Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3332,2,Mod(1,3332)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3332, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3332.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.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: | \(26.6061539535\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 3 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 476) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3332.1 |
$q$-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 | ||||||||
\(3\) | 1.30278 | 0.752158 | 0.376079 | − | 0.926588i | \(-0.377272\pi\) | ||||
0.376079 | + | 0.926588i | \(0.377272\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.30278 | 1.02983 | 0.514916 | − | 0.857240i | \(-0.327823\pi\) | ||||
0.514916 | + | 0.857240i | \(0.327823\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.30278 | −0.434259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.60555 | −1.83205 | −0.916025 | − | 0.401121i | \(-0.868621\pi\) | ||||
−0.916025 | + | 0.401121i | \(0.868621\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.00000 | 0.774597 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.60555 | −1.51542 | −0.757709 | − | 0.652593i | \(-0.773681\pi\) | ||||
−0.757709 | + | 0.652593i | \(0.773681\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.302776 | 0.0605551 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.60555 | −1.07879 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.30278 | −0.772801 | −0.386401 | − | 0.922331i | \(-0.626282\pi\) | ||||
−0.386401 | + | 0.922331i | \(0.626282\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.60555 | −0.428350 | −0.214175 | − | 0.976795i | \(-0.568706\pi\) | ||||
−0.214175 | + | 0.976795i | \(0.568706\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.60555 | −1.37799 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.90833 | −0.610378 | −0.305189 | − | 0.952292i | \(-0.598720\pi\) | ||||
−0.305189 | + | 0.952292i | \(0.598720\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.30278 | 1.11366 | 0.556831 | − | 0.830626i | \(-0.312017\pi\) | ||||
0.556831 | + | 0.830626i | \(0.312017\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | −0.447214 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.60555 | −0.671789 | −0.335894 | − | 0.941900i | \(-0.609039\pi\) | ||||
−0.335894 | + | 0.941900i | \(0.609039\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.30278 | −0.182425 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.69722 | −0.507853 | −0.253926 | − | 0.967224i | \(-0.581722\pi\) | ||||
−0.253926 | + | 0.967224i | \(0.581722\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.60555 | −1.13983 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.21110 | −1.19918 | −0.599592 | − | 0.800306i | \(-0.704670\pi\) | ||||
−0.599592 | + | 0.800306i | \(0.704670\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.90833 | 1.01256 | 0.506279 | − | 0.862370i | \(-0.331021\pi\) | ||||
0.506279 | + | 0.862370i | \(0.331021\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.2111 | −1.88671 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.69722 | −0.207349 | −0.103674 | − | 0.994611i | \(-0.533060\pi\) | ||||
−0.103674 | + | 0.994611i | \(0.533060\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.81665 | −0.927666 | −0.463833 | − | 0.885923i | \(-0.653526\pi\) | ||||
−0.463833 | + | 0.885923i | \(0.653526\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.90833 | 0.925600 | 0.462800 | − | 0.886463i | \(-0.346845\pi\) | ||||
0.462800 | + | 0.886463i | \(0.346845\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.394449 | 0.0455470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.6056 | 1.41824 | 0.709118 | − | 0.705090i | \(-0.249093\pi\) | ||||
0.709118 | + | 0.705090i | \(0.249093\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.39445 | −0.377161 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.30278 | −0.249771 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.6056 | 1.76018 | 0.880092 | − | 0.474802i | \(-0.157480\pi\) | ||||
0.880092 | + | 0.474802i | \(0.157480\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.60555 | −0.581269 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.2111 | −1.56063 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.30278 | 0.639950 | 0.319975 | − | 0.947426i | \(-0.396325\pi\) | ||||
0.319975 | + | 0.947426i | \(0.396325\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −19.8167 | −1.97183 | −0.985915 | − | 0.167245i | \(-0.946513\pi\) | ||||
−0.985915 | + | 0.167245i | \(0.946513\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.21110 | 0.710531 | 0.355266 | − | 0.934765i | \(-0.384390\pi\) | ||||
0.355266 | + | 0.934765i | \(0.384390\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.39445 | −0.134806 | −0.0674032 | − | 0.997726i | \(-0.521471\pi\) | ||||
−0.0674032 | + | 0.997726i | \(0.521471\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.42221 | 0.806701 | 0.403350 | − | 0.915046i | \(-0.367846\pi\) | ||||
0.403350 | + | 0.915046i | \(0.367846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.39445 | −0.322187 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.60555 | 0.433254 | 0.216627 | − | 0.976254i | \(-0.430494\pi\) | ||||
0.216627 | + | 0.976254i | \(0.430494\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.60555 | 0.795583 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.09167 | −0.459101 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.8167 | −0.967471 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9083 | 1.32290 | 0.661450 | − | 0.749989i | \(-0.269941\pi\) | ||||
0.661450 | + | 0.749989i | \(0.269941\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.51388 | 0.837650 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.2111 | 1.85322 | 0.926611 | − | 0.376021i | \(-0.122708\pi\) | ||||
0.926611 | + | 0.376021i | \(0.122708\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.9083 | −1.11097 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.6972 | −1.08480 | −0.542399 | − | 0.840121i | \(-0.682484\pi\) | ||||
−0.542399 | + | 0.840121i | \(0.682484\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.09167 | −0.601508 | −0.300754 | − | 0.953702i | \(-0.597238\pi\) | ||||
−0.300754 | + | 0.953702i | \(0.597238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.7250 | 1.45209 | 0.726044 | − | 0.687649i | \(-0.241357\pi\) | ||||
0.726044 | + | 0.687649i | \(0.241357\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1194 | −0.904886 | −0.452443 | − | 0.891793i | \(-0.649447\pi\) | ||||
−0.452443 | + | 0.891793i | \(0.649447\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.30278 | 0.105323 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.90833 | −0.795856 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.21110 | 0.575509 | 0.287754 | − | 0.957704i | \(-0.407091\pi\) | ||||
0.287754 | + | 0.957704i | \(0.407091\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.81665 | −0.381985 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.6056 | 0.987343 | 0.493671 | − | 0.869648i | \(-0.335655\pi\) | ||||
0.493671 | + | 0.869648i | \(0.335655\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.7250 | 1.83589 | 0.917947 | − | 0.396703i | \(-0.129846\pi\) | ||||
0.917947 | + | 0.396703i | \(0.129846\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.6333 | 2.35641 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.60555 | 0.658083 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.3028 | −1.31551 | −0.657753 | − | 0.753234i | \(-0.728493\pi\) | ||||
−0.657753 | + | 0.753234i | \(0.728493\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.0000 | −0.901975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.90833 | 0.740583 | 0.370292 | − | 0.928916i | \(-0.379258\pi\) | ||||
0.370292 | + | 0.928916i | \(0.379258\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.3028 | 0.761603 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | −0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.7250 | 1.49961 | 0.749803 | − | 0.661661i | \(-0.230148\pi\) | ||||
0.749803 | + | 0.661661i | \(0.230148\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8167 | −0.850581 | −0.425291 | − | 0.905057i | \(-0.639828\pi\) | ||||
−0.425291 | + | 0.905057i | \(0.639828\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19.8167 | −1.41910 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.60555 | −0.328132 | −0.164066 | − | 0.986449i | \(-0.552461\pi\) | ||||
−0.164066 | + | 0.986449i | \(0.552461\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.1194 | −1.49712 | −0.748558 | − | 0.663069i | \(-0.769254\pi\) | ||||
−0.748558 | + | 0.663069i | \(0.769254\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.21110 | −0.155959 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | −0.628587 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.0278 | −1.44761 | −0.723805 | − | 0.690004i | \(-0.757609\pi\) | ||||
−0.723805 | + | 0.690004i | \(0.757609\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.1833 | −0.697751 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.8167 | 1.14689 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.3028 | 0.696197 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.60555 | 0.444337 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.02776 | 0.604543 | 0.302272 | − | 0.953222i | \(-0.402255\pi\) | ||||
0.302272 | + | 0.953222i | \(0.402255\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.394449 | −0.0262966 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.51388 | −0.365969 | −0.182984 | − | 0.983116i | \(-0.558576\pi\) | ||||
−0.182984 | + | 0.983116i | \(0.558576\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.7889 | −0.712950 | −0.356475 | − | 0.934305i | \(-0.616022\pi\) | ||||
−0.356475 | + | 0.934305i | \(0.616022\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.8167 | −0.905159 | −0.452580 | − | 0.891724i | \(-0.649496\pi\) | ||||
−0.452580 | + | 0.891724i | \(0.649496\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.6056 | −0.691830 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.4222 | 1.06674 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3028 | 0.731116 | 0.365558 | − | 0.930789i | \(-0.380878\pi\) | ||||
0.365558 | + | 0.930789i | \(0.380878\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.48612 | −0.546639 | −0.273320 | − | 0.961923i | \(-0.588122\pi\) | ||||
−0.273320 | + | 0.961923i | \(0.588122\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.3944 | 0.795104 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 43.6333 | 2.77632 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.81665 | −0.495360 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.18335 | −0.264050 | −0.132025 | − | 0.991246i | \(-0.542148\pi\) | ||||
−0.132025 | + | 0.991246i | \(0.542148\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.00000 | −0.187867 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.21110 | −0.200303 | −0.100152 | − | 0.994972i | \(-0.531933\pi\) | ||||
−0.100152 | + | 0.994972i | \(0.531933\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.4222 | −1.13596 | −0.567981 | − | 0.823042i | \(-0.692275\pi\) | ||||
−0.567981 | + | 0.823042i | \(0.692275\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.51388 | −0.523003 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.6333 | 1.32394 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.2111 | −0.927437 | −0.463719 | − | 0.885983i | \(-0.653485\pi\) | ||||
−0.463719 | + | 0.885983i | \(0.653485\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.21110 | 0.0735692 | 0.0367846 | − | 0.999323i | \(-0.488288\pi\) | ||||
0.0367846 | + | 0.999323i | \(0.488288\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.4222 | −1.34722 | −0.673610 | − | 0.739087i | \(-0.735257\pi\) | ||||
−0.673610 | + | 0.739087i | \(0.735257\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.60555 | 0.335596 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.69722 | 0.220558 | 0.110279 | − | 0.993901i | \(-0.464826\pi\) | ||||
0.110279 | + | 0.993901i | \(0.464826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.51388 | 0.565541 | 0.282771 | − | 0.959188i | \(-0.408746\pi\) | ||||
0.282771 | + | 0.959188i | \(0.408746\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −19.8167 | −1.17384 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.21110 | 0.481343 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.6333 | 1.26383 | 0.631916 | − | 0.775037i | \(-0.282269\pi\) | ||||
0.631916 | + | 0.775037i | \(0.282269\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.2111 | −1.23496 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.8167 | −1.48313 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.2111 | 1.04276 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.21110 | 0.0691213 | 0.0345606 | − | 0.999403i | \(-0.488997\pi\) | ||||
0.0345606 | + | 0.999403i | \(0.488997\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.39445 | 0.534432 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.88057 | 0.106637 | 0.0533187 | − | 0.998578i | \(-0.483020\pi\) | ||||
0.0533187 | + | 0.998578i | \(0.483020\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.3305 | −1.88395 | −0.941977 | − | 0.335679i | \(-0.891034\pi\) | ||||
−0.941977 | + | 0.335679i | \(0.891034\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.00000 | −0.336994 | −0.168497 | − | 0.985702i | \(-0.553891\pi\) | ||||
−0.168497 | + | 0.985702i | \(0.553891\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.81665 | −0.101396 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.60555 | 0.367543 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.9722 | 0.606766 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.69722 | 0.313148 | 0.156574 | − | 0.987666i | \(-0.449955\pi\) | ||||
0.156574 | + | 0.987666i | \(0.449955\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.39445 | 0.186015 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.90833 | −0.213535 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.0000 | −0.871576 | −0.435788 | − | 0.900049i | \(-0.643530\pi\) | ||||
−0.435788 | + | 0.900049i | \(0.643530\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.0000 | −1.61048 | −0.805242 | − | 0.592946i | \(-0.797965\pi\) | ||||
−0.805242 | + | 0.592946i | \(0.797965\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.2111 | −1.56363 | −0.781817 | − | 0.623508i | \(-0.785707\pi\) | ||||
−0.781817 | + | 0.623508i | \(0.785707\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 37.0278 | 1.97640 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6333 | 0.832077 | 0.416039 | − | 0.909347i | \(-0.363418\pi\) | ||||
0.416039 | + | 0.909347i | \(0.363418\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.0000 | −0.955341 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.90833 | 0.364608 | 0.182304 | − | 0.983242i | \(-0.441645\pi\) | ||||
0.182304 | + | 0.983242i | \(0.441645\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.6333 | 1.29649 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.3305 | −0.752158 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.2111 | 0.953213 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.33053 | −0.330451 | −0.165226 | − | 0.986256i | \(-0.552835\pi\) | ||||
−0.165226 | + | 0.986256i | \(0.552835\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.09167 | 0.265062 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.9361 | −1.60181 | −0.800905 | − | 0.598792i | \(-0.795648\pi\) | ||||
−0.800905 | + | 0.598792i | \(0.795648\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.0917 | −0.727691 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.78890 | −0.348722 | −0.174361 | − | 0.984682i | \(-0.555786\pi\) | ||||
−0.174361 | + | 0.984682i | \(0.555786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.4222 | 0.995030 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.4222 | −0.941331 | −0.470665 | − | 0.882312i | \(-0.655986\pi\) | ||||
−0.470665 | + | 0.882312i | \(0.655986\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.51388 | −0.483618 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.1194 | −0.513075 | −0.256538 | − | 0.966534i | \(-0.582582\pi\) | ||||
−0.256538 | + | 0.966534i | \(0.582582\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 27.6333 | 1.39392 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 29.0278 | 1.46054 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.9361 | 1.10094 | 0.550470 | − | 0.834855i | \(-0.314448\pi\) | ||||
0.550470 | + | 0.834855i | \(0.314448\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.6056 | −0.829242 | −0.414621 | − | 0.909994i | \(-0.636086\pi\) | ||||
−0.414621 | + | 0.909994i | \(0.636086\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.4222 | 1.41581 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.81665 | −0.388413 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.6056 | 1.31556 | 0.657780 | − | 0.753210i | \(-0.271496\pi\) | ||||
0.657780 | + | 0.753210i | \(0.271496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.5416 | −0.815939 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.8167 | −0.678233 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.23886 | −0.452429 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.5139 | 0.855609 | 0.427804 | − | 0.903871i | \(-0.359287\pi\) | ||||
0.427804 | + | 0.903871i | \(0.359287\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.9361 | −1.50773 | −0.753866 | − | 0.657028i | \(-0.771813\pi\) | ||||
−0.753866 | + | 0.657028i | \(0.771813\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.00000 | 0.291730 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.302776 | −0.0146868 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.6333 | −0.753030 | −0.376515 | − | 0.926411i | \(-0.622878\pi\) | ||||
−0.376515 | + | 0.926411i | \(0.622878\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.81665 | −0.183417 | −0.0917083 | − | 0.995786i | \(-0.529233\pi\) | ||||
−0.0917083 | + | 0.995786i | \(0.529233\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.90833 | 0.377444 | 0.188722 | − | 0.982031i | \(-0.439566\pi\) | ||||
0.188722 | + | 0.982031i | \(0.439566\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.2111 | −1.00777 | −0.503885 | − | 0.863771i | \(-0.668096\pi\) | ||||
−0.503885 | + | 0.863771i | \(0.668096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 38.2389 | 1.81270 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.0917 | 1.09220 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.2389 | −1.52145 | −0.760723 | − | 0.649077i | \(-0.775155\pi\) | ||||
−0.760723 | + | 0.649077i | \(0.775155\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.4861 | −0.680617 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.09167 | −0.144622 | −0.0723112 | − | 0.997382i | \(-0.523037\pi\) | ||||
−0.0723112 | + | 0.997382i | \(0.523037\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.60555 | 0.261645 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.8167 | 1.48185 | 0.740925 | − | 0.671588i | \(-0.234388\pi\) | ||||
0.740925 | + | 0.671588i | \(0.234388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.6972 | −0.775986 | −0.387993 | − | 0.921662i | \(-0.626832\pi\) | ||||
−0.387993 | + | 0.921662i | \(0.626832\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.9083 | −0.598609 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.4500 | 1.64043 | 0.820214 | − | 0.572056i | \(-0.193854\pi\) | ||||
0.820214 | + | 0.572056i | \(0.193854\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.39445 | 0.432873 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00000 | −0.0917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.81665 | 0.220539 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.5139 | −0.663156 | −0.331578 | − | 0.943428i | \(-0.607581\pi\) | ||||
−0.331578 | + | 0.943428i | \(0.607581\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.2111 | 0.784759 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.5139 | 0.659041 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.21110 | 0.236138 | 0.118069 | − | 0.993005i | \(-0.462330\pi\) | ||||
0.118069 | + | 0.993005i | \(0.462330\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.4222 | 0.742638 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.3305 | −1.14315 | −0.571575 | − | 0.820550i | \(-0.693668\pi\) | ||||
−0.571575 | + | 0.820550i | \(0.693668\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.57779 | 0.0706318 | 0.0353159 | − | 0.999376i | \(-0.488756\pi\) | ||||
0.0353159 | + | 0.999376i | \(0.488756\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.9083 | 1.38088 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.1472 | −0.942906 | −0.471453 | − | 0.881891i | \(-0.656270\pi\) | ||||
−0.471453 | + | 0.881891i | \(0.656270\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.6333 | −2.03066 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 39.9083 | 1.77239 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.0278 | 0.488797 | 0.244398 | − | 0.969675i | \(-0.421410\pi\) | ||||
0.244398 | + | 0.969675i | \(0.421410\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 37.0278 | 1.63482 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.6056 | 0.731728 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.5416 | −0.989468 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.3583 | −1.72432 | −0.862159 | − | 0.506638i | \(-0.830888\pi\) | ||||
−0.862159 | + | 0.506638i | \(0.830888\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.7889 | −0.471766 | −0.235883 | − | 0.971782i | \(-0.575798\pi\) | ||||
−0.235883 | + | 0.971782i | \(0.575798\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.30278 | 0.187432 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.8167 | 1.11824 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.21110 | −0.138828 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.9083 | 0.557035 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.0555 | 1.80811 | 0.904054 | − | 0.427419i | \(-0.140577\pi\) | ||||
0.904054 | + | 0.427419i | \(0.140577\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.2389 | −0.782704 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.3944 | 0.830767 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.2111 | −1.33449 | −0.667245 | − | 0.744838i | \(-0.732527\pi\) | ||||
−0.667245 | + | 0.744838i | \(0.732527\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.3028 | −0.439712 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.81665 | −0.331798 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.6333 | 1.42509 | 0.712544 | − | 0.701627i | \(-0.247543\pi\) | ||||
0.712544 | + | 0.701627i | \(0.247543\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.2389 | −2.04029 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.6333 | 1.16461 | 0.582303 | − | 0.812972i | \(-0.302152\pi\) | ||||
0.582303 | + | 0.812972i | \(0.302152\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.6056 | 0.446179 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.88057 | 0.204604 | 0.102302 | − | 0.994753i | \(-0.467379\pi\) | ||||
0.102302 | + | 0.994753i | \(0.467379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.02776 | −0.377800 | −0.188900 | − | 0.981996i | \(-0.560492\pi\) | ||||
−0.188900 | + | 0.981996i | \(0.560492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.0000 | 1.12794 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.2389 | −1.17560 | −0.587800 | − | 0.809007i | \(-0.700006\pi\) | ||||
−0.587800 | + | 0.809007i | \(0.700006\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.3944 | −0.639771 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.8167 | 0.819318 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.6056 | 0.437738 | 0.218869 | − | 0.975754i | \(-0.429763\pi\) | ||||
0.218869 | + | 0.975754i | \(0.429763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.4222 | 1.17112 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −43.8167 | −1.79933 | −0.899667 | − | 0.436576i | \(-0.856191\pi\) | ||||
−0.899667 | + | 0.436576i | \(0.856191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −27.5139 | −1.12607 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.9638 | 1.79631 | 0.898157 | − | 0.439675i | \(-0.144906\pi\) | ||||
0.898157 | + | 0.439675i | \(0.144906\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.21110 | 0.0900431 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −25.3305 | −1.02983 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5139 | 0.873221 | 0.436611 | − | 0.899651i | \(-0.356179\pi\) | ||||
0.436611 | + | 0.899651i | \(0.356179\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.4222 | 1.23075 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.1472 | 1.17724 | 0.588622 | − | 0.808408i | \(-0.299671\pi\) | ||||
0.588622 | + | 0.808408i | \(0.299671\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.7250 | −0.472797 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.0000 | −0.966204 | −0.483102 | − | 0.875564i | \(-0.660490\pi\) | ||||
−0.483102 | + | 0.875564i | \(0.660490\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.6333 | 1.75377 | 0.876885 | − | 0.480700i | \(-0.159617\pi\) | ||||
0.876885 | + | 0.480700i | \(0.159617\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.4222 | −1.05689 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.60555 | 0.103890 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.11943 | −0.323229 | −0.161615 | − | 0.986854i | \(-0.551670\pi\) | ||||
−0.161615 | + | 0.986854i | \(0.551670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −27.3944 | −1.08883 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 34.3305 | 1.36237 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.1833 | 0.402847 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.8444 | −0.507324 | −0.253662 | − | 0.967293i | \(-0.581635\pi\) | ||||
−0.253662 | + | 0.967293i | \(0.581635\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.1472 | −1.50438 | −0.752189 | − | 0.658947i | \(-0.771002\pi\) | ||||
−0.752189 | + | 0.658947i | \(0.771002\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.9083 | 0.862640 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.4222 | −0.724252 | −0.362126 | − | 0.932129i | \(-0.617949\pi\) | ||||
−0.362126 | + | 0.932129i | \(0.617949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.0555 | 1.09790 | 0.548949 | − | 0.835856i | \(-0.315028\pi\) | ||||
0.548949 | + | 0.835856i | \(0.315028\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48.8444 | 1.90851 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.3028 | −0.401950 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.3028 | 1.49206 | 0.746032 | − | 0.665910i | \(-0.231957\pi\) | ||||
0.746032 | + | 0.665910i | \(0.231957\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.1833 | 0.551668 | 0.275834 | − | 0.961205i | \(-0.411046\pi\) | ||||
0.275834 | + | 0.961205i | \(0.411046\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.60555 | 0.334212 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.7611 | 0.454712 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.1833 | −0.778011 | −0.389005 | − | 0.921235i | \(-0.627181\pi\) | ||||
−0.389005 | + | 0.921235i | \(0.627181\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.69722 | −0.0653262 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −48.4222 | −1.86102 | −0.930508 | − | 0.366271i | \(-0.880634\pi\) | ||||
−0.930508 | + | 0.366271i | \(0.880634\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.18335 | −0.275266 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.4500 | 1.58604 | 0.793019 | − | 0.609196i | \(-0.208508\pi\) | ||||
0.793019 | + | 0.609196i | \(0.208508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.2389 | −1.11716 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.0555 | −0.536251 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.4222 | 0.930412 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.4861 | −1.12170 | −0.560852 | − | 0.827916i | \(-0.689527\pi\) | ||||
−0.560852 | + | 0.827916i | \(0.689527\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.3305 | −0.619452 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.90833 | 0.148038 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.0000 | −0.680823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.8444 | −0.711744 | −0.355872 | − | 0.934535i | \(-0.615816\pi\) | ||||
−0.355872 | + | 0.934535i | \(0.615816\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.2111 | 0.649129 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.8167 | −0.520365 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.1833 | 0.457555 | 0.228778 | − | 0.973479i | \(-0.426527\pi\) | ||||
0.228778 | + | 0.973479i | \(0.426527\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.4222 | −0.615881 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.7250 | 0.549914 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.3028 | 1.09281 | 0.546405 | − | 0.837521i | \(-0.315996\pi\) | ||||
0.546405 | + | 0.837521i | \(0.315996\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.0555 | −0.411159 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.4222 | 0.831594 | 0.415797 | − | 0.909458i | \(-0.363503\pi\) | ||||
0.415797 | + | 0.909458i | \(0.363503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.3305 | 0.975205 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.30278 | −0.270103 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.2389 | 1.11690 | 0.558449 | − | 0.829539i | \(-0.311397\pi\) | ||||
0.558449 | + | 0.829539i | \(0.311397\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.3583 | −0.932820 | −0.466410 | − | 0.884569i | \(-0.654453\pi\) | ||||
−0.466410 | + | 0.884569i | \(0.654453\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 56.8444 | 2.08823 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.81665 | 0.0666466 | 0.0333233 | − | 0.999445i | \(-0.489391\pi\) | ||||
0.0333233 | + | 0.999445i | \(0.489391\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.8167 | 1.49541 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.81665 | 0.285996 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.6056 | 0.678926 | 0.339463 | − | 0.940619i | \(-0.389755\pi\) | ||||
0.339463 | + | 0.940619i | \(0.389755\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.44996 | −0.198608 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.6056 | −0.931881 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.7250 | −1.66190 | −0.830951 | − | 0.556345i | \(-0.812203\pi\) | ||||
−0.830951 | + | 0.556345i | \(0.812203\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.8167 | −1.37085 | −0.685426 | − | 0.728142i | \(-0.740384\pi\) | ||||
−0.685426 | + | 0.728142i | \(0.740384\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.00000 | 0.108465 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 60.8444 | 2.19696 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 53.2666 | 1.92084 | 0.960422 | − | 0.278550i | \(-0.0898539\pi\) | ||||
0.960422 | + | 0.278550i | \(0.0898539\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.18335 | −0.150660 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.8167 | −0.928560 | −0.464280 | − | 0.885688i | \(-0.653687\pi\) | ||||
−0.464280 | + | 0.885688i | \(0.653687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.30278 | −0.0467971 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.8167 | 0.924978 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.6056 | 0.592678 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.42221 | −0.0863423 | −0.0431711 | − | 0.999068i | \(-0.513746\pi\) | ||||
−0.0431711 | + | 0.999068i | \(0.513746\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.0000 | −0.854423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −52.2389 | −1.85506 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.0917 | −0.393381 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.422205 | −0.0149553 | −0.00747764 | − | 0.999972i | \(-0.502380\pi\) | ||||
−0.00747764 | + | 0.999972i | \(0.502380\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.60555 | 0.162933 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21.6333 | −0.764375 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.8167 | −0.697579 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.6056 | 1.42762 | 0.713808 | − | 0.700342i | \(-0.246969\pi\) | ||||
0.713808 | + | 0.700342i | \(0.246969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.09167 | −0.143678 | −0.0718390 | − | 0.997416i | \(-0.522887\pi\) | ||||
−0.0718390 | + | 0.997416i | \(0.522887\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.57779 | 0.0553357 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29.0278 | 1.01680 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −48.2389 | −1.68766 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.6056 | −0.370136 | −0.185068 | − | 0.982726i | \(-0.559251\pi\) | ||||
−0.185068 | + | 0.982726i | \(0.559251\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.8722 | 1.52929 | 0.764644 | − | 0.644453i | \(-0.222915\pi\) | ||||
0.764644 | + | 0.644453i | \(0.222915\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.6333 | 0.960904 | 0.480452 | − | 0.877021i | \(-0.340473\pi\) | ||||
0.480452 | + | 0.877021i | \(0.340473\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.6056 | 0.924049 | 0.462024 | − | 0.886867i | \(-0.347123\pi\) | ||||
0.462024 | + | 0.886867i | \(0.347123\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.2111 | −1.01332 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.6333 | 1.89066 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.1194 | 0.833689 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.4222 | −0.636005 | −0.318003 | − | 0.948090i | \(-0.603012\pi\) | ||||
−0.318003 | + | 0.948090i | \(0.603012\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.81665 | 0.165894 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 70.5416 | 2.42671 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.3944 | 0.425376 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.4222 | 0.562286 | 0.281143 | − | 0.959666i | \(-0.409287\pi\) | ||||
0.281143 | + | 0.959666i | \(0.409287\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.8167 | 0.677715 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.5416 | 1.17992 | 0.589960 | − | 0.807433i | \(-0.299144\pi\) | ||||
0.589960 | + | 0.807433i | \(0.299144\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.4500 | −1.27778 | −0.638888 | − | 0.769300i | \(-0.720605\pi\) | ||||
−0.638888 | + | 0.769300i | \(0.720605\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.9083 | 0.643647 | 0.321823 | − | 0.946800i | \(-0.395704\pi\) | ||||
0.321823 | + | 0.946800i | \(0.395704\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.8444 | −1.35475 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.30278 | 0.0442446 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.2111 | 0.379874 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.21110 | −0.277904 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.6056 | −1.10101 | −0.550506 | − | 0.834831i | \(-0.685565\pi\) | ||||
−0.550506 | + | 0.834831i | \(0.685565\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.1833 | 0.950601 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.69722 | 0.326708 | 0.163354 | − | 0.986568i | \(-0.447769\pi\) | ||||
0.163354 | + | 0.986568i | \(0.447769\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.6695 | −0.493667 | −0.246833 | − | 0.969058i | \(-0.579390\pi\) | ||||
−0.246833 | + | 0.969058i | \(0.579390\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.6333 | −0.928883 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.9083 | 1.64218 | 0.821090 | − | 0.570798i | \(-0.193366\pi\) | ||||
0.821090 | + | 0.570798i | \(0.193366\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.4222 | 1.01804 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.8167 | 0.762677 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.69722 | 0.123172 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −32.2389 | −1.07166 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.8444 | −0.758536 | −0.379268 | − | 0.925287i | \(-0.623824\pi\) | ||||
−0.379268 | + | 0.925287i | \(0.623824\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 25.8167 | 0.856284 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.8167 | 1.25292 | 0.626461 | − | 0.779453i | \(-0.284503\pi\) | ||||
0.626461 | + | 0.779453i | \(0.284503\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 23.7250 | 0.784324 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.3305 | 0.802590 | 0.401295 | − | 0.915949i | \(-0.368560\pi\) | ||||
0.401295 | + | 0.915949i | \(0.368560\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.57779 | 0.0519901 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 51.6333 | 1.69953 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.788897 | −0.0259388 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.39445 | −0.308554 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.9361 | −1.76959 | −0.884793 | − | 0.465985i | \(-0.845700\pi\) | ||||
−0.884793 | + | 0.465985i | \(0.845700\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.44996 | 0.0802081 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.78890 | 0.221784 | 0.110892 | − | 0.993832i | \(-0.464629\pi\) | ||||
0.110892 | + | 0.993832i | \(0.464629\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −43.4222 | −1.41703 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.275019 | 0.00896537 | 0.00448269 | − | 0.999990i | \(-0.498573\pi\) | ||||
0.00448269 | + | 0.999990i | \(0.498573\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.8444 | 1.58723 | 0.793615 | − | 0.608420i | \(-0.208196\pi\) | ||||
0.793615 | + | 0.608420i | \(0.208196\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −52.2389 | −1.69575 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.81665 | −0.253472 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.5139 | 0.567330 | 0.283665 | − | 0.958923i | \(-0.408450\pi\) | ||||
0.283665 | + | 0.958923i | \(0.408450\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 47.7250 | 1.54434 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.4861 | −0.402778 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.81665 | 0.0585409 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.2111 | −0.875956 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.5139 | 0.531051 | 0.265525 | − | 0.964104i | \(-0.414455\pi\) | ||||
0.265525 | + | 0.964104i | \(0.414455\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.60555 | 0.276450 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.8444 | −1.18239 | −0.591197 | − | 0.806527i | \(-0.701344\pi\) | ||||
−0.591197 | + | 0.806527i | \(0.701344\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.60555 | −0.0834444 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.1472 | −1.06047 | −0.530236 | − | 0.847850i | \(-0.677897\pi\) | ||||
−0.530236 | + | 0.847850i | \(0.677897\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.9722 | −0.350317 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.0917 | −0.736510 | −0.368255 | − | 0.929725i | \(-0.620045\pi\) | ||||
−0.368255 | + | 0.929725i | \(0.620045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.6056 | −0.337921 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.0000 | 0.444725 | 0.222362 | − | 0.974964i | \(-0.428623\pi\) | ||||
0.222362 | + | 0.974964i | \(0.428623\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.42221 | 0.235537 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48.6333 | −1.54178 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.1472 | −0.448046 | −0.224023 | − | 0.974584i | \(-0.571919\pi\) | ||||
−0.224023 | + | 0.974584i | \(0.571919\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.6056 | 0.462099 |
(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 | 3332.2.a.j.1.2 | 2 | ||
7.6 | odd | 2 | 476.2.a.d.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 4284.2.a.n.1.2 | 2 | |||
28.27 | even | 2 | 1904.2.a.h.1.2 | 2 | |||
56.13 | odd | 2 | 7616.2.a.q.1.2 | 2 | |||
56.27 | even | 2 | 7616.2.a.v.1.1 | 2 | |||
119.118 | odd | 2 | 8092.2.a.k.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
476.2.a.d.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
1904.2.a.h.1.2 | 2 | 28.27 | even | 2 | |||
3332.2.a.j.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4284.2.a.n.1.2 | 2 | 21.20 | even | 2 | |||
7616.2.a.q.1.2 | 2 | 56.13 | odd | 2 | |||
7616.2.a.v.1.1 | 2 | 56.27 | even | 2 | |||
8092.2.a.k.1.2 | 2 | 119.118 | odd | 2 |