Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, 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("2736.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.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: | \(21.8470699930\) |
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: | no (minimal twist has level 1368) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.91729\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1 |
$q$-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 | ||||||||
\(5\) | −3.91729 | −1.75186 | −0.875932 | − | 0.482435i | \(-0.839752\pi\) | ||||
−0.875932 | + | 0.482435i | \(0.839752\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.32401 | 1.63432 | 0.817162 | − | 0.576408i | \(-0.195546\pi\) | ||||
0.817162 | + | 0.576408i | \(0.195546\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0827140 | −0.0249392 | −0.0124696 | − | 0.999922i | \(-0.503969\pi\) | ||||
−0.0124696 | + | 0.999922i | \(0.503969\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.02112 | −1.94731 | −0.973653 | − | 0.228033i | \(-0.926771\pi\) | ||||
−0.973653 | + | 0.228033i | \(0.926771\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.10383 | 1.23786 | 0.618930 | − | 0.785446i | \(-0.287566\pi\) | ||||
0.618930 | + | 0.785446i | \(0.287566\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.83457 | −1.63362 | −0.816811 | − | 0.576906i | \(-0.804260\pi\) | ||||
−0.816811 | + | 0.576906i | \(0.804260\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.3451 | 2.06903 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.81346 | 0.522446 | 0.261223 | − | 0.965279i | \(-0.415874\pi\) | ||||
0.261223 | + | 0.965279i | \(0.415874\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −16.9384 | −2.86311 | ||||||||
\(36\) | 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 | ||||||||
\(41\) | −1.02112 | −0.159471 | −0.0797357 | − | 0.996816i | \(-0.525408\pi\) | ||||
−0.0797357 | + | 0.996816i | \(0.525408\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.324014 | −0.0494117 | −0.0247059 | − | 0.999695i | \(-0.507865\pi\) | ||||
−0.0247059 | + | 0.999695i | \(0.507865\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.73074 | −0.981780 | −0.490890 | − | 0.871222i | \(-0.663328\pi\) | ||||
−0.490890 | + | 0.871222i | \(0.663328\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.6971 | 1.67101 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.85569 | −1.21642 | −0.608211 | − | 0.793775i | \(-0.708113\pi\) | ||||
−0.608211 | + | 0.793775i | \(0.708113\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.324014 | 0.0436901 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.0422 | 1.82814 | 0.914071 | − | 0.405553i | \(-0.132921\pi\) | ||||
0.914071 | + | 0.405553i | \(0.132921\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.34513 | 1.19652 | 0.598261 | − | 0.801302i | \(-0.295859\pi\) | ||||
0.598261 | + | 0.801302i | \(0.295859\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 27.5037 | 3.41142 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.62691 | −0.198759 | −0.0993796 | − | 0.995050i | \(-0.531686\pi\) | ||||
−0.0993796 | + | 0.995050i | \(0.531686\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.62691 | 0.193079 | 0.0965396 | − | 0.995329i | \(-0.469223\pi\) | ||||
0.0965396 | + | 0.995329i | \(0.469223\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.30290 | 0.386575 | 0.193288 | − | 0.981142i | \(-0.438085\pi\) | ||||
0.193288 | + | 0.981142i | \(0.438085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.357657 | −0.0407587 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.0211 | 1.46499 | 0.732495 | − | 0.680772i | \(-0.238356\pi\) | ||||
0.732495 | + | 0.680772i | \(0.238356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.81346 | −0.747874 | −0.373937 | − | 0.927454i | \(-0.621992\pi\) | ||||
−0.373937 | + | 0.927454i | \(0.621992\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19.9932 | −2.16856 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.18654 | 0.125773 | 0.0628867 | − | 0.998021i | \(-0.479969\pi\) | ||||
0.0628867 | + | 0.998021i | \(0.479969\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −30.3594 | −3.18253 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.91729 | −0.401905 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.66914 | −0.575614 | −0.287807 | − | 0.957688i | \(-0.592926\pi\) | ||||
−0.287807 | + | 0.957688i | \(0.592926\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.02112 | 0.897635 | 0.448817 | − | 0.893624i | \(-0.351845\pi\) | ||||
0.448817 | + | 0.893624i | \(0.351845\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.04223 | −0.792424 | −0.396212 | − | 0.918159i | \(-0.629676\pi\) | ||||
−0.396212 | + | 0.918159i | \(0.629676\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.46149 | 0.527982 | 0.263991 | − | 0.964525i | \(-0.414961\pi\) | ||||
0.263991 | + | 0.964525i | \(0.414961\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.6691 | 1.11770 | 0.558851 | − | 0.829268i | \(-0.311243\pi\) | ||||
0.558851 | + | 0.829268i | \(0.311243\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.4826 | 0.986120 | 0.493060 | − | 0.869995i | \(-0.335878\pi\) | ||||
0.493060 | + | 0.869995i | \(0.335878\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 30.6903 | 2.86188 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 22.0690 | 2.02306 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9932 | −0.999378 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −20.9384 | −1.87279 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.373086 | −0.0331061 | −0.0165530 | − | 0.999863i | \(-0.505269\pi\) | ||||
−0.0165530 | + | 0.999863i | \(0.505269\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.5442 | 1.18336 | 0.591681 | − | 0.806172i | \(-0.298464\pi\) | ||||
0.591681 | + | 0.806172i | \(0.298464\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.32401 | 0.374940 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.5653 | 1.58614 | 0.793071 | − | 0.609129i | \(-0.208481\pi\) | ||||
0.793071 | + | 0.609129i | \(0.208481\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.32401 | 0.706034 | 0.353017 | − | 0.935617i | \(-0.385156\pi\) | ||||
0.353017 | + | 0.935617i | \(0.385156\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.580745 | 0.0485643 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.0211 | −0.915254 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.7519 | 0.962750 | 0.481375 | − | 0.876515i | \(-0.340138\pi\) | ||||
0.481375 | + | 0.876515i | \(0.340138\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.0211 | 1.05964 | 0.529822 | − | 0.848109i | \(-0.322259\pi\) | ||||
0.529822 | + | 0.848109i | \(0.322259\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.5037 | −1.88786 | ||||||||
\(156\) | 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 | ||||||||
\(161\) | −33.8768 | −2.66987 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0422 | 0.786568 | 0.393284 | − | 0.919417i | \(-0.371339\pi\) | ||||
0.393284 | + | 0.919417i | \(0.371339\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.16543 | 0.322330 | 0.161165 | − | 0.986927i | \(-0.448475\pi\) | ||||
0.161165 | + | 0.986927i | \(0.448475\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 36.2961 | 2.79200 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.4826 | 1.10109 | 0.550546 | − | 0.834805i | \(-0.314420\pi\) | ||||
0.550546 | + | 0.834805i | \(0.314420\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 44.7325 | 3.38146 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.4615 | −1.30513 | −0.652566 | − | 0.757732i | \(-0.726308\pi\) | ||||
−0.652566 | + | 0.757732i | \(0.726308\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.39420 | 0.103630 | 0.0518151 | − | 0.998657i | \(-0.483499\pi\) | ||||
0.0518151 | + | 0.998657i | \(0.483499\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.6691 | −1.15202 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.422158 | −0.0308713 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.73074 | 0.487019 | 0.243510 | − | 0.969898i | \(-0.421701\pi\) | ||||
0.243510 | + | 0.969898i | \(0.421701\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0211 | 0.937280 | 0.468640 | − | 0.883389i | \(-0.344744\pi\) | ||||
0.468640 | + | 0.883389i | \(0.344744\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.0211 | 1.78268 | 0.891340 | − | 0.453335i | \(-0.149766\pi\) | ||||
0.891340 | + | 0.453335i | \(0.149766\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.324014 | −0.0229688 | −0.0114844 | − | 0.999934i | \(-0.503656\pi\) | ||||
−0.0114844 | + | 0.999934i | \(0.503656\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.1654 | 0.853846 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | 0.279372 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0827140 | −0.00572145 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.6691 | −1.35408 | −0.677040 | − | 0.735946i | \(-0.736738\pi\) | ||||
−0.677040 | + | 0.735946i | \(0.736738\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.26926 | 0.0865626 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.9441 | 1.76120 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −35.8346 | −2.41049 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.6903 | −1.38552 | −0.692761 | − | 0.721167i | \(-0.743606\pi\) | ||||
−0.692761 | + | 0.721167i | \(0.743606\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.16543 | 0.276469 | 0.138235 | − | 0.990400i | \(-0.455857\pi\) | ||||
0.138235 | + | 0.990400i | \(0.455857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.697101 | 0.0460657 | 0.0230329 | − | 0.999735i | \(-0.492668\pi\) | ||||
0.0230329 | + | 0.999735i | \(0.492668\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.9806 | 1.50551 | 0.752756 | − | 0.658300i | \(-0.228724\pi\) | ||||
0.752756 | + | 0.658300i | \(0.228724\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.3662 | 1.71994 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.9806 | −1.22775 | −0.613877 | − | 0.789401i | \(-0.710391\pi\) | ||||
−0.613877 | + | 0.789401i | \(0.710391\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.6903 | −1.33278 | −0.666388 | − | 0.745605i | \(-0.732161\pi\) | ||||
−0.666388 | + | 0.745605i | \(0.732161\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −45.8209 | −2.92739 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.02112 | −0.446743 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.1249 | 1.64899 | 0.824496 | − | 0.565868i | \(-0.191459\pi\) | ||||
0.824496 | + | 0.565868i | \(0.191459\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.648029 | 0.0407412 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.02112 | 0.0636954 | 0.0318477 | − | 0.999493i | \(-0.489861\pi\) | ||||
0.0318477 | + | 0.999493i | \(0.489861\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.2961 | 1.07472 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.8962 | −0.918537 | −0.459269 | − | 0.888297i | \(-0.651888\pi\) | ||||
−0.459269 | + | 0.888297i | \(0.651888\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 34.6903 | 2.13101 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.81346 | 0.415424 | 0.207712 | − | 0.978190i | \(-0.433398\pi\) | ||||
0.207712 | + | 0.978190i | \(0.433398\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.3383 | −1.66068 | −0.830341 | − | 0.557255i | \(-0.811855\pi\) | ||||
−0.830341 | + | 0.557255i | \(0.811855\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.855687 | −0.0515999 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.99316 | 0.119757 | 0.0598786 | − | 0.998206i | \(-0.480929\pi\) | ||||
0.0598786 | + | 0.998206i | \(0.480929\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.1095 | −0.722393 | −0.361197 | − | 0.932490i | \(-0.617632\pi\) | ||||
−0.361197 | + | 0.932490i | \(0.617632\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.63376 | 0.0971167 | 0.0485583 | − | 0.998820i | \(-0.484537\pi\) | ||||
0.0485583 | + | 0.998820i | \(0.484537\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.41532 | −0.260628 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.04907 | 0.532298 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.3942 | −0.665656 | −0.332828 | − | 0.942987i | \(-0.608003\pi\) | ||||
−0.332828 | + | 0.942987i | \(0.608003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −55.0074 | −3.20266 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 55.0074 | 3.18116 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.40104 | −0.0807548 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −36.6075 | −2.09614 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.6691 | −1.12258 | −0.561289 | − | 0.827620i | \(-0.689694\pi\) | ||||
−0.561289 | + | 0.827620i | \(0.689694\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.9384 | 0.960489 | 0.480244 | − | 0.877135i | \(-0.340548\pi\) | ||||
0.480244 | + | 0.877135i | \(0.340548\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.3383 | −1.20611 | −0.603056 | − | 0.797699i | \(-0.706050\pi\) | ||||
−0.603056 | + | 0.797699i | \(0.706050\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.0211 | −0.731339 | −0.365669 | − | 0.930745i | \(-0.619160\pi\) | ||||
−0.365669 | + | 0.930745i | \(0.619160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.232712 | −0.0130294 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.10383 | 0.283985 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −72.6343 | −4.02903 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −29.1038 | −1.60455 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.7114 | 1.41322 | 0.706612 | − | 0.707601i | \(-0.250222\pi\) | ||||
0.706612 | + | 0.707601i | \(0.250222\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.37309 | 0.348199 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.6691 | 0.744606 | 0.372303 | − | 0.928111i | \(-0.378568\pi\) | ||||
0.372303 | + | 0.928111i | \(0.378568\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.496284 | −0.0268753 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.3103 | 1.09665 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.58643 | 0.407261 | 0.203630 | − | 0.979048i | \(-0.434726\pi\) | ||||
0.203630 | + | 0.979048i | \(0.434726\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.7393 | −1.21721 | −0.608604 | − | 0.793474i | \(-0.708270\pi\) | ||||
−0.608604 | + | 0.793474i | \(0.708270\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.2961 | −0.707678 | −0.353839 | − | 0.935306i | \(-0.615124\pi\) | ||||
−0.353839 | + | 0.935306i | \(0.615124\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.37309 | −0.338248 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.19223 | −0.221257 | −0.110629 | − | 0.993862i | \(-0.535286\pi\) | ||||
−0.110629 | + | 0.993862i | \(0.535286\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.9384 | −0.677227 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.04223 | 0.106604 | 0.0533018 | − | 0.998578i | \(-0.483025\pi\) | ||||
0.0533018 | + | 0.998578i | \(0.483025\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −38.2921 | −1.98803 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.3383 | −1.00130 | −0.500649 | − | 0.865650i | \(-0.666905\pi\) | ||||
−0.500649 | + | 0.865650i | \(0.666905\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.7536 | −1.01736 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.64803 | 0.238753 | 0.119377 | − | 0.992849i | \(-0.461910\pi\) | ||||
0.119377 | + | 0.992849i | \(0.461910\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.8768 | −1.73102 | −0.865512 | − | 0.500888i | \(-0.833007\pi\) | ||||
−0.865512 | + | 0.500888i | \(0.833007\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.40104 | 0.0714038 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.6287 | 1.09662 | 0.548308 | − | 0.836276i | \(-0.315272\pi\) | ||||
0.548308 | + | 0.836276i | \(0.315272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.9863 | −2.02219 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −51.0074 | −2.56646 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.65487 | −0.133244 | −0.0666221 | − | 0.997778i | \(-0.521222\pi\) | ||||
−0.0666221 | + | 0.997778i | \(0.521222\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.30974 | −0.165281 | −0.0826403 | − | 0.996579i | \(-0.526335\pi\) | ||||
−0.0826403 | + | 0.996579i | \(0.526335\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −42.1267 | −2.09848 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.330856 | −0.0163999 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.25383 | −0.0619978 | −0.0309989 | − | 0.999519i | \(-0.509869\pi\) | ||||
−0.0309989 | + | 0.999519i | \(0.509869\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 60.7188 | 2.98778 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.6903 | 1.31017 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.4826 | −1.09835 | −0.549173 | − | 0.835708i | \(-0.685057\pi\) | ||||
−0.549173 | + | 0.835708i | \(0.685057\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.9441 | −1.65433 | −0.827167 | − | 0.561957i | \(-0.810049\pi\) | ||||
−0.827167 | + | 0.561957i | \(0.810049\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 52.7998 | 2.56117 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 40.4085 | 1.95550 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.8346 | 1.34074 | 0.670372 | − | 0.742025i | \(-0.266135\pi\) | ||||
0.670372 | + | 0.742025i | \(0.266135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.62691 | −0.174298 | −0.0871492 | − | 0.996195i | \(-0.527776\pi\) | ||||
−0.0871492 | + | 0.996195i | \(0.527776\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.83457 | −0.374778 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.9230 | −0.807689 | −0.403845 | − | 0.914828i | \(-0.632326\pi\) | ||||
−0.403845 | + | 0.914828i | \(0.632326\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.2556 | 1.48500 | 0.742499 | − | 0.669848i | \(-0.233641\pi\) | ||||
0.742499 | + | 0.669848i | \(0.233641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.64803 | −0.220338 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.35197 | 0.0638035 | 0.0319017 | − | 0.999491i | \(-0.489844\pi\) | ||||
0.0319017 | + | 0.999491i | \(0.489844\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0844605 | 0.00397709 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 118.926 | 5.57536 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.2892 | 1.46365 | 0.731824 | − | 0.681494i | \(-0.238669\pi\) | ||||
0.731824 | + | 0.681494i | \(0.238669\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.7519 | 1.29253 | 0.646266 | − | 0.763112i | \(-0.276329\pi\) | ||||
0.646266 | + | 0.763112i | \(0.276329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.28178 | 0.106044 | 0.0530218 | − | 0.998593i | \(-0.483115\pi\) | ||||
0.0530218 | + | 0.998593i | \(0.483115\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.79803 | −0.407124 | −0.203562 | − | 0.979062i | \(-0.565252\pi\) | ||||
−0.203562 | + | 0.979062i | \(0.565252\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.03480 | −0.324837 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.0268005 | 0.00123229 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.3451 | 0.474667 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.8768 | −1.18234 | −0.591171 | − | 0.806547i | \(-0.701334\pi\) | ||||
−0.591171 | + | 0.806547i | \(0.701334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.0845 | −1.28054 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.2077 | 1.00840 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.97888 | −0.316243 | −0.158122 | − | 0.987420i | \(-0.550544\pi\) | ||||
−0.158122 | + | 0.987420i | \(0.550544\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.77123 | −0.215322 | −0.107661 | − | 0.994188i | \(-0.534336\pi\) | ||||
−0.107661 | + | 0.994188i | \(0.534336\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.3594 | 0.646715 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.03480 | 0.315554 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0143 | 1.03026 | 0.515130 | − | 0.857112i | \(-0.327744\pi\) | ||||
0.515130 | + | 0.857112i | \(0.327744\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.41926 | 0.152457 | 0.0762285 | − | 0.997090i | \(-0.475712\pi\) | ||||
0.0762285 | + | 0.997090i | \(0.475712\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.3383 | −1.57253 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.2288 | 0.675004 | 0.337502 | − | 0.941325i | \(-0.390418\pi\) | ||||
0.337502 | + | 0.941325i | \(0.390418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.2818 | 0.631789 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.5037 | 1.38822 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.556727 | 0.0244848 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.3172 | −0.452004 | −0.226002 | − | 0.974127i | \(-0.572566\pi\) | ||||
−0.226002 | + | 0.974127i | \(0.572566\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.6058 | −0.463759 | −0.231880 | − | 0.972744i | \(-0.574488\pi\) | ||||
−0.231880 | + | 0.972744i | \(0.574488\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.6230 | 1.33396 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 38.3805 | 1.66872 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.16937 | 0.310540 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.3942 | −0.924952 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.967514 | −0.0416738 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.7393 | 0.461720 | 0.230860 | − | 0.972987i | \(-0.425846\pi\) | ||||
0.230860 | + | 0.972987i | \(0.425846\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −45.7114 | −1.95806 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.0633 | −1.41369 | −0.706843 | − | 0.707370i | \(-0.749881\pi\) | ||||
−0.706843 | + | 0.707370i | \(0.749881\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.81346 | 0.119857 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 56.3035 | 2.39427 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.5442 | 0.743372 | 0.371686 | − | 0.928359i | \(-0.378780\pi\) | ||||
0.371686 | + | 0.928359i | \(0.378780\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.27494 | 0.0962198 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.71137 | −0.409286 | −0.204643 | − | 0.978837i | \(-0.565603\pi\) | ||||
−0.204643 | + | 0.978837i | \(0.565603\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −41.0633 | −1.72755 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.8135 | −0.788701 | −0.394351 | − | 0.918960i | \(-0.629030\pi\) | ||||
−0.394351 | + | 0.918960i | \(0.629030\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.0422 | −0.755044 | −0.377522 | − | 0.926001i | \(-0.623224\pi\) | ||||
−0.377522 | + | 0.926001i | \(0.623224\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −81.0497 | −3.38000 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.2470 | −0.718001 | −0.359001 | − | 0.933337i | \(-0.616882\pi\) | ||||
−0.359001 | + | 0.933337i | \(0.616882\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.4615 | −1.22227 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.732489 | 0.0303366 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.91729 | −0.326781 | −0.163391 | − | 0.986561i | \(-0.552243\pi\) | ||||
−0.163391 | + | 0.986561i | \(0.552243\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00000 | 0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.25383 | −0.133619 | −0.0668093 | − | 0.997766i | \(-0.521282\pi\) | ||||
−0.0668093 | + | 0.997766i | \(0.521282\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −86.4507 | −3.54413 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.7114 | −1.54084 | −0.770422 | − | 0.637534i | \(-0.779955\pi\) | ||||
−0.770422 | + | 0.637534i | \(0.779955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.0211 | 1.34696 | 0.673480 | − | 0.739206i | \(-0.264799\pi\) | ||||
0.673480 | + | 0.739206i | \(0.264799\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 43.0633 | 1.75077 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.6269 | 1.12134 | 0.560671 | − | 0.828039i | \(-0.310543\pi\) | ||||
0.560671 | + | 0.828039i | \(0.310543\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 47.2573 | 1.91183 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.9932 | 0.565178 | 0.282589 | − | 0.959241i | \(-0.408807\pi\) | ||||
0.282589 | + | 0.959241i | \(0.408807\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.68457 | 0.0678184 | 0.0339092 | − | 0.999425i | \(-0.489204\pi\) | ||||
0.0339092 | + | 0.999425i | \(0.489204\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.0000 | 1.12542 | 0.562708 | − | 0.826656i | \(-0.309760\pi\) | ||||
0.562708 | + | 0.826656i | \(0.309760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.13063 | 0.205554 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 30.2961 | 1.21184 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.4153 | 0.814012 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.4085 | 0.812449 | 0.406224 | − | 0.913773i | \(-0.366845\pi\) | ||||
0.406224 | + | 0.913773i | \(0.366845\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.46149 | 0.0579973 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −82.1267 | −3.25398 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.8135 | 0.743087 | 0.371543 | − | 0.928416i | \(-0.378829\pi\) | ||||
0.371543 | + | 0.928416i | \(0.378829\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.6623 | −1.24864 | −0.624320 | − | 0.781169i | \(-0.714624\pi\) | ||||
−0.624320 | + | 0.781169i | \(0.714624\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.1038 | −0.986933 | −0.493467 | − | 0.869765i | \(-0.664271\pi\) | ||||
−0.493467 | + | 0.869765i | \(0.664271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.16149 | −0.0455924 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.4632 | −0.526857 | −0.263428 | − | 0.964679i | \(-0.584853\pi\) | ||||
−0.263428 | + | 0.964679i | \(0.584853\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −53.0565 | −2.07309 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.1306 | −1.44640 | −0.723202 | − | 0.690637i | \(-0.757330\pi\) | ||||
−0.723202 | + | 0.690637i | \(0.757330\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0422 | 0.701761 | 0.350881 | − | 0.936420i | \(-0.385882\pi\) | ||||
0.350881 | + | 0.936420i | \(0.385882\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.9384 | −0.656843 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.0422 | −0.853479 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.772973 | −0.0298403 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.3172 | 1.16864 | 0.584321 | − | 0.811523i | \(-0.301361\pi\) | ||||
0.584321 | + | 0.811523i | \(0.301361\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.10951 | 0.311674 | 0.155837 | − | 0.987783i | \(-0.450193\pi\) | ||||
0.155837 | + | 0.987783i | \(0.450193\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.5135 | −0.940740 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.6230 | −0.712588 | −0.356294 | − | 0.934374i | \(-0.615960\pi\) | ||||
−0.356294 | + | 0.934374i | \(0.615960\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −72.7256 | −2.77870 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 62.1768 | 2.36875 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.9298 | −0.415790 | −0.207895 | − | 0.978151i | \(-0.566661\pi\) | ||||
−0.207895 | + | 0.978151i | \(0.566661\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −32.6075 | −1.23687 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.21160 | −0.197403 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.6132 | 1.64725 | 0.823624 | − | 0.567136i | \(-0.191948\pi\) | ||||
0.823624 | + | 0.567136i | \(0.191948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 39.0074 | 1.46703 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.2538 | −0.798204 | −0.399102 | − | 0.916906i | \(-0.630678\pi\) | ||||
−0.399102 | + | 0.916906i | \(0.630678\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −47.0074 | −1.76044 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.27494 | −0.0850780 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.0616 | −0.561703 | −0.280851 | − | 0.959751i | \(-0.590617\pi\) | ||||
−0.280851 | + | 0.959751i | \(0.590617\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.7747 | −1.29508 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.1056 | 1.08095 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.0702 | 0.633098 | 0.316549 | − | 0.948576i | \(-0.397476\pi\) | ||||
0.316549 | + | 0.948576i | \(0.397476\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.65371 | −0.0611648 | ||||||||
\(732\) | 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 | ||||||||
\(737\) | 0.134569 | 0.00495690 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.4085 | 1.33931 | 0.669654 | − | 0.742673i | \(-0.266443\pi\) | ||||
0.669654 | + | 0.742673i | \(0.266443\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.3805 | 1.37136 | 0.685679 | − | 0.727904i | \(-0.259505\pi\) | ||||
0.685679 | + | 0.727904i | \(0.259505\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −46.0354 | −1.68661 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.6155 | 0.862893 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.35197 | −0.0493341 | −0.0246671 | − | 0.999696i | \(-0.507853\pi\) | ||||
−0.0246671 | + | 0.999696i | \(0.507853\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −51.0074 | −1.85635 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.61264 | −0.167649 | −0.0838246 | − | 0.996481i | \(-0.526714\pi\) | ||||
−0.0838246 | + | 0.996481i | \(0.526714\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.7804 | 1.58704 | 0.793519 | − | 0.608545i | \(-0.208247\pi\) | ||||
0.793519 | + | 0.608545i | \(0.208247\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 50.4575 | 1.82669 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −98.5921 | −3.55995 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.3874 | 0.987613 | 0.493807 | − | 0.869572i | \(-0.335605\pi\) | ||||
0.493807 | + | 0.869572i | \(0.335605\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.9789 | −0.682623 | −0.341312 | − | 0.939950i | \(-0.610871\pi\) | ||||
−0.341312 | + | 0.939950i | \(0.610871\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 62.0708 | 2.22965 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.02112 | −0.0365852 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.134569 | −0.00481524 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.83457 | −0.279628 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.3383 | 0.689336 | 0.344668 | − | 0.938725i | \(-0.387992\pi\) | ||||
0.344668 | + | 0.938725i | \(0.387992\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45.3269 | 1.61164 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −65.6132 | −2.32999 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.6480 | −0.943922 | −0.471961 | − | 0.881620i | \(-0.656454\pi\) | ||||
−0.471961 | + | 0.881620i | \(0.656454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.3526 | −1.21531 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.273196 | −0.00964088 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 132.705 | 4.67724 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.4843 | −1.07177 | −0.535886 | − | 0.844290i | \(-0.680022\pi\) | ||||
−0.535886 | + | 0.844290i | \(0.680022\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.5710 | −1.38953 | −0.694763 | − | 0.719239i | \(-0.744491\pi\) | ||||
−0.694763 | + | 0.719239i | \(0.744491\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −39.3383 | −1.37796 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.324014 | −0.0113358 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.0827 | −0.421690 | −0.210845 | − | 0.977520i | \(-0.567621\pi\) | ||||
−0.210845 | + | 0.977520i | \(0.567621\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.7045 | 1.59316 | 0.796580 | − | 0.604533i | \(-0.206640\pi\) | ||||
0.796580 | + | 0.604533i | \(0.206640\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.6766 | 1.48401 | 0.742005 | − | 0.670394i | \(-0.233875\pi\) | ||||
0.742005 | + | 0.670394i | \(0.233875\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.3805 | 0.881502 | 0.440751 | − | 0.897629i | \(-0.354712\pi\) | ||||
0.440751 | + | 0.897629i | \(0.354712\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 59.7000 | 2.06848 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.3172 | −0.564679 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.1306 | −1.55808 | −0.779041 | − | 0.626973i | \(-0.784294\pi\) | ||||
−0.779041 | + | 0.626973i | \(0.784294\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0845 | −0.727050 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −142.182 | −4.89121 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −47.5346 | −1.63331 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.3383 | −1.07426 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.6343 | −0.911943 | −0.455971 | − | 0.889994i | \(-0.650708\pi\) | ||||
−0.455971 | + | 0.889994i | \(0.650708\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.2749 | 0.829216 | 0.414608 | − | 0.910000i | \(-0.363919\pi\) | ||||
0.414608 | + | 0.910000i | \(0.363919\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.0987 | −1.47051 | −0.735255 | − | 0.677791i | \(-0.762938\pi\) | ||||
−0.735255 | + | 0.677791i | \(0.762938\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.5921 | 0.905206 | 0.452603 | − | 0.891712i | \(-0.350495\pi\) | ||||
0.452603 | + | 0.891712i | \(0.350495\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −56.7325 | −1.92896 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.07703 | −0.0365357 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.4227 | 0.387045 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −90.5379 | −3.06074 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.9441 | −0.740999 | −0.370500 | − | 0.928833i | \(-0.620814\pi\) | ||||
−0.370500 | + | 0.928833i | \(0.620814\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.68457 | 0.326282 | 0.163141 | − | 0.986603i | \(-0.447838\pi\) | ||||
0.163141 | + | 0.986603i | \(0.447838\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.2681 | −1.15321 | −0.576607 | − | 0.817022i | \(-0.695623\pi\) | ||||
−0.576607 | + | 0.817022i | \(0.695623\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.7884 | −0.362239 | −0.181120 | − | 0.983461i | \(-0.557972\pi\) | ||||
−0.181120 | + | 0.983461i | \(0.557972\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.61323 | −0.0541060 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.73074 | −0.225236 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 68.4016 | 2.28641 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.8807 | 0.563004 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.1979 | −1.50576 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.46149 | −0.181546 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.43643 | 0.114105 | 0.0570524 | − | 0.998371i | \(-0.481830\pi\) | ||||
0.0570524 | + | 0.998371i | \(0.481830\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.1306 | 1.76030 | 0.880148 | − | 0.474699i | \(-0.157443\pi\) | ||||
0.880148 | + | 0.474699i | \(0.157443\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.563568 | 0.0186514 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 58.5653 | 1.93400 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.3805 | −0.573330 | −0.286665 | − | 0.958031i | \(-0.592547\pi\) | ||||
−0.286665 | + | 0.958031i | \(0.592547\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.4227 | −0.375984 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 41.3805 | 1.36058 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.6269 | −0.447085 | −0.223542 | − | 0.974694i | \(-0.571762\pi\) | ||||
−0.223542 | + | 0.974694i | \(0.571762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.6971 | 0.383357 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.65371 | 0.0540822 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.7256 | 1.00376 | 0.501882 | − | 0.864936i | \(-0.332641\pi\) | ||||
0.501882 | + | 0.864936i | \(0.332641\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.2362 | −1.11607 | −0.558034 | − | 0.829818i | \(-0.688444\pi\) | ||||
−0.558034 | + | 0.829818i | \(0.688444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.00000 | 0.260516 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.2710 | −1.73108 | −0.865538 | − | 0.500844i | \(-0.833023\pi\) | ||||
−0.865538 | + | 0.500844i | \(0.833023\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.1900 | −0.752780 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.0633 | 1.78368 | 0.891838 | − | 0.452354i | \(-0.149416\pi\) | ||||
0.891838 | + | 0.452354i | \(0.149416\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.3662 | −0.853192 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 80.2767 | 2.59227 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −51.0074 | −1.64199 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.0845 | 1.16040 | 0.580199 | − | 0.814475i | \(-0.302975\pi\) | ||||
0.580199 | + | 0.814475i | \(0.302975\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.0000 | 1.28366 | 0.641831 | − | 0.766846i | \(-0.278175\pi\) | ||||
0.641831 | + | 0.766846i | \(0.278175\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.9932 | 1.15389 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.85569 | 0.283319 | 0.141659 | − | 0.989915i | \(-0.454756\pi\) | ||||
0.141659 | + | 0.989915i | \(0.454756\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0981437 | −0.00313669 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.92297 | 0.0932283 | 0.0466142 | − | 0.998913i | \(-0.485157\pi\) | ||||
0.0466142 | + | 0.998913i | \(0.485157\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −98.0149 | −3.12301 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.53851 | 0.0807201 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.7747 | −1.16819 | −0.584094 | − | 0.811686i | \(-0.698550\pi\) | ||||
−0.584094 | + | 0.811686i | \(0.698550\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.26926 | 0.0402382 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.8375 | −0.343226 | −0.171613 | − | 0.985164i | \(-0.554898\pi\) | ||||
−0.171613 | + | 0.985164i | \(0.554898\pi\) | |||||||
\(998\) | 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 | 2736.2.a.bc.1.1 | 3 | ||
3.2 | odd | 2 | 2736.2.a.be.1.3 | 3 | |||
4.3 | odd | 2 | 1368.2.a.m.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 1368.2.a.o.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.a.m.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
1368.2.a.o.1.3 | yes | 3 | 12.11 | even | 2 | ||
2736.2.a.bc.1.1 | 3 | 1.1 | even | 1 | trivial | ||
2736.2.a.be.1.3 | 3 | 3.2 | odd | 2 |