||
0.515089 | + | 0.857137i | \(0.327759\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.0703 | 1.14035 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.41995 | 0.324056 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0629 | −0.689369 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.55641 | −0.0876325 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0777 | 0.482010 | 0.241005 | − | 0.970524i | \(-0.422523\pi\) | ||||
0.241005 | + | 0.970524i | \(0.422523\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.9963 | 1.05881 | 0.529407 | − | 0.848368i | \(-0.322415\pi\) | ||||
0.529407 | + | 0.848368i | \(0.322415\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.2464 | −1.47555 | −0.737774 | − | 0.675048i | \(-0.764123\pi\) | ||||
−0.737774 | + | 0.675048i | \(0.764123\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.9575 | −0.441077 | −0.220539 | − | 0.975378i | \(-0.570782\pi\) | ||||
−0.220539 | + | 0.975378i | \(0.570782\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.830917 | 0.0282520 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.23568 | 0.0758401 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 76.6267 | 2.59640 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.28574 | 0.280109 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.7181 | −0.395692 | −0.197846 | − | 0.980233i | \(-0.563395\pi\) | ||||
−0.197846 | + | 0.980233i | \(0.563395\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.3510 | −0.955169 | −0.477585 | − | 0.878586i | \(-0.658488\pi\) | ||||
−0.477585 | + | 0.878586i | \(0.658488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.3378 | 0.751726 | 0.375863 | − | 0.926675i | \(-0.377346\pi\) | ||||
0.375863 | + | 0.926675i | \(0.377346\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.5490 | −1.22720 | −0.613598 | − | 0.789619i | \(-0.710278\pi\) | ||||
−0.613598 | + | 0.789619i | \(0.710278\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.5601 | 0.857258 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.55892 | −0.252950 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.10912 | 0.204205 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −47.2708 | −1.57657 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −55.2320 | −1.84004 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.11784 | −0.236605 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.3097 | 1.57089 | 0.785446 | − | 0.618931i | \(-0.212434\pi\) | ||||
0.785446 | + | 0.618931i | \(0.212434\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.8396 | −1.25368 | −0.626842 | − | 0.779147i | \(-0.715653\pi\) | ||||
−0.626842 | + | 0.779147i | \(0.715653\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.3097 | 1.69810 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 50.9198 | 1.68152 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.5915 | −1.43795 | −0.718976 | − | 0.695035i | \(-0.755389\pi\) | ||||
−0.718976 | + | 0.695035i | \(0.755389\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −76.6267 | −2.52220 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.5915 | −0.644166 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.7569 | −0.779440 | −0.389720 | − | 0.920933i | \(-0.627428\pi\) | ||||
−0.389720 | + | 0.920933i | \(0.627428\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.137255 | 0.00449836 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.79459 | −0.189504 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.4894 | −1.48608 | −0.743038 | − | 0.669250i | \(-0.766616\pi\) | ||||
−0.743038 | + | 0.669250i | \(0.766616\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48.7482 | 1.58915 | 0.794573 | − | 0.607168i | \(-0.207695\pi\) | ||||
0.794573 | + | 0.607168i | \(0.207695\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.00000 | −0.260516 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.94876 | −0.193309 | −0.0966543 | − | 0.995318i | \(-0.530814\pi\) | ||||
−0.0966543 | + | 0.995318i | \(0.530814\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 98.6581 | 3.20258 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.4473 | 0.467993 | 0.233997 | − | 0.972237i | \(-0.424819\pi\) | ||||
0.233997 | + | 0.972237i | \(0.424819\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.41546 | −0.0781624 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.6065 | −0.923751 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.165390 | −0.00532410 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.0703 | 0.581101 | 0.290551 | − | 0.956860i | \(-0.406162\pi\) | ||||
0.290551 | + | 0.956860i | \(0.406162\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.0000 | −1.28366 | −0.641831 | − | 0.766846i | \(-0.721825\pi\) | ||||
−0.641831 | + | 0.766846i | \(0.721825\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.3415 | 0.555942 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.1567 | −0.420919 | −0.210460 | − | 0.977603i | \(-0.567496\pi\) | ||||
−0.210460 | + | 0.977603i | \(0.567496\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.7532 | −0.535436 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.23568 | −0.198887 | −0.0994436 | − | 0.995043i | \(-0.531706\pi\) | ||||
−0.0994436 | + | 0.995043i | \(0.531706\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.66922 | 0.116911 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.882162 | 0.0280511 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.8661 | −1.52052 | −0.760258 | − | 0.649622i | \(-0.774927\pi\) | ||||
−0.760258 | + | 0.649622i | \(0.774927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.441081 | −0.0139832 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.9256 | 1.42281 | 0.711405 | − | 0.702783i | \(-0.248059\pi\) | ||||
0.711405 | + | 0.702783i | \(0.248059\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1368.2.a.m.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 1368.2.a.o.1.2 | yes | 3 | ||
4.3 | odd | 2 | 2736.2.a.bc.1.2 | 3 | |||
12.11 | even | 2 | 2736.2.a.be.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.a.m.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1368.2.a.o.1.2 | yes | 3 | 3.2 | odd | 2 | ||
2736.2.a.bc.1.2 | 3 | 4.3 | odd | 2 | |||
2736.2.a.be.1.2 | 3 | 12.11 | even | 2 |