Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4704,2,Mod(1,4704)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4704, 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("4704.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4704 = 2^{5} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4704.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: | \(37.5616291108\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4704.1 |
$q$-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 | ||||||||
\(5\) | 3.46410 | 1.54919 | 0.774597 | − | 0.632456i | \(-0.217953\pi\) | ||||
0.774597 | + | 0.632456i | \(0.217953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.46410 | −1.64749 | −0.823744 | − | 0.566961i | \(-0.808119\pi\) | ||||
−0.823744 | + | 0.566961i | \(0.808119\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.46410 | 0.894427 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.46410 | −1.81031 | −0.905155 | − | 0.425081i | \(-0.860246\pi\) | ||||
−0.905155 | + | 0.425081i | \(0.860246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.92820 | −1.58944 | −0.794719 | − | 0.606977i | \(-0.792382\pi\) | ||||
−0.794719 | + | 0.606977i | \(0.792382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.46410 | −1.13934 | −0.569672 | − | 0.821872i | \(-0.692930\pi\) | ||||
−0.569672 | + | 0.821872i | \(0.692930\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.00000 | 1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.92820 | 1.65793 | 0.828963 | − | 0.559304i | \(-0.188931\pi\) | ||||
0.828963 | + | 0.559304i | \(0.188931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.92820 | 0.525921 | 0.262960 | − | 0.964807i | \(-0.415301\pi\) | ||||
0.262960 | + | 0.964807i | \(0.415301\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.46410 | −0.951178 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.53590 | −0.708388 | −0.354194 | − | 0.935172i | \(-0.615245\pi\) | ||||
−0.354194 | + | 0.935172i | \(0.615245\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.46410 | 0.516398 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.92820 | −0.427122 | −0.213561 | − | 0.976930i | \(-0.568506\pi\) | ||||
−0.213561 | + | 0.976930i | \(0.568506\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.46410 | −1.04518 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.9282 | −2.55228 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.92820 | −0.917663 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.9282 | −1.94349 | −0.971743 | − | 0.236040i | \(-0.924150\pi\) | ||||
−0.971743 | + | 0.236040i | \(0.924150\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.92820 | −0.630992 | −0.315496 | − | 0.948927i | \(-0.602171\pi\) | ||||
−0.315496 | + | 0.948927i | \(0.602171\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.92820 | −0.859338 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.9282 | −1.33509 | −0.667546 | − | 0.744568i | \(-0.732655\pi\) | ||||
−0.667546 | + | 0.744568i | \(0.732655\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.46410 | −0.657801 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.53590 | −0.300956 | −0.150478 | − | 0.988613i | \(-0.548081\pi\) | ||||
−0.150478 | + | 0.988613i | \(0.548081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.928203 | 0.108638 | 0.0543190 | − | 0.998524i | \(-0.482701\pi\) | ||||
0.0543190 | + | 0.998524i | \(0.482701\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.00000 | 0.808290 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.92820 | −0.329449 | −0.164724 | − | 0.986340i | \(-0.552673\pi\) | ||||
−0.164724 | + | 0.986340i | \(0.552673\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −25.8564 | −2.80452 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.92820 | 0.957204 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.46410 | 0.367194 | 0.183597 | − | 0.983002i | \(-0.441226\pi\) | ||||
0.183597 | + | 0.983002i | \(0.441226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.92820 | 0.303641 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −24.0000 | −2.46235 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.92820 | −0.500383 | −0.250192 | − | 0.968196i | \(-0.580494\pi\) | ||||
−0.250192 | + | 0.968196i | \(0.580494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.46410 | −0.549163 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.53590 | 0.849354 | 0.424677 | − | 0.905345i | \(-0.360388\pi\) | ||||
0.424677 | + | 0.905345i | \(0.360388\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.92820 | 0.288524 | 0.144262 | − | 0.989539i | \(-0.453919\pi\) | ||||
0.144262 | + | 0.989539i | \(0.453919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.39230 | 0.811315 | 0.405657 | − | 0.914025i | \(-0.367043\pi\) | ||||
0.405657 | + | 0.914025i | \(0.367043\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.85641 | 0.739069 | 0.369534 | − | 0.929217i | \(-0.379517\pi\) | ||||
0.369534 | + | 0.929217i | \(0.379517\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.9282 | −1.76506 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.8564 | 1.71422 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.53590 | −0.408988 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9282 | 0.969721 | 0.484861 | − | 0.874591i | \(-0.338870\pi\) | ||||
0.484861 | + | 0.874591i | \(0.338870\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.46410 | 0.298142 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.92820 | 0.421045 | 0.210522 | − | 0.977589i | \(-0.432484\pi\) | ||||
0.210522 | + | 0.977589i | \(0.432484\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.85641 | 0.836009 | 0.418005 | − | 0.908445i | \(-0.362730\pi\) | ||||
0.418005 | + | 0.908445i | \(0.362730\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.92820 | −0.246599 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.9282 | 0.913862 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30.9282 | 2.56845 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.85641 | 0.476588 | 0.238294 | − | 0.971193i | \(-0.423412\pi\) | ||||
0.238294 | + | 0.971193i | \(0.423412\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.46410 | −0.603437 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.1436 | 0.814753 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.9282 | −1.03178 | −0.515891 | − | 0.856654i | \(-0.672539\pi\) | ||||
−0.515891 | + | 0.856654i | \(0.672539\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.92820 | 0.229355 | 0.114677 | − | 0.993403i | \(-0.463417\pi\) | ||||
0.114677 | + | 0.993403i | \(0.463417\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18.9282 | −1.47356 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.92820 | 0.226591 | 0.113296 | − | 0.993561i | \(-0.463859\pi\) | ||||
0.113296 | + | 0.993561i | \(0.463859\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.92820 | −0.529813 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.60770 | −0.122231 | −0.0611154 | − | 0.998131i | \(-0.519466\pi\) | ||||
−0.0611154 | + | 0.998131i | \(0.519466\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.9282 | −1.12207 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.53590 | −0.189542 | −0.0947710 | − | 0.995499i | \(-0.530212\pi\) | ||||
−0.0947710 | + | 0.995499i | \(0.530212\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.92820 | −0.364303 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.92820 | −0.509372 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 40.7846 | 2.98247 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.53590 | −0.183491 | −0.0917456 | − | 0.995782i | \(-0.529245\pi\) | ||||
−0.0917456 | + | 0.995782i | \(0.529245\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8564 | −0.853443 | −0.426721 | − | 0.904383i | \(-0.640332\pi\) | ||||
−0.426721 | + | 0.904383i | \(0.640332\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.92820 | −0.496139 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.8564 | 1.41471 | 0.707355 | − | 0.706858i | \(-0.249888\pi\) | ||||
0.707355 | + | 0.706858i | \(0.249888\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.8564 | −1.54936 | −0.774680 | − | 0.632354i | \(-0.782089\pi\) | ||||
−0.774680 | + | 0.632354i | \(0.782089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.9282 | −0.770816 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.7128 | −1.09743 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.46410 | −0.379781 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 37.8564 | 2.61858 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.53590 | −0.173757 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27.7128 | 1.89000 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.928203 | 0.0627222 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.9282 | 1.00418 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.0000 | −1.60716 | −0.803579 | − | 0.595198i | \(-0.797074\pi\) | ||||
−0.803579 | + | 0.595198i | \(0.797074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.07180 | −0.602116 | −0.301058 | − | 0.953606i | \(-0.597340\pi\) | ||||
−0.301058 | + | 0.953606i | \(0.597340\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.143594 | 0.00948893 | 0.00474446 | − | 0.999989i | \(-0.498490\pi\) | ||||
0.00474446 | + | 0.999989i | \(0.498490\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.928203 | −0.0608086 | −0.0304043 | − | 0.999538i | \(-0.509679\pi\) | ||||
−0.0304043 | + | 0.999538i | \(0.509679\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1436 | −0.661695 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.92820 | −0.190207 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.4641 | −1.38840 | −0.694199 | − | 0.719783i | \(-0.744241\pi\) | ||||
−0.694199 | + | 0.719783i | \(0.744241\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.9282 | 1.09044 | 0.545221 | − | 0.838293i | \(-0.316446\pi\) | ||||
0.545221 | + | 0.838293i | \(0.316446\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.8564 | 0.881662 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.9282 | −1.44722 | −0.723608 | − | 0.690212i | \(-0.757517\pi\) | ||||
−0.723608 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.8564 | 1.87706 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −25.8564 | −1.61919 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.53590 | −0.282942 | −0.141471 | − | 0.989942i | \(-0.545183\pi\) | ||||
−0.141471 | + | 0.989942i | \(0.545183\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.92820 | 0.552642 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.39230 | 0.517492 | 0.258746 | − | 0.965945i | \(-0.416691\pi\) | ||||
0.258746 | + | 0.965945i | \(0.416691\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.92820 | −0.425596 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.46410 | 0.212000 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.46410 | 0.211210 | 0.105605 | − | 0.994408i | \(-0.466322\pi\) | ||||
0.105605 | + | 0.994408i | \(0.466322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.9282 | −0.663841 | −0.331921 | − | 0.943307i | \(-0.607697\pi\) | ||||
−0.331921 | + | 0.943307i | \(0.607697\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −38.2487 | −2.30648 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.8564 | 1.67373 | 0.836865 | − | 0.547410i | \(-0.184386\pi\) | ||||
0.836865 | + | 0.547410i | \(0.184386\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.92820 | 0.175307 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.928203 | −0.0553720 | −0.0276860 | − | 0.999617i | \(-0.508814\pi\) | ||||
−0.0276860 | + | 0.999617i | \(0.508814\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.07180 | −0.0637117 | −0.0318559 | − | 0.999492i | \(-0.510142\pi\) | ||||
−0.0318559 | + | 0.999492i | \(0.510142\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −24.0000 | −1.42164 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.7128 | 2.27722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.92820 | −0.288896 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.4641 | −1.37079 | −0.685394 | − | 0.728173i | \(-0.740370\pi\) | ||||
−0.685394 | + | 0.728173i | \(0.740370\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −51.7128 | −3.01084 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.46410 | −0.317059 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.9282 | 0.631994 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.53590 | 0.490375 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.0718 | −0.977528 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.07180 | 0.517755 | 0.258877 | − | 0.965910i | \(-0.416647\pi\) | ||||
0.258877 | + | 0.965910i | \(0.416647\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.92820 | 0.166580 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.07180 | 0.287595 | 0.143798 | − | 0.989607i | \(-0.454069\pi\) | ||||
0.143798 | + | 0.989607i | \(0.454069\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.8564 | 1.56457 | 0.782286 | − | 0.622920i | \(-0.214054\pi\) | ||||
0.782286 | + | 0.622920i | \(0.214054\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −48.7846 | −2.73141 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.39230 | 0.468413 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 51.7128 | 2.87738 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.0000 | −0.776580 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.00000 | −0.110600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.0000 | −1.31916 | −0.659580 | − | 0.751635i | \(-0.729266\pi\) | ||||
−0.659580 | + | 0.751635i | \(0.729266\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.00000 | −0.109599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −37.8564 | −2.06832 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.8564 | −1.08165 | −0.540824 | − | 0.841136i | \(-0.681887\pi\) | ||||
−0.540824 | + | 0.841136i | \(0.681887\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.85641 | 0.426701 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.0000 | −0.866449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18.9282 | −1.01906 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.3205 | 0.607717 | 0.303858 | − | 0.952717i | \(-0.401725\pi\) | ||||
0.303858 | + | 0.952717i | \(0.401725\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.7846 | 1.64786 | 0.823931 | − | 0.566690i | \(-0.191776\pi\) | ||||
0.823931 | + | 0.566690i | \(0.191776\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.4641 | −0.823071 | −0.411536 | − | 0.911394i | \(-0.635007\pi\) | ||||
−0.411536 | + | 0.911394i | \(0.635007\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.78461 | −0.466239 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.3205 | 1.44192 | 0.720961 | − | 0.692976i | \(-0.243701\pi\) | ||||
0.720961 | + | 0.692976i | \(0.243701\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.0000 | 1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.8564 | 0.989705 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.21539 | 0.168301 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.53590 | −0.236129 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.0000 | 1.55334 | 0.776671 | − | 0.629907i | \(-0.216907\pi\) | ||||
0.776671 | + | 0.629907i | \(0.216907\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.92820 | 0.357771 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.8564 | −0.919652 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000 | 0.410932 | 0.205466 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205466 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.9282 | 0.559869 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.7128 | −1.00728 | −0.503639 | − | 0.863914i | \(-0.668006\pi\) | ||||
−0.503639 | + | 0.863914i | \(0.668006\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.00000 | 0.406663 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.7846 | −1.35803 | −0.679017 | − | 0.734123i | \(-0.737594\pi\) | ||||
−0.679017 | + | 0.734123i | \(0.737594\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.7846 | 2.06257 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000 | 0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.1436 | −0.510380 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.7846 | 1.54504 | 0.772518 | − | 0.634993i | \(-0.218997\pi\) | ||||
0.772518 | + | 0.634993i | \(0.218997\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.92820 | −0.445853 | −0.222927 | − | 0.974835i | \(-0.571561\pi\) | ||||
−0.222927 | + | 0.974835i | \(0.571561\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.85641 | −0.291728 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.46410 | 0.172133 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.9282 | 0.541691 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.92820 | 0.441471 | 0.220736 | − | 0.975334i | \(-0.429154\pi\) | ||||
0.220736 | + | 0.975334i | \(0.429154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.92820 | 0.243090 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.8564 | −0.680184 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.85641 | 0.482670 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.9282 | 1.51094 | 0.755471 | − | 0.655182i | \(-0.227408\pi\) | ||||
0.755471 | + | 0.655182i | \(0.227408\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.8564 | −1.55259 | −0.776293 | − | 0.630372i | \(-0.782902\pi\) | ||||
−0.776293 | + | 0.630372i | \(0.782902\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.92820 | −0.142374 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −52.2487 | −2.53443 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.9282 | 0.527619 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.2487 | −1.84238 | −0.921188 | − | 0.389118i | \(-0.872780\pi\) | ||||
−0.921188 | + | 0.389118i | \(0.872780\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.143594 | 0.00690067 | 0.00345033 | − | 0.999994i | \(-0.498902\pi\) | ||||
0.00345033 | + | 0.999994i | \(0.498902\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 30.9282 | 1.48289 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 37.8564 | 1.81092 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.8564 | −0.661330 | −0.330665 | − | 0.943748i | \(-0.607273\pi\) | ||||
−0.330665 | + | 0.943748i | \(0.607273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.60770 | 0.361453 | 0.180726 | − | 0.983533i | \(-0.442155\pi\) | ||||
0.180726 | + | 0.983533i | \(0.442155\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | 0.568855 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.0000 | −0.851371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.8564 | −0.937082 | −0.468541 | − | 0.883442i | \(-0.655220\pi\) | ||||
−0.468541 | + | 0.883442i | \(0.655220\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.7846 | 1.16706 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.85641 | 0.275158 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.7128 | −0.828570 | −0.414285 | − | 0.910147i | \(-0.635968\pi\) | ||||
−0.414285 | + | 0.910147i | \(0.635968\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.46410 | −0.348394 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.1769 | −1.63835 | −0.819176 | − | 0.573542i | \(-0.805569\pi\) | ||||
−0.819176 | + | 0.573542i | \(0.805569\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.78461 | 0.408255 | 0.204128 | − | 0.978944i | \(-0.434564\pi\) | ||||
0.204128 | + | 0.978944i | \(0.434564\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.1436 | 0.470398 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.7846 | −0.961797 | −0.480899 | − | 0.876776i | \(-0.659689\pi\) | ||||
−0.480899 | + | 0.876776i | \(0.659689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.9282 | −0.595700 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −43.7128 | −2.00992 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −48.4974 | −2.22521 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.9282 | −0.864852 | −0.432426 | − | 0.901670i | \(-0.642342\pi\) | ||||
−0.432426 | + | 0.901670i | \(0.642342\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.0718 | −0.775190 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.7128 | −1.25579 | −0.627894 | − | 0.778299i | \(-0.716083\pi\) | ||||
−0.627894 | + | 0.778299i | \(0.716083\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.92820 | 0.132418 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.4641 | 0.607626 | 0.303813 | − | 0.952732i | \(-0.401740\pi\) | ||||
0.303813 | + | 0.952732i | \(0.401740\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −66.6410 | −3.00136 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.9282 | −0.850759 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.85641 | −0.262169 | −0.131084 | − | 0.991371i | \(-0.541846\pi\) | ||||
−0.131084 | + | 0.991371i | \(0.541846\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.92820 | 0.130822 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.0000 | −0.713405 | −0.356702 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356702 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.5692 | 1.31581 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | −0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.24871 | −0.365618 | −0.182809 | − | 0.983148i | \(-0.558519\pi\) | ||||
−0.182809 | + | 0.983148i | \(0.558519\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.92820 | −0.305888 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.1436 | 0.446980 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.0000 | 0.703679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.60770 | −0.0705700 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.60770 | −0.420921 | −0.210460 | − | 0.977602i | \(-0.567496\pi\) | ||||
−0.210460 | + | 0.977602i | \(0.567496\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.0000 | 1.22435 | 0.612177 | − | 0.790721i | \(-0.290294\pi\) | ||||
0.612177 | + | 0.790721i | \(0.290294\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.8564 | −0.952080 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.85641 | 0.298105 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.9282 | −0.647829 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.07180 | 0.392943 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.0718 | 1.25688 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.53590 | −0.109432 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.8564 | 0.853694 | 0.426847 | − | 0.904324i | \(-0.359624\pi\) | ||||
0.426847 | + | 0.904324i | \(0.359624\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.00000 | 0.257485 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.92820 | −0.296772 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.92820 | 0.125201 | 0.0626005 | − | 0.998039i | \(-0.480061\pi\) | ||||
0.0626005 | + | 0.998039i | \(0.480061\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.92820 | −0.210331 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −61.8564 | −2.63517 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.92820 | −0.294086 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.8564 | −1.34980 | −0.674900 | − | 0.737910i | \(-0.735813\pi\) | ||||
−0.674900 | + | 0.737910i | \(0.735813\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.7846 | 1.72193 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 46.9282 | 1.97779 | 0.988894 | − | 0.148623i | \(-0.0474840\pi\) | ||||
0.988894 | + | 0.148623i | \(0.0474840\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.2154 | 1.14496 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.0718 | −0.464154 | −0.232077 | − | 0.972697i | \(-0.574552\pi\) | ||||
−0.232077 | + | 0.972697i | \(0.574552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.7846 | 1.03720 | 0.518602 | − | 0.855016i | \(-0.326453\pi\) | ||||
0.518602 | + | 0.855016i | \(0.326453\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.53590 | −0.105939 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.2487 | −1.59508 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.85641 | 0.160544 | 0.0802722 | − | 0.996773i | \(-0.474421\pi\) | ||||
0.0802722 | + | 0.996773i | \(0.474421\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.8564 | −0.492735 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.9282 | 0.452600 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.92820 | −0.286446 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.7846 | 0.857873 | 0.428936 | − | 0.903335i | \(-0.358888\pi\) | ||||
0.428936 | + | 0.903335i | \(0.358888\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.2872 | −0.835919 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.8564 | 0.816783 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.4641 | −0.635035 | −0.317517 | − | 0.948252i | \(-0.602849\pi\) | ||||
−0.317517 | + | 0.948252i | \(0.602849\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.8564 | −0.894523 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.60770 | 0.310842 | 0.155421 | − | 0.987848i | \(-0.450327\pi\) | ||||
0.155421 | + | 0.987848i | \(0.450327\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.5692 | 1.61406 | 0.807031 | − | 0.590509i | \(-0.201073\pi\) | ||||
0.807031 | + | 0.590509i | \(0.201073\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.9282 | −0.445031 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 65.3205 | 2.65566 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.8564 | −0.562414 | −0.281207 | − | 0.959647i | \(-0.590735\pi\) | ||||
−0.281207 | + | 0.959647i | \(0.590735\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.85641 | 0.236925 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.143594 | 0.00579969 | 0.00289984 | − | 0.999996i | \(-0.499077\pi\) | ||||
0.00289984 | + | 0.999996i | \(0.499077\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.7128 | −0.633602 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.7846 | −0.917274 | −0.458637 | − | 0.888624i | \(-0.651662\pi\) | ||||
−0.458637 | + | 0.888624i | \(0.651662\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.46410 | −0.219267 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 37.8564 | 1.51184 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.9282 | 0.595226 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.0718 | −0.520380 | −0.260190 | − | 0.965557i | \(-0.583785\pi\) | ||||
−0.260190 | + | 0.965557i | \(0.583785\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.0000 | 0.635943 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.8564 | 1.50229 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.53590 | −0.100319 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.7846 | 1.37391 | 0.686955 | − | 0.726700i | \(-0.258947\pi\) | ||||
0.686955 | + | 0.726700i | \(0.258947\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.7846 | 1.13515 | 0.567577 | − | 0.823320i | \(-0.307881\pi\) | ||||
0.567577 | + | 0.823320i | \(0.307881\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.7128 | 1.09119 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.9282 | −0.744144 | −0.372072 | − | 0.928204i | \(-0.621353\pi\) | ||||
−0.372072 | + | 0.928204i | \(0.621353\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 81.5692 | 3.20187 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.07180 | −0.276741 | −0.138370 | − | 0.990381i | \(-0.544186\pi\) | ||||
−0.138370 | + | 0.990381i | \(0.544186\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41.5692 | 1.62424 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.928203 | 0.0362127 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.4641 | −0.836123 | −0.418061 | − | 0.908419i | \(-0.637290\pi\) | ||||
−0.418061 | + | 0.908419i | \(0.637290\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.7846 | 0.575055 | 0.287527 | − | 0.957772i | \(-0.407167\pi\) | ||||
0.287527 | + | 0.957772i | \(0.407167\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.9282 | 0.579763 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.7846 | −1.88895 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.0000 | −0.927894 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.9282 | 1.03955 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.14359 | 0.159724 | 0.0798619 | − | 0.996806i | \(-0.474552\pi\) | ||||
0.0798619 | + | 0.996806i | \(0.474552\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.00000 | 0.269430 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.3923 | 0.860606 | 0.430303 | − | 0.902684i | \(-0.358407\pi\) | ||||
0.430303 | + | 0.902684i | \(0.358407\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.07180 | −0.347632 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.2487 | −1.15743 | −0.578717 | − | 0.815528i | \(-0.696447\pi\) | ||||
−0.578717 | + | 0.815528i | \(0.696447\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.0718 | 0.652280 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.143594 | 0.00547844 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.00000 | 0.152388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.1436 | −0.538048 | −0.269024 | − | 0.963134i | \(-0.586701\pi\) | ||||
−0.269024 | + | 0.963134i | \(0.586701\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 34.1436 | 1.29514 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.8564 | 1.28240 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.928203 | −0.0351079 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.6410 | −1.53499 | −0.767495 | − | 0.641055i | \(-0.778497\pi\) | ||||
−0.767495 | + | 0.641055i | \(0.778497\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.8564 | 0.522604 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.1436 | −0.382030 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.7128 | −1.41633 | −0.708167 | − | 0.706045i | \(-0.750478\pi\) | ||||
−0.708167 | + | 0.706045i | \(0.750478\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.92820 | −0.109816 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.0000 | −0.599205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.8564 | 1.41575 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.4641 | −0.801592 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.8564 | 0.516757 | 0.258378 | − | 0.966044i | \(-0.416812\pi\) | ||||
0.258378 | + | 0.966044i | \(0.416812\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.9282 | 0.629567 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 62.4974 | 2.32110 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.9282 | 1.29542 | 0.647708 | − | 0.761889i | \(-0.275728\pi\) | ||||
0.647708 | + | 0.761889i | \(0.275728\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −59.7128 | −2.20856 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.7128 | 1.83618 | 0.918092 | − | 0.396367i | \(-0.129729\pi\) | ||||
0.918092 | + | 0.396367i | \(0.129729\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 59.7128 | 2.19955 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.9282 | 1.87342 | 0.936712 | − | 0.350101i | \(-0.113853\pi\) | ||||
0.936712 | + | 0.350101i | \(0.113853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.8564 | 0.509028 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.3923 | −1.18836 | −0.594179 | − | 0.804333i | \(-0.702523\pi\) | ||||
−0.594179 | + | 0.804333i | \(0.702523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −62.3538 | −2.28447 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.00000 | −0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.7128 | 1.01125 | 0.505627 | − | 0.862752i | \(-0.331261\pi\) | ||||
0.505627 | + | 0.862752i | \(0.331261\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.9282 | −0.835550 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.2872 | 0.738326 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.0000 | −0.944986 | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||||
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.8564 | 1.08372 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.5359 | −0.744426 | −0.372213 | − | 0.928147i | \(-0.621401\pi\) | ||||
−0.372213 | + | 0.928147i | \(0.621401\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −25.8564 | −0.934840 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29.8564 | 1.07805 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.8564 | −1.14877 | −0.574386 | − | 0.818585i | \(-0.694759\pi\) | ||||
−0.574386 | + | 0.818585i | \(0.694759\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.53590 | −0.163356 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.3205 | −1.05459 | −0.527293 | − | 0.849684i | \(-0.676793\pi\) | ||||
−0.527293 | + | 0.849684i | \(0.676793\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.4974 | 0.736289 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.4256 | 1.12594 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8564 | 0.495821 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.92820 | 0.319068 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44.7846 | −1.59843 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.7128 | −1.13044 | −0.565220 | − | 0.824940i | \(-0.691209\pi\) | ||||
−0.565220 | + | 0.824940i | \(0.691209\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.39230 | 0.298774 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.85641 | 0.350011 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.92820 | −0.245718 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.3923 | 0.509802 | 0.254901 | − | 0.966967i | \(-0.417957\pi\) | ||||
0.254901 | + | 0.966967i | \(0.417957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.8564 | 0.773224 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.46410 | 0.122398 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.07180 | −0.178980 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.46410 | 0.121942 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.0000 | −1.33601 | −0.668004 | − | 0.744157i | \(-0.732851\pi\) | ||||
−0.668004 | + | 0.744157i | \(0.732851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.5692 | 1.60015 | 0.800076 | − | 0.599899i | \(-0.204793\pi\) | ||||
0.800076 | + | 0.599899i | \(0.204793\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.9282 | −0.383269 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.1436 | 0.355315 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −55.4256 | −1.93910 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.8564 | −1.39100 | −0.695499 | − | 0.718527i | \(-0.744817\pi\) | ||||
−0.695499 | + | 0.718527i | \(0.744817\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.9282 | 1.21752 | 0.608760 | − | 0.793354i | \(-0.291667\pi\) | ||||
0.608760 | + | 0.793354i | \(0.291667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −38.2487 | −1.33165 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.1769 | −0.875487 | −0.437744 | − | 0.899100i | \(-0.644222\pi\) | ||||
−0.437744 | + | 0.899100i | \(0.644222\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.7128 | 1.17089 | 0.585447 | − | 0.810711i | \(-0.300919\pi\) | ||||
0.585447 | + | 0.810711i | \(0.300919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.8564 | 0.966328 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.1436 | 0.351034 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.92820 | 0.101214 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.92820 | 0.101093 | 0.0505464 | − | 0.998722i | \(-0.483904\pi\) | ||||
0.0505464 | + | 0.998722i | \(0.483904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.7128 | 1.74872 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.928203 | −0.0319690 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31.1769 | −1.07252 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.07180 | −0.0367840 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.9282 | 0.374614 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.9282 | −1.26440 | −0.632199 | − | 0.774806i | \(-0.717847\pi\) | ||||
−0.632199 | + | 0.774806i | \(0.717847\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24.0000 | −0.820783 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.17691 | 0.245159 | 0.122579 | − | 0.992459i | \(-0.460883\pi\) | ||||
0.122579 | + | 0.992459i | \(0.460883\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.0718 | −0.855439 | −0.427719 | − | 0.903912i | \(-0.640683\pi\) | ||||
−0.427719 | + | 0.903912i | \(0.640683\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.53590 | 0.0863230 | 0.0431615 | − | 0.999068i | \(-0.486257\pi\) | ||||
0.0431615 | + | 0.999068i | \(0.486257\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.56922 | −0.189359 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.7128 | 1.31476 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.0000 | 0.542763 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.8564 | 0.740576 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.92820 | −0.166794 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.8564 | 1.21078 | 0.605392 | − | 0.795927i | \(-0.293016\pi\) | ||||
0.605392 | + | 0.795927i | \(0.293016\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.4641 | −0.791425 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.3205 | −0.718306 | −0.359153 | − | 0.933279i | \(-0.616934\pi\) | ||||
−0.359153 | + | 0.933279i | \(0.616934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.5692 | −1.66814 | −0.834069 | − | 0.551661i | \(-0.813994\pi\) | ||||
−0.834069 | + | 0.551661i | \(0.813994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −51.7128 | −1.73831 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.0718 | −0.438908 | −0.219454 | − | 0.975623i | \(-0.570428\pi\) | ||||
−0.219454 | + | 0.975623i | \(0.570428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.46410 | −0.183054 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.2872 | 0.678885 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.78461 | −0.293637 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.9282 | 0.364882 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.1436 | 0.871938 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.9282 | 0.497331 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.7846 | 0.690904 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.7128 | −0.388918 | −0.194459 | − | 0.980911i | \(-0.562295\pi\) | ||||
−0.194459 | + | 0.980911i | \(0.562295\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.53590 | 0.283118 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.1769 | 1.09920 | 0.549600 | − | 0.835428i | \(-0.314780\pi\) | ||||
0.549600 | + | 0.835428i | \(0.314780\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.8564 | 0.723341 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.0718 | −0.564376 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.0000 | 1.31948 | 0.659739 | − | 0.751495i | \(-0.270667\pi\) | ||||
0.659739 | + | 0.751495i | \(0.270667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.07180 | 0.298926 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.07180 | 0.166940 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.0000 | −0.460317 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.92820 | 0.0961748 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.3923 | −1.12837 | −0.564187 | − | 0.825647i | \(-0.690810\pi\) | ||||
−0.564187 | + | 0.825647i | \(0.690810\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.07180 | 0.166043 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 141.282 | 4.62042 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.0000 | −0.849383 | −0.424691 | − | 0.905338i | \(-0.639617\pi\) | ||||
−0.424691 | + | 0.905338i | \(0.639617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000 | 0.456873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.4641 | 1.41689 | 0.708445 | − | 0.705766i | \(-0.249397\pi\) | ||||
0.708445 | + | 0.705766i | \(0.249397\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.7846 | 0.807098 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.2487 | 0.722986 | 0.361493 | − | 0.932375i | \(-0.382267\pi\) | ||||
0.361493 | + | 0.932375i | \(0.382267\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.85641 | −0.0602615 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.8564 | 0.903306 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.0000 | −0.712650 | −0.356325 | − | 0.934362i | \(-0.615970\pi\) | ||||
−0.356325 | + | 0.934362i | \(0.615970\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.78461 | −0.284263 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −48.7846 | −1.57698 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.4256 | −0.723407 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.39230 | 0.270438 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −41.0718 | −1.32215 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.0718 | −0.677623 | −0.338812 | − | 0.940854i | \(-0.610025\pi\) | ||||
−0.338812 | + | 0.940854i | \(0.610025\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 51.7128 | 1.66125 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.8564 | −0.829772 | −0.414886 | − | 0.909873i | \(-0.636178\pi\) | ||||
−0.414886 | + | 0.909873i | \(0.636178\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.0000 | −0.448359 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −58.4974 | −1.87150 | −0.935749 | − | 0.352666i | \(-0.885275\pi\) | ||||
−0.935749 | + | 0.352666i | \(0.885275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.9282 | −0.604948 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.7128 | 1.64938 | 0.824691 | − | 0.565583i | \(-0.191349\pi\) | ||||
0.824691 | + | 0.565583i | \(0.191349\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 68.7846 | 2.19166 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −43.7128 | −1.38999 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0000 | 1.27064 | 0.635321 | − | 0.772248i | \(-0.280868\pi\) | ||||
0.635321 | + | 0.772248i | \(0.280868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.0000 | −0.761617 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −75.7128 | −2.40026 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.9282 | −1.42289 | −0.711445 | − | 0.702742i | \(-0.751959\pi\) | ||||
−0.711445 | + | 0.702742i | \(0.751959\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 4704.2.a.bn.1.2 | 2 | ||
4.3 | odd | 2 | 4704.2.a.bm.1.2 | 2 | |||
7.6 | odd | 2 | 672.2.a.i.1.1 | ✓ | 2 | ||
8.3 | odd | 2 | 9408.2.a.dx.1.1 | 2 | |||
8.5 | even | 2 | 9408.2.a.do.1.1 | 2 | |||
21.20 | even | 2 | 2016.2.a.t.1.2 | 2 | |||
28.27 | even | 2 | 672.2.a.j.1.1 | yes | 2 | ||
56.13 | odd | 2 | 1344.2.a.v.1.2 | 2 | |||
56.27 | even | 2 | 1344.2.a.u.1.2 | 2 | |||
84.83 | odd | 2 | 2016.2.a.s.1.2 | 2 | |||
112.13 | odd | 4 | 5376.2.c.bh.2689.2 | 4 | |||
112.27 | even | 4 | 5376.2.c.bn.2689.1 | 4 | |||
112.69 | odd | 4 | 5376.2.c.bh.2689.3 | 4 | |||
112.83 | even | 4 | 5376.2.c.bn.2689.4 | 4 | |||
168.83 | odd | 2 | 4032.2.a.br.1.1 | 2 | |||
168.125 | even | 2 | 4032.2.a.bs.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.a.i.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
672.2.a.j.1.1 | yes | 2 | 28.27 | even | 2 | ||
1344.2.a.u.1.2 | 2 | 56.27 | even | 2 | |||
1344.2.a.v.1.2 | 2 | 56.13 | odd | 2 | |||
2016.2.a.s.1.2 | 2 | 84.83 | odd | 2 | |||
2016.2.a.t.1.2 | 2 | 21.20 | even | 2 | |||
4032.2.a.br.1.1 | 2 | 168.83 | odd | 2 | |||
4032.2.a.bs.1.1 | 2 | 168.125 | even | 2 | |||
4704.2.a.bm.1.2 | 2 | 4.3 | odd | 2 | |||
4704.2.a.bn.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5376.2.c.bh.2689.2 | 4 | 112.13 | odd | 4 | |||
5376.2.c.bh.2689.3 | 4 | 112.69 | odd | 4 | |||
5376.2.c.bn.2689.1 | 4 | 112.27 | even | 4 | |||
5376.2.c.bn.2689.4 | 4 | 112.83 | even | 4 | |||
9408.2.a.do.1.1 | 2 | 8.5 | even | 2 | |||
9408.2.a.dx.1.1 | 2 | 8.3 | odd | 2 |