Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1241,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8280.1241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.p (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(66.1161328736\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1241.22 | ||
Character | \(\chi\) | \(=\) | 8280.1241 |
Dual form | 8280.2.p.a.1241.27 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8280\mathbb{Z}\right)^\times\).
\(n\) | \(1657\) | \(2071\) | \(3961\) | \(4141\) | \(4601\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.669780i | − | 0.253153i | −0.991957 | − | 0.126577i | \(-0.959601\pi\) | ||
0.991957 | − | 0.126577i | \(-0.0403989\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.53199 | 1.96947 | 0.984734 | − | 0.174064i | \(-0.0556898\pi\) | ||||
0.984734 | + | 0.174064i | \(0.0556898\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.67759 | −0.465280 | −0.232640 | − | 0.972563i | \(-0.574736\pi\) | ||||
−0.232640 | + | 0.972563i | \(0.574736\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.86583 | 1.18014 | 0.590068 | − | 0.807353i | \(-0.299101\pi\) | ||||
0.590068 | + | 0.807353i | \(0.299101\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.93620i | 1.82069i | 0.413851 | + | 0.910345i | \(0.364183\pi\) | ||||
−0.413851 | + | 0.910345i | \(0.635817\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.87865 | + | 3.83580i | −0.600241 | + | 0.799819i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.55690i | 1.03189i | 0.856621 | + | 0.515946i | \(0.172559\pi\) | ||||
−0.856621 | + | 0.515946i | \(0.827441\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.03194 | −0.364948 | −0.182474 | − | 0.983211i | \(-0.558410\pi\) | ||||
−0.182474 | + | 0.983211i | \(0.558410\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.669780i | 0.113214i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.940522i | − | 0.154621i | −0.997007 | − | 0.0773105i | \(-0.975367\pi\) | ||
0.997007 | − | 0.0773105i | \(-0.0246333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.80249i | 0.437675i | 0.975761 | + | 0.218838i | \(0.0702265\pi\) | ||||
−0.975761 | + | 0.218838i | \(0.929773\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.91885i | − | 1.05511i | −0.849519 | − | 0.527557i | \(-0.823108\pi\) | ||
0.849519 | − | 0.527557i | \(-0.176892\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.23598i | 0.326151i | 0.986614 | + | 0.163076i | \(0.0521414\pi\) | ||||
−0.986614 | + | 0.163076i | \(0.947859\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.55139 | 0.935913 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.97773 | −0.821104 | −0.410552 | − | 0.911837i | \(-0.634664\pi\) | ||||
−0.410552 | + | 0.911837i | \(0.634664\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.53199 | −0.880773 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.74853i | 0.357829i | 0.983865 | + | 0.178914i | \(0.0572585\pi\) | ||||
−0.983865 | + | 0.178914i | \(0.942741\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.34487i | − | 0.172193i | −0.996287 | − | 0.0860967i | \(-0.972561\pi\) | ||
0.996287 | − | 0.0860967i | \(-0.0274394\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.67759 | 0.208080 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.66113i | 0.325109i | 0.986700 | + | 0.162554i | \(0.0519733\pi\) | ||||
−0.986700 | + | 0.162554i | \(0.948027\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.57789i | − | 0.543295i | −0.962397 | − | 0.271648i | \(-0.912432\pi\) | ||
0.962397 | − | 0.271648i | \(-0.0875685\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.52129 | −0.412136 | −0.206068 | − | 0.978538i | \(-0.566067\pi\) | ||||
−0.206068 | + | 0.978538i | \(0.566067\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.37500i | − | 0.498577i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.7290i | 1.54464i | 0.635236 | + | 0.772318i | \(0.280903\pi\) | ||||
−0.635236 | + | 0.772318i | \(0.719097\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.0656 | −1.43414 | −0.717068 | − | 0.697003i | \(-0.754516\pi\) | ||||
−0.717068 | + | 0.697003i | \(0.754516\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.86583 | −0.527773 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.3026 | −1.41007 | −0.705034 | − | 0.709173i | \(-0.749068\pi\) | ||||
−0.705034 | + | 0.709173i | \(0.749068\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.12362i | 0.117787i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 7.93620i | − | 0.814237i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.14141i | 0.217428i | 0.994073 | + | 0.108714i | \(0.0346732\pi\) | ||||
−0.994073 | + | 0.108714i | \(0.965327\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 4.83776i | − | 0.481375i | −0.970603 | − | 0.240688i | \(-0.922627\pi\) | ||
0.970603 | − | 0.240688i | \(-0.0773729\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2379i | 1.20584i | 0.797802 | + | 0.602919i | \(0.205996\pi\) | ||||
−0.797802 | + | 0.602919i | \(0.794004\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.8635 | −1.24356 | −0.621782 | − | 0.783190i | \(-0.713591\pi\) | ||||
−0.621782 | + | 0.783190i | \(0.713591\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.24388i | 0.693838i | 0.937895 | + | 0.346919i | \(0.112772\pi\) | ||||
−0.937895 | + | 0.346919i | \(0.887228\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.24581 | 0.399412 | 0.199706 | − | 0.979856i | \(-0.436001\pi\) | ||||
0.199706 | + | 0.979856i | \(0.436001\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.87865 | − | 3.83580i | 0.268436 | − | 0.357690i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.25903i | − | 0.298755i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31.6669 | 2.87881 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.97859 | −0.530514 | −0.265257 | − | 0.964178i | \(-0.585457\pi\) | ||||
−0.265257 | + | 0.964178i | \(0.585457\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.7326i | − | 0.937710i | −0.883275 | − | 0.468855i | \(-0.844667\pi\) | ||
0.883275 | − | 0.468855i | \(-0.155333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.31551 | 0.460913 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.24036 | 0.191407 | 0.0957033 | − | 0.995410i | \(-0.469490\pi\) | ||||
0.0957033 | + | 0.995410i | \(0.469490\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0068 | 1.69695 | 0.848476 | − | 0.529234i | \(-0.177520\pi\) | ||||
0.848476 | + | 0.529234i | \(0.177520\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.9580 | −0.916355 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 5.55690i | − | 0.461476i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.8878 | −1.13773 | −0.568866 | − | 0.822430i | \(-0.692618\pi\) | ||||
−0.568866 | + | 0.822430i | \(0.692618\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.1907 | −1.64309 | −0.821547 | − | 0.570141i | \(-0.806889\pi\) | ||||
−0.821547 | + | 0.570141i | \(0.806889\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.03194 | 0.163210 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 18.9416i | − | 1.51170i | −0.654743 | − | 0.755852i | \(-0.727223\pi\) | ||
0.654743 | − | 0.755852i | \(-0.272777\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.56914 | + | 1.92807i | 0.202477 | + | 0.151953i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.1105 | 1.41852 | 0.709261 | − | 0.704946i | \(-0.249029\pi\) | ||||
0.709261 | + | 0.704946i | \(0.249029\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 21.2004i | − | 1.64054i | −0.571978 | − | 0.820269i | \(-0.693824\pi\) | ||
0.571978 | − | 0.820269i | \(-0.306176\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1857 | −0.783514 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.5587i | 1.63908i | 0.573021 | + | 0.819540i | \(0.305771\pi\) | ||||
−0.573021 | + | 0.819540i | \(0.694229\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.669780i | − | 0.0506306i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 13.3629i | − | 0.998788i | −0.866375 | − | 0.499394i | \(-0.833556\pi\) | ||
0.866375 | − | 0.499394i | \(-0.166444\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3173i | 1.28719i | 0.765368 | + | 0.643593i | \(0.222557\pi\) | ||||
−0.765368 | + | 0.643593i | \(0.777443\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.940522i | 0.0691486i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.7835 | 2.32424 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.07752 | 0.222682 | 0.111341 | − | 0.993782i | \(-0.464485\pi\) | ||||
0.111341 | + | 0.993782i | \(0.464485\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.7424 | 1.20514 | 0.602572 | − | 0.798065i | \(-0.294143\pi\) | ||||
0.602572 | + | 0.798065i | \(0.294143\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.57646i | − | 0.254812i | −0.991851 | − | 0.127406i | \(-0.959335\pi\) | ||
0.991851 | − | 0.127406i | \(-0.0406651\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.5351i | 1.81014i | 0.425264 | + | 0.905069i | \(0.360181\pi\) | ||||
−0.425264 | + | 0.905069i | \(0.639819\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.72190 | 0.261226 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 2.80249i | − | 0.195734i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 51.8392i | 3.58579i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6623 | 0.940550 | 0.470275 | − | 0.882520i | \(-0.344155\pi\) | ||||
0.470275 | + | 0.882520i | \(0.344155\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.91885i | 0.471862i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.36096i | 0.0923877i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.16287 | −0.549094 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.76892 | 0.118456 | 0.0592278 | − | 0.998244i | \(-0.481136\pi\) | ||||
0.0592278 | + | 0.998244i | \(0.481136\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.40585 | −0.159682 | −0.0798409 | − | 0.996808i | \(-0.525441\pi\) | ||||
−0.0798409 | + | 0.996808i | \(0.525441\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.5202i | − | 0.761279i | −0.924723 | − | 0.380640i | \(-0.875704\pi\) | ||
0.924723 | − | 0.380640i | \(-0.124296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 8.11652i | − | 0.531731i | −0.964010 | − | 0.265866i | \(-0.914342\pi\) | ||
0.964010 | − | 0.265866i | \(-0.0856577\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2.23598i | − | 0.145859i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.1582i | 0.786451i | 0.919442 | + | 0.393226i | \(0.128641\pi\) | ||||
−0.919442 | + | 0.393226i | \(0.871359\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.09653i | 0.199465i | 0.995014 | + | 0.0997327i | \(0.0317988\pi\) | ||||
−0.995014 | + | 0.0997327i | \(0.968201\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.55139 | −0.418553 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 13.3137i | − | 0.847130i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.07435 | 0.509649 | 0.254824 | − | 0.966987i | \(-0.417982\pi\) | ||||
0.254824 | + | 0.966987i | \(0.417982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.8033 | + | 25.0554i | −1.18216 | + | 1.57522i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 11.0766i | − | 0.690942i | −0.938429 | − | 0.345471i | \(-0.887719\pi\) | ||
0.938429 | − | 0.345471i | \(-0.112281\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.629943 | −0.0391428 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.352558 | −0.0217397 | −0.0108698 | − | 0.999941i | \(-0.503460\pi\) | ||||
−0.0108698 | + | 0.999941i | \(0.503460\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.97773 | 0.367209 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.6847i | 0.712432i | 0.934404 | + | 0.356216i | \(0.115933\pi\) | ||||
−0.934404 | + | 0.356216i | \(0.884067\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.62513 | 0.402448 | 0.201224 | − | 0.979545i | \(-0.435508\pi\) | ||||
0.201224 | + | 0.979545i | \(0.435508\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.53199 | 0.393894 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.25382 | 0.135419 | 0.0677093 | − | 0.997705i | \(-0.478431\pi\) | ||||
0.0677093 | + | 0.997705i | \(0.478431\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.2793 | −0.672870 | −0.336435 | − | 0.941707i | \(-0.609221\pi\) | ||||
−0.336435 | + | 0.941707i | \(0.609221\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.03403i | − | 0.0614668i | −0.999528 | − | 0.0307334i | \(-0.990216\pi\) | ||
0.999528 | − | 0.0307334i | \(-0.00978428\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.87705 | 0.110799 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.67627 | 0.392722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.84176 | −0.458121 | −0.229060 | − | 0.973412i | \(-0.573565\pi\) | ||||
−0.229060 | + | 0.973412i | \(0.573565\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.74853i | − | 0.160026i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.82920 | − | 6.43490i | 0.279280 | − | 0.372140i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.63411 | −0.267106 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.34487i | 0.0770072i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.0617 | −1.54449 | −0.772247 | − | 0.635323i | \(-0.780867\pi\) | ||||
−0.772247 | + | 0.635323i | \(0.780867\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.8664i | 1.41005i | 0.709184 | + | 0.705023i | \(0.249063\pi\) | ||||
−0.709184 | + | 0.705023i | \(0.750937\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.0768i | 1.53047i | 0.643750 | + | 0.765236i | \(0.277378\pi\) | ||||
−0.643750 | + | 0.765236i | \(0.722622\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.3848i | 0.920261i | 0.887851 | + | 0.460131i | \(0.152197\pi\) | ||||
−0.887851 | + | 0.460131i | \(0.847803\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.2976i | 2.03228i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 38.6162i | 2.14866i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.67759 | −0.0930560 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.49761 | 0.0825662 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.8287 | 1.30974 | 0.654872 | − | 0.755740i | \(-0.272722\pi\) | ||||
0.654872 | + | 0.755740i | \(0.272722\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 2.66113i | − | 0.145393i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.72528i | 0.0939817i | 0.998895 | + | 0.0469909i | \(0.0149632\pi\) | ||||
−0.998895 | + | 0.0469909i | \(0.985037\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.2726 | −0.718753 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.07646i | − | 0.490083i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.1433i | 1.72554i | 0.505594 | + | 0.862772i | \(0.331274\pi\) | ||||
−0.505594 | + | 0.862772i | \(0.668726\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.1946 | −0.545704 | −0.272852 | − | 0.962056i | \(-0.587967\pi\) | ||||
−0.272852 | + | 0.962056i | \(0.587967\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.09406i | − | 0.0582310i | −0.999576 | − | 0.0291155i | \(-0.990731\pi\) | ||
0.999576 | − | 0.0291155i | \(-0.00926906\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.57789i | 0.242969i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.0047 | 1.21414 | 0.607070 | − | 0.794649i | \(-0.292345\pi\) | ||||
0.607070 | + | 0.794649i | \(0.292345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −43.9833 | −2.31491 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.52129 | 0.184313 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.5207i | 1.59317i | 0.604529 | + | 0.796583i | \(0.293361\pi\) | ||||
−0.604529 | + | 0.796583i | \(0.706639\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.00377i | 0.207865i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 16.8273i | − | 0.871282i | −0.900120 | − | 0.435641i | \(-0.856522\pi\) | ||
0.900120 | − | 0.435641i | \(-0.143478\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 9.32221i | − | 0.480118i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.56133i | − | 0.337033i | −0.985699 | − | 0.168516i | \(-0.946102\pi\) | ||
0.985699 | − | 0.168516i | \(-0.0538976\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 37.2581 | 1.90380 | 0.951899 | − | 0.306411i | \(-0.0991282\pi\) | ||||
0.951899 | + | 0.306411i | \(0.0991282\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.37500i | 0.222970i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.3098 | −1.63817 | −0.819087 | − | 0.573670i | \(-0.805519\pi\) | ||||
−0.819087 | + | 0.573670i | \(0.805519\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.0070 | + | 18.6643i | −0.708366 | + | 0.943896i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 13.7290i | − | 0.690783i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.5346 | −0.578904 | −0.289452 | − | 0.957193i | \(-0.593473\pi\) | ||||
−0.289452 | + | 0.957193i | \(0.593473\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.03309 | −0.401154 | −0.200577 | − | 0.979678i | \(-0.564282\pi\) | ||||
−0.200577 | + | 0.979678i | \(0.564282\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.40877 | 0.169803 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6.14348i | − | 0.304521i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.7487 | −0.531490 | −0.265745 | − | 0.964043i | \(-0.585618\pi\) | ||||
−0.265745 | + | 0.964043i | \(0.585618\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.84091 | 0.0905855 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.0656 | 0.641365 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.2851 | 0.942140 | 0.471070 | − | 0.882096i | \(-0.343868\pi\) | ||||
0.471070 | + | 0.882096i | \(0.343868\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.4742i | 0.802903i | 0.915880 | + | 0.401451i | \(0.131494\pi\) | ||||
−0.915880 | + | 0.401451i | \(0.868506\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.86583 | 0.236027 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.900770 | −0.0435913 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.94237 | 0.141729 | 0.0708645 | − | 0.997486i | \(-0.477424\pi\) | ||||
0.0708645 | + | 0.997486i | \(0.477424\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.8972i | 1.05231i | 0.850389 | + | 0.526155i | \(0.176367\pi\) | ||||
−0.850389 | + | 0.526155i | \(0.823633\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −30.4417 | − | 22.8456i | −1.45622 | − | 1.09285i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.5219 | 1.12264 | 0.561320 | − | 0.827599i | \(-0.310294\pi\) | ||||
0.561320 | + | 0.827599i | \(0.310294\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 8.84084i | − | 0.420041i | −0.977697 | − | 0.210020i | \(-0.932647\pi\) | ||
0.977697 | − | 0.210020i | \(-0.0673530\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.3026 | 0.630602 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.3766i | 1.29198i | 0.763346 | + | 0.645990i | \(0.223555\pi\) | ||||
−0.763346 | + | 0.645990i | \(0.776445\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.3058i | 0.861988i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1.12362i | − | 0.0526760i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 36.5250i | − | 1.70857i | −0.519808 | − | 0.854283i | \(-0.673996\pi\) | ||
0.519808 | − | 0.854283i | \(-0.326004\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.1897i | 1.63895i | 0.573115 | + | 0.819475i | \(0.305735\pi\) | ||||
−0.573115 | + | 0.819475i | \(0.694265\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.7369 | 0.870778 | 0.435389 | − | 0.900243i | \(-0.356611\pi\) | ||||
0.435389 | + | 0.900243i | \(0.356611\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.8152 | −1.19459 | −0.597293 | − | 0.802023i | \(-0.703757\pi\) | ||||
−0.597293 | + | 0.802023i | \(0.703757\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.78237 | 0.0823023 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 45.1938i | − | 2.07802i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.93620i | 0.364138i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.91066 | 0.224374 | 0.112187 | − | 0.993687i | \(-0.464214\pi\) | ||||
0.112187 | + | 0.993687i | \(0.464214\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.57781i | 0.0719420i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2.14141i | − | 0.0972366i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.7414 | 0.939881 | 0.469941 | − | 0.882698i | \(-0.344275\pi\) | ||||
0.469941 | + | 0.882698i | \(0.344275\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.7369i | 0.935844i | 0.883770 | + | 0.467922i | \(0.154997\pi\) | ||||
−0.883770 | + | 0.467922i | \(0.845003\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.0389i | 1.21777i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.06618 | −0.137537 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.0473 | −1.03174 | −0.515870 | − | 0.856667i | \(-0.672531\pi\) | ||||
−0.515870 | + | 0.856667i | \(0.672531\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.6799 | −1.01125 | −0.505624 | − | 0.862754i | \(-0.668738\pi\) | ||||
−0.505624 | + | 0.862754i | \(0.668738\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.83776i | 0.215278i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 6.03904i | − | 0.267676i | −0.991003 | − | 0.133838i | \(-0.957270\pi\) | ||
0.991003 | − | 0.133838i | \(-0.0427302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.35849i | 0.104334i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 12.2379i | − | 0.539267i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.6054i | 0.642344i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.0984 | −1.36244 | −0.681222 | − | 0.732077i | \(-0.738551\pi\) | ||||
−0.681222 | + | 0.732077i | \(0.738551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.6962i | 1.16734i | 0.811989 | + | 0.583672i | \(0.198385\pi\) | ||||
−0.811989 | + | 0.583672i | \(0.801615\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.88708 | −0.430688 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.42670 | − | 22.0839i | −0.279422 | − | 0.960168i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.70143i | − | 0.203642i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.8635 | 0.556139 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 42.7936 | 1.84325 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.9894 | 0.601452 | 0.300726 | − | 0.953711i | \(-0.402771\pi\) | ||||
0.300726 | + | 0.953711i | \(0.402771\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 7.24388i | − | 0.310294i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.5455 | 1.60533 | 0.802665 | − | 0.596429i | \(-0.203414\pi\) | ||||
0.802665 | + | 0.596429i | \(0.203414\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −44.1007 | −1.87875 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.19543 | 0.391030 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.71665 | 0.115108 | 0.0575541 | − | 0.998342i | \(-0.481670\pi\) | ||||
0.0575541 | + | 0.998342i | \(0.481670\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.6070i | 0.490924i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.4941 | 1.32732 | 0.663659 | − | 0.748035i | \(-0.269002\pi\) | ||||
0.663659 | + | 0.748035i | \(0.269002\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.24581 | −0.178622 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.4946 | 0.607646 | 0.303823 | − | 0.952728i | \(-0.401737\pi\) | ||||
0.303823 | + | 0.952728i | \(0.401737\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0190i | 0.461130i | 0.973057 | + | 0.230565i | \(0.0740574\pi\) | ||||
−0.973057 | + | 0.230565i | \(0.925943\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.87865 | + | 3.83580i | −0.120048 | + | 0.159964i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.4467 | 1.18425 | 0.592125 | − | 0.805846i | \(-0.298289\pi\) | ||||
0.592125 | + | 0.805846i | \(0.298289\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.75108i | 0.363056i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −39.0465 | −1.61714 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.28618i | − | 0.342007i | −0.985270 | − | 0.171004i | \(-0.945299\pi\) | ||
0.985270 | − | 0.171004i | \(-0.0547010\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 16.1259i | − | 0.664456i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.9404i | 1.27057i | 0.772278 | + | 0.635285i | \(0.219117\pi\) | ||||
−0.772278 | + | 0.635285i | \(0.780883\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.25903i | 0.133607i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.8074i | 0.441576i | 0.975322 | + | 0.220788i | \(0.0708630\pi\) | ||||
−0.975322 | + | 0.220788i | \(0.929137\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.7779 | 0.765967 | 0.382983 | − | 0.923755i | \(-0.374897\pi\) | ||||
0.382983 | + | 0.923755i | \(0.374897\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −31.6669 | −1.28744 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.6596 | 0.919725 | 0.459862 | − | 0.887990i | \(-0.347899\pi\) | ||||
0.459862 | + | 0.887990i | \(0.347899\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.75106i | − | 0.151752i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 15.0213i | − | 0.606705i | −0.952878 | − | 0.303353i | \(-0.901894\pi\) | ||
0.952878 | − | 0.303353i | \(-0.0981060\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.9666 | −1.24667 | −0.623333 | − | 0.781956i | \(-0.714222\pi\) | ||||
−0.623333 | + | 0.781956i | \(0.714222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.2693i | − | 1.13624i | −0.822946 | − | 0.568119i | \(-0.807671\pi\) | ||
0.822946 | − | 0.568119i | \(-0.192329\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.90979i | 0.356963i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 4.57642i | − | 0.182474i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9.29055i | − | 0.369851i | −0.982753 | − | 0.184925i | \(-0.940796\pi\) | ||
0.982753 | − | 0.184925i | \(-0.0592043\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.97859 | 0.237253 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.9906 | −0.435462 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.1330 | 0.597717 | 0.298859 | − | 0.954297i | \(-0.403394\pi\) | ||||
0.298859 | + | 0.954297i | \(0.403394\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.49585i | 0.256171i | 0.991763 | + | 0.128086i | \(0.0408832\pi\) | ||||
−0.991763 | + | 0.128086i | \(0.959117\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 16.9943i | − | 0.668116i | −0.942552 | − | 0.334058i | \(-0.891582\pi\) | ||
0.942552 | − | 0.334058i | \(-0.108418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.9534i | 0.704733i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.3036i | 0.872807i | 0.899751 | + | 0.436403i | \(0.143748\pi\) | ||||
−0.899751 | + | 0.436403i | \(0.856252\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.7326i | 0.419357i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.4672 | −1.14788 | −0.573940 | − | 0.818897i | \(-0.694586\pi\) | ||||
−0.573940 | + | 0.818897i | \(0.694586\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.62468i | 0.218775i | 0.993999 | + | 0.109387i | \(0.0348889\pi\) | ||||
−0.993999 | + | 0.109387i | \(0.965111\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.31551 | −0.206127 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.3152 | − | 15.9964i | −0.825326 | − | 0.619383i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 8.78470i | − | 0.339130i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.85261 | 0.187055 | 0.0935273 | − | 0.995617i | \(-0.470186\pi\) | ||||
0.0935273 | + | 0.995617i | \(0.470186\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.5803 | −0.521932 | −0.260966 | − | 0.965348i | \(-0.584041\pi\) | ||||
−0.260966 | + | 0.965348i | \(0.584041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.43428 | 0.0550425 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.30907i | 0.0500901i | 0.999686 | + | 0.0250451i | \(0.00797293\pi\) | ||||
−0.999686 | + | 0.0250451i | \(0.992027\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.24036 | −0.0855996 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.0282 | 0.382043 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.9593 | 1.82446 | 0.912229 | − | 0.409681i | \(-0.134360\pi\) | ||||
0.912229 | + | 0.409681i | \(0.134360\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.0068 | −0.758900 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.6364i | 0.516517i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.6365 | 0.930509 | 0.465254 | − | 0.885177i | \(-0.345963\pi\) | ||||
0.465254 | + | 0.885177i | \(0.345963\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.46417 | 0.281517 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.24024 | −0.121862 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 5.58949i | − | 0.209918i | −0.994477 | − | 0.104959i | \(-0.966529\pi\) | ||
0.994477 | − | 0.104959i | \(-0.0334711\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.84926 | − | 7.79412i | 0.219057 | − | 0.291892i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.9580 | 0.409806 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 41.4071i | − | 1.54422i | −0.635487 | − | 0.772112i | \(-0.719201\pi\) | ||
0.635487 | − | 0.772112i | \(-0.280799\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.19672 | 0.305262 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.55690i | 0.206378i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.25287i | 0.120642i | 0.998179 | + | 0.0603211i | \(0.0192125\pi\) | ||||
−0.998179 | + | 0.0603211i | \(0.980788\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 33.6659i | − | 1.24518i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 32.9050i | − | 1.21537i | −0.794177 | − | 0.607687i | \(-0.792098\pi\) | ||
0.794177 | − | 0.607687i | \(-0.207902\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.3825i | 0.640291i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.1180 | −1.03434 | −0.517168 | − | 0.855884i | \(-0.673014\pi\) | ||||
−0.517168 | + | 0.855884i | \(0.673014\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.2581 | 1.33018 | 0.665090 | − | 0.746763i | \(-0.268393\pi\) | ||||
0.665090 | + | 0.746763i | \(0.268393\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.8878 | 0.508809 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.61574i | 0.314812i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 46.0578i | − | 1.68067i | −0.542066 | − | 0.840336i | \(-0.682358\pi\) | ||
0.542066 | − | 0.840336i | \(-0.317642\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.1907 | 0.734814 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.16778i | 0.187826i | 0.995580 | + | 0.0939132i | \(0.0299376\pi\) | ||||
−0.995580 | + | 0.0939132i | \(0.970062\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.8894i | 0.539741i | 0.962897 | + | 0.269871i | \(0.0869809\pi\) | ||||
−0.962897 | + | 0.269871i | \(0.913019\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.85181 | 0.175647 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 4.61092i | − | 0.166491i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 20.3215i | − | 0.732812i | −0.930455 | − | 0.366406i | \(-0.880588\pi\) | ||
0.930455 | − | 0.366406i | \(-0.119412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.0773 | −1.00987 | −0.504935 | − | 0.863158i | \(-0.668483\pi\) | ||||
−0.504935 | + | 0.863158i | \(0.668483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.03194 | −0.0729895 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.2411 | −0.796871 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 29.9027i | − | 1.07000i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.9416i | 0.676054i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.6563i | 1.16407i | 0.813163 | + | 0.582036i | \(0.197744\pi\) | ||||
−0.813163 | + | 0.582036i | \(0.802256\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.84376i | − | 0.101112i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.25615i | 0.0801182i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −50.7925 | −1.79916 | −0.899582 | − | 0.436753i | \(-0.856128\pi\) | ||||
−0.899582 | + | 0.436753i | \(0.856128\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.8799i | 0.384903i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.0011 | −0.811690 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.56914 | − | 1.92807i | −0.0905504 | − | 0.0679554i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 51.8554i | − | 1.82314i | −0.411145 | − | 0.911570i | \(-0.634871\pi\) | ||
0.411145 | − | 0.911570i | \(-0.365129\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.5785 | −0.722609 | −0.361304 | − | 0.932448i | \(-0.617668\pi\) | ||||
−0.361304 | + | 0.932448i | \(0.617668\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.1105 | −0.634383 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 54.9094 | 1.92104 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 5.31025i | − | 0.185329i | −0.995697 | − | 0.0926644i | \(-0.970462\pi\) | ||
0.995697 | − | 0.0926644i | \(-0.0295384\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.99207 | 0.313444 | 0.156722 | − | 0.987643i | \(-0.449907\pi\) | ||||
0.156722 | + | 0.987643i | \(0.449907\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.4390 | 0.849827 | 0.424914 | − | 0.905234i | \(-0.360304\pi\) | ||||
0.424914 | + | 0.905234i | \(0.360304\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.0122 | 0.660321 | 0.330161 | − | 0.943925i | \(-0.392897\pi\) | ||||
0.330161 | + | 0.943925i | \(0.392897\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.8779 | 1.10451 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.2004i | 0.733671i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.4446 | 0.464160 | 0.232080 | − | 0.972697i | \(-0.425447\pi\) | ||||
0.232080 | + | 0.972697i | \(0.425447\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.87918 | −0.0647994 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.1857 | 0.350398 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 21.2099i | − | 0.728779i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.60765 | + | 2.70744i | 0.123669 | + | 0.0928098i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.1737 | −1.03313 | −0.516564 | − | 0.856249i | \(-0.672789\pi\) | ||||
−0.516564 | + | 0.856249i | \(0.672789\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.4362i | 0.868886i | 0.900699 | + | 0.434443i | \(0.143055\pi\) | ||||
−0.900699 | + | 0.434443i | \(0.856945\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.0900 | −1.40197 | −0.700987 | − | 0.713174i | \(-0.747257\pi\) | ||||
−0.700987 | + | 0.713174i | \(0.747257\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 29.6332i | − | 1.00872i | −0.863492 | − | 0.504362i | \(-0.831728\pi\) | ||
0.863492 | − | 0.504362i | \(-0.168272\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 21.5587i | − | 0.733019i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 89.6779i | 3.04211i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.46429i | − | 0.151267i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.669780i | 0.0226427i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.5310 | 0.963422 | 0.481711 | − | 0.876330i | \(-0.340016\pi\) | ||||
0.481711 | + | 0.876330i | \(0.340016\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.1718 | 1.69033 | 0.845166 | − | 0.534504i | \(-0.179501\pi\) | ||||
0.845166 | + | 0.534504i | \(0.179501\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.77640 | 0.127086 | 0.0635430 | − | 0.997979i | \(-0.479760\pi\) | ||||
0.0635430 | + | 0.997979i | \(0.479760\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 33.3132i | − | 1.11855i | −0.828983 | − | 0.559273i | \(-0.811080\pi\) | ||
0.828983 | − | 0.559273i | \(-0.188920\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.00434i | 0.134301i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.7452 | −0.593820 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.3629i | 0.446672i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 11.2913i | − | 0.376586i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.0866 | −0.969015 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 17.3173i | − | 0.575647i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.3967i | 0.876489i | 0.898856 | + | 0.438245i | \(0.144400\pi\) | ||||
−0.898856 | + | 0.438245i | \(0.855600\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.1399 | −0.501606 | −0.250803 | − | 0.968038i | \(-0.580695\pi\) | ||||
−0.250803 | + | 0.968038i | \(0.580695\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −85.3444 | −2.82449 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.18847 | −0.237384 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.5909i | 0.646243i | 0.946358 | + | 0.323121i | \(0.104732\pi\) | ||||
−0.946358 | + | 0.323121i | \(0.895268\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.67982i | 0.252784i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 0.940522i | − | 0.0309242i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 20.2980i | − | 0.665957i | −0.942934 | − | 0.332978i | \(-0.891946\pi\) | ||
0.942934 | − | 0.332978i | \(-0.108054\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.9932i | 1.70401i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −31.7835 | −1.03943 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.82383i | 0.320931i | 0.987041 | + | 0.160465i | \(0.0512995\pi\) | ||||
−0.987041 | + | 0.160465i | \(0.948701\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.9699 | 0.553203 | 0.276602 | − | 0.960985i | \(-0.410792\pi\) | ||||
0.276602 | + | 0.960985i | \(0.410792\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.7498 | − | 8.06740i | −0.350061 | − | 0.262711i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 53.5451i | − | 1.73998i | −0.493068 | − | 0.869990i | \(-0.664125\pi\) | ||
0.493068 | − | 0.869990i | \(-0.335875\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.90729 | 0.191759 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.2172 | −1.20558 | −0.602791 | − | 0.797899i | \(-0.705945\pi\) | ||||
−0.602791 | + | 0.797899i | \(0.705945\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.07752 | −0.0995864 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1.50055i | − | 0.0484552i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.8712 | −0.866813 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.7424 | −0.538957 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.8671 | 1.63578 | 0.817888 | − | 0.575377i | \(-0.195145\pi\) | ||||
0.817888 | + | 0.575377i | \(0.195145\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.47694 | −0.143672 | −0.0718359 | − | 0.997416i | \(-0.522886\pi\) | ||||
−0.0718359 | + | 0.997416i | \(0.522886\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 13.4001i | − | 0.429589i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.9288 | −1.46939 | −0.734697 | − | 0.678396i | \(-0.762676\pi\) | ||||
−0.734697 | + | 0.678396i | \(0.762676\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −86.8922 | −2.77709 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.3406 | 1.12719 | 0.563594 | − | 0.826052i | \(-0.309418\pi\) | ||||
0.563594 | + | 0.826052i | \(0.309418\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.57646i | 0.113955i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.5393 | + | 19.9170i | 0.843901 | + | 0.633323i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.9076 | 1.74420 | 0.872098 | − | 0.489331i | \(-0.162759\pi\) | ||||
0.872098 | + | 0.489331i | \(0.162759\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 25.5351i | − | 0.809519i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.6966 | 1.63725 | 0.818623 | − | 0.574331i | \(-0.194738\pi\) | ||||
0.818623 | + | 0.574331i | \(0.194738\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8280.2.p.a.1241.22 | ✓ | 48 | |
3.2 | odd | 2 | 8280.2.p.b.1241.22 | yes | 48 | ||
23.22 | odd | 2 | 8280.2.p.b.1241.27 | yes | 48 | ||
69.68 | even | 2 | inner | 8280.2.p.a.1241.27 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.p.a.1241.22 | ✓ | 48 | 1.1 | even | 1 | trivial | |
8280.2.p.a.1241.27 | yes | 48 | 69.68 | even | 2 | inner | |
8280.2.p.b.1241.22 | yes | 48 | 3.2 | odd | 2 | ||
8280.2.p.b.1241.27 | yes | 48 | 23.22 | odd | 2 |