Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(1,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1620.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(95.5830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.560145.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 90x + 192 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(8.76746\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.949584 | 0.0512727 | 0.0256364 | − | 0.999671i | \(-0.491839\pi\) | ||||
0.0256364 | + | 0.999671i | \(0.491839\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 62.6552 | 1.71739 | 0.858693 | − | 0.512491i | \(-0.171277\pi\) | ||||
0.858693 | + | 0.512491i | \(0.171277\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.94958 | 0.148267 | 0.0741334 | − | 0.997248i | \(-0.476381\pi\) | ||||
0.0741334 | + | 0.997248i | \(0.476381\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −103.411 | −1.47535 | −0.737673 | − | 0.675158i | \(-0.764075\pi\) | ||||
−0.737673 | + | 0.675158i | \(0.764075\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 73.8064 | 0.891176 | 0.445588 | − | 0.895238i | \(-0.352995\pi\) | ||||
0.445588 | + | 0.895238i | \(0.352995\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 86.1591 | 0.781105 | 0.390552 | − | 0.920581i | \(-0.372284\pi\) | ||||
0.390552 | + | 0.920581i | \(0.372284\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −55.5624 | −0.355782 | −0.177891 | − | 0.984050i | \(-0.556927\pi\) | ||||
−0.177891 | + | 0.984050i | \(0.556927\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 199.865 | 1.15796 | 0.578980 | − | 0.815342i | \(-0.303451\pi\) | ||||
0.578980 | + | 0.815342i | \(0.303451\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.74792 | 0.0229299 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −18.9070 | −0.0840078 | −0.0420039 | − | 0.999117i | \(-0.513374\pi\) | ||||
−0.0420039 | + | 0.999117i | \(0.513374\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −57.3025 | −0.218272 | −0.109136 | − | 0.994027i | \(-0.534808\pi\) | ||||
−0.109136 | + | 0.994027i | \(0.534808\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 296.032 | 1.04987 | 0.524935 | − | 0.851142i | \(-0.324090\pi\) | ||||
0.524935 | + | 0.851142i | \(0.324090\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 57.5384 | 0.178571 | 0.0892856 | − | 0.996006i | \(-0.471542\pi\) | ||||
0.0892856 | + | 0.996006i | \(0.471542\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −342.098 | −0.997371 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 672.005 | 1.74164 | 0.870821 | − | 0.491600i | \(-0.163588\pi\) | ||||
0.870821 | + | 0.491600i | \(0.163588\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 313.276 | 0.768038 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −546.644 | −1.20622 | −0.603110 | − | 0.797658i | \(-0.706072\pi\) | ||||
−0.603110 | + | 0.797658i | \(0.706072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −791.559 | −1.66146 | −0.830728 | − | 0.556679i | \(-0.812075\pi\) | ||||
−0.830728 | + | 0.556679i | \(0.812075\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 34.7479 | 0.0663069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 631.560 | 1.15160 | 0.575801 | − | 0.817590i | \(-0.304690\pi\) | ||||
0.575801 | + | 0.817590i | \(0.304690\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 102.942 | 0.172069 | 0.0860346 | − | 0.996292i | \(-0.472580\pi\) | ||||
0.0860346 | + | 0.996292i | \(0.472580\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −200.652 | −0.321707 | −0.160853 | − | 0.986978i | \(-0.551425\pi\) | ||||
−0.160853 | + | 0.986978i | \(0.551425\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 59.4963 | 0.0880550 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −665.931 | −0.948394 | −0.474197 | − | 0.880419i | \(-0.657262\pi\) | ||||
−0.474197 | + | 0.880419i | \(0.657262\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1347.41 | 1.78189 | 0.890946 | − | 0.454109i | \(-0.150042\pi\) | ||||
0.890946 | + | 0.454109i | \(0.150042\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −517.056 | −0.659795 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.6866 | −0.0151099 | −0.00755496 | − | 0.999971i | \(-0.502405\pi\) | ||||
−0.00755496 | + | 0.999971i | \(0.502405\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.59922 | 0.00760204 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 369.032 | 0.398546 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −637.379 | −0.667175 | −0.333588 | − | 0.942719i | \(-0.608259\pi\) | ||||
−0.333588 | + | 0.942719i | \(0.608259\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −736.903 | −0.725986 | −0.362993 | − | 0.931792i | \(-0.618245\pi\) | ||||
−0.362993 | + | 0.931792i | \(0.618245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1396.64 | −1.33607 | −0.668034 | − | 0.744130i | \(-0.732864\pi\) | ||||
−0.668034 | + | 0.744130i | \(0.732864\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −181.225 | −0.163735 | −0.0818677 | − | 0.996643i | \(-0.526089\pi\) | ||||
−0.0818677 | + | 0.996643i | \(0.526089\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1495.62 | 1.31426 | 0.657132 | − | 0.753775i | \(-0.271769\pi\) | ||||
0.657132 | + | 0.753775i | \(0.271769\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2238.50 | 1.86354 | 0.931771 | − | 0.363048i | \(-0.118264\pi\) | ||||
0.931771 | + | 0.363048i | \(0.118264\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 430.795 | 0.349321 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −98.1976 | −0.0756450 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2594.67 | 1.94941 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1163.69 | 0.813075 | 0.406537 | − | 0.913634i | \(-0.366736\pi\) | ||||
0.406537 | + | 0.913634i | \(0.366736\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −98.9947 | −0.0660245 | −0.0330122 | − | 0.999455i | \(-0.510510\pi\) | ||||
−0.0330122 | + | 0.999455i | \(0.510510\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 70.0854 | 0.0456930 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 174.907 | 0.109076 | 0.0545378 | − | 0.998512i | \(-0.482631\pi\) | ||||
0.0545378 | + | 0.998512i | \(0.482631\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 981.514 | 0.598928 | 0.299464 | − | 0.954108i | \(-0.403192\pi\) | ||||
0.299464 | + | 0.954108i | \(0.403192\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 435.427 | 0.254631 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −277.812 | −0.159111 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2306.94 | 1.26840 | 0.634200 | − | 0.773169i | \(-0.281330\pi\) | ||||
0.634200 | + | 0.773169i | \(0.281330\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1981.80 | −1.06806 | −0.534029 | − | 0.845466i | \(-0.679323\pi\) | ||||
−0.534029 | + | 0.845466i | \(0.679323\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 999.323 | 0.517855 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −433.147 | −0.220184 | −0.110092 | − | 0.993921i | \(-0.535115\pi\) | ||||
−0.110092 | + | 0.993921i | \(0.535115\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 81.8153 | 0.0400494 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3447.72 | 1.65673 | 0.828363 | − | 0.560192i | \(-0.189273\pi\) | ||||
0.828363 | + | 0.560192i | \(0.189273\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1054.89 | 0.488801 | 0.244401 | − | 0.969674i | \(-0.421409\pi\) | ||||
0.244401 | + | 0.969674i | \(0.421409\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2148.70 | −0.978017 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 632.144 | 0.277809 | 0.138905 | − | 0.990306i | \(-0.455642\pi\) | ||||
0.138905 | + | 0.990306i | \(0.455642\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23.7396 | 0.0102545 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1329.33 | 0.555078 | 0.277539 | − | 0.960714i | \(-0.410481\pi\) | ||||
0.277539 | + | 0.960714i | \(0.410481\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1468.52 | 0.603062 | 0.301531 | − | 0.953456i | \(-0.402502\pi\) | ||||
0.301531 | + | 0.953456i | \(0.402502\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −94.5349 | −0.0375694 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6479.24 | −2.53374 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 482.390 | 0.182746 | 0.0913732 | − | 0.995817i | \(-0.470874\pi\) | ||||
0.0913732 | + | 0.995817i | \(0.470874\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −343.353 | −0.128057 | −0.0640287 | − | 0.997948i | \(-0.520395\pi\) | ||||
−0.0640287 | + | 0.997948i | \(0.520395\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4507.54 | 1.63020 | 0.815099 | − | 0.579321i | \(-0.196682\pi\) | ||||
0.815099 | + | 0.579321i | \(0.196682\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1750.03 | −0.623397 | −0.311699 | − | 0.950181i | \(-0.600898\pi\) | ||||
−0.311699 | + | 0.950181i | \(0.600898\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −52.7612 | −0.0182419 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −286.512 | −0.0976141 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4624.35 | 1.53049 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5200.05 | −1.69662 | −0.848308 | − | 0.529502i | \(-0.822379\pi\) | ||||
−0.848308 | + | 0.529502i | \(0.822379\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1480.16 | 0.469516 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 189.788 | 0.0593717 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −718.664 | −0.218745 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2905.47 | −0.872489 | −0.436244 | − | 0.899828i | \(-0.643692\pi\) | ||||
−0.436244 | + | 0.899828i | \(0.643692\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1734.02 | 0.507009 | 0.253504 | − | 0.967334i | \(-0.418417\pi\) | ||||
0.253504 | + | 0.967334i | \(0.418417\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3472.97 | 1.00218 | 0.501092 | − | 0.865394i | \(-0.332932\pi\) | ||||
0.501092 | + | 0.865394i | \(0.332932\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −595.216 | −0.167356 | −0.0836779 | − | 0.996493i | \(-0.526667\pi\) | ||||
−0.0836779 | + | 0.996493i | \(0.526667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 287.692 | 0.0798595 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2179.16 | 0.589784 | 0.294892 | − | 0.955531i | \(-0.404716\pi\) | ||||
0.294892 | + | 0.955531i | \(0.404716\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4362.16 | −1.16594 | −0.582970 | − | 0.812494i | \(-0.698109\pi\) | ||||
−0.582970 | + | 0.812494i | \(0.698109\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1710.49 | −0.446038 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 512.924 | 0.132132 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2738.00 | 0.688531 | 0.344266 | − | 0.938872i | \(-0.388128\pi\) | ||||
0.344266 | + | 0.938872i | \(0.388128\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5398.31 | 1.34146 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1995.09 | −0.484243 | −0.242122 | − | 0.970246i | \(-0.577843\pi\) | ||||
−0.242122 | + | 0.970246i | \(0.577843\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.9538 | −0.00430731 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2553.56 | −0.598705 | −0.299352 | − | 0.954143i | \(-0.596771\pi\) | ||||
−0.299352 | + | 0.954143i | \(0.596771\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3360.03 | 0.778886 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4534.66 | 1.02782 | 0.513909 | − | 0.857845i | \(-0.328197\pi\) | ||||
0.513909 | + | 0.857845i | \(0.328197\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4390.49 | 0.984145 | 0.492073 | − | 0.870554i | \(-0.336239\pi\) | ||||
0.492073 | + | 0.870554i | \(0.336239\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1566.38 | 0.343477 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6726.79 | 1.45911 | 0.729555 | − | 0.683922i | \(-0.239727\pi\) | ||||
0.729555 | + | 0.683922i | \(0.239727\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7238.73 | 1.53675 | 0.768374 | − | 0.640001i | \(-0.221066\pi\) | ||||
0.768374 | + | 0.640001i | \(0.221066\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7453.35 | 1.56557 | 0.782784 | − | 0.622293i | \(-0.213799\pi\) | ||||
0.782784 | + | 0.622293i | \(0.213799\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −54.4135 | −0.0111914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5780.86 | 1.17665 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3064.73 | 0.611071 | 0.305535 | − | 0.952181i | \(-0.401165\pi\) | ||||
0.305535 | + | 0.952181i | \(0.401165\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2733.22 | −0.539438 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 598.770 | 0.115812 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 281.107 | 0.0538297 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3957.80 | −0.743026 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7427.82 | 1.38087 | 0.690437 | − | 0.723393i | \(-0.257418\pi\) | ||||
0.690437 | + | 0.723393i | \(0.257418\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7574.79 | 1.38111 | 0.690557 | − | 0.723278i | \(-0.257365\pi\) | ||||
0.690557 | + | 0.723278i | \(0.257365\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8628.60 | −1.55820 | −0.779101 | − | 0.626898i | \(-0.784324\pi\) | ||||
−0.779101 | + | 0.626898i | \(0.784324\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2946.09 | 0.521983 | 0.260992 | − | 0.965341i | \(-0.415951\pi\) | ||||
0.260992 | + | 0.965341i | \(0.415951\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3481.27 | −0.611015 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7632.40 | −1.31479 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 173.740 | 0.0296534 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 54.6376 | 0.00915583 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3137.45 | 0.520996 | 0.260498 | − | 0.965474i | \(-0.416113\pi\) | ||||
0.260498 | + | 0.965474i | \(0.416113\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3157.80 | 0.515012 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3715.74 | −0.600621 | −0.300311 | − | 0.953841i | \(-0.597090\pi\) | ||||
−0.300311 | + | 0.953841i | \(0.597090\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12522.5 | 1.98866 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −650.559 | −0.102411 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6060.02 | 0.937518 | 0.468759 | − | 0.883326i | \(-0.344701\pi\) | ||||
0.468759 | + | 0.883326i | \(0.344701\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5634.65 | −0.864229 | −0.432115 | − | 0.901819i | \(-0.642232\pi\) | ||||
−0.432115 | + | 0.901819i | \(0.642232\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4557.89 | 0.687229 | 0.343614 | − | 0.939111i | \(-0.388349\pi\) | ||||
0.343614 | + | 0.939111i | \(0.388349\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 514.708 | 0.0769517 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3206.54 | −0.471406 | −0.235703 | − | 0.971825i | \(-0.575739\pi\) | ||||
−0.235703 | + | 0.971825i | \(0.575739\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1411.62 | −0.205805 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1003.26 | −0.143872 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8700.21 | −1.23746 | −0.618730 | − | 0.785604i | \(-0.712352\pi\) | ||||
−0.618730 | + | 0.785604i | \(0.712352\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 638.126 | 0.0892987 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12722.5 | 1.76607 | 0.883035 | − | 0.469308i | \(-0.155497\pi\) | ||||
0.883035 | + | 0.469308i | \(0.155497\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −386.135 | −0.0527506 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1339.34 | 0.181523 | 0.0907613 | − | 0.995873i | \(-0.471070\pi\) | ||||
0.0907613 | + | 0.995873i | \(0.471070\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4729.50 | −0.630982 | −0.315491 | − | 0.948928i | \(-0.602169\pi\) | ||||
−0.315491 | + | 0.948928i | \(0.602169\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 297.482 | 0.0393794 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4838.38 | −0.630631 | −0.315316 | − | 0.948987i | \(-0.602110\pi\) | ||||
−0.315316 | + | 0.948987i | \(0.602110\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8909.81 | −1.15240 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3329.66 | −0.424135 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7768.23 | −0.982056 | −0.491028 | − | 0.871144i | \(-0.663379\pi\) | ||||
−0.491028 | + | 0.871144i | \(0.663379\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5207.07 | −0.648450 | −0.324225 | − | 0.945980i | \(-0.605104\pi\) | ||||
−0.324225 | + | 0.945980i | \(0.605104\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1388.98 | 0.171687 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1184.62 | −0.144274 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7831.43 | −0.946795 | −0.473398 | − | 0.880849i | \(-0.656973\pi\) | ||||
−0.473398 | + | 0.880849i | \(0.656973\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −519.085 | −0.0618462 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6737.03 | 0.796886 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11700.2 | −1.36419 | −0.682093 | − | 0.731265i | \(-0.738930\pi\) | ||||
−0.682093 | + | 0.731265i | \(0.738930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3235.99 | −0.374614 | −0.187307 | − | 0.982301i | \(-0.559976\pi\) | ||||
−0.187307 | + | 0.982301i | \(0.559976\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2585.28 | −0.295069 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −751.652 | −0.0851874 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7828.48 | 0.874907 | 0.437453 | − | 0.899241i | \(-0.355881\pi\) | ||||
0.437453 | + | 0.899241i | \(0.355881\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11016.3 | −1.22265 | −0.611327 | − | 0.791378i | \(-0.709364\pi\) | ||||
−0.611327 | + | 0.791378i | \(0.709364\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6359.09 | 0.696102 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −648.915 | −0.0705491 | −0.0352745 | − | 0.999378i | \(-0.511231\pi\) | ||||
−0.0352745 | + | 0.999378i | \(0.511231\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 914.423 | 0.0980712 | 0.0490356 | − | 0.998797i | \(-0.484385\pi\) | ||||
0.0490356 | + | 0.998797i | \(0.484385\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −63.4332 | −0.00675736 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9663.37 | 1.01569 | 0.507843 | − | 0.861450i | \(-0.330443\pi\) | ||||
0.507843 | + | 0.861450i | \(0.330443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3590.30 | −0.374857 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 32.9961 | 0.00339974 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8945.84 | 0.915686 | 0.457843 | − | 0.889033i | \(-0.348622\pi\) | ||||
0.457843 | + | 0.889033i | \(0.348622\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6388.10 | −0.645388 | −0.322694 | − | 0.946503i | \(-0.604588\pi\) | ||||
−0.322694 | + | 0.946503i | \(0.604588\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −189.765 | −0.0190478 | −0.00952389 | − | 0.999955i | \(-0.503032\pi\) | ||||
−0.00952389 | + | 0.999955i | \(0.503032\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17087.3 | 1.69317 | 0.846583 | − | 0.532257i | \(-0.178656\pi\) | ||||
0.846583 | + | 0.532257i | \(0.178656\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 599.719 | 0.0590458 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18547.9 | 1.80303 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1845.16 | 0.178235 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7748.19 | −0.739089 | −0.369545 | − | 0.929213i | \(-0.620486\pi\) | ||||
−0.369545 | + | 0.929213i | \(0.620486\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −131.396 | −0.0124556 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3186.89 | −0.298370 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5330.93 | 0.496032 | 0.248016 | − | 0.968756i | \(-0.420221\pi\) | ||||
0.248016 | + | 0.968756i | \(0.420221\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14497.8 | −1.33254 | −0.666269 | − | 0.745712i | \(-0.732110\pi\) | ||||
−0.666269 | + | 0.745712i | \(0.732110\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5745.77 | 0.524901 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 97.7516 | 0.00882246 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3062.84 | −0.274772 | −0.137386 | − | 0.990518i | \(-0.543870\pi\) | ||||
−0.137386 | + | 0.990518i | \(0.543870\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10683.8 | −0.947055 | −0.473527 | − | 0.880779i | \(-0.657020\pi\) | ||||
−0.473527 | + | 0.880779i | \(0.657020\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3684.52 | −0.324671 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14374.4 | 1.25174 | 0.625868 | − | 0.779929i | \(-0.284745\pi\) | ||||
0.625868 | + | 0.779929i | \(0.284745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −190.536 | −0.0164948 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6983.20 | −0.597508 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3605.08 | 0.306676 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9386.82 | −0.789336 | −0.394668 | − | 0.918824i | \(-0.629140\pi\) | ||||
−0.394668 | + | 0.918824i | \(0.629140\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15352.7 | 1.28361 | 0.641805 | − | 0.766868i | \(-0.278186\pi\) | ||||
0.641805 | + | 0.766868i | \(0.278186\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20668.2 | −1.70839 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4743.62 | −0.389876 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −398.229 | −0.0323625 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −906.125 | −0.0732247 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21434.2 | −1.71287 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23730.6 | −1.88588 | −0.942938 | − | 0.332968i | \(-0.891950\pi\) | ||||
−0.942938 | + | 0.332968i | \(0.891950\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7478.12 | 0.587757 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13140.6 | −1.02715 | −0.513577 | − | 0.858043i | \(-0.671680\pi\) | ||||
−0.513577 | + | 0.858043i | \(0.671680\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4100.86 | −0.317064 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −632.358 | −0.0486268 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19848.3 | −1.50987 | −0.754935 | − | 0.655800i | \(-0.772332\pi\) | ||||
−0.754935 | + | 0.655800i | \(0.772332\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2057.30 | 0.155661 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18601.9 | 1.39250 | 0.696250 | − | 0.717800i | \(-0.254851\pi\) | ||||
0.696250 | + | 0.717800i | \(0.254851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11192.5 | 0.833401 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19378.0 | 1.42771 | 0.713857 | − | 0.700292i | \(-0.246947\pi\) | ||||
0.713857 | + | 0.700292i | \(0.246947\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4682.33 | 0.343169 | 0.171584 | − | 0.985169i | \(-0.445111\pi\) | ||||
0.171584 | + | 0.985169i | \(0.445111\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2153.98 | 0.156221 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20543.6 | −1.48222 | −0.741111 | − | 0.671382i | \(-0.765701\pi\) | ||||
−0.741111 | + | 0.671382i | \(0.765701\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1279.48 | 0.0913625 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42104.6 | 2.99107 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3698.34 | −0.260046 | −0.130023 | − | 0.991511i | \(-0.541505\pi\) | ||||
−0.130023 | + | 0.991511i | \(0.541505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14751.3 | 1.03195 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9685.31 | −0.670705 | −0.335353 | − | 0.942093i | \(-0.608855\pi\) | ||||
−0.335353 | + | 0.942093i | \(0.608855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −490.988 | −0.0338295 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14009.7 | −0.955629 | −0.477814 | − | 0.878461i | \(-0.658571\pi\) | ||||
−0.477814 | + | 0.878461i | \(0.658571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3243.57 | −0.220146 | −0.110073 | − | 0.993923i | \(-0.535108\pi\) | ||||
−0.110073 | + | 0.993923i | \(0.535108\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12973.3 | 0.871804 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11726.6 | −0.784135 | −0.392068 | − | 0.919936i | \(-0.628240\pi\) | ||||
−0.392068 | + | 0.919936i | \(0.628240\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 399.868 | 0.0264762 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20343.9 | 1.34043 | 0.670215 | − | 0.742167i | \(-0.266202\pi\) | ||||
0.670215 | + | 0.742167i | \(0.266202\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21893.5 | −1.42852 | −0.714260 | − | 0.699880i | \(-0.753237\pi\) | ||||
−0.714260 | + | 0.699880i | \(0.753237\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29767.0 | 1.93285 | 0.966426 | − | 0.256944i | \(-0.0827157\pi\) | ||||
0.966426 | + | 0.256944i | \(0.0827157\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0470 | −0.000774726 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1955.19 | 0.123941 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6594.67 | −0.416054 | −0.208027 | − | 0.978123i | \(-0.566704\pi\) | ||||
−0.208027 | + | 0.978123i | \(0.566704\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5818.43 | 0.363618 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2377.44 | −0.147877 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16161.4 | −0.995847 | −0.497923 | − | 0.867221i | \(-0.665904\pi\) | ||||
−0.497923 | + | 0.867221i | \(0.665904\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15876.2 | −0.973710 | −0.486855 | − | 0.873483i | \(-0.661856\pi\) | ||||
−0.486855 | + | 0.873483i | \(0.661856\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 624.258 | 0.0379322 | 0.0189661 | − | 0.999820i | \(-0.493963\pi\) | ||||
0.0189661 | + | 0.999820i | \(0.493963\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34250.1 | −2.07155 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10146.4 | −0.608053 | −0.304027 | − | 0.952664i | \(-0.598331\pi\) | ||||
−0.304027 | + | 0.952664i | \(0.598331\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −494.973 | −0.0295270 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24050.3 | −1.42165 | −0.710826 | − | 0.703368i | \(-0.751679\pi\) | ||||
−0.710826 | + | 0.703368i | \(0.751679\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −986.004 | −0.0580198 | −0.0290099 | − | 0.999579i | \(-0.509235\pi\) | ||||
−0.0290099 | + | 0.999579i | \(0.509235\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 350.427 | 0.0204345 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4787.20 | −0.277903 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −49595.3 | −2.85336 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30055.5 | 1.72148 | 0.860739 | − | 0.509046i | \(-0.170002\pi\) | ||||
0.860739 | + | 0.509046i | \(0.170002\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22370.6 | −1.26997 | −0.634986 | − | 0.772523i | \(-0.718994\pi\) | ||||
−0.634986 | + | 0.772523i | \(0.718994\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −605.245 | −0.0342079 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27040.9 | −1.51492 | −0.757460 | − | 0.652881i | \(-0.773560\pi\) | ||||
−0.757460 | + | 0.652881i | \(0.773560\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 874.537 | 0.0487801 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4670.16 | 0.258228 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22601.5 | −1.24429 | −0.622143 | − | 0.782904i | \(-0.713738\pi\) | ||||
−0.622143 | + | 0.782904i | \(0.713738\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4907.57 | 0.267849 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5925.72 | 0.322027 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20238.5 | 1.09044 | 0.545219 | − | 0.838294i | \(-0.316446\pi\) | ||||
0.545219 | + | 0.838294i | \(0.316446\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1395.46 | −0.0748658 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −699.752 | −0.0372233 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7959.77 | 0.421630 | 0.210815 | − | 0.977526i | \(-0.432388\pi\) | ||||
0.210815 | + | 0.977526i | \(0.432388\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17220.1 | 0.904488 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2177.14 | 0.113875 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22376.4 | 1.16064 | 0.580320 | − | 0.814389i | \(-0.302928\pi\) | ||||
0.580320 | + | 0.814389i | \(0.302928\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1326.23 | −0.0685039 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1389.06 | −0.0711564 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13278.2 | 0.677389 | 0.338694 | − | 0.940896i | \(-0.390015\pi\) | ||||
0.338694 | + | 0.940896i | \(0.390015\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30613.0 | −1.54892 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11726.7 | −0.590906 | −0.295453 | − | 0.955357i | \(-0.595471\pi\) | ||||
−0.295453 | + | 0.955357i | \(0.595471\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39570.5 | 1.97774 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10822.8 | −0.538733 | −0.269366 | − | 0.963038i | \(-0.586814\pi\) | ||||
−0.269366 | + | 0.963038i | \(0.586814\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15108.6 | 0.746003 | 0.373002 | − | 0.927831i | \(-0.378329\pi\) | ||||
0.373002 | + | 0.927831i | \(0.378329\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11534.7 | 0.567246 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −172.088 | −0.00839516 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3929.51 | −0.190932 | −0.0954659 | − | 0.995433i | \(-0.530434\pi\) | ||||
−0.0954659 | + | 0.995433i | \(0.530434\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9909.01 | −0.477650 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32082.2 | −1.54035 | −0.770176 | − | 0.637831i | \(-0.779832\pi\) | ||||
−0.770176 | + | 0.637831i | \(0.779832\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29348.1 | −1.39799 | −0.698994 | − | 0.715128i | \(-0.746368\pi\) | ||||
−0.698994 | + | 0.715128i | \(0.746368\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1420.22 | 0.0673860 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3798.95 | −0.178842 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15550.8 | 0.729230 | 0.364615 | − | 0.931158i | \(-0.381201\pi\) | ||||
0.364615 | + | 0.931158i | \(0.381201\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29954.5 | −1.39378 | −0.696888 | − | 0.717180i | \(-0.745433\pi\) | ||||
−0.696888 | + | 0.717180i | \(0.745433\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4996.62 | 0.231592 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4229.29 | −0.194519 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6449.82 | 0.295509 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2165.73 | −0.0984692 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15602.2 | −0.706683 | −0.353341 | − | 0.935494i | \(-0.614955\pi\) | ||||
−0.353341 | + | 0.935494i | \(0.614955\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2125.64 | 0.0955488 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5501.01 | −0.246339 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30628.9 | −1.36127 | −0.680635 | − | 0.732623i | \(-0.738296\pi\) | ||||
−0.680635 | + | 0.732623i | \(0.738296\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5950.12 | −0.263454 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12571.9 | −0.552494 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 409.076 | 0.0179106 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19959.7 | −0.867425 | −0.433713 | − | 0.901051i | \(-0.642797\pi\) | ||||
−0.433713 | + | 0.901051i | \(0.642797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3768.40 | 0.163165 | 0.0815823 | − | 0.996667i | \(-0.474003\pi\) | ||||
0.0815823 | + | 0.996667i | \(0.474003\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17238.6 | 0.740910 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21849.0 | 0.935619 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29287.6 | 1.24500 | 0.622500 | − | 0.782620i | \(-0.286117\pi\) | ||||
0.622500 | + | 0.782620i | \(0.286117\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1061.18 | −0.0449459 | −0.0224729 | − | 0.999747i | \(-0.507154\pi\) | ||||
−0.0224729 | + | 0.999747i | \(0.507154\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43016.7 | −1.80875 | −0.904375 | − | 0.426739i | \(-0.859662\pi\) | ||||
−0.904375 | + | 0.426739i | \(0.859662\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27947.5 | −1.17088 | −0.585439 | − | 0.810716i | \(-0.699078\pi\) | ||||
−0.585439 | + | 0.810716i | \(0.699078\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35376.8 | 1.47147 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5274.45 | 0.218599 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13095.6 | 0.538866 | 0.269433 | − | 0.963019i | \(-0.413164\pi\) | ||||
0.269433 | + | 0.963019i | \(0.413164\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21301.8 | −0.873419 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10743.5 | −0.437382 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2463.86 | 0.0999517 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1629.01 | −0.0656189 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32225.5 | 1.29353 | 0.646764 | − | 0.762690i | \(-0.276122\pi\) | ||||
0.646764 | + | 0.762690i | \(0.276122\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5251.95 | −0.209339 | −0.104669 | − | 0.994507i | \(-0.533378\pi\) | ||||
−0.104669 | + | 0.994507i | \(0.533378\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35129.6 | −1.39535 | −0.697675 | − | 0.716414i | \(-0.745782\pi\) | ||||
−0.697675 | + | 0.716414i | \(0.745782\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −47402.3 | −1.86975 | −0.934874 | − | 0.354979i | \(-0.884488\pi\) | ||||
−0.934874 | + | 0.354979i | \(0.884488\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3160.72 | 0.124240 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41724.0 | −1.62876 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4389.08 | 0.170744 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 118.698 | 0.00458597 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23727.3 | 0.913584 | 0.456792 | − | 0.889573i | \(-0.348998\pi\) | ||||
0.456792 | + | 0.889573i | \(0.348998\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43690.9 | 1.67081 | 0.835406 | − | 0.549634i | \(-0.185233\pi\) | ||||
0.835406 | + | 0.549634i | \(0.185233\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7852.57 | 0.299275 | 0.149638 | − | 0.988741i | \(-0.452189\pi\) | ||||
0.149638 | + | 0.988741i | \(0.452189\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16014.3 | 0.606209 | 0.303105 | − | 0.952957i | \(-0.401977\pi\) | ||||
0.303105 | + | 0.952957i | \(0.401977\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1105.02 | 0.0416886 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4246.71 | 0.159138 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6646.66 | 0.248238 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11105.0 | −0.411981 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −69492.8 | −2.56952 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7342.60 | 0.269698 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25873.3 | 0.947200 | 0.473600 | − | 0.880740i | \(-0.342954\pi\) | ||||
0.473600 | + | 0.880740i | \(0.342954\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23293.1 | −0.847128 | −0.423564 | − | 0.905866i | \(-0.639221\pi\) | ||||
−0.423564 | + | 0.905866i | \(0.639221\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 84421.9 | 3.06020 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −94.0038 | −0.00338525 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42422.5 | 1.52273 | 0.761365 | − | 0.648323i | \(-0.224529\pi\) | ||||
0.761365 | + | 0.648323i | \(0.224529\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 715.401 | 0.0255121 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −472.674 | −0.0168016 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34596.0 | −1.22181 | −0.610903 | − | 0.791705i | \(-0.709193\pi\) | ||||
−0.610903 | + | 0.791705i | \(0.709193\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25249.0 | −0.888833 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −32396.2 | −1.13312 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17173.8 | 0.598767 | 0.299383 | − | 0.954133i | \(-0.403219\pi\) | ||||
0.299383 | + | 0.954133i | \(0.403219\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33493.5 | 1.16032 | 0.580158 | − | 0.814504i | \(-0.302991\pi\) | ||||
0.580158 | + | 0.814504i | \(0.302991\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4937.13 | −0.170493 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21477.0 | −0.736968 | −0.368484 | − | 0.929634i | \(-0.620123\pi\) | ||||
−0.368484 | + | 0.929634i | \(0.620123\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1394.45 | −0.0476984 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19415.1 | −0.659934 | −0.329967 | − | 0.943992i | \(-0.607038\pi\) | ||||
−0.329967 | + | 0.943992i | \(0.607038\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2411.95 | 0.0817266 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 166.089 | 0.00559260 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10154.9 | 0.340870 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1716.77 | −0.0572691 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54931.8 | −1.82677 | −0.913386 | − | 0.407094i | \(-0.866542\pi\) | ||||
−0.913386 | + | 0.407094i | \(0.866542\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.202715 | −6.69972e−6 0 | −3.34986e−6 | − | 1.00000i | \(-0.500001\pi\) | ||||
−3.34986e−6 | 1.00000i | \(0.500001\pi\) | ||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 932.030 | 0.0307086 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22873.5 | 0.749015 | 0.374508 | − | 0.927224i | \(-0.377812\pi\) | ||||
0.374508 | + | 0.927224i | \(0.377812\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −794.884 | −0.0259495 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26259.5 | −0.852032 | −0.426016 | − | 0.904716i | \(-0.640083\pi\) | ||||
−0.426016 | + | 0.904716i | \(0.640083\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22537.7 | 0.729047 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25505.8 | 0.820058 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40250.1 | −1.29020 | −0.645099 | − | 0.764099i | \(-0.723184\pi\) | ||||
−0.645099 | + | 0.764099i | \(0.723184\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8750.13 | −0.278792 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59087.1 | −1.87694 | −0.938469 | − | 0.345362i | \(-0.887756\pi\) | ||||
−0.938469 | + | 0.345362i | \(0.887756\pi\) | |||||||
\(998\) | 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 | 1620.4.a.f.1.2 | yes | 3 | |
3.2 | odd | 2 | 1620.4.a.d.1.2 | ✓ | 3 | ||
9.2 | odd | 6 | 1620.4.i.u.1081.2 | 6 | |||
9.4 | even | 3 | 1620.4.i.s.541.2 | 6 | |||
9.5 | odd | 6 | 1620.4.i.u.541.2 | 6 | |||
9.7 | even | 3 | 1620.4.i.s.1081.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.4.a.d.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
1620.4.a.f.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
1620.4.i.s.541.2 | 6 | 9.4 | even | 3 | |||
1620.4.i.s.1081.2 | 6 | 9.7 | even | 3 | |||
1620.4.i.u.541.2 | 6 | 9.5 | odd | 6 | |||
1620.4.i.u.1081.2 | 6 | 9.2 | odd | 6 |