Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9450,2,Mod(1,9450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9450, 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("9450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9450.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: | \(75.4586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{10}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.16228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9450.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.16228 | 1.15441 | 0.577204 | − | 0.816600i | \(-0.304144\pi\) | ||||
0.577204 | + | 0.816600i | \(0.304144\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.32456 | 1.77647 | 0.888233 | − | 0.459394i | \(-0.151933\pi\) | ||||
0.888233 | + | 0.459394i | \(0.151933\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | 0.688247 | 0.344124 | − | 0.938924i | \(-0.388176\pi\) | ||||
0.344124 | + | 0.938924i | \(0.388176\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | 1.16228 | 0.242352 | 0.121176 | − | 0.992631i | \(-0.461334\pi\) | ||||
0.121176 | + | 0.992631i | \(0.461334\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.16228 | 0.816290 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 1.83772 | 0.341256 | 0.170628 | − | 0.985335i | \(-0.445420\pi\) | ||||
0.170628 | + | 0.985335i | \(0.445420\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.32456 | −1.13592 | −0.567962 | − | 0.823055i | \(-0.692268\pi\) | ||||
−0.567962 | + | 0.823055i | \(0.692268\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.32456 | 1.25615 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.48683 | 1.23083 | 0.615414 | − | 0.788204i | \(-0.288989\pi\) | ||||
0.615414 | + | 0.788204i | \(0.288989\pi\) | |||||||
\(38\) | 3.00000 | 0.486664 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | 0.624695 | 0.312348 | − | 0.949968i | \(-0.398885\pi\) | ||||
0.312348 | + | 0.949968i | \(0.398885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.16228 | 0.482243 | 0.241121 | − | 0.970495i | \(-0.422485\pi\) | ||||
0.241121 | + | 0.970495i | \(0.422485\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.16228 | 0.171368 | ||||||||
\(47\) | −10.4868 | −1.52966 | −0.764831 | − | 0.644231i | \(-0.777178\pi\) | ||||
−0.764831 | + | 0.644231i | \(0.777178\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.16228 | 0.577204 | ||||||||
\(53\) | −0.162278 | −0.0222906 | −0.0111453 | − | 0.999938i | \(-0.503548\pi\) | ||||
−0.0111453 | + | 0.999938i | \(0.503548\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.83772 | 0.241305 | ||||||||
\(59\) | −0.324555 | −0.0422535 | −0.0211268 | − | 0.999777i | \(-0.506725\pi\) | ||||
−0.0211268 | + | 0.999777i | \(0.506725\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.83772 | −0.491370 | −0.245685 | − | 0.969350i | \(-0.579013\pi\) | ||||
−0.245685 | + | 0.969350i | \(0.579013\pi\) | |||||||
\(62\) | −6.32456 | −0.803219 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.48683 | −0.425984 | −0.212992 | − | 0.977054i | \(-0.568321\pi\) | ||||
−0.212992 | + | 0.977054i | \(0.568321\pi\) | |||||||
\(68\) | 7.32456 | 0.888233 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.3246 | −1.22530 | −0.612650 | − | 0.790355i | \(-0.709896\pi\) | ||||
−0.612650 | + | 0.790355i | \(0.709896\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.32456 | −0.506151 | −0.253075 | − | 0.967447i | \(-0.581442\pi\) | ||||
−0.253075 | + | 0.967447i | \(0.581442\pi\) | |||||||
\(74\) | 7.48683 | 0.870327 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.00000 | 0.344124 | ||||||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.4868 | −1.62990 | −0.814948 | − | 0.579534i | \(-0.803235\pi\) | ||||
−0.814948 | + | 0.579534i | \(0.803235\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.00000 | 0.441726 | ||||||||
\(83\) | 3.16228 | 0.347105 | 0.173553 | − | 0.984825i | \(-0.444475\pi\) | ||||
0.173553 | + | 0.984825i | \(0.444475\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.16228 | 0.340997 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | 5.00000 | 0.529999 | 0.264999 | − | 0.964249i | \(-0.414628\pi\) | ||||
0.264999 | + | 0.964249i | \(0.414628\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.16228 | 0.436325 | ||||||||
\(92\) | 1.16228 | 0.121176 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.4868 | −1.08163 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.4868 | −1.16631 | −0.583156 | − | 0.812360i | \(-0.698182\pi\) | ||||
−0.583156 | + | 0.812360i | \(0.698182\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4868 | 1.54100 | 0.770499 | − | 0.637442i | \(-0.220007\pi\) | ||||
0.770499 | + | 0.637442i | \(0.220007\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.32456 | −0.623177 | −0.311588 | − | 0.950217i | \(-0.600861\pi\) | ||||
−0.311588 | + | 0.950217i | \(0.600861\pi\) | |||||||
\(104\) | 4.16228 | 0.408145 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.162278 | −0.0157618 | ||||||||
\(107\) | 8.32456 | 0.804765 | 0.402383 | − | 0.915472i | \(-0.368182\pi\) | ||||
0.402383 | + | 0.915472i | \(0.368182\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.4868 | 1.48337 | 0.741685 | − | 0.670749i | \(-0.234027\pi\) | ||||
0.741685 | + | 0.670749i | \(0.234027\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −14.6491 | −1.37807 | −0.689036 | − | 0.724727i | \(-0.741966\pi\) | ||||
−0.689036 | + | 0.724727i | \(0.741966\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.83772 | 0.170628 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.324555 | −0.0298777 | ||||||||
\(119\) | 7.32456 | 0.671441 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −3.83772 | −0.347451 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.32456 | −0.567962 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.48683 | −0.398142 | −0.199071 | − | 0.979985i | \(-0.563792\pi\) | ||||
−0.199071 | + | 0.979985i | \(0.563792\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.48683 | −0.479387 | −0.239693 | − | 0.970849i | \(-0.577047\pi\) | ||||
−0.239693 | + | 0.970849i | \(0.577047\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | 0.260133 | ||||||||
\(134\) | −3.48683 | −0.301216 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.32456 | 0.628075 | ||||||||
\(137\) | −2.51317 | −0.214714 | −0.107357 | − | 0.994221i | \(-0.534239\pi\) | ||||
−0.107357 | + | 0.994221i | \(0.534239\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.3246 | 1.04536 | 0.522678 | − | 0.852530i | \(-0.324933\pi\) | ||||
0.522678 | + | 0.852530i | \(0.324933\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.3246 | −0.866417 | ||||||||
\(143\) | 8.32456 | 0.696134 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.32456 | −0.357903 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.48683 | 0.615414 | ||||||||
\(149\) | 18.4868 | 1.51450 | 0.757250 | − | 0.653125i | \(-0.226542\pi\) | ||||
0.757250 | + | 0.653125i | \(0.226542\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.16228 | −0.664237 | −0.332118 | − | 0.943238i | \(-0.607763\pi\) | ||||
−0.332118 | + | 0.943238i | \(0.607763\pi\) | |||||||
\(152\) | 3.00000 | 0.243332 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.1623 | 1.92836 | 0.964180 | − | 0.265249i | \(-0.0854543\pi\) | ||||
0.964180 | + | 0.265249i | \(0.0854543\pi\) | |||||||
\(158\) | −14.4868 | −1.15251 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.16228 | 0.0916003 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.324555 | 0.0254211 | 0.0127106 | − | 0.999919i | \(-0.495954\pi\) | ||||
0.0127106 | + | 0.999919i | \(0.495954\pi\) | |||||||
\(164\) | 4.00000 | 0.312348 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.16228 | 0.245440 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.32456 | 0.332658 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.16228 | 0.241121 | ||||||||
\(173\) | 12.8377 | 0.976034 | 0.488017 | − | 0.872834i | \(-0.337720\pi\) | ||||
0.488017 | + | 0.872834i | \(0.337720\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.00000 | 0.374766 | ||||||||
\(179\) | 12.6754 | 0.947407 | 0.473704 | − | 0.880684i | \(-0.342917\pi\) | ||||
0.473704 | + | 0.880684i | \(0.342917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.83772 | −0.731232 | −0.365616 | − | 0.930766i | \(-0.619142\pi\) | ||||
−0.365616 | + | 0.930766i | \(0.619142\pi\) | |||||||
\(182\) | 4.16228 | 0.308529 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.16228 | 0.0856842 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.6491 | 1.07125 | ||||||||
\(188\) | −10.4868 | −0.764831 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.6754 | −1.05636 | −0.528181 | − | 0.849132i | \(-0.677126\pi\) | ||||
−0.528181 | + | 0.849132i | \(0.677126\pi\) | |||||||
\(194\) | −11.4868 | −0.824707 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −12.8114 | −0.912774 | −0.456387 | − | 0.889781i | \(-0.650857\pi\) | ||||
−0.456387 | + | 0.889781i | \(0.650857\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.1359 | −1.71095 | −0.855476 | − | 0.517843i | \(-0.826735\pi\) | ||||
−0.855476 | + | 0.517843i | \(0.826735\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.4868 | 1.08965 | ||||||||
\(203\) | 1.83772 | 0.128983 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.32456 | −0.440653 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.16228 | 0.288602 | ||||||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.324555 | 0.0223433 | 0.0111717 | − | 0.999938i | \(-0.496444\pi\) | ||||
0.0111717 | + | 0.999938i | \(0.496444\pi\) | |||||||
\(212\) | −0.162278 | −0.0111453 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.32456 | 0.569055 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.32456 | −0.429339 | ||||||||
\(218\) | 15.4868 | 1.04890 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.4868 | 2.05077 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.837722 | 0.0560980 | 0.0280490 | − | 0.999607i | \(-0.491071\pi\) | ||||
0.0280490 | + | 0.999607i | \(0.491071\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.6491 | −0.974444 | ||||||||
\(227\) | −9.81139 | −0.651205 | −0.325602 | − | 0.945507i | \(-0.605567\pi\) | ||||
−0.325602 | + | 0.945507i | \(0.605567\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.8377 | 1.17875 | 0.589375 | − | 0.807860i | \(-0.299374\pi\) | ||||
0.589375 | + | 0.807860i | \(0.299374\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.83772 | 0.120652 | ||||||||
\(233\) | −15.4868 | −1.01458 | −0.507288 | − | 0.861777i | \(-0.669352\pi\) | ||||
−0.507288 | + | 0.861777i | \(0.669352\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.324555 | −0.0211268 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.32456 | 0.474780 | ||||||||
\(239\) | 25.8114 | 1.66960 | 0.834800 | − | 0.550553i | \(-0.185583\pi\) | ||||
0.834800 | + | 0.550553i | \(0.185583\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.4868 | −1.51292 | −0.756460 | − | 0.654040i | \(-0.773073\pi\) | ||||
−0.756460 | + | 0.654040i | \(0.773073\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.83772 | −0.245685 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.4868 | 0.794518 | ||||||||
\(248\) | −6.32456 | −0.401610 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.67544 | −0.231992 | −0.115996 | − | 0.993250i | \(-0.537006\pi\) | ||||
−0.115996 | + | 0.993250i | \(0.537006\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.32456 | 0.146144 | ||||||||
\(254\) | −4.48683 | −0.281529 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.0000 | −1.18519 | −0.592594 | − | 0.805502i | \(-0.701896\pi\) | ||||
−0.592594 | + | 0.805502i | \(0.701896\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.48683 | 0.465209 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.48683 | −0.338978 | ||||||||
\(263\) | 16.3246 | 1.00662 | 0.503308 | − | 0.864107i | \(-0.332116\pi\) | ||||
0.503308 | + | 0.864107i | \(0.332116\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.00000 | 0.183942 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.48683 | −0.212992 | ||||||||
\(269\) | 22.6491 | 1.38094 | 0.690470 | − | 0.723361i | \(-0.257404\pi\) | ||||
0.690470 | + | 0.723361i | \(0.257404\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.32456 | −0.141207 | −0.0706033 | − | 0.997504i | \(-0.522492\pi\) | ||||
−0.0706033 | + | 0.997504i | \(0.522492\pi\) | |||||||
\(272\) | 7.32456 | 0.444116 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.51317 | −0.151826 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.32456 | 0.500174 | 0.250087 | − | 0.968223i | \(-0.419541\pi\) | ||||
0.250087 | + | 0.968223i | \(0.419541\pi\) | |||||||
\(278\) | 12.3246 | 0.739178 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.83772 | 0.527214 | 0.263607 | − | 0.964630i | \(-0.415088\pi\) | ||||
0.263607 | + | 0.964630i | \(0.415088\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.6491 | −1.28691 | −0.643453 | − | 0.765486i | \(-0.722499\pi\) | ||||
−0.643453 | + | 0.765486i | \(0.722499\pi\) | |||||||
\(284\) | −10.3246 | −0.612650 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.32456 | 0.492241 | ||||||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.6491 | 2.15583 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.32456 | −0.253075 | ||||||||
\(293\) | 24.1359 | 1.41004 | 0.705018 | − | 0.709189i | \(-0.250939\pi\) | ||||
0.705018 | + | 0.709189i | \(0.250939\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.48683 | 0.435163 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.4868 | 1.07091 | ||||||||
\(299\) | 4.83772 | 0.279773 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.16228 | 0.182271 | ||||||||
\(302\) | −8.16228 | −0.469686 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.00000 | 0.172062 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.64911 | 0.379485 | 0.189742 | − | 0.981834i | \(-0.439235\pi\) | ||||
0.189742 | + | 0.981834i | \(0.439235\pi\) | |||||||
\(308\) | 2.00000 | 0.113961 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.0000 | 1.02069 | 0.510343 | − | 0.859971i | \(-0.329518\pi\) | ||||
0.510343 | + | 0.859971i | \(0.329518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.16228 | 0.291789 | 0.145895 | − | 0.989300i | \(-0.453394\pi\) | ||||
0.145895 | + | 0.989300i | \(0.453394\pi\) | |||||||
\(314\) | 24.1623 | 1.36356 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.4868 | −0.814948 | ||||||||
\(317\) | −21.8377 | −1.22653 | −0.613264 | − | 0.789878i | \(-0.710144\pi\) | ||||
−0.613264 | + | 0.789878i | \(0.710144\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.67544 | 0.205785 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.16228 | 0.0647712 | ||||||||
\(323\) | 21.9737 | 1.22265 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.324555 | 0.0179755 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.00000 | 0.220863 | ||||||||
\(329\) | −10.4868 | −0.578158 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.18861 | −0.120297 | −0.0601485 | − | 0.998189i | \(-0.519157\pi\) | ||||
−0.0601485 | + | 0.998189i | \(0.519157\pi\) | |||||||
\(332\) | 3.16228 | 0.173553 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.3246 | 0.725835 | 0.362917 | − | 0.931821i | \(-0.381781\pi\) | ||||
0.362917 | + | 0.931821i | \(0.381781\pi\) | |||||||
\(338\) | 4.32456 | 0.235225 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.6491 | −0.684988 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 3.16228 | 0.170499 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.8377 | 0.690160 | ||||||||
\(347\) | −23.0000 | −1.23470 | −0.617352 | − | 0.786687i | \(-0.711795\pi\) | ||||
−0.617352 | + | 0.786687i | \(0.711795\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.8114 | −0.578720 | −0.289360 | − | 0.957220i | \(-0.593443\pi\) | ||||
−0.289360 | + | 0.957220i | \(0.593443\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.00000 | 0.106600 | ||||||||
\(353\) | 24.0000 | 1.27739 | 0.638696 | − | 0.769460i | \(-0.279474\pi\) | ||||
0.638696 | + | 0.769460i | \(0.279474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.00000 | 0.264999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.6754 | 0.669918 | ||||||||
\(359\) | 22.0000 | 1.16112 | 0.580558 | − | 0.814219i | \(-0.302835\pi\) | ||||
0.580558 | + | 0.814219i | \(0.302835\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | −9.83772 | −0.517059 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.16228 | 0.218163 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.4605 | 1.59003 | 0.795013 | − | 0.606593i | \(-0.207464\pi\) | ||||
0.795013 | + | 0.606593i | \(0.207464\pi\) | |||||||
\(368\) | 1.16228 | 0.0605879 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.162278 | −0.00842504 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.32456 | −0.223917 | −0.111958 | − | 0.993713i | \(-0.535712\pi\) | ||||
−0.111958 | + | 0.993713i | \(0.535712\pi\) | |||||||
\(374\) | 14.6491 | 0.757487 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.4868 | −0.540817 | ||||||||
\(377\) | 7.64911 | 0.393949 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.83772 | −0.248497 | −0.124249 | − | 0.992251i | \(-0.539652\pi\) | ||||
−0.124249 | + | 0.992251i | \(0.539652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.3246 | 1.34512 | 0.672561 | − | 0.740042i | \(-0.265194\pi\) | ||||
0.672561 | + | 0.740042i | \(0.265194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.6754 | −0.746960 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.4868 | −0.583156 | ||||||||
\(389\) | −26.4868 | −1.34294 | −0.671468 | − | 0.741034i | \(-0.734336\pi\) | ||||
−0.671468 | + | 0.741034i | \(0.734336\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.51317 | 0.430529 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.8114 | −0.645428 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.8114 | −0.944117 | −0.472058 | − | 0.881567i | \(-0.656489\pi\) | ||||
−0.472058 | + | 0.881567i | \(0.656489\pi\) | |||||||
\(398\) | −24.1359 | −1.20983 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.16228 | 0.457542 | 0.228771 | − | 0.973480i | \(-0.426529\pi\) | ||||
0.228771 | + | 0.973480i | \(0.426529\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.3246 | −1.31132 | ||||||||
\(404\) | 15.4868 | 0.770499 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.83772 | 0.0912046 | ||||||||
\(407\) | 14.9737 | 0.742217 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.1359 | 0.995658 | 0.497829 | − | 0.867275i | \(-0.334131\pi\) | ||||
0.497829 | + | 0.867275i | \(0.334131\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.32456 | −0.311588 | ||||||||
\(413\) | −0.324555 | −0.0159703 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.16228 | 0.204072 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.00000 | 0.293470 | ||||||||
\(419\) | −20.1359 | −0.983705 | −0.491853 | − | 0.870678i | \(-0.663680\pi\) | ||||
−0.491853 | + | 0.870678i | \(0.663680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.35089 | −0.260786 | −0.130393 | − | 0.991462i | \(-0.541624\pi\) | ||||
−0.130393 | + | 0.991462i | \(0.541624\pi\) | |||||||
\(422\) | 0.324555 | 0.0157991 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.162278 | −0.00788090 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.83772 | −0.185720 | ||||||||
\(428\) | 8.32456 | 0.402383 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.9737 | 1.49195 | 0.745974 | − | 0.665975i | \(-0.231984\pi\) | ||||
0.745974 | + | 0.665975i | \(0.231984\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.3246 | 1.45731 | 0.728653 | − | 0.684884i | \(-0.240147\pi\) | ||||
0.728653 | + | 0.684884i | \(0.240147\pi\) | |||||||
\(434\) | −6.32456 | −0.303588 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.4868 | 0.741685 | ||||||||
\(437\) | 3.48683 | 0.166798 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.8114 | 1.61373 | 0.806865 | − | 0.590736i | \(-0.201163\pi\) | ||||
0.806865 | + | 0.590736i | \(0.201163\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.4868 | 1.45011 | ||||||||
\(443\) | −28.6228 | −1.35991 | −0.679955 | − | 0.733254i | \(-0.738001\pi\) | ||||
−0.679955 | + | 0.733254i | \(0.738001\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.837722 | 0.0396673 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 25.1623 | 1.18748 | 0.593741 | − | 0.804656i | \(-0.297651\pi\) | ||||
0.593741 | + | 0.804656i | \(0.297651\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | −14.6491 | −0.689036 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.81139 | −0.460471 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.6228 | −1.43247 | −0.716237 | − | 0.697858i | \(-0.754137\pi\) | ||||
−0.716237 | + | 0.697858i | \(0.754137\pi\) | |||||||
\(458\) | 17.8377 | 0.833502 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.16228 | −0.240431 | −0.120216 | − | 0.992748i | \(-0.538359\pi\) | ||||
−0.120216 | + | 0.992748i | \(0.538359\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.4868 | −0.952104 | −0.476052 | − | 0.879417i | \(-0.657933\pi\) | ||||
−0.476052 | + | 0.879417i | \(0.657933\pi\) | |||||||
\(464\) | 1.83772 | 0.0853141 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.4868 | −0.717414 | ||||||||
\(467\) | 10.3246 | 0.477763 | 0.238882 | − | 0.971049i | \(-0.423219\pi\) | ||||
0.238882 | + | 0.971049i | \(0.423219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.48683 | −0.161007 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.324555 | −0.0149389 | ||||||||
\(473\) | 6.32456 | 0.290803 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.32456 | 0.335720 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.8114 | 1.18059 | ||||||||
\(479\) | −4.16228 | −0.190179 | −0.0950897 | − | 0.995469i | \(-0.530314\pi\) | ||||
−0.0950897 | + | 0.995469i | \(0.530314\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.1623 | 1.42088 | ||||||||
\(482\) | −23.4868 | −1.06980 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.9737 | −1.22229 | −0.611147 | − | 0.791517i | \(-0.709291\pi\) | ||||
−0.611147 | + | 0.791517i | \(0.709291\pi\) | |||||||
\(488\) | −3.83772 | −0.173726 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.3246 | −0.781846 | −0.390923 | − | 0.920423i | \(-0.627844\pi\) | ||||
−0.390923 | + | 0.920423i | \(0.627844\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.4605 | 0.606230 | ||||||||
\(494\) | 12.4868 | 0.561809 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.32456 | −0.283981 | ||||||||
\(497\) | −10.3246 | −0.463120 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.83772 | 0.216566 | 0.108283 | − | 0.994120i | \(-0.465465\pi\) | ||||
0.108283 | + | 0.994120i | \(0.465465\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.67544 | −0.164043 | ||||||||
\(503\) | 30.0000 | 1.33763 | 0.668817 | − | 0.743427i | \(-0.266801\pi\) | ||||
0.668817 | + | 0.743427i | \(0.266801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.32456 | 0.103339 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.48683 | −0.199071 | ||||||||
\(509\) | −19.4868 | −0.863739 | −0.431869 | − | 0.901936i | \(-0.642146\pi\) | ||||
−0.431869 | + | 0.901936i | \(0.642146\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.32456 | −0.191307 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.0000 | −0.838054 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.9737 | −0.922421 | ||||||||
\(518\) | 7.48683 | 0.328953 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.3246 | −1.37235 | −0.686177 | − | 0.727435i | \(-0.740712\pi\) | ||||
−0.686177 | + | 0.727435i | \(0.740712\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.3246 | −1.19482 | −0.597410 | − | 0.801936i | \(-0.703803\pi\) | ||||
−0.597410 | + | 0.801936i | \(0.703803\pi\) | |||||||
\(524\) | −5.48683 | −0.239693 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.3246 | 0.711784 | ||||||||
\(527\) | −46.3246 | −2.01793 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6491 | −0.941266 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.00000 | 0.130066 | ||||||||
\(533\) | 16.6491 | 0.721153 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.48683 | −0.150608 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22.6491 | 0.976472 | ||||||||
\(539\) | 2.00000 | 0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.8114 | −0.765771 | −0.382886 | − | 0.923796i | \(-0.625070\pi\) | ||||
−0.382886 | + | 0.923796i | \(0.625070\pi\) | |||||||
\(542\) | −2.32456 | −0.0998482 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.32456 | 0.314038 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.2982 | −1.42373 | −0.711865 | − | 0.702317i | \(-0.752149\pi\) | ||||
−0.711865 | + | 0.702317i | \(0.752149\pi\) | |||||||
\(548\) | −2.51317 | −0.107357 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.51317 | 0.234869 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.4868 | −0.616043 | ||||||||
\(554\) | 8.32456 | 0.353676 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.3246 | 0.522678 | ||||||||
\(557\) | 1.18861 | 0.0503631 | 0.0251815 | − | 0.999683i | \(-0.491984\pi\) | ||||
0.0251815 | + | 0.999683i | \(0.491984\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.1623 | 0.556705 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.83772 | 0.372797 | ||||||||
\(563\) | −14.4605 | −0.609437 | −0.304719 | − | 0.952442i | \(-0.598562\pi\) | ||||
−0.304719 | + | 0.952442i | \(0.598562\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −21.6491 | −0.909980 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.3246 | −0.433209 | ||||||||
\(569\) | 24.0000 | 1.00613 | 0.503066 | − | 0.864248i | \(-0.332205\pi\) | ||||
0.503066 | + | 0.864248i | \(0.332205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.2982 | 1.64458 | 0.822290 | − | 0.569069i | \(-0.192696\pi\) | ||||
0.822290 | + | 0.569069i | \(0.192696\pi\) | |||||||
\(572\) | 8.32456 | 0.348067 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.00000 | 0.166957 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.0000 | −1.16566 | −0.582828 | − | 0.812596i | \(-0.698054\pi\) | ||||
−0.582828 | + | 0.812596i | \(0.698054\pi\) | |||||||
\(578\) | 36.6491 | 1.52440 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.16228 | 0.131193 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.324555 | −0.0134417 | ||||||||
\(584\) | −4.32456 | −0.178951 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.1359 | 0.997047 | ||||||||
\(587\) | 18.8377 | 0.777516 | 0.388758 | − | 0.921340i | \(-0.372904\pi\) | ||||
0.388758 | + | 0.921340i | \(0.372904\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.9737 | −0.781796 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.48683 | 0.307707 | ||||||||
\(593\) | 0.675445 | 0.0277372 | 0.0138686 | − | 0.999904i | \(-0.495585\pi\) | ||||
0.0138686 | + | 0.999904i | \(0.495585\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.4868 | 0.757250 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.83772 | 0.197829 | ||||||||
\(599\) | 20.1359 | 0.822732 | 0.411366 | − | 0.911470i | \(-0.365052\pi\) | ||||
0.411366 | + | 0.911470i | \(0.365052\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.6754 | −0.884160 | −0.442080 | − | 0.896976i | \(-0.645759\pi\) | ||||
−0.442080 | + | 0.896976i | \(0.645759\pi\) | |||||||
\(602\) | 3.16228 | 0.128885 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.16228 | −0.332118 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.8377 | −0.845777 | −0.422889 | − | 0.906182i | \(-0.638984\pi\) | ||||
−0.422889 | + | 0.906182i | \(0.638984\pi\) | |||||||
\(608\) | 3.00000 | 0.121666 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.6491 | −1.76585 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.8114 | −0.477057 | −0.238529 | − | 0.971135i | \(-0.576665\pi\) | ||||
−0.238529 | + | 0.971135i | \(0.576665\pi\) | |||||||
\(614\) | 6.64911 | 0.268336 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | 0.0805823 | ||||||||
\(617\) | −37.4868 | −1.50916 | −0.754582 | − | 0.656206i | \(-0.772160\pi\) | ||||
−0.754582 | + | 0.656206i | \(0.772160\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.97367 | 0.360682 | 0.180341 | − | 0.983604i | \(-0.442280\pi\) | ||||
0.180341 | + | 0.983604i | \(0.442280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.0000 | 0.721734 | ||||||||
\(623\) | 5.00000 | 0.200321 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.16228 | 0.206326 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.1623 | 0.964180 | ||||||||
\(629\) | 54.8377 | 2.18652 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.8377 | −0.948965 | −0.474482 | − | 0.880265i | \(-0.657365\pi\) | ||||
−0.474482 | + | 0.880265i | \(0.657365\pi\) | |||||||
\(632\) | −14.4868 | −0.576255 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.8377 | −0.867287 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.16228 | 0.164915 | ||||||||
\(638\) | 3.67544 | 0.145512 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.3246 | −0.407795 | −0.203898 | − | 0.978992i | \(-0.565361\pi\) | ||||
−0.203898 | + | 0.978992i | \(0.565361\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.35089 | −0.0927100 | −0.0463550 | − | 0.998925i | \(-0.514761\pi\) | ||||
−0.0463550 | + | 0.998925i | \(0.514761\pi\) | |||||||
\(644\) | 1.16228 | 0.0458002 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.9737 | 0.864542 | ||||||||
\(647\) | −1.13594 | −0.0446586 | −0.0223293 | − | 0.999751i | \(-0.507108\pi\) | ||||
−0.0223293 | + | 0.999751i | \(0.507108\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.649111 | −0.0254798 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.324555 | 0.0127106 | ||||||||
\(653\) | −21.5132 | −0.841875 | −0.420938 | − | 0.907090i | \(-0.638299\pi\) | ||||
−0.420938 | + | 0.907090i | \(0.638299\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.00000 | 0.156174 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.4868 | −0.408819 | ||||||||
\(659\) | 6.35089 | 0.247396 | 0.123698 | − | 0.992320i | \(-0.460525\pi\) | ||||
0.123698 | + | 0.992320i | \(0.460525\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.64911 | 0.103038 | 0.0515192 | − | 0.998672i | \(-0.483594\pi\) | ||||
0.0515192 | + | 0.998672i | \(0.483594\pi\) | |||||||
\(662\) | −2.18861 | −0.0850628 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.16228 | 0.122720 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.13594 | 0.0827041 | ||||||||
\(668\) | −12.0000 | −0.464294 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.67544 | −0.296307 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.9737 | −1.34814 | −0.674068 | − | 0.738669i | \(-0.735454\pi\) | ||||
−0.674068 | + | 0.738669i | \(0.735454\pi\) | |||||||
\(674\) | 13.3246 | 0.513243 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.32456 | 0.166329 | ||||||||
\(677\) | −3.67544 | −0.141259 | −0.0706294 | − | 0.997503i | \(-0.522501\pi\) | ||||
−0.0706294 | + | 0.997503i | \(0.522501\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.4868 | −0.440824 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.6491 | −0.484359 | ||||||||
\(683\) | 20.0000 | 0.765279 | 0.382639 | − | 0.923898i | \(-0.375015\pi\) | ||||
0.382639 | + | 0.923898i | \(0.375015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.16228 | 0.120561 | ||||||||
\(689\) | −0.675445 | −0.0257324 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.2982 | −0.886306 | −0.443153 | − | 0.896446i | \(-0.646140\pi\) | ||||
−0.443153 | + | 0.896446i | \(0.646140\pi\) | |||||||
\(692\) | 12.8377 | 0.488017 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23.0000 | −0.873068 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.2982 | 1.10975 | ||||||||
\(698\) | −10.8114 | −0.409217 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.3246 | 0.616570 | 0.308285 | − | 0.951294i | \(-0.400245\pi\) | ||||
0.308285 | + | 0.951294i | \(0.400245\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.4605 | 0.847114 | ||||||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.0000 | 0.903252 | ||||||||
\(707\) | 15.4868 | 0.582442 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.32456 | 0.237524 | 0.118762 | − | 0.992923i | \(-0.462108\pi\) | ||||
0.118762 | + | 0.992923i | \(0.462108\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.00000 | 0.187383 | ||||||||
\(713\) | −7.35089 | −0.275293 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.6754 | 0.473704 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.0000 | 0.821033 | ||||||||
\(719\) | −1.83772 | −0.0685355 | −0.0342677 | − | 0.999413i | \(-0.510910\pi\) | ||||
−0.0342677 | + | 0.999413i | \(0.510910\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.32456 | −0.235539 | ||||||||
\(722\) | −10.0000 | −0.372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.83772 | −0.365616 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.1623 | −0.933217 | −0.466609 | − | 0.884464i | \(-0.654524\pi\) | ||||
−0.466609 | + | 0.884464i | \(0.654524\pi\) | |||||||
\(728\) | 4.16228 | 0.154264 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.1623 | 0.856688 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.1359 | 0.928417 | 0.464209 | − | 0.885726i | \(-0.346339\pi\) | ||||
0.464209 | + | 0.885726i | \(0.346339\pi\) | |||||||
\(734\) | 30.4605 | 1.12432 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.16228 | 0.0428421 | ||||||||
\(737\) | −6.97367 | −0.256878 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.64911 | −0.244591 | −0.122296 | − | 0.992494i | \(-0.539026\pi\) | ||||
−0.122296 | + | 0.992494i | \(0.539026\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.162278 | −0.00595740 | ||||||||
\(743\) | −39.2982 | −1.44171 | −0.720856 | − | 0.693085i | \(-0.756251\pi\) | ||||
−0.720856 | + | 0.693085i | \(0.756251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.32456 | −0.158333 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14.6491 | 0.535625 | ||||||||
\(749\) | 8.32456 | 0.304173 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.9473 | −1.09279 | −0.546397 | − | 0.837526i | \(-0.684001\pi\) | ||||
−0.546397 | + | 0.837526i | \(0.684001\pi\) | |||||||
\(752\) | −10.4868 | −0.382415 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.64911 | 0.278564 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 53.1096 | 1.93030 | 0.965151 | − | 0.261694i | \(-0.0842812\pi\) | ||||
0.965151 | + | 0.261694i | \(0.0842812\pi\) | |||||||
\(758\) | −4.83772 | −0.175714 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.9473 | 1.48434 | 0.742170 | − | 0.670212i | \(-0.233797\pi\) | ||||
0.742170 | + | 0.670212i | \(0.233797\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.4868 | 0.560661 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.3246 | 0.951145 | ||||||||
\(767\) | −1.35089 | −0.0487778 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.0000 | 0.576975 | 0.288487 | − | 0.957484i | \(-0.406848\pi\) | ||||
0.288487 | + | 0.957484i | \(0.406848\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.6754 | −0.528181 | ||||||||
\(773\) | 36.0000 | 1.29483 | 0.647415 | − | 0.762138i | \(-0.275850\pi\) | ||||
0.647415 | + | 0.762138i | \(0.275850\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11.4868 | −0.412353 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.4868 | −0.949599 | ||||||||
\(779\) | 12.0000 | 0.429945 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.6491 | −0.738883 | ||||||||
\(782\) | 8.51317 | 0.304430 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.9737 | −0.605046 | −0.302523 | − | 0.953142i | \(-0.597829\pi\) | ||||
−0.302523 | + | 0.953142i | \(0.597829\pi\) | |||||||
\(788\) | −12.8114 | −0.456387 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.6491 | −0.520862 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.9737 | −0.567242 | ||||||||
\(794\) | −18.8114 | −0.667591 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −24.1359 | −0.855476 | ||||||||
\(797\) | −2.51317 | −0.0890209 | −0.0445105 | − | 0.999009i | \(-0.514173\pi\) | ||||
−0.0445105 | + | 0.999009i | \(0.514173\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −76.8114 | −2.71739 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.16228 | 0.323531 | ||||||||
\(803\) | −8.64911 | −0.305220 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −26.3246 | −0.927243 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.4868 | 0.544825 | ||||||||
\(809\) | −6.00000 | −0.210949 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.3246 | 0.573233 | 0.286616 | − | 0.958045i | \(-0.407470\pi\) | ||||
0.286616 | + | 0.958045i | \(0.407470\pi\) | |||||||
\(812\) | 1.83772 | 0.0644914 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.9737 | 0.524827 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.48683 | 0.331902 | ||||||||
\(818\) | 20.1359 | 0.704037 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.4605 | −1.51678 | −0.758391 | − | 0.651800i | \(-0.774014\pi\) | ||||
−0.758391 | + | 0.651800i | \(0.774014\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.701779 | −0.0244625 | −0.0122312 | − | 0.999925i | \(-0.503893\pi\) | ||||
−0.0122312 | + | 0.999925i | \(0.503893\pi\) | |||||||
\(824\) | −6.32456 | −0.220326 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.324555 | −0.0112927 | ||||||||
\(827\) | 52.6228 | 1.82987 | 0.914937 | − | 0.403598i | \(-0.132240\pi\) | ||||
0.914937 | + | 0.403598i | \(0.132240\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.1096 | 1.11521 | 0.557606 | − | 0.830105i | \(-0.311720\pi\) | ||||
0.557606 | + | 0.830105i | \(0.311720\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.16228 | 0.144301 | ||||||||
\(833\) | 7.32456 | 0.253781 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.00000 | 0.207514 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.1359 | −0.695585 | ||||||||
\(839\) | 49.7851 | 1.71877 | 0.859385 | − | 0.511328i | \(-0.170846\pi\) | ||||
0.859385 | + | 0.511328i | \(0.170846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.6228 | −0.883544 | ||||||||
\(842\) | −5.35089 | −0.184404 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.324555 | 0.0111717 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.00000 | −0.240523 | ||||||||
\(848\) | −0.162278 | −0.00557264 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.70178 | 0.298293 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.6228 | −1.49362 | −0.746808 | − | 0.665040i | \(-0.768414\pi\) | ||||
−0.746808 | + | 0.665040i | \(0.768414\pi\) | |||||||
\(854\) | −3.83772 | −0.131324 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.32456 | 0.284527 | ||||||||
\(857\) | 57.5964 | 1.96746 | 0.983728 | − | 0.179661i | \(-0.0575002\pi\) | ||||
0.983728 | + | 0.179661i | \(0.0575002\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.0000 | 0.818869 | 0.409435 | − | 0.912339i | \(-0.365726\pi\) | ||||
0.409435 | + | 0.912339i | \(0.365726\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.9737 | 1.05497 | ||||||||
\(863\) | −8.18861 | −0.278744 | −0.139372 | − | 0.990240i | \(-0.544508\pi\) | ||||
−0.139372 | + | 0.990240i | \(0.544508\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 30.3246 | 1.03047 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.32456 | −0.214669 | ||||||||
\(869\) | −28.9737 | −0.982864 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.5132 | −0.491760 | ||||||||
\(872\) | 15.4868 | 0.524450 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.48683 | 0.117944 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.9737 | −0.505625 | −0.252812 | − | 0.967515i | \(-0.581356\pi\) | ||||
−0.252812 | + | 0.967515i | \(0.581356\pi\) | |||||||
\(878\) | 33.8114 | 1.14108 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.0263 | −0.337796 | −0.168898 | − | 0.985634i | \(-0.554021\pi\) | ||||
−0.168898 | + | 0.985634i | \(0.554021\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.9737 | −1.85001 | −0.925006 | − | 0.379954i | \(-0.875940\pi\) | ||||
−0.925006 | + | 0.379954i | \(0.875940\pi\) | |||||||
\(884\) | 30.4868 | 1.02538 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.6228 | −0.961601 | ||||||||
\(887\) | −30.3246 | −1.01820 | −0.509099 | − | 0.860708i | \(-0.670021\pi\) | ||||
−0.509099 | + | 0.860708i | \(0.670021\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.48683 | −0.150484 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.837722 | 0.0280490 | ||||||||
\(893\) | −31.4605 | −1.05279 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.1623 | 0.839676 | ||||||||
\(899\) | −11.6228 | −0.387641 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.18861 | −0.0395984 | ||||||||
\(902\) | 8.00000 | 0.266371 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.6491 | −0.487222 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.9737 | 0.762828 | 0.381414 | − | 0.924404i | \(-0.375437\pi\) | ||||
0.381414 | + | 0.924404i | \(0.375437\pi\) | |||||||
\(908\) | −9.81139 | −0.325602 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.2982 | 1.50080 | 0.750399 | − | 0.660986i | \(-0.229862\pi\) | ||||
0.750399 | + | 0.660986i | \(0.229862\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.32456 | 0.209312 | ||||||||
\(914\) | −30.6228 | −1.01291 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.8377 | 0.589375 | ||||||||
\(917\) | −5.48683 | −0.181191 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.2982 | 0.768537 | 0.384269 | − | 0.923221i | \(-0.374454\pi\) | ||||
0.384269 | + | 0.923221i | \(0.374454\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.16228 | −0.170011 | ||||||||
\(923\) | −42.9737 | −1.41450 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −20.4868 | −0.673239 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.83772 | 0.0603262 | ||||||||
\(929\) | 14.2982 | 0.469109 | 0.234555 | − | 0.972103i | \(-0.424637\pi\) | ||||
0.234555 | + | 0.972103i | \(0.424637\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.00000 | 0.0983210 | ||||||||
\(932\) | −15.4868 | −0.507288 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.3246 | 0.337830 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.1359 | 0.396464 | 0.198232 | − | 0.980155i | \(-0.436480\pi\) | ||||
0.198232 | + | 0.980155i | \(0.436480\pi\) | |||||||
\(938\) | −3.48683 | −0.113849 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.7851 | −0.481979 | −0.240989 | − | 0.970528i | \(-0.577472\pi\) | ||||
−0.240989 | + | 0.970528i | \(0.577472\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.64911 | 0.151396 | ||||||||
\(944\) | −0.324555 | −0.0105634 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.32456 | 0.205629 | ||||||||
\(947\) | −46.0000 | −1.49480 | −0.747400 | − | 0.664375i | \(-0.768698\pi\) | ||||
−0.747400 | + | 0.664375i | \(0.768698\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.0000 | −0.584305 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.32456 | 0.237390 | ||||||||
\(953\) | −24.7851 | −0.802867 | −0.401433 | − | 0.915888i | \(-0.631488\pi\) | ||||
−0.401433 | + | 0.915888i | \(0.631488\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 25.8114 | 0.834800 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.16228 | −0.134477 | ||||||||
\(959\) | −2.51317 | −0.0811544 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.00000 | 0.290323 | ||||||||
\(962\) | 31.1623 | 1.00471 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.4868 | −0.756460 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.4868 | −0.723128 | −0.361564 | − | 0.932347i | \(-0.617757\pi\) | ||||
−0.361564 | + | 0.932347i | \(0.617757\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.4605 | 1.49099 | 0.745494 | − | 0.666512i | \(-0.232214\pi\) | ||||
0.745494 | + | 0.666512i | \(0.232214\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.3246 | 0.395107 | ||||||||
\(974\) | −26.9737 | −0.864292 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.83772 | −0.122842 | ||||||||
\(977\) | −40.4605 | −1.29445 | −0.647223 | − | 0.762301i | \(-0.724070\pi\) | ||||
−0.647223 | + | 0.762301i | \(0.724070\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.0000 | 0.319601 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.3246 | −0.552849 | ||||||||
\(983\) | 58.4342 | 1.86376 | 0.931880 | − | 0.362766i | \(-0.118168\pi\) | ||||
0.931880 | + | 0.362766i | \(0.118168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.4605 | 0.428670 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.4868 | 0.397259 | ||||||||
\(989\) | 3.67544 | 0.116872 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.4868 | 1.85790 | 0.928948 | − | 0.370211i | \(-0.120715\pi\) | ||||
0.928948 | + | 0.370211i | \(0.120715\pi\) | |||||||
\(992\) | −6.32456 | −0.200805 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.3246 | −0.327475 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.97367 | −0.284199 | −0.142099 | − | 0.989852i | \(-0.545385\pi\) | ||||
−0.142099 | + | 0.989852i | \(0.545385\pi\) | |||||||
\(998\) | 4.83772 | 0.153135 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9450.2.a.ex.1.2 | yes | 2 | |
3.2 | odd | 2 | 9450.2.a.eh.1.2 | yes | 2 | ||
5.4 | even | 2 | 9450.2.a.ee.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 9450.2.a.em.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9450.2.a.ee.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
9450.2.a.eh.1.2 | yes | 2 | 3.2 | odd | 2 | ||
9450.2.a.em.1.1 | yes | 2 | 15.14 | odd | 2 | ||
9450.2.a.ex.1.2 | yes | 2 | 1.1 | even | 1 | trivial |