Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 31 x^{10} + 131 x^{9} + 309 x^{8} - 1453 x^{7} - 1072 x^{6} + 6350 x^{5} + \cdots + 3008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.619387\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.619387 | −0.276999 | −0.138499 | − | 0.990363i | \(-0.544228\pi\) | ||||
−0.138499 | + | 0.990363i | \(0.544228\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.954126 | 0.360626 | 0.180313 | − | 0.983609i | \(-0.442289\pi\) | ||||
0.180313 | + | 0.983609i | \(0.442289\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.25107 | 1.88477 | 0.942385 | − | 0.334531i | \(-0.108578\pi\) | ||||
0.942385 | + | 0.334531i | \(0.108578\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.92641 | 0.811641 | 0.405820 | − | 0.913953i | \(-0.366986\pi\) | ||||
0.405820 | + | 0.913953i | \(0.366986\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.619387 | −0.159925 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.33666 | 1.29433 | 0.647165 | − | 0.762350i | \(-0.275954\pi\) | ||||
0.647165 | + | 0.762350i | \(0.275954\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.94423 | 0.675454 | 0.337727 | − | 0.941244i | \(-0.390342\pi\) | ||||
0.337727 | + | 0.941244i | \(0.390342\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.954126 | 0.208207 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.33637 | −0.487167 | −0.243583 | − | 0.969880i | \(-0.578323\pi\) | ||||
−0.243583 | + | 0.969880i | \(0.578323\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61636 | −0.923272 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47124 | 0.830289 | 0.415144 | − | 0.909756i | \(-0.363731\pi\) | ||||
0.415144 | + | 0.909756i | \(0.363731\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.45595 | −0.620707 | −0.310353 | − | 0.950621i | \(-0.600447\pi\) | ||||
−0.310353 | + | 0.950621i | \(0.600447\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.25107 | 1.08817 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.590974 | −0.0998928 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.26640 | 0.701392 | 0.350696 | − | 0.936489i | \(-0.385945\pi\) | ||||
0.350696 | + | 0.936489i | \(0.385945\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.92641 | 0.468601 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.8203 | −1.68985 | −0.844925 | − | 0.534885i | \(-0.820355\pi\) | ||||
−0.844925 | + | 0.534885i | \(0.820355\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.32390 | −0.201893 | −0.100947 | − | 0.994892i | \(-0.532187\pi\) | ||||
−0.100947 | + | 0.994892i | \(0.532187\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.619387 | −0.0923328 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.37095 | 0.491704 | 0.245852 | − | 0.969307i | \(-0.420932\pi\) | ||||
0.245852 | + | 0.969307i | \(0.420932\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.08964 | −0.869949 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.33666 | 0.747282 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.72269 | 0.786072 | 0.393036 | − | 0.919523i | \(-0.371425\pi\) | ||||
0.393036 | + | 0.919523i | \(0.371425\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.87184 | −0.522078 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.94423 | 0.389973 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.0347 | −1.30641 | −0.653204 | − | 0.757182i | \(-0.726575\pi\) | ||||
−0.653204 | + | 0.757182i | \(0.726575\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.8490 | 1.51711 | 0.758556 | − | 0.651608i | \(-0.225905\pi\) | ||||
0.758556 | + | 0.651608i | \(0.225905\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.954126 | 0.120209 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.81258 | −0.224823 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.604492 | 0.0738505 | 0.0369252 | − | 0.999318i | \(-0.488244\pi\) | ||||
0.0369252 | + | 0.999318i | \(0.488244\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.33637 | −0.281266 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.74739 | −1.15680 | −0.578401 | − | 0.815752i | \(-0.696323\pi\) | ||||
−0.578401 | + | 0.815752i | \(0.696323\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.1654 | −1.30681 | −0.653404 | − | 0.757009i | \(-0.726660\pi\) | ||||
−0.653404 | + | 0.757009i | \(0.726660\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.61636 | −0.533051 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.96431 | 0.679697 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.74411 | 0.758772 | 0.379386 | − | 0.925239i | \(-0.376135\pi\) | ||||
0.379386 | + | 0.925239i | \(0.376135\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.00272570 | 0.000299184 0 | 0.000149592 | − | 1.00000i | \(-0.499952\pi\) | ||||
0.000149592 | 1.00000i | \(0.499952\pi\) | ||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.30546 | −0.358528 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.47124 | 0.479367 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.85457 | 1.04458 | 0.522291 | − | 0.852767i | \(-0.325077\pi\) | ||||
0.522291 | + | 0.852767i | \(0.325077\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.79217 | 0.292699 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.45595 | −0.358365 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.82362 | −0.187100 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.92479 | −0.906175 | −0.453088 | − | 0.891466i | \(-0.649678\pi\) | ||||
−0.453088 | + | 0.891466i | \(0.649678\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.25107 | 0.628256 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.91531 | 0.190580 | 0.0952901 | − | 0.995450i | \(-0.469622\pi\) | ||||
0.0952901 | + | 0.995450i | \(0.469622\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.90694 | 0.582028 | 0.291014 | − | 0.956719i | \(-0.406007\pi\) | ||||
0.291014 | + | 0.956719i | \(0.406007\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.590974 | −0.0576732 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.36790 | −0.712282 | −0.356141 | − | 0.934432i | \(-0.615908\pi\) | ||||
−0.356141 | + | 0.934432i | \(0.615908\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.19031 | 0.880272 | 0.440136 | − | 0.897931i | \(-0.354930\pi\) | ||||
0.440136 | + | 0.897931i | \(0.354930\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.26640 | 0.404949 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9146 | −1.21490 | −0.607451 | − | 0.794357i | \(-0.707808\pi\) | ||||
−0.607451 | + | 0.794357i | \(0.707808\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.44712 | 0.134944 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.92641 | 0.270547 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.09185 | 0.466769 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 28.0759 | 2.55236 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.8203 | −0.975635 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.95625 | 0.532743 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.28542 | 0.823948 | 0.411974 | − | 0.911196i | \(-0.364839\pi\) | ||||
0.411974 | + | 0.911196i | \(0.364839\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.32390 | −0.116563 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.24628 | −0.196259 | −0.0981293 | − | 0.995174i | \(-0.531286\pi\) | ||||
−0.0981293 | + | 0.995174i | \(0.531286\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.80917 | 0.243586 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.619387 | −0.0533084 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.893884 | −0.0763696 | −0.0381848 | − | 0.999271i | \(-0.512158\pi\) | ||||
−0.0381848 | + | 0.999271i | \(0.512158\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.11800 | 0.0948276 | 0.0474138 | − | 0.998875i | \(-0.484902\pi\) | ||||
0.0474138 | + | 0.998875i | \(0.484902\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.37095 | 0.283885 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.2932 | 1.52976 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.76943 | −0.229989 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.08964 | −0.502265 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.8738 | −0.890814 | −0.445407 | − | 0.895328i | \(-0.646941\pi\) | ||||
−0.445407 | + | 0.895328i | \(0.646941\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.9232 | 1.94684 | 0.973421 | − | 0.229023i | \(-0.0735530\pi\) | ||||
0.973421 | + | 0.229023i | \(0.0735530\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.33666 | 0.431443 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.14057 | 0.171935 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4595 | 0.834758 | 0.417379 | − | 0.908733i | \(-0.362949\pi\) | ||||
0.417379 | + | 0.908733i | \(0.362949\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.72269 | 0.453839 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.22919 | −0.175685 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.79788 | −0.140821 | −0.0704103 | − | 0.997518i | \(-0.522431\pi\) | ||||
−0.0704103 | + | 0.997518i | \(0.522431\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.87184 | −0.301422 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.43611 | −0.341240 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.94423 | 0.225151 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.35455 | 0.483127 | 0.241564 | − | 0.970385i | \(-0.422340\pi\) | ||||
0.241564 | + | 0.970385i | \(0.422340\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.40459 | −0.332956 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.0347 | −0.754255 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.3384 | 1.14645 | 0.573224 | − | 0.819399i | \(-0.305693\pi\) | ||||
0.573224 | + | 0.819399i | \(0.305693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.95349 | 0.219531 | 0.109766 | − | 0.993958i | \(-0.464990\pi\) | ||||
0.109766 | + | 0.993958i | \(0.464990\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.8490 | 0.875904 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.64256 | −0.194285 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 33.3598 | 2.43951 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.954126 | 0.0694025 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.76766 | 0.127903 | 0.0639515 | − | 0.997953i | \(-0.479630\pi\) | ||||
0.0639515 | + | 0.997953i | \(0.479630\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.2653 | −0.810897 | −0.405448 | − | 0.914118i | \(-0.632885\pi\) | ||||
−0.405448 | + | 0.914118i | \(0.632885\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.81258 | −0.129802 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.9384 | −1.49180 | −0.745901 | − | 0.666057i | \(-0.767981\pi\) | ||||
−0.745901 | + | 0.666057i | \(0.767981\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.8279 | 0.909347 | 0.454674 | − | 0.890658i | \(-0.349756\pi\) | ||||
0.454674 | + | 0.890658i | \(0.349756\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.604492 | 0.0426376 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.26613 | 0.299424 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.70197 | 0.468086 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.33637 | −0.162389 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.4046 | 1.27307 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.08886 | −0.556860 | −0.278430 | − | 0.960457i | \(-0.589814\pi\) | ||||
−0.278430 | + | 0.960457i | \(0.589814\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.74739 | −0.667880 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.820009 | 0.0559242 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.29741 | −0.223843 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.1654 | −0.754486 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.6173 | 1.05053 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.7517 | 1.65750 | 0.828749 | − | 0.559620i | \(-0.189053\pi\) | ||||
0.828749 | + | 0.559620i | \(0.189053\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.61636 | −0.307757 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.26183 | −0.0837504 | −0.0418752 | − | 0.999123i | \(-0.513333\pi\) | ||||
−0.0418752 | + | 0.999123i | \(0.513333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.5768 | 0.831096 | 0.415548 | − | 0.909571i | \(-0.363590\pi\) | ||||
0.415548 | + | 0.909571i | \(0.363590\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.96431 | 0.392423 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.6215 | 1.02340 | 0.511698 | − | 0.859165i | \(-0.329017\pi\) | ||||
0.511698 | + | 0.859165i | \(0.329017\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.08793 | −0.136201 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.74411 | 0.438077 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.8379 | −1.80068 | −0.900341 | − | 0.435185i | \(-0.856683\pi\) | ||||
−0.900341 | + | 0.435185i | \(0.856683\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −31.0024 | −1.99704 | −0.998521 | − | 0.0543633i | \(-0.982687\pi\) | ||||
−0.998521 | + | 0.0543633i | \(0.982687\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.77185 | 0.240975 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.61604 | 0.548226 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.00272570 | 0.000172734 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.88623 | 0.182177 | 0.0910885 | − | 0.995843i | \(-0.470965\pi\) | ||||
0.0910885 | + | 0.995843i | \(0.470965\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.6048 | −0.918197 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.30546 | −0.206996 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.5265 | −0.656626 | −0.328313 | − | 0.944569i | \(-0.606480\pi\) | ||||
−0.328313 | + | 0.944569i | \(0.606480\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.07069 | 0.252940 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.47124 | 0.276763 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.9049 | −0.857415 | −0.428708 | − | 0.903443i | \(-0.641031\pi\) | ||||
−0.428708 | + | 0.903443i | \(0.641031\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.54456 | −0.217741 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.85457 | 0.603090 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.54423 | 0.520951 | 0.260475 | − | 0.965480i | \(-0.416121\pi\) | ||||
0.260475 | + | 0.965480i | \(0.416121\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.35225 | 0.203635 | 0.101817 | − | 0.994803i | \(-0.467534\pi\) | ||||
0.101817 | + | 0.994803i | \(0.467534\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.79217 | 0.168990 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −28.8572 | −1.74015 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.5788 | −0.695700 | −0.347850 | − | 0.937550i | \(-0.613088\pi\) | ||||
−0.347850 | + | 0.937550i | \(0.613088\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.45595 | −0.206902 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.10103 | −0.423612 | −0.211806 | − | 0.977312i | \(-0.567935\pi\) | ||||
−0.211806 | + | 0.977312i | \(0.567935\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.58868 | −0.213325 | −0.106662 | − | 0.994295i | \(-0.534016\pi\) | ||||
−0.106662 | + | 0.994295i | \(0.534016\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.82362 | −0.108022 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.3240 | −0.609404 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.4799 | 0.675291 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.92479 | −0.523180 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.4842 | −1.37196 | −0.685982 | − | 0.727619i | \(-0.740627\pi\) | ||||
−0.685982 | + | 0.727619i | \(0.740627\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.21537 | 0.361873 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.25107 | 0.362724 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.83718 | −0.395404 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.26317 | −0.0728080 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.91531 | 0.110031 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.33913 | −0.420237 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.96744 | 0.226433 | 0.113217 | − | 0.993570i | \(-0.463885\pi\) | ||||
0.113217 | + | 0.993570i | \(0.463885\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.90694 | 0.336034 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.69973 | 0.0963829 | 0.0481915 | − | 0.998838i | \(-0.484654\pi\) | ||||
0.0481915 | + | 0.998838i | \(0.484654\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.65206 | 0.545566 | 0.272783 | − | 0.962076i | \(-0.412056\pi\) | ||||
0.272783 | + | 0.962076i | \(0.412056\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.590974 | −0.0332976 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.58465 | −0.482162 | −0.241081 | − | 0.970505i | \(-0.577502\pi\) | ||||
−0.241081 | + | 0.970505i | \(0.577502\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.9501 | 1.56490 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.36790 | −0.411236 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.7124 | 0.874260 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.5094 | −0.749365 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.19031 | 0.508225 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.21631 | 0.177321 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.0207 | 0.715683 | 0.357841 | − | 0.933782i | \(-0.383513\pi\) | ||||
0.357841 | + | 0.933782i | \(0.383513\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.26640 | 0.233797 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.374415 | −0.0204565 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.58095 | 0.0861199 | 0.0430600 | − | 0.999072i | \(-0.486289\pi\) | ||||
0.0430600 | + | 0.999072i | \(0.486289\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.9146 | −0.701424 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.6034 | −1.16989 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.4892 | −0.674352 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.44712 | 0.0779102 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.4617 | 1.09844 | 0.549220 | − | 0.835678i | \(-0.314925\pi\) | ||||
0.549220 | + | 0.835678i | \(0.314925\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.71699 | 0.198966 | 0.0994831 | − | 0.995039i | \(-0.468281\pi\) | ||||
0.0994831 | + | 0.995039i | \(0.468281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.92641 | 0.156200 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.2105 | 1.18214 | 0.591072 | − | 0.806619i | \(-0.298705\pi\) | ||||
0.591072 | + | 0.806619i | \(0.298705\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.03741 | 0.320433 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.09185 | 0.269489 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.53420 | −0.186528 | −0.0932640 | − | 0.995641i | \(-0.529730\pi\) | ||||
−0.0932640 | + | 0.995641i | \(0.529730\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.3315 | −0.543762 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.0759 | 1.47360 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.91569 | 0.361984 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2786 | 0.536537 | 0.268268 | − | 0.963344i | \(-0.413549\pi\) | ||||
0.268268 | + | 0.963344i | \(0.413549\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.8203 | −0.563283 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.46017 | 0.283478 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.5828 | −1.16929 | −0.584647 | − | 0.811288i | \(-0.698767\pi\) | ||||
−0.584647 | + | 0.811288i | \(0.698767\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.95625 | 0.307580 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.0847 | 0.673896 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3926 | 0.533834 | 0.266917 | − | 0.963720i | \(-0.413995\pi\) | ||||
0.266917 | + | 0.963720i | \(0.413995\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.28542 | 0.475707 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.01014 | 0.307104 | 0.153552 | − | 0.988141i | \(-0.450929\pi\) | ||||
0.153552 | + | 0.988141i | \(0.450929\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.69422 | −0.188275 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.32390 | −0.0672978 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.9823 | −1.16525 | −0.582626 | − | 0.812741i | \(-0.697975\pi\) | ||||
−0.582626 | + | 0.812741i | \(0.697975\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.4684 | −0.630555 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.24628 | −0.113310 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.17722 | −0.210179 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −38.2310 | −1.91876 | −0.959381 | − | 0.282115i | \(-0.908964\pi\) | ||||
−0.959381 | + | 0.282115i | \(0.908964\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.80917 | 0.140634 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.9593 | −1.14653 | −0.573266 | − | 0.819370i | \(-0.694324\pi\) | ||||
−0.573266 | + | 0.819370i | \(0.694324\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.1135 | −0.503791 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.619387 | −0.0307776 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.6696 | 1.32196 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.3129 | 1.05386 | 0.526928 | − | 0.849910i | \(-0.323344\pi\) | ||||
0.526928 | + | 0.849910i | \(0.323344\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.893884 | −0.0440920 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.57438 | −0.471124 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.00168826 | −8.28736e−5 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.11800 | 0.0547487 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.8211 | −1.55456 | −0.777281 | − | 0.629154i | \(-0.783402\pi\) | ||||
−0.777281 | + | 0.629154i | \(0.783402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.234009 | −0.0114049 | −0.00570245 | − | 0.999984i | \(-0.501815\pi\) | ||||
−0.00570245 | + | 0.999984i | \(0.501815\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.37095 | 0.163901 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.6359 | −1.19502 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.3055 | 0.547110 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.2932 | 0.883205 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.97830 | −0.480638 | −0.240319 | − | 0.970694i | \(-0.577252\pi\) | ||||
−0.240319 | + | 0.970694i | \(0.577252\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.2262 | 1.50064 | 0.750318 | − | 0.661077i | \(-0.229901\pi\) | ||||
0.750318 | + | 0.661077i | \(0.229901\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.76943 | −0.132784 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.87882 | −0.329059 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.4486 | −0.737320 | −0.368660 | − | 0.929564i | \(-0.620183\pi\) | ||||
−0.368660 | + | 0.929564i | \(0.620183\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.08964 | −0.289983 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.04906 | −0.192377 | −0.0961883 | − | 0.995363i | \(-0.530665\pi\) | ||||
−0.0961883 | + | 0.995363i | \(0.530665\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.10380 | −0.289348 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.8738 | −0.514312 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.16361 | −0.149300 | −0.0746500 | − | 0.997210i | \(-0.523784\pi\) | ||||
−0.0746500 | + | 0.997210i | \(0.523784\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −67.6386 | −3.18498 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.9232 | 1.12401 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.72943 | −0.0810771 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.9553 | −1.02702 | −0.513512 | − | 0.858083i | \(-0.671656\pi\) | ||||
−0.513512 | + | 0.858083i | \(0.671656\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.33666 | 0.249094 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.4993 | −1.18762 | −0.593811 | − | 0.804604i | \(-0.702378\pi\) | ||||
−0.593811 | + | 0.804604i | \(0.702378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.891709 | 0.0414412 | 0.0207206 | − | 0.999785i | \(-0.493404\pi\) | ||||
0.0207206 | + | 0.999785i | \(0.493404\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.14057 | 0.0992666 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.2712 | 1.40079 | 0.700393 | − | 0.713758i | \(-0.253008\pi\) | ||||
0.700393 | + | 0.713758i | \(0.253008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.576762 | 0.0266324 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.4595 | 0.481948 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.27582 | −0.380523 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.5916 | −0.623627 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.72269 | 0.262024 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.73323 | −0.0791932 | −0.0395966 | − | 0.999216i | \(-0.512607\pi\) | ||||
−0.0395966 | + | 0.999216i | \(0.512607\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.4852 | 0.569278 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.22919 | −0.101432 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.52790 | 0.251009 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.7612 | 1.89238 | 0.946190 | − | 0.323612i | \(-0.104897\pi\) | ||||
0.946190 | + | 0.323612i | \(0.104897\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.79788 | −0.0813029 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.6055 | 1.56173 | 0.780863 | − | 0.624703i | \(-0.214780\pi\) | ||||
0.780863 | + | 0.624703i | \(0.214780\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.8615 | 1.07467 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.87184 | −0.174026 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.30024 | −0.417173 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.8402 | 0.798636 | 0.399318 | − | 0.916813i | \(-0.369247\pi\) | ||||
0.399318 | + | 0.916813i | \(0.369247\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.0372 | −1.11635 | −0.558176 | − | 0.829722i | \(-0.688499\pi\) | ||||
−0.558176 | + | 0.829722i | \(0.688499\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.18632 | −0.0527904 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.43611 | −0.197015 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.2180 | −0.718852 | −0.359426 | − | 0.933174i | \(-0.617027\pi\) | ||||
−0.359426 | + | 0.933174i | \(0.617027\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.6532 | −0.471269 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.94423 | 0.129991 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.65868 | −0.161221 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.0721 | 0.926748 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.35455 | 0.278934 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.8985 | −1.04701 | −0.523506 | − | 0.852022i | \(-0.675376\pi\) | ||||
−0.523506 | + | 0.852022i | \(0.675376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.56408 | −0.330754 | −0.165377 | − | 0.986230i | \(-0.552884\pi\) | ||||
−0.165377 | + | 0.986230i | \(0.552884\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.40459 | −0.192232 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.4432 | −0.803399 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5414 | −0.762669 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.0347 | −0.435469 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31.6647 | −1.37155 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.56358 | 0.197301 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.3384 | 0.661901 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −38.0668 | −1.63965 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.93874 | 0.255326 | 0.127663 | − | 0.991818i | \(-0.459252\pi\) | ||||
0.127663 | + | 0.991818i | \(0.459252\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.95349 | 0.126746 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.69236 | −0.243834 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.2274 | −0.608319 | −0.304159 | − | 0.952621i | \(-0.598376\pi\) | ||||
−0.304159 | + | 0.952621i | \(0.598376\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.8490 | 0.505704 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.1644 | 0.560822 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.43473 | 0.273633 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.64256 | −0.112170 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.7728 | 1.85471 | 0.927356 | − | 0.374179i | \(-0.122076\pi\) | ||||
0.927356 | + | 0.374179i | \(0.122076\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.87429 | −0.163865 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 33.3598 | 1.40845 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.51748 | 0.0639541 | 0.0319770 | − | 0.999489i | \(-0.489820\pi\) | ||||
0.0319770 | + | 0.999489i | \(0.489820\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.99913 | 0.336526 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.954126 | 0.0400695 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.3447 | 1.31404 | 0.657019 | − | 0.753874i | \(-0.271817\pi\) | ||||
0.657019 | + | 0.753874i | \(0.271817\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.7936 | −1.37237 | −0.686184 | − | 0.727428i | \(-0.740716\pi\) | ||||
−0.686184 | + | 0.727428i | \(0.740716\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.76766 | 0.0738449 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.7855 | 0.449787 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.2365 | 0.717565 | 0.358782 | − | 0.933421i | \(-0.383192\pi\) | ||||
0.358782 | + | 0.933421i | \(0.383192\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.2653 | −0.468171 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.00260066 | 0.000107894 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.7729 | 1.48156 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.81258 | −0.0749411 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.9256 | 0.616045 | 0.308023 | − | 0.951379i | \(-0.400333\pi\) | ||||
0.308023 | + | 0.951379i | \(0.400333\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.1751 | −0.419259 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.9384 | −0.861293 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.00970 | −0.0414635 | −0.0207318 | − | 0.999785i | \(-0.506600\pi\) | ||||
−0.0207318 | + | 0.999785i | \(0.506600\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.15383 | −0.129294 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.8279 | 0.525012 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.66824 | 0.0681624 | 0.0340812 | − | 0.999419i | \(-0.489150\pi\) | ||||
0.0340812 | + | 0.999419i | \(0.489150\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.4063 | −0.873182 | −0.436591 | − | 0.899660i | \(-0.643814\pi\) | ||||
−0.436591 | + | 0.899660i | \(0.643814\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.604492 | 0.0246168 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.3899 | −0.706999 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.1471 | 1.46716 | 0.733582 | − | 0.679601i | \(-0.237847\pi\) | ||||
0.733582 | + | 0.679601i | \(0.237847\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.26613 | 0.172872 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.86479 | 0.399087 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.3272 | −1.10373 | −0.551867 | − | 0.833932i | \(-0.686084\pi\) | ||||
−0.551867 | + | 0.833932i | \(0.686084\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.70197 | 0.270250 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.4624 | 0.622491 | 0.311246 | − | 0.950330i | \(-0.399254\pi\) | ||||
0.311246 | + | 0.950330i | \(0.399254\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.42786 | 0.378938 | 0.189469 | − | 0.981887i | \(-0.439323\pi\) | ||||
0.189469 | + | 0.981887i | \(0.439323\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.33637 | −0.0937553 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.40251 | 0.376704 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.3926 | 0.775703 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.4046 | 0.735010 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.7683 | 0.907833 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.25940 | −0.129755 | −0.0648774 | − | 0.997893i | \(-0.520666\pi\) | ||||
−0.0648774 | + | 0.997893i | \(0.520666\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.08886 | −0.321503 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.75127 | −0.228232 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.8208 | −0.706086 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.74739 | −0.385601 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.6986 | −1.29152 | −0.645758 | − | 0.763542i | \(-0.723458\pi\) | ||||
−0.645758 | + | 0.763542i | \(0.723458\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.9513 | 1.73327 | 0.866635 | − | 0.498943i | \(-0.166278\pi\) | ||||
0.866635 | + | 0.498943i | \(0.166278\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.820009 | 0.0322878 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.4757 | −1.47332 | −0.736661 | − | 0.676262i | \(-0.763599\pi\) | ||||
−0.736661 | + | 0.676262i | \(0.763599\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −62.7277 | −2.46228 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.29741 | −0.129236 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.0885 | −1.25572 | −0.627860 | − | 0.778326i | \(-0.716069\pi\) | ||||
−0.627860 | + | 0.778326i | \(0.716069\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.39132 | 0.0543633 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.1654 | −0.435603 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 48.8689 | 1.90366 | 0.951831 | − | 0.306623i | \(-0.0991990\pi\) | ||||
0.951831 | + | 0.306623i | \(0.0991990\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.28040 | −0.0498018 | −0.0249009 | − | 0.999690i | \(-0.507927\pi\) | ||||
−0.0249009 | + | 0.999690i | \(0.507927\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.6173 | 0.606524 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.73997 | −0.0674730 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.4465 | −0.404489 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.7517 | 0.956957 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 74.0691 | 2.85940 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.53994 | 0.290643 | 0.145322 | − | 0.989384i | \(-0.453578\pi\) | ||||
0.145322 | + | 0.989384i | \(0.453578\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.61636 | −0.177684 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.9878 | −1.15253 | −0.576263 | − | 0.817264i | \(-0.695490\pi\) | ||||
−0.576263 | + | 0.817264i | \(0.695490\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.51538 | −0.326790 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.26183 | −0.0483533 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.5606 | 0.710201 | 0.355100 | − | 0.934828i | \(-0.384447\pi\) | ||||
0.355100 | + | 0.934828i | \(0.384447\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.553660 | 0.0211543 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.5768 | 0.479834 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.7469 | 0.638008 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.4157 | −0.966857 | −0.483429 | − | 0.875384i | \(-0.660609\pi\) | ||||
−0.483429 | + | 0.875384i | \(0.660609\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.96431 | 0.226566 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.692476 | −0.0262671 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −57.7444 | −2.18722 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.6215 | 0.590858 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.05383 | −0.0398026 | −0.0199013 | − | 0.999802i | \(-0.506335\pi\) | ||||
−0.0199013 | + | 0.999802i | \(0.506335\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.5613 | 0.473758 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.08793 | −0.0786358 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.82744 | 0.0687281 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.33736 | −0.0502257 | −0.0251129 | − | 0.999685i | \(-0.507995\pi\) | ||||
−0.0251129 | + | 0.999685i | \(0.507995\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.74411 | 0.252924 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.07437 | 0.302388 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.3306 | −0.423740 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.8379 | −1.03962 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.81276 | 0.254073 | 0.127037 | − | 0.991898i | \(-0.459453\pi\) | ||||
0.127037 | + | 0.991898i | \(0.459453\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.63597 | 0.209894 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −31.0024 | −1.15299 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.6409 | −0.766582 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.6649 | 0.766419 | 0.383210 | − | 0.923661i | \(-0.374819\pi\) | ||||
0.383210 | + | 0.923661i | \(0.374819\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.06522 | −0.261317 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.2674 | −1.33957 | −0.669784 | − | 0.742556i | \(-0.733613\pi\) | ||||
−0.669784 | + | 0.742556i | \(0.733613\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.77185 | 0.139127 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.77872 | 0.139191 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.6388 | 0.612069 | 0.306034 | − | 0.952020i | \(-0.400998\pi\) | ||||
0.306034 | + | 0.952020i | \(0.400998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.61604 | 0.316518 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.04095 | 0.148248 | 0.0741241 | − | 0.997249i | \(-0.476384\pi\) | ||||
0.0741241 | + | 0.997249i | \(0.476384\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.73508 | 0.246754 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.00272570 | 9.97281e−5 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.02991 | −0.256867 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.2195 | −0.920272 | −0.460136 | − | 0.887849i | \(-0.652199\pi\) | ||||
−0.460136 | + | 0.887849i | \(0.652199\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.88623 | 0.105180 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.8177 | −0.539272 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.8414 | 0.830184 | 0.415092 | − | 0.909779i | \(-0.363749\pi\) | ||||
0.415092 | + | 0.909779i | \(0.363749\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14.6048 | −0.530121 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.8230 | −1.11733 | −0.558666 | − | 0.829392i | \(-0.688687\pi\) | ||||
−0.558666 | + | 0.829392i | \(0.688687\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.76872 | 0.317449 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.30546 | −0.119509 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29.3657 | −1.06033 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.8669 | −0.824600 | −0.412300 | − | 0.911048i | \(-0.635274\pi\) | ||||
−0.412300 | + | 0.911048i | \(0.635274\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.5265 | −0.379103 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.4906 | −1.13264 | −0.566320 | − | 0.824186i | \(-0.691633\pi\) | ||||
−0.566320 | + | 0.824186i | \(0.691633\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.9539 | 0.573081 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.07069 | 0.146035 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −31.8576 | −1.14142 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.9317 | −2.18031 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.47124 | 0.159789 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.47848 | −0.231227 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.5858 | −0.626866 | −0.313433 | − | 0.949610i | \(-0.601479\pi\) | ||||
−0.313433 | + | 0.949610i | \(0.601479\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.9049 | −0.495029 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.3221 | −0.438125 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.6751 | 1.23135 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.54456 | −0.125713 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.0559 | 0.639573 | 0.319787 | − | 0.947490i | \(-0.396389\pi\) | ||||
0.319787 | + | 0.947490i | \(0.396389\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.9896 | 0.636427 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.85457 | 0.348194 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −69.7955 | −2.46303 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.38073 | 0.0486645 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.54423 | 0.300771 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.6237 | 1.63920 | 0.819600 | − | 0.572936i | \(-0.194195\pi\) | ||||
0.819600 | + | 0.572936i | \(0.194195\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.3725 | 0.610030 | 0.305015 | − | 0.952348i | \(-0.401339\pi\) | ||||
0.305015 | + | 0.952348i | \(0.401339\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.35225 | 0.117569 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.11358 | 0.0390071 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.89788 | −0.136370 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.79217 | 0.0975662 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.23612 | −0.217642 | −0.108821 | − | 0.994061i | \(-0.534708\pi\) | ||||
−0.108821 | + | 0.994061i | \(0.534708\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.4109 | −0.641762 | −0.320881 | − | 0.947120i | \(-0.603979\pi\) | ||||
−0.320881 | + | 0.947120i | \(0.603979\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −28.8572 | −1.00468 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.54468 | −0.0884873 | −0.0442436 | − | 0.999021i | \(-0.514088\pi\) | ||||
−0.0442436 | + | 0.999021i | \(0.514088\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.5243 | 1.40747 | 0.703734 | − | 0.710463i | \(-0.251515\pi\) | ||||
0.703734 | + | 0.710463i | \(0.251515\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.5788 | −0.401663 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −32.4984 | −1.12600 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.619387 | −0.0214348 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.45595 | −0.119455 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.9352 | 0.757287 | 0.378643 | − | 0.925543i | \(-0.376391\pi\) | ||||
0.378643 | + | 0.925543i | \(0.376391\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00799 | −0.310620 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.10103 | −0.244573 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.74767 | 0.0945228 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.7880 | 0.920445 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.58868 | −0.123163 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.96789 | −0.341695 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.93334 | 0.271632 | 0.135816 | − | 0.990734i | \(-0.456634\pi\) | ||||
0.135816 | + | 0.990734i | \(0.456634\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.82362 | −0.0623666 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45.3773 | −1.55006 | −0.775029 | − | 0.631926i | \(-0.782265\pi\) | ||||
−0.775029 | + | 0.631926i | \(0.782265\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.9407 | 0.578010 | 0.289005 | − | 0.957328i | \(-0.406676\pi\) | ||||
0.289005 | + | 0.957328i | \(0.406676\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.3240 | −0.351839 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.2827 | −0.792551 | −0.396275 | − | 0.918132i | \(-0.629697\pi\) | ||||
−0.396275 | + | 0.918132i | \(0.629697\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.93593 | −0.133826 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.4799 | 0.389879 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.1579 | 1.43011 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.76899 | 0.0599400 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.92479 | −0.302058 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.68302 | 0.192121 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.5659 | 1.09967 | 0.549836 | − | 0.835272i | \(-0.314690\pi\) | ||||
0.549836 | + | 0.835272i | \(0.314690\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.4842 | −0.792104 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.9764 | 0.706712 | 0.353356 | − | 0.935489i | \(-0.385040\pi\) | ||||
0.353356 | + | 0.935489i | \(0.385040\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.1958 | 1.01617 | 0.508084 | − | 0.861307i | \(-0.330354\pi\) | ||||
0.508084 | + | 0.861307i | \(0.330354\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.21537 | 0.208927 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37.7926 | −1.26895 | −0.634475 | − | 0.772943i | \(-0.718784\pi\) | ||||
−0.634475 | + | 0.772943i | \(0.718784\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.85947 | 0.297137 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.25107 | 0.209419 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.92487 | 0.332123 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.50042 | −0.317564 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.83718 | −0.228287 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.4524 | −0.515366 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.5400 | 1.01744 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.26317 | −0.0420357 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.82935 | −0.0608098 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.2201 | −0.538581 | −0.269291 | − | 0.963059i | \(-0.586789\pi\) | ||||
−0.269291 | + | 0.963059i | \(0.586789\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.91531 | 0.0635267 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.1700 | −1.19837 | −0.599183 | − | 0.800612i | \(-0.704508\pi\) | ||||
−0.599183 | + | 0.800612i | \(0.704508\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.0170385 | 0.000563894 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.33913 | −0.242624 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.14324 | −0.0707759 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.1395 | 1.52200 | 0.761000 | − | 0.648752i | \(-0.224709\pi\) | ||||
0.761000 | + | 0.648752i | \(0.224709\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.96744 | 0.130731 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.5249 | −0.938908 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.6952 | −0.647576 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.90694 | 0.194009 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.7751 | −1.27217 | −0.636084 | − | 0.771619i | \(-0.719447\pi\) | ||||
−0.636084 | + | 0.771619i | \(0.719447\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.9293 | −0.587610 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.69973 | 0.0556467 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.6627 | −0.675742 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.0137 | −0.359802 | −0.179901 | − | 0.983685i | \(-0.557578\pi\) | ||||
−0.179901 | + | 0.983685i | \(0.557578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.65206 | 0.314983 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 59.1291 | 1.92755 | 0.963776 | − | 0.266713i | \(-0.0859374\pi\) | ||||
0.963776 | + | 0.266713i | \(0.0859374\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.2803 | 0.823239 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.590974 | −0.0192244 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.8243 | −1.00165 | −0.500827 | − | 0.865547i | \(-0.666971\pi\) | ||||
−0.500827 | + | 0.865547i | \(0.666971\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.6745 | −1.06066 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.58465 | −0.278376 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.3635 | −0.594852 | −0.297426 | − | 0.954745i | \(-0.596128\pi\) | ||||
−0.297426 | + | 0.954745i | \(0.596128\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.09486 | −0.0354290 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.9501 | 0.903497 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.852878 | −0.0275409 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0564 | −0.614723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.36790 | −0.237427 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.97761 | 0.224617 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.11727 | −0.164560 | −0.0822802 | − | 0.996609i | \(-0.526220\pi\) | ||||
−0.0822802 | + | 0.996609i | \(0.526220\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.7124 | 0.504754 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.0924 | −1.80009 | −0.900045 | − | 0.435797i | \(-0.856467\pi\) | ||||
−0.900045 | + | 0.435797i | \(0.856467\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.06671 | 0.0341973 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.5094 | −0.432646 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.10703 | −0.291360 | −0.145680 | − | 0.989332i | \(-0.546537\pi\) | ||||
−0.145680 | + | 0.989332i | \(0.546537\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 61.6016 | 1.96880 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.19031 | 0.293424 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.4710 | −1.19514 | −0.597570 | − | 0.801817i | \(-0.703867\pi\) | ||||
−0.597570 | + | 0.801817i | \(0.703867\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.9690 | 0.413227 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.21631 | 0.102376 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.09313 | 0.0983558 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.6068 | −1.06756 | −0.533778 | − | 0.845625i | \(-0.679228\pi\) | ||||
−0.533778 | + | 0.845625i | \(0.679228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.0207 | 0.413200 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.94546 | −0.251888 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.8355 | −0.343164 | −0.171582 | − | 0.985170i | \(-0.554888\pi\) | ||||
−0.171582 | + | 0.985170i | \(0.554888\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.26640 | 0.134983 |
(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 | 4008.2.a.l.1.6 | ✓ | 12 | |
4.3 | odd | 2 | 8016.2.a.bf.1.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.l.1.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8016.2.a.bf.1.6 | 12 | 4.3 | odd | 2 |