Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(673,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.673");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.c (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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - x^{10} - 861 x^{8} - 2158 x^{7} + 8654 x^{6} + 118244 x^{5} + 707300 x^{4} + \cdots + 43264 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 673.6 | ||
Root | \(1.59395 - 5.94871i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.673 |
Dual form | 1344.4.c.g.673.7 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 17.4720i | 1.56275i | 0.624065 | + | 0.781373i | \(0.285480\pi\) | ||||
−0.624065 | + | 0.781373i | \(0.714520\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 37.3882i | − 1.02481i | −0.858743 | − | 0.512407i | \(-0.828754\pi\) | ||||
0.858743 | − | 0.512407i | \(-0.171246\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.32287i | 0.0922269i | 0.998936 | + | 0.0461134i | \(0.0146836\pi\) | ||||
−0.998936 | + | 0.0461134i | \(0.985316\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 52.4161 | 0.902251 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.453383 | −0.00646833 | −0.00323416 | − | 0.999995i | \(-0.501029\pi\) | ||||
−0.00323416 | + | 0.999995i | \(0.501029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 58.2551i | 0.703402i | 0.936112 | + | 0.351701i | \(0.114397\pi\) | ||||
−0.936112 | + | 0.351701i | \(0.885603\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 21.0000i | − 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 181.686 | 1.64714 | 0.823568 | − | 0.567218i | \(-0.191980\pi\) | ||||
0.823568 | + | 0.567218i | \(0.191980\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −180.272 | −1.44217 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 255.263i | − 1.63452i | −0.576266 | − | 0.817262i | \(-0.695491\pi\) | ||||
0.576266 | − | 0.817262i | \(-0.304509\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 30.0965 | 0.174370 | 0.0871852 | − | 0.996192i | \(-0.472213\pi\) | ||||
0.0871852 | + | 0.996192i | \(0.472213\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −112.165 | −0.591677 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 122.304i | 0.590662i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 135.620i | 0.602589i | 0.953531 | + | 0.301294i | \(0.0974187\pi\) | ||||
−0.953531 | + | 0.301294i | \(0.902581\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.9686 | 0.0532472 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 30.5603 | 0.116408 | 0.0582039 | − | 0.998305i | \(-0.481463\pi\) | ||||
0.0582039 | + | 0.998305i | \(0.481463\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 423.547i | − 1.50210i | −0.660245 | − | 0.751051i | \(-0.729547\pi\) | ||||
0.660245 | − | 0.751051i | \(-0.270453\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 157.248i | − 0.520915i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 28.9804 | 0.0899408 | 0.0449704 | − | 0.998988i | \(-0.485681\pi\) | ||||
0.0449704 | + | 0.998988i | \(0.485681\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.36015i | 0.00373449i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 117.967i | − 0.305736i | −0.988247 | − | 0.152868i | \(-0.951149\pi\) | ||||
0.988247 | − | 0.152868i | \(-0.0488509\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 653.247 | 1.60152 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 174.765 | 0.406110 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 447.313i | 0.987036i | 0.869735 | + | 0.493518i | \(0.164289\pi\) | ||||
−0.869735 | + | 0.493518i | \(0.835711\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 22.4253i | 0.0470699i | 0.999723 | + | 0.0235350i | \(0.00749211\pi\) | ||||
−0.999723 | + | 0.0235350i | \(0.992508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −75.5294 | −0.144127 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 246.131i | − 0.448802i | −0.974497 | − | 0.224401i | \(-0.927957\pi\) | ||||
0.974497 | − | 0.224401i | \(-0.0720426\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 545.058i | − 0.950974i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 56.3796 | 0.0942398 | 0.0471199 | − | 0.998889i | \(-0.484996\pi\) | ||||
0.0471199 | + | 0.998889i | \(0.484996\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 268.070 | 0.429797 | 0.214899 | − | 0.976636i | \(-0.431058\pi\) | ||||
0.214899 | + | 0.976636i | \(0.431058\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 540.815i | 0.832639i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 261.717i | − 0.387343i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 964.677 | 1.37386 | 0.686928 | − | 0.726725i | \(-0.258959\pi\) | ||||
0.686928 | + | 0.726725i | \(0.258959\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1289.25i | 1.70498i | 0.522742 | + | 0.852491i | \(0.324909\pi\) | ||||
−0.522742 | + | 0.852491i | \(0.675091\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 7.92152i | − 0.0101083i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −765.790 | −0.943693 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −269.033 | −0.320420 | −0.160210 | − | 0.987083i | \(-0.551217\pi\) | ||||
−0.160210 | + | 0.987083i | \(0.551217\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 30.2601i | 0.0348585i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 90.2894i | − 0.100673i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1017.83 | −1.09924 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 968.154 | 1.01341 | 0.506707 | − | 0.862118i | \(-0.330863\pi\) | ||||
0.506707 | + | 0.862118i | \(0.330863\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 336.494i | 0.341605i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1665.47i | 1.64080i | 0.571793 | + | 0.820398i | \(0.306248\pi\) | ||||
−0.571793 | + | 0.820398i | \(0.693752\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 368.792 | 0.352798 | 0.176399 | − | 0.984319i | \(-0.443555\pi\) | ||||
0.176399 | + | 0.984319i | \(0.443555\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 366.912 | 0.341019 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 476.639i | 0.430640i | 0.976544 | + | 0.215320i | \(0.0690794\pi\) | ||||
−0.976544 | + | 0.215320i | \(0.930921\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1263.41i | 1.11021i | 0.831780 | + | 0.555106i | \(0.187322\pi\) | ||||
−0.831780 | + | 0.555106i | \(0.812678\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 406.860 | 0.347905 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −505.593 | −0.420905 | −0.210452 | − | 0.977604i | \(-0.567494\pi\) | ||||
−0.210452 | + | 0.977604i | \(0.567494\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3174.42i | 2.57405i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 38.9059i | − 0.0307423i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.17368 | −0.00244480 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −66.8758 | −0.0502448 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 91.6809i | − 0.0672080i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 965.706i | − 0.691003i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −703.892 | −0.491813 | −0.245907 | − | 0.969294i | \(-0.579086\pi\) | ||||
−0.245907 | + | 0.969294i | \(0.579086\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1270.64 | −0.867239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1171.40i | 0.781267i | 0.920546 | + | 0.390634i | \(0.127744\pi\) | ||||
−0.920546 | + | 0.390634i | \(0.872256\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 407.786i | 0.265861i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −471.745 | −0.300750 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2953.17 | 1.84165 | 0.920827 | − | 0.389972i | \(-0.127515\pi\) | ||||
0.920827 | + | 0.389972i | \(0.127515\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2649.44i | − 1.61671i | −0.588698 | − | 0.808353i | \(-0.700359\pi\) | ||||
0.588698 | − | 0.808353i | \(-0.299641\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 86.9411i | − 0.0519274i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 161.624 | 0.0945155 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4459.97 | 2.55435 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 147.000i | − 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2667.36i | − 1.46657i | −0.679923 | − | 0.733284i | \(-0.737987\pi\) | ||||
0.679923 | − | 0.733284i | \(-0.262013\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2149.89 | 1.15864 | 0.579322 | − | 0.815099i | \(-0.303317\pi\) | ||||
0.579322 | + | 0.815099i | \(0.303317\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.08045 | 0.00215611 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 525.846i | 0.272497i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 852.825i | 0.433521i | 0.976225 | + | 0.216761i | \(0.0695491\pi\) | ||||
−0.976225 | + | 0.216761i | \(0.930451\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −353.901 | −0.176517 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1271.80 | 0.622559 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2823.90i | 1.35696i | 0.734618 | + | 0.678481i | \(0.237362\pi\) | ||||
−0.734618 | + | 0.678481i | \(0.762638\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 1959.74i | − 0.924640i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2418.95 | −1.12086 | −0.560431 | − | 0.828201i | \(-0.689364\pi\) | ||||
−0.560431 | + | 0.828201i | \(0.689364\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2178.31 | 0.991494 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 524.296i | − 0.234467i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1578.81i | 0.693844i | 0.937894 | + | 0.346922i | \(0.112773\pi\) | ||||
−0.937894 | + | 0.346922i | \(0.887227\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1261.90 | −0.545090 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1341.94 | 0.569866 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1952.03i | 0.815093i | 0.913184 | + | 0.407547i | \(0.133616\pi\) | ||||
−0.913184 | + | 0.407547i | \(0.866384\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1098.00i | − 0.450904i | −0.974254 | − | 0.225452i | \(-0.927614\pi\) | ||||
0.974254 | − | 0.225452i | \(-0.0723859\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 67.2759 | 0.0271758 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2369.55 | −0.941693 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.9512i | 0.00662883i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2749.65 | 1.04166 | 0.520831 | − | 0.853660i | \(-0.325622\pi\) | ||||
0.520831 | + | 0.853660i | \(0.325622\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4324.91 | 1.61302 | 0.806512 | − | 0.591218i | \(-0.201353\pi\) | ||||
0.806512 | + | 0.591218i | \(0.201353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 226.588i | 0.0832118i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4628.81i | − 1.67406i | −0.547161 | − | 0.837028i | \(-0.684291\pi\) | ||||
0.547161 | − | 0.837028i | \(-0.315709\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5309.40 | 1.89132 | 0.945661 | − | 0.325153i | \(-0.105416\pi\) | ||||
0.945661 | + | 0.325153i | \(0.105416\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −738.394 | −0.259116 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1786.84i | − 0.617792i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 533.950i | 0.181916i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1635.17 | −0.549045 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2178.05 | 0.720857 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3782.53i | − 1.23412i | −0.786915 | − | 0.617061i | \(-0.788323\pi\) | ||||
0.786915 | − | 0.617061i | \(-0.211677\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 169.139i | − 0.0544094i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7400.23 | 2.34740 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 210.675 | 0.0659058 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 804.209i | − 0.248143i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1.95992i | 0 0.000596554i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1866.79 | 0.560580 | 0.280290 | − | 0.959915i | \(-0.409569\pi\) | ||||
0.280290 | + | 0.959915i | \(0.409569\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1622.44 | 0.480724 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4551.03i | 1.33067i | 0.746545 | + | 0.665335i | \(0.231711\pi\) | ||||
−0.746545 | + | 0.665335i | \(0.768289\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 5784.65i | − 1.66926i | −0.550811 | − | 0.834630i | \(-0.685681\pi\) | ||||
0.550811 | − | 0.834630i | \(-0.314319\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −785.152 | −0.223633 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2286.02 | −0.642757 | −0.321379 | − | 0.946951i | \(-0.604146\pi\) | ||||
−0.321379 | + | 0.946951i | \(0.604146\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 506.345i | 0.140555i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2894.03i | − 0.793196i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1448.66 | 0.392074 | 0.196037 | − | 0.980596i | \(-0.437193\pi\) | ||||
0.196037 | + | 0.980596i | \(0.437193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −778.931 | −0.208197 | −0.104098 | − | 0.994567i | \(-0.533196\pi\) | ||||
−0.104098 | + | 0.994567i | \(0.533196\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 856.129i | 0.223249i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −251.830 | −0.0648726 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3867.75 | 0.984372 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1351.67i | 0.339907i | 0.985452 | + | 0.169954i | \(0.0543618\pi\) | ||||
−0.985452 | + | 0.169954i | \(0.945638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 6792.90i | − 1.68801i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −23.7646 | −0.00583606 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5562.00 | −1.34999 | −0.674996 | − | 0.737821i | \(-0.735855\pi\) | ||||
−0.674996 | + | 0.737821i | \(0.735855\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 949.340i | 0.227757i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2297.37i | 0.544842i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 761.231 | 0.178477 | 0.0892387 | − | 0.996010i | \(-0.471557\pi\) | ||||
0.0892387 | + | 0.996010i | \(0.471557\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2061.12 | 0.477787 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 807.098i | 0.184995i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1069.55i | − 0.242422i | −0.992627 | − | 0.121211i | \(-0.961322\pi\) | ||||
0.992627 | − | 0.121211i | \(-0.0386778\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −132.954 | −0.0298022 | −0.0149011 | − | 0.999889i | \(-0.504743\pi\) | ||||
−0.0149011 | + | 0.999889i | \(0.504743\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 90.7804 | 0.0201256 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6740.02i | 1.47796i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4583.31i | − 0.994168i | −0.867703 | − | 0.497084i | \(-0.834404\pi\) | ||||
0.867703 | − | 0.497084i | \(-0.165596\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −270.868 | −0.0581235 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7961.29 | 1.69014 | 0.845072 | − | 0.534652i | \(-0.179557\pi\) | ||||
0.845072 | + | 0.534652i | \(0.179557\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8316.15i | 1.74680i | 0.487005 | + | 0.873399i | \(0.338089\pi\) | ||||
−0.487005 | + | 0.873399i | \(0.661911\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3053.50i | 0.634646i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 213.922 | 0.0439980 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4912.79 | −0.999958 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 2904.46i | − 0.585095i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 175.584i | − 0.0350093i | −0.999847 | − | 0.0175046i | \(-0.994428\pi\) | ||||
0.999847 | − | 0.0175046i | \(-0.00557218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7815.46 | −1.54249 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1009.48 | 0.197226 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 785.405i | 0.151910i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2964.83i | − 0.567741i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4996.41 | 0.947314 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −391.815 | −0.0735583 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 5368.85i | − 0.998100i | −0.866573 | − | 0.499050i | \(-0.833682\pi\) | ||||
0.866573 | − | 0.499050i | \(-0.166318\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1106.38i | − 0.203688i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4211.61 | 0.767906 | 0.383953 | − | 0.923353i | \(-0.374562\pi\) | ||||
0.383953 | + | 0.923353i | \(0.374562\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6473.79 | −1.16907 | −0.584537 | − | 0.811367i | \(-0.698724\pi\) | ||||
−0.584537 | + | 0.811367i | \(0.698724\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1100.74i | − 0.196887i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8116.09i | 1.43800i | 0.695011 | + | 0.718999i | \(0.255399\pi\) | ||||
−0.695011 | + | 0.718999i | \(0.744601\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9543.83 | −1.67508 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1429.92 | 0.248630 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 26.4119i | − 0.00454984i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 779.291i | − 0.133007i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3790.24 | 0.640981 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 202.862 | 0.0339944 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 2109.02i | − 0.350218i | −0.984549 | − | 0.175109i | \(-0.943972\pi\) | ||||
0.984549 | − | 0.175109i | \(-0.0560278\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 1220.58i | − 0.200863i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4300.41 | 0.701363 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4799.81 | 0.775852 | 0.387926 | − | 0.921690i | \(-0.373192\pi\) | ||||
0.387926 | + | 0.921690i | \(0.373192\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1516.78i | 0.243009i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1125.25i | − 0.178697i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9523.26 | 1.48613 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 6198.46i | − 0.958937i | −0.877559 | − | 0.479468i | \(-0.840830\pi\) | ||||
0.877559 | − | 0.479468i | \(-0.159170\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8792.41i | 1.34856i | 0.738476 | + | 0.674279i | \(0.235546\pi\) | ||||
−0.738476 | + | 0.674279i | \(0.764454\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −116.718 | −0.0177491 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10149.1 | −1.53027 | −0.765133 | − | 0.643872i | \(-0.777327\pi\) | ||||
−0.765133 | + | 0.643872i | \(0.777327\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 985.066i | 0.147273i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.52104i | 0.00141150i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1114.46 | 0.163842 | 0.0819208 | − | 0.996639i | \(-0.473895\pi\) | ||||
0.0819208 | + | 0.996639i | \(0.473895\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3465.34 | 0.505225 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 200.627i | 0.0290088i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4683.72i | 0.671663i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4455.22 | −0.633680 | −0.316840 | − | 0.948479i | \(-0.602622\pi\) | ||||
−0.316840 | + | 0.948479i | \(0.602622\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −275.043 | −0.0388026 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 825.768i | − 0.115557i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12462.7i | 1.73001i | 0.501762 | + | 0.865006i | \(0.332685\pi\) | ||||
−0.501762 | + | 0.865006i | \(0.667315\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2897.12 | −0.398951 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1103.47 | 0.150747 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8572.04i | 1.16178i | 0.813981 | + | 0.580892i | \(0.197296\pi\) | ||||
−0.813981 | + | 0.580892i | \(0.802704\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2111.67i | 0.283948i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1512.38 | 0.201772 | 0.100886 | − | 0.994898i | \(-0.467832\pi\) | ||||
0.100886 | + | 0.994898i | \(0.467832\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4572.73 | 0.605319 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3811.93i | 0.500700i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7534.31i | 0.982017i | 0.871155 | + | 0.491008i | \(0.163372\pi\) | ||||
−0.871155 | + | 0.491008i | \(0.836628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −82.3733 | −0.0106542 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3514.21 | 0.451065 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16854.9i | 2.14699i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1732.14i | − 0.218977i | −0.993988 | − | 0.109488i | \(-0.965079\pi\) | ||||
0.993988 | − | 0.109488i | \(-0.0349213\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1223.36 | 0.153495 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4360.84 | 0.543068 | 0.271534 | − | 0.962429i | \(-0.412469\pi\) | ||||
0.271534 | + | 0.962429i | \(0.412469\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 130.103i | 0.0160816i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1415.23i | 0.173638i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5070.58 | 0.617542 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4793.15 | −0.579476 | −0.289738 | − | 0.957106i | \(-0.593568\pi\) | ||||
−0.289738 | + | 0.957106i | \(0.593568\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 8859.52i | − 1.06328i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3131.19i | 0.373065i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22525.8 | −2.66445 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7948.31 | −0.933406 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5001.59i | 0.583159i | 0.956547 | + | 0.291580i | \(0.0941808\pi\) | ||||
−0.956547 | + | 0.291580i | \(0.905819\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 15021.2i | − 1.73892i | −0.494001 | − | 0.869461i | \(-0.664466\pi\) | ||||
0.494001 | − | 0.869461i | \(-0.335534\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −260.823 | −0.0299803 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 81.7321 | 0.00932844 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 156.977i | 0.0177908i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 484.873i | − 0.0545685i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8850.80 | −0.989160 | −0.494580 | − | 0.869132i | \(-0.664678\pi\) | ||||
−0.494580 | + | 0.869132i | \(0.664678\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9712.52 | 1.07795 | 0.538977 | − | 0.842321i | \(-0.318811\pi\) | ||||
0.538977 | + | 0.842321i | \(0.318811\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 13379.9i | − 1.47475i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10584.1i | 1.15860i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9005.22 | 0.979033 | 0.489517 | − | 0.871994i | \(-0.337173\pi\) | ||||
0.489517 | + | 0.871994i | \(0.337173\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −441.000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14131.1i | 1.51555i | 0.652519 | + | 0.757773i | \(0.273712\pi\) | ||||
−0.652519 | + | 0.757773i | \(0.726288\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 4700.54i | − 0.500735i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8002.08 | −0.846723 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17279.4 | −1.81619 | −0.908093 | − | 0.418769i | \(-0.862462\pi\) | ||||
−0.908093 | + | 0.418769i | \(0.862462\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1142.59i | − 0.119296i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 6449.66i | − 0.668944i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −528.706 | −0.0544749 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11926.0 | −1.22073 | −0.610365 | − | 0.792120i | \(-0.708977\pi\) | ||||
−0.610365 | + | 0.792120i | \(0.708977\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 12.2413i | − 0.00124483i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 771.769i | − 0.0779715i | −0.999240 | − | 0.0389858i | \(-0.987587\pi\) | ||||
0.999240 | − | 0.0389858i | \(-0.0124127\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3467.01 | −0.348003 | −0.174002 | − | 0.984745i | \(-0.555670\pi\) | ||||
−0.174002 | + | 0.984745i | \(0.555670\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1577.54 | 0.157326 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 7236.61i | − 0.717067i | −0.933517 | − | 0.358533i | \(-0.883277\pi\) | ||||
0.933517 | − | 0.358533i | \(-0.116723\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 1722.92i | − 0.169631i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2558.47 | 0.250294 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15835.7 | −1.53938 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 10501.7i | − 1.01443i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1061.70i | 0.101912i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6144.44 | 0.586110 | 0.293055 | − | 0.956096i | \(-0.405328\pi\) | ||||
0.293055 | + | 0.956096i | \(0.405328\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −586.268 | −0.0555749 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 3815.40i | − 0.359434i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16915.6i | 1.58371i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12917.5 | 1.20195 | 0.600974 | − | 0.799268i | \(-0.294779\pi\) | ||||
0.600974 | + | 0.799268i | \(0.294779\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8471.70 | 0.783443 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7964.15i | 0.732011i | 0.930613 | + | 0.366005i | \(0.119275\pi\) | ||||
−0.930613 | + | 0.366005i | \(0.880725\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 115.732i | 0.0105726i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5879.22 | −0.533841 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 394.657 | 0.0356193 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 17549.3i | − 1.57437i | −0.616714 | − | 0.787187i | \(-0.711537\pi\) | ||||
0.616714 | − | 0.787187i | \(-0.288463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7256.85i | 0.647130i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12194.7 | 1.08098 | 0.540492 | − | 0.841349i | \(-0.318238\pi\) | ||||
0.540492 | + | 0.841349i | \(0.318238\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29099.1 | −2.56415 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 6534.94i | − 0.572439i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10089.8i | 0.878633i | 0.898332 | + | 0.439316i | \(0.144779\pi\) | ||||
−0.898332 | + | 0.439316i | \(0.855221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1876.49 | 0.162448 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1572.89 | −0.135370 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6443.55i | 0.551333i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1083.52i | − 0.0921727i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4736.44 | 0.400591 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17003.4 | −1.42982 | −0.714908 | − | 0.699218i | \(-0.753532\pi\) | ||||
−0.714908 | + | 0.699218i | \(0.753532\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3626.50i | 0.303204i | 0.988442 | + | 0.151602i | \(0.0484432\pi\) | ||||
−0.988442 | + | 0.151602i | \(0.951557\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3785.70i | 0.314708i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.6452 | −0.00112789 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20842.8 | 1.71306 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 4025.81i | − 0.329012i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 132.108i | 0.0107359i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8327.85 | −0.672980 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5856.09 | 0.470594 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1832.02i | − 0.146402i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 13102.4i | − 1.04125i | −0.853786 | − | 0.520624i | \(-0.825699\pi\) | ||||
0.853786 | − | 0.520624i | \(-0.174301\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3294.00 | −0.260330 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −22074.4 | −1.73498 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 19947.4i | − 1.55921i | −0.626269 | − | 0.779607i | \(-0.715419\pi\) | ||||
0.626269 | − | 0.779607i | \(-0.284581\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 201.828i | − 0.0156900i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14870.4 | 1.14973 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6752.74 | 0.519269 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7108.66i | 0.543686i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 17285.5i | − 1.31492i | −0.753489 | − | 0.657461i | \(-0.771630\pi\) | ||||
0.753489 | − | 0.657461i | \(-0.228370\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1830.94 | 0.138534 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 50.8535 | 0.00382716 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 26089.4i | − 1.95300i | −0.215519 | − | 0.976500i | \(-0.569144\pi\) | ||||
0.215519 | − | 0.976500i | \(-0.430856\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 8833.74i | − 0.657767i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10919.5 | 0.804513 | 0.402257 | − | 0.915527i | \(-0.368226\pi\) | ||||
0.402257 | + | 0.915527i | \(0.368226\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1828.86i | 0.134037i | 0.997752 | + | 0.0670186i | \(0.0213487\pi\) | ||||
−0.997752 | + | 0.0670186i | \(0.978651\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 8248.94i | − 0.601404i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32752.8 | −2.37545 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16607.3 | 1.19822 | 0.599110 | − | 0.800667i | \(-0.295521\pi\) | ||||
0.599110 | + | 0.800667i | \(0.295521\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 12974.7i | − 0.931279i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9024.75i | 0.644423i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4410.57 | −0.313322 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 679.764 | 0.0480424 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 14955.1i | − 1.05156i | −0.850621 | − | 0.525779i | \(-0.823774\pi\) | ||||
0.850621 | − | 0.525779i | \(-0.176226\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1753.27i | 0.122653i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13886.4 | −0.966516 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11985.7 | −0.830003 | −0.415002 | − | 0.909821i | \(-0.636219\pi\) | ||||
−0.415002 | + | 0.909821i | \(0.636219\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 55.4506i | − 0.00382060i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 15928.2i | − 1.09196i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4441.72 | −0.302978 | −0.151489 | − | 0.988459i | \(-0.548407\pi\) | ||||
−0.151489 | + | 0.988459i | \(0.548407\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16036.0 | −1.08839 | −0.544194 | − | 0.838959i | \(-0.683164\pi\) | ||||
−0.544194 | + | 0.838959i | \(0.683164\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2215.18i | 0.149601i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 1168.46i | − 0.0785198i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27300.6 | 1.82553 | 0.912765 | − | 0.408484i | \(-0.133943\pi\) | ||||
0.912765 | + | 0.408484i | \(0.133943\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5360.53 | −0.356683 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 125.278i | 0.00829496i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9028.45i | 0.594871i | 0.954742 | + | 0.297435i | \(0.0961312\pi\) | ||||
−0.954742 | + | 0.297435i | \(0.903869\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1601.85 | 0.105029 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13495.7 | −0.880580 | −0.440290 | − | 0.897856i | \(-0.645124\pi\) | ||||
−0.440290 | + | 0.897856i | \(0.645124\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 20208.8i | − 1.31222i | −0.754667 | − | 0.656108i | \(-0.772202\pi\) | ||||
0.754667 | − | 0.656108i | \(-0.227798\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4905.52i | 0.316991i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1883.23 | −0.121107 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5661.11 | −0.362311 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 6534.16i | − 0.416187i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 61.4878i | − 0.00389774i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11819.1 | −0.745657 | −0.372828 | − | 0.927900i | \(-0.621612\pi\) | ||||
−0.372828 | + | 0.927900i | \(0.621612\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11347.6 | −0.712521 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 12298.4i | − 0.768579i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 211.821i | 0.0131753i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −507.416 | −0.0314133 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21519.7 | −1.32602 | −0.663009 | − | 0.748611i | \(-0.730721\pi\) | ||||
−0.663009 | + | 0.748611i | \(0.730721\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 12695.3i | − 0.778621i | −0.921107 | − | 0.389311i | \(-0.872713\pi\) | ||||
0.921107 | − | 0.389311i | \(-0.127287\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 22200.7i | − 1.35527i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19246.1 | −1.16946 | −0.584732 | − | 0.811227i | \(-0.698800\pi\) | ||||
−0.584732 | + | 0.811227i | \(0.698800\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16724.2 | 1.01153 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 632.026i | − 0.0380508i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 11147.0i | − 0.668020i | −0.942569 | − | 0.334010i | \(-0.891598\pi\) | ||||
0.942569 | − | 0.334010i | \(-0.108402\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20466.8 | −1.22092 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2412.63 | −0.143266 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5236.88i | 0.309560i | 0.987949 | + | 0.154780i | \(0.0494669\pi\) | ||||
−0.987949 | + | 0.154780i | \(0.950533\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 5099.28i | − 0.300059i | −0.988682 | − | 0.150030i | \(-0.952063\pi\) | ||||
0.988682 | − | 0.150030i | \(-0.0479369\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.87975 | −0.000344420 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7124.84 | −0.415473 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 46377.8i | − 2.69228i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 5600.37i | − 0.323651i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 838.441 | 0.0482380 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 653.573 | 0.0374344 | 0.0187172 | − | 0.999825i | \(-0.494042\pi\) | ||||
0.0187172 | + | 0.999825i | \(0.494042\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 4867.33i | − 0.277546i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1139.25i | − 0.0646751i | −0.999477 | − | 0.0323375i | \(-0.989705\pi\) | ||||
0.999477 | − | 0.0323375i | \(-0.0102951\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6777.08 | 0.383034 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13653.1 | 0.768263 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29280.6i | 1.64040i | 0.572079 | + | 0.820199i | \(0.306137\pi\) | ||||
−0.572079 | + | 0.820199i | \(0.693863\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 51597.9i | 2.87804i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17354.0 | −0.963748 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 509.956 | 0.0281971 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6960.69i | 0.383208i | 0.981472 | + | 0.191604i | \(0.0613690\pi\) | ||||
−0.981472 | + | 0.191604i | \(0.938631\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2355.46i | 0.129114i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 46291.0 | 2.52650 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.8555 | −0.000752963 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6858.07i | 0.371096i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 8817.36i | − 0.475074i | −0.971378 | − | 0.237537i | \(-0.923660\pi\) | ||||
0.971378 | − | 0.237537i | \(-0.0763401\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7900.56 | −0.423862 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1519.04 | 0.0811492 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11658.3i | 0.620163i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27251.2i | 1.44350i | 0.692155 | + | 0.721749i | \(0.256661\pi\) | ||||
−0.692155 | + | 0.721749i | \(0.743339\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8682.09 | −0.457952 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5468.10 | 0.287212 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2823.91i | 0.147704i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 4345.97i | − 0.226364i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19977.3 | −1.03620 | −0.518099 | − | 0.855321i | \(-0.673360\pi\) | ||||
−0.518099 | + | 0.855321i | \(0.673360\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2581.55 | 0.133345 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2336.79i | 0.120202i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 46016.7i | 2.35727i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20613.8 | 1.05161 | 0.525807 | − | 0.850604i | \(-0.323763\pi\) | ||||
0.525807 | + | 0.850604i | \(0.323763\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 192.029i | 0.00971608i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20567.6i | 1.03640i | 0.855259 | + | 0.518200i | \(0.173398\pi\) | ||||
−0.855259 | + | 0.518200i | \(0.826602\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2568.39 | 0.128893 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9202.41 | −0.459939 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 12830.6i | − 0.638673i | −0.947641 | − | 0.319337i | \(-0.896540\pi\) | ||||
0.947641 | − | 0.319337i | \(-0.103460\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 755.489i | 0.0374542i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11598.4 | 0.572686 | 0.286343 | − | 0.958127i | \(-0.407560\pi\) | ||||
0.286343 | + | 0.958127i | \(0.407560\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 46604.2 | 2.29187 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 11603.2i | − 0.568327i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3336.48i | 0.162767i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20829.8 | −1.01210 | −0.506052 | − | 0.862503i | \(-0.668895\pi\) | ||||
−0.506052 | + | 0.862503i | \(0.668895\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4055.01 | 0.196245 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 37562.9i | 1.81067i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9455.66i | 0.453992i | 0.973896 | + | 0.226996i | \(0.0728904\pi\) | ||||
−0.973896 | + | 0.226996i | \(0.927110\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20378.7 | −0.974572 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18076.5 | −0.861070 | −0.430535 | − | 0.902574i | \(-0.641675\pi\) | ||||
−0.430535 | + | 0.902574i | \(0.641675\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8843.89i | 0.419620i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 71.2937i | 0.00336945i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1933.68 | −0.0910313 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19101.1 | −0.895713 | −0.447857 | − | 0.894105i | \(-0.647813\pi\) | ||||
−0.447857 | + | 0.894105i | \(0.647813\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16686.0i | 0.779419i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 23720.6i | − 1.10371i | −0.833939 | − | 0.551857i | \(-0.813919\pi\) | ||||
0.833939 | − | 0.551857i | \(-0.186081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5425.54 | −0.251472 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2848.02 | 0.131496 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1780.29i | 0.0818815i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 2107.93i | − 0.0965783i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6892.11 | 0.314564 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14900.6 | −0.677483 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25919.3i | 1.17398i | 0.809593 | + | 0.586991i | \(0.199688\pi\) | ||||
−0.809593 | + | 0.586991i | \(0.800312\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 2283.69i | − 0.103044i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3539.15 | −0.159087 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −96.9418 | −0.00434112 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 6183.36i | − 0.275851i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18011.6i | 0.800505i | 0.916405 | + | 0.400253i | \(0.131078\pi\) | ||||
−0.916405 | + | 0.400253i | \(0.868922\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.1392 | −0.000581767 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2421.29 | 0.106807 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 10022.6i | − 0.440462i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22220.9i | 0.972901i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3208.65 | −0.139963 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8800.52 | −0.382459 | −0.191230 | − | 0.981545i | \(-0.561248\pi\) | ||||
−0.191230 | + | 0.981545i | \(0.561248\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 36022.4i | − 1.55970i | −0.625967 | − | 0.779850i | \(-0.715296\pi\) | ||||
0.625967 | − | 0.779850i | \(-0.284704\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 398.862i | 0.0172063i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −49339.2 | −2.12059 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24673.8 | 1.05658 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 272.341i | − 0.0116195i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17624.7i | 0.749216i | 0.927183 | + | 0.374608i | \(0.122223\pi\) | ||||
−0.927183 | + | 0.374608i | \(0.877777\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3193.42 | −0.135256 | −0.0676280 | − | 0.997711i | \(-0.521543\pi\) | ||||
−0.0676280 | + | 0.997711i | \(0.521543\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20220.1 | 0.853300 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35413.5i | 1.48906i | 0.667591 | + | 0.744528i | \(0.267325\pi\) | ||||
−0.667591 | + | 0.744528i | \(0.732675\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 41344.0i | − 1.73213i | −0.499932 | − | 0.866065i | \(-0.666642\pi\) | ||||
0.499932 | − | 0.866065i | \(-0.333358\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13749.9 | −0.573983 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.2158 | −0.000924047 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 42263.9i | − 1.75162i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 812.605i | 0.0335576i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39777.5 | 1.63679 | 0.818397 | − | 0.574653i | \(-0.194863\pi\) | ||||
0.818397 | + | 0.574653i | \(0.194863\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −40770.4 | −1.67167 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 23883.9i | − 0.975805i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 38059.5i | 1.54945i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −468.131 | −0.0189907 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24948.5 | 1.00851 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24640.2i | 0.992545i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 27194.4i | − 1.09158i | −0.837922 | − | 0.545790i | \(-0.816230\pi\) | ||||
0.837922 | − | 0.545790i | \(-0.183770\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9160.51 | 0.366413 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18965.3 | −0.755943 | −0.377972 | − | 0.925817i | \(-0.623378\pi\) | ||||
−0.377972 | + | 0.925817i | \(0.623378\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 32183.8i | − 1.27834i | −0.769064 | − | 0.639172i | \(-0.779277\pi\) | ||||
0.769064 | − | 0.639172i | \(-0.220723\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 641.766i | − 0.0254022i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3324.30 | −0.131125 | −0.0655624 | − | 0.997848i | \(-0.520884\pi\) | ||||
−0.0655624 | + | 0.997848i | \(0.520884\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27585.1 | −1.08430 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14738.4i | 0.577326i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 36067.5i | − 1.40795i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1064.00 | 0.0413916 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8713.38 | −0.337805 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 6759.94i | − 0.261174i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22741.2i | 0.875618i | 0.899068 | + | 0.437809i | \(0.144245\pi\) | ||||
−0.899068 | + | 0.437809i | \(0.855755\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −526.751 | −0.0202126 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34545.2 | 1.32107 | 0.660533 | − | 0.750797i | \(-0.270330\pi\) | ||||
0.660533 | + | 0.750797i | \(0.270330\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31171.3i | 1.18799i | 0.804467 | + | 0.593997i | \(0.202451\pi\) | ||||
−0.804467 | + | 0.593997i | \(0.797549\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23446.4i | 0.890555i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11015.2 | 0.416974 | 0.208487 | − | 0.978025i | \(-0.433146\pi\) | ||||
0.208487 | + | 0.978025i | \(0.433146\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4927.24 | −0.185888 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 3028.44i | − 0.113868i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1688.25i | 0.0632646i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34105.9 | −1.27378 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2356.22 | 0.0877054 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 7682.53i | − 0.285013i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53.4842i | 0.00197760i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8894.49 | −0.327785 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19184.3 | 0.704649 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28824.5i | 1.05524i | 0.849481 | + | 0.527620i | \(0.176915\pi\) | ||||
−0.849481 | + | 0.527620i | \(0.823085\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 14989.2i | − 0.546932i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4484.99 | 0.163111 | 0.0815556 | − | 0.996669i | \(-0.474011\pi\) | ||||
0.0815556 | + | 0.996669i | \(0.474011\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48202.7 | 1.74729 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1175.45i | 0.0424689i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8199.83i | 0.295291i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35988.2 | 1.29177 | 0.645887 | − | 0.763433i | \(-0.276488\pi\) | ||||
0.645887 | + | 0.763433i | \(0.276488\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16106.6 | −0.576253 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 243.722i | 0.00869145i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 24448.4i | − 0.869037i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3319.13 | −0.117599 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4954.03 | 0.174958 | 0.0874792 | − | 0.996166i | \(-0.472119\pi\) | ||||
0.0874792 | + | 0.996166i | \(0.472119\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2854.50i | 0.100486i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 12634.8i | − 0.443351i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −296.171 | −0.0103592 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17123.9 | −0.597027 | −0.298513 | − | 0.954405i | \(-0.596491\pi\) | ||||
−0.298513 | + | 0.954405i | \(0.596491\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19421.4i | 0.674965i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 54586.0i | − 1.89102i | −0.325590 | − | 0.945511i | \(-0.605563\pi\) | ||||
0.325590 | − | 0.945511i | \(-0.394437\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5552.37 | 0.191739 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3302.21 | −0.113673 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 24841.2i | − 0.852409i | −0.904627 | − | 0.426204i | \(-0.859850\pi\) | ||||
0.904627 | − | 0.426204i | \(-0.140150\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1158.83i | 0.0396388i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24348.3 | 0.830228 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20388.7 | −0.693028 | −0.346514 | − | 0.938045i | \(-0.612635\pi\) | ||||
−0.346514 | + | 0.938045i | \(0.612635\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48041.9i | 1.62785i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28631.5i | 0.967111i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20672.2 | 0.696080 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28885.2 | −0.969595 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 4289.75i | − 0.143547i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 75564.8i | 2.52074i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27543.1 | −0.915952 | −0.457976 | − | 0.888964i | \(-0.651425\pi\) | ||||
−0.457976 | + | 0.888964i | \(0.651425\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −79.2357 | −0.00262685 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 5698.52i | − 0.188336i | −0.995556 | − | 0.0941680i | \(-0.969981\pi\) | ||||
0.995556 | − | 0.0941680i | \(-0.0300191\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 18546.0i | − 0.611057i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2337.87 | −0.0767917 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25368.3 | −0.830711 | −0.415355 | − | 0.909659i | \(-0.636343\pi\) | ||||
−0.415355 | + | 0.909659i | \(0.636343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10058.6i | 0.328371i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 11370.7i | − 0.370070i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18984.9 | 0.615995 | 0.307998 | − | 0.951387i | \(-0.400341\pi\) | ||||
0.307998 | + | 0.951387i | \(0.400341\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 80874.6 | 2.61612 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 608.587i | − 0.0196267i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 76952.6i | − 2.47416i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52094.6 | 1.66987 | 0.834935 | − | 0.550349i | \(-0.185505\pi\) | ||||
0.834935 | + | 0.550349i | \(0.185505\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6327.06 | −0.202199 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 92765.9i | 2.95566i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 37144.6i | − 1.17992i | −0.807432 | − | 0.589961i | \(-0.799143\pi\) | ||||
0.807432 | − | 0.589961i | \(-0.200857\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3661.74 | −0.115968 |
(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 | 1344.4.c.g.673.6 | yes | 12 | |
4.3 | odd | 2 | 1344.4.c.f.673.12 | yes | 12 | ||
8.3 | odd | 2 | 1344.4.c.f.673.1 | ✓ | 12 | ||
8.5 | even | 2 | inner | 1344.4.c.g.673.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.c.f.673.1 | ✓ | 12 | 8.3 | odd | 2 | ||
1344.4.c.f.673.12 | yes | 12 | 4.3 | odd | 2 | ||
1344.4.c.g.673.6 | yes | 12 | 1.1 | even | 1 | trivial | |
1344.4.c.g.673.7 | yes | 12 | 8.5 | even | 2 | inner |