Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(895,1344)]
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([1, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.895");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.b (of order \(2\), degree \(1\), not 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: | \(24\) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.9 | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.j.895.16 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 5.77465i | − | 0.516501i | −0.966078 | − | 0.258250i | \(-0.916854\pi\) | ||
0.966078 | − | 0.258250i | \(-0.0831460\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.77600 | − | 18.1312i | −0.203885 | − | 0.978995i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 14.5391i | − | 0.398519i | −0.979947 | − | 0.199260i | \(-0.936146\pi\) | ||
0.979947 | − | 0.199260i | \(-0.0638537\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 75.4995i | 1.61075i | 0.592764 | + | 0.805376i | \(0.298037\pi\) | ||||
−0.592764 | + | 0.805376i | \(0.701963\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 17.3240i | − | 0.298202i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 81.5687i | 1.16372i | 0.813287 | + | 0.581862i | \(0.197676\pi\) | ||||
−0.813287 | + | 0.581862i | \(0.802324\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 89.0300 | 1.07499 | 0.537497 | − | 0.843266i | \(-0.319370\pi\) | ||||
0.537497 | + | 0.843266i | \(0.319370\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.3280 | − | 54.3937i | −0.117713 | − | 0.565223i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.53823i | 0.0864721i | 0.999065 | + | 0.0432361i | \(0.0137668\pi\) | ||||
−0.999065 | + | 0.0432361i | \(0.986233\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 91.6534 | 0.733227 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −259.288 | −1.66030 | −0.830148 | − | 0.557543i | \(-0.811744\pi\) | ||||
−0.830148 | + | 0.557543i | \(0.811744\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −13.5154 | −0.0783042 | −0.0391521 | − | 0.999233i | \(-0.512466\pi\) | ||||
−0.0391521 | + | 0.999233i | \(0.512466\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 43.6174i | − | 0.230085i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −104.702 | + | 21.8051i | −0.505652 | + | 0.105307i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 196.934 | 0.875020 | 0.437510 | − | 0.899214i | \(-0.355860\pi\) | ||||
0.437510 | + | 0.899214i | \(0.355860\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 226.498i | 0.929968i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 341.451i | 1.30063i | 0.759666 | + | 0.650313i | \(0.225362\pi\) | ||||
−0.759666 | + | 0.650313i | \(0.774638\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 535.198i | 1.89807i | 0.315173 | + | 0.949034i | \(0.397938\pi\) | ||||
−0.315173 | + | 0.949034i | \(0.602062\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 51.9719i | − | 0.172167i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −26.7703 | −0.0830818 | −0.0415409 | − | 0.999137i | \(-0.513227\pi\) | ||||
−0.0415409 | + | 0.999137i | \(0.513227\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −314.484 | + | 136.927i | −0.916862 | + | 0.399204i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 244.706i | 0.671877i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 671.696 | 1.74084 | 0.870420 | − | 0.492310i | \(-0.163847\pi\) | ||||
0.870420 | + | 0.492310i | \(0.163847\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −83.9585 | −0.205836 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 267.090 | 0.620648 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 546.205 | 1.20525 | 0.602626 | − | 0.798024i | \(-0.294121\pi\) | ||||
0.602626 | + | 0.798024i | \(0.294121\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 815.566i | − | 1.71184i | −0.517105 | − | 0.855922i | \(-0.672990\pi\) | ||
0.517105 | − | 0.855922i | \(-0.327010\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −33.9840 | − | 163.181i | −0.0679615 | − | 0.326332i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 435.983 | 0.831955 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 605.151i | − | 1.10345i | −0.834027 | − | 0.551723i | \(-0.813970\pi\) | ||
0.834027 | − | 0.551723i | \(-0.186030\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 28.6147i | 0.0499247i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 287.911i | − | 0.481250i | −0.970618 | − | 0.240625i | \(-0.922648\pi\) | ||
0.970618 | − | 0.240625i | \(-0.0773525\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 64.3771i | − | 0.103216i | −0.998667 | − | 0.0516080i | \(-0.983565\pi\) | ||
0.998667 | − | 0.0516080i | \(-0.0164346\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 274.960 | 0.423329 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −263.612 | + | 54.8997i | −0.390148 | + | 0.0812519i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 131.742i | 0.187622i | 0.995590 | + | 0.0938111i | \(0.0299050\pi\) | ||||
−0.995590 | + | 0.0938111i | \(0.970095\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 822.082 | 1.08717 | 0.543586 | − | 0.839353i | \(-0.317066\pi\) | ||||
0.543586 | + | 0.839353i | \(0.317066\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 471.031 | 0.601065 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −777.864 | −0.958572 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 737.170i | 0.877976i | 0.898493 | + | 0.438988i | \(0.144663\pi\) | ||||
−0.898493 | + | 0.438988i | \(0.855337\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1368.90 | − | 285.086i | 1.57692 | − | 0.328408i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −40.5461 | −0.0452090 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 514.117i | − | 0.555235i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 348.816i | − | 0.365122i | −0.983194 | − | 0.182561i | \(-0.941561\pi\) | ||
0.983194 | − | 0.182561i | \(-0.0584388\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 130.852i | − | 0.132840i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 947.473i | − | 0.933436i | −0.884406 | − | 0.466718i | \(-0.845436\pi\) | ||
0.884406 | − | 0.466718i | \(-0.154564\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −467.433 | −0.447161 | −0.223580 | − | 0.974686i | \(-0.571774\pi\) | ||||
−0.223580 | + | 0.974686i | \(0.571774\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −314.105 | + | 65.4152i | −0.291938 | + | 0.0607988i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 277.654i | − | 0.250859i | −0.992103 | − | 0.125429i | \(-0.959969\pi\) | ||
0.992103 | − | 0.125429i | \(-0.0400308\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1225.56 | 1.07695 | 0.538474 | − | 0.842642i | \(-0.319001\pi\) | ||||
0.538474 | + | 0.842642i | \(0.319001\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 590.802 | 0.505193 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1993.16 | −1.65930 | −0.829648 | − | 0.558287i | \(-0.811459\pi\) | ||||
−0.829648 | + | 0.558287i | \(0.811459\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 55.0800 | 0.0446629 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 679.495i | 0.536918i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1478.94 | − | 308.003i | 1.13928 | − | 0.237265i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1119.61 | 0.841182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1024.35i | 0.750917i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1251.10i | − | 0.895213i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1972.83i | 1.37843i | 0.724558 | + | 0.689213i | \(0.242044\pi\) | ||||
−0.724558 | + | 0.689213i | \(0.757956\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1605.59i | 1.09585i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2251.70 | 1.50177 | 0.750886 | − | 0.660432i | \(-0.229627\pi\) | ||||
0.750886 | + | 0.660432i | \(0.229627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −336.177 | − | 1614.22i | −0.219175 | − | 1.05241i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 155.916i | − | 0.0994006i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1185.62 | 0.739377 | 0.369689 | − | 0.929156i | \(-0.379464\pi\) | ||||
0.369689 | + | 0.929156i | \(0.379464\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2597.62 | 1.58509 | 0.792544 | − | 0.609814i | \(-0.208756\pi\) | ||||
0.792544 | + | 0.609814i | \(0.208756\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −80.3108 | −0.0479673 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1097.70 | 0.641916 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1497.30i | 0.857544i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −943.451 | + | 410.781i | −0.529351 | + | 0.230480i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1445.20 | −0.794601 | −0.397300 | − | 0.917689i | \(-0.630053\pi\) | ||||
−0.397300 | + | 0.917689i | \(0.630053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1876.14i | 1.01111i | 0.862793 | + | 0.505557i | \(0.168713\pi\) | ||||
−0.862793 | + | 0.505557i | \(0.831287\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 734.118i | 0.387908i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 78.0466i | 0.0404442i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 371.136i | 0.188661i | 0.995541 | + | 0.0943307i | \(0.0300711\pi\) | ||||
−0.995541 | + | 0.0943307i | \(0.969929\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2015.09 | 1.00507 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 172.940 | − | 36.0163i | 0.0846558 | − | 0.0176303i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 766.086i | − | 0.368126i | −0.982914 | − | 0.184063i | \(-0.941075\pi\) | ||
0.982914 | − | 0.184063i | \(-0.0589250\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −251.875 | −0.118839 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2296.51 | −1.06413 | −0.532064 | − | 0.846704i | \(-0.678583\pi\) | ||||
−0.532064 | + | 0.846704i | \(0.678583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3503.17 | −1.59452 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 801.270 | 0.358331 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1486.15i | 0.653119i | 0.945177 | + | 0.326560i | \(0.105889\pi\) | ||||
−0.945177 | + | 0.326560i | \(0.894111\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −346.083 | − | 1661.79i | −0.149494 | − | 0.717825i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1638.62 | 0.695853 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1165.15i | 0.486523i | 0.969961 | + | 0.243262i | \(0.0782173\pi\) | ||||
−0.969961 | + | 0.243262i | \(0.921783\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1623.96i | 0.666894i | 0.942769 | + | 0.333447i | \(0.108212\pi\) | ||||
−0.942769 | + | 0.333447i | \(0.891788\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2446.70i | − | 0.988333i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1137.23i | − | 0.451949i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1185.94 | 0.463767 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −101.952 | − | 489.543i | −0.0392376 | − | 0.188408i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1614.70i | − | 0.611705i | −0.952079 | − | 0.305852i | \(-0.901059\pi\) | ||
0.952079 | − | 0.305852i | \(-0.0989414\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1997.58 | −0.745021 | −0.372510 | − | 0.928028i | \(-0.621503\pi\) | ||||
−0.372510 | + | 0.928028i | \(0.621503\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1307.95 | 0.480329 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1574.98 | −0.569606 | −0.284803 | − | 0.958586i | \(-0.591928\pi\) | ||||
−0.284803 | + | 0.958586i | \(0.591928\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3994.83 | 1.42305 | 0.711523 | − | 0.702663i | \(-0.248006\pi\) | ||||
0.711523 | + | 0.702663i | \(0.248006\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 1815.45i | − | 0.637075i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 979.070 | + | 4701.21i | 0.338509 | + | 1.62542i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1971.76 | 0.671775 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 85.8441i | 0.0288240i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1294.42i | − | 0.428406i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 808.768i | − | 0.263876i | −0.991258 | − | 0.131938i | \(-0.957880\pi\) | ||
0.991258 | − | 0.131938i | \(-0.0421200\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 863.734i | − | 0.277850i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3090.58 | 0.980354 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 51.0340 | + | 245.050i | 0.0159650 | + | 0.0766595i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 193.131i | − | 0.0595918i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6158.39 | −1.87447 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5103.24 | 1.53246 | 0.766229 | − | 0.642567i | \(-0.222131\pi\) | ||||
0.766229 | + | 0.642567i | \(0.222131\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 824.880 | 0.244409 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2534.63 | 0.741099 | 0.370549 | − | 0.928813i | \(-0.379169\pi\) | ||||
0.370549 | + | 0.928813i | \(0.379169\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2323.15i | 0.670386i | 0.942150 | + | 0.335193i | \(0.108802\pi\) | ||||
−0.942150 | + | 0.335193i | \(0.891198\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −790.837 | + | 164.699i | −0.225252 | + | 0.0469108i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1272.46 | −0.357776 | −0.178888 | − | 0.983869i | \(-0.557250\pi\) | ||||
−0.178888 | + | 0.983869i | \(0.557250\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 154.589i | 0.0429118i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 395.226i | 0.108324i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 312.303i | 0.0845239i | 0.999107 | + | 0.0422620i | \(0.0134564\pi\) | ||||
−0.999107 | + | 0.0422620i | \(0.986544\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1090.73i | − | 0.291536i | −0.989319 | − | 0.145768i | \(-0.953435\pi\) | ||
0.989319 | − | 0.145768i | \(-0.0465653\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 790.706 | + | 1816.03i | 0.206189 | + | 0.473560i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6721.72i | 1.73155i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2466.25 | 0.627679 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4320.91 | −1.08659 | −0.543294 | − | 0.839543i | \(-0.682823\pi\) | ||||
−0.543294 | + | 0.839543i | \(0.682823\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 138.678 | 0.0344608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1413.09 | 0.347025 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 138.980i | 0.0337327i | 0.999858 | + | 0.0168664i | \(0.00536899\pi\) | ||||
−0.999858 | + | 0.0168664i | \(0.994631\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −743.622 | − | 3570.66i | −0.178403 | − | 0.856640i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2333.59 | −0.553432 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6782.11i | 1.59012i | 0.606528 | + | 0.795062i | \(0.292562\pi\) | ||||
−0.606528 | + | 0.795062i | \(0.707438\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3878.81i | − | 0.899145i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2211.51i | 0.506899i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 5605.82i | − | 1.27061i | −0.772263 | − | 0.635303i | \(-0.780875\pi\) | ||
0.772263 | − | 0.635303i | \(-0.219125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −747.876 | −0.167639 | −0.0838196 | − | 0.996481i | \(-0.526712\pi\) | ||||
−0.0838196 | + | 0.996481i | \(0.526712\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4106.70 | − | 855.257i | 0.910434 | − | 0.189606i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1332.56i | − | 0.292205i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5603.44 | 1.21544 | 0.607722 | − | 0.794150i | \(-0.292083\pi\) | ||||
0.607722 | + | 0.794150i | \(0.292083\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −121.638 | −0.0261014 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1954.56 | 0.414945 | 0.207472 | − | 0.978241i | \(-0.433476\pi\) | ||||
0.207472 | + | 0.978241i | \(0.433476\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5011.56 | −1.05267 | −0.526336 | − | 0.850277i | \(-0.676435\pi\) | ||||
−0.526336 | + | 0.850277i | \(0.676435\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 1542.35i | − | 0.320565i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6190.93 | − | 1289.32i | 1.27331 | − | 0.265178i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1740.45 | −0.354254 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1046.45i | − | 0.210804i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8253.06i | 1.64556i | 0.568361 | + | 0.822779i | \(0.307578\pi\) | ||||
−0.568361 | + | 0.822779i | \(0.692422\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3154.15i | − | 0.622514i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 392.557i | − | 0.0766951i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −720.131 | −0.139285 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9703.81 | − | 2020.91i | 1.85820 | − | 0.386987i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2842.42i | − | 0.538920i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4709.61 | −0.884169 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10554.1 | 1.96207 | 0.981034 | − | 0.193837i | \(-0.0620932\pi\) | ||||
0.981034 | + | 0.193837i | \(0.0620932\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1402.30 | −0.258168 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9756.96 | 1.77899 | 0.889496 | − | 0.456943i | \(-0.151056\pi\) | ||||
0.889496 | + | 0.456943i | \(0.151056\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8663.75i | − | 1.56455i | −0.622934 | − | 0.782275i | \(-0.714059\pi\) | ||
0.622934 | − | 0.782275i | \(-0.285941\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −942.315 | + | 196.246i | −0.168551 | + | 0.0351022i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9685.17 | −1.71600 | −0.858002 | − | 0.513646i | \(-0.828294\pi\) | ||||
−0.858002 | + | 0.513646i | \(0.828294\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3769.82i | 0.661660i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 832.963i | − | 0.144833i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7262.06i | 1.25100i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6919.78i | 1.18105i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3676.68 | 0.621776 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 101.084 | + | 485.378i | 0.0169391 | + | 0.0813366i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 10134.4i | − | 1.68288i | −0.540347 | − | 0.841442i | \(-0.681707\pi\) | ||
0.540347 | − | 0.841442i | \(-0.318293\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1772.41 | 0.291673 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3494.54 | −0.569931 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 700.301 | 0.113198 | 0.0565992 | − | 0.998397i | \(-0.481974\pi\) | ||||
0.0565992 | + | 0.998397i | \(0.481974\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5979.47 | −0.957995 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 196.502i | 0.0312058i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3670.14 | + | 5184.94i | 0.577753 | + | 0.816212i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 165.240 | 0.0257861 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6590.30i | 1.01955i | 0.860306 | + | 0.509777i | \(0.170272\pi\) | ||||
−0.860306 | + | 0.509777i | \(0.829728\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2636.31i | 0.404351i | 0.979349 | + | 0.202175i | \(0.0648011\pi\) | ||||
−0.979349 | + | 0.202175i | \(0.935199\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2038.49i | 0.309989i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5950.82i | 0.897252i | 0.893720 | + | 0.448626i | \(0.148086\pi\) | ||||
−0.893720 | + | 0.448626i | \(0.851914\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1662.59 | −0.248566 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4436.82 | − | 924.009i | 0.657764 | − | 0.136985i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 921.748i | − | 0.135510i | −0.997702 | − | 0.0677549i | \(-0.978416\pi\) | ||
0.997702 | − | 0.0677549i | \(-0.0215836\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1067.34 | 0.155611 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3358.84 | 0.485657 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −371.756 | −0.0533112 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2627.64 | −0.373738 | −0.186869 | − | 0.982385i | \(-0.559834\pi\) | ||||
−0.186869 | + | 0.982385i | \(0.559834\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3073.06i | 0.433542i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2536.32 | − | 12178.7i | −0.354930 | − | 1.70427i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2183.43 | −0.303093 | −0.151546 | − | 0.988450i | \(-0.548425\pi\) | ||||
−0.151546 | + | 0.988450i | \(0.548425\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 3753.29i | − | 0.516852i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 19576.1i | − | 2.67433i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5540.25i | − | 0.750880i | −0.926847 | − | 0.375440i | \(-0.877492\pi\) | ||
0.926847 | − | 0.375440i | \(-0.122508\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5918.48i | 0.795835i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4048.48 | −0.540124 | −0.270062 | − | 0.962843i | \(-0.587044\pi\) | ||||
−0.270062 | + | 0.962843i | \(0.587044\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 317.027 | + | 1522.27i | 0.0419667 | + | 0.201512i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4816.78i | 0.632690i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3380.49 | −0.440611 | −0.220305 | − | 0.975431i | \(-0.570705\pi\) | ||||
−0.220305 | + | 0.975431i | \(0.570705\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −778.021 | −0.100630 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6755.10 | 0.867048 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 760.765 | 0.0969070 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11865.9i | 1.50008i | 0.661392 | + | 0.750040i | \(0.269966\pi\) | ||||
−0.661392 | + | 0.750040i | \(0.730034\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1008.53 | − | 4842.67i | −0.126541 | − | 0.607611i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4336.29 | −0.540011 | −0.270005 | − | 0.962859i | \(-0.587025\pi\) | ||||
−0.270005 | + | 0.962859i | \(0.587025\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1020.40i | − | 0.126129i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 467.747i | − | 0.0573890i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2863.25i | − | 0.348712i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11019.1i | 1.33217i | 0.745874 | + | 0.666087i | \(0.232032\pi\) | ||||
−0.745874 | + | 0.666087i | \(0.767968\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3556.87 | 0.426880 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2062.47 | − | 9903.38i | −0.245732 | − | 1.17994i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4747.24i | − | 0.561525i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7792.86 | 0.915151 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9791.38 | −1.14162 | −0.570812 | − | 0.821081i | \(-0.693371\pi\) | ||||
−0.570812 | + | 0.821081i | \(0.693371\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10701.6 | 1.23887 | 0.619437 | − | 0.785046i | \(-0.287361\pi\) | ||||
0.619437 | + | 0.785046i | \(0.287361\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −240.932 | −0.0276939 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7476.04i | 0.853274i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14787.2 | + | 3079.57i | −1.67589 | + | 0.349019i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3293.09 | 0.370610 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 11506.1i | − | 1.28592i | −0.765901 | − | 0.642959i | \(-0.777707\pi\) | ||
0.765901 | − | 0.642959i | \(-0.222293\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1134.62i | 0.125926i | 0.998016 | + | 0.0629632i | \(0.0200551\pi\) | ||||
−0.998016 | + | 0.0629632i | \(0.979945\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4491.90i | 0.495103i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 849.188i | 0.0929570i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4908.19 | −0.533611 | −0.266806 | − | 0.963750i | \(-0.585968\pi\) | ||||
−0.266806 | + | 0.963750i | \(0.585968\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2830.35 | + | 1232.34i | −0.305621 | + | 0.133068i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 127.763i | 0.0137025i | 0.999977 | + | 0.00685124i | \(0.00218083\pi\) | ||||
−0.999977 | + | 0.00685124i | \(0.997819\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4256.90 | 0.453475 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4335.60 | −0.458763 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6741.08 | −0.708533 | −0.354267 | − | 0.935144i | \(-0.615269\pi\) | ||||
−0.354267 | + | 0.935144i | \(0.615269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4964.40 | 0.518325 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5628.42i | 0.583767i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1646.27 | − | 7904.92i | −0.169623 | − | 0.814480i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2976.15 | 0.304635 | 0.152318 | − | 0.988332i | \(-0.451326\pi\) | ||||
0.152318 | + | 0.988332i | \(0.451326\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2202.35i | 0.223959i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 6326.93i | − | 0.639207i | −0.947551 | − | 0.319604i | \(-0.896450\pi\) | ||
0.947551 | − | 0.319604i | \(-0.103550\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13109.7i | 1.31589i | 0.753066 | + | 0.657945i | \(0.228574\pi\) | ||||
−0.753066 | + | 0.657945i | \(0.771426\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 234.140i | 0.0233505i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2556.42 | 0.253313 | 0.126656 | − | 0.991947i | \(-0.459575\pi\) | ||||
0.126656 | + | 0.991947i | \(0.459575\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10972.1 | + | 2285.05i | −1.08027 | + | 0.224976i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1113.41i | 0.108924i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7781.32 | 0.756417 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8159.90 | 0.788214 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6045.26 | 0.580280 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4199.36 | 0.400571 | 0.200286 | − | 0.979738i | \(-0.435813\pi\) | ||||
0.200286 | + | 0.979738i | \(0.435813\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14868.4i | 1.40944i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 518.820 | − | 108.049i | 0.0488760 | − | 0.0101789i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2014.29 | −0.188586 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4659.54i | 0.433561i | 0.976220 | + | 0.216780i | \(0.0695555\pi\) | ||||
−0.976220 | + | 0.216780i | \(0.930444\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2298.26i | − | 0.212538i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6311.43i | − | 0.580104i | −0.957011 | − | 0.290052i | \(-0.906327\pi\) | ||
0.957011 | − | 0.290052i | \(-0.0936726\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 21149.8i | − | 1.93213i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −755.626 | −0.0686119 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5220.19 | + | 1087.15i | −0.471142 | + | 0.0981195i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3080.68i | − | 0.276373i | −0.990406 | − | 0.138187i | \(-0.955873\pi\) | ||
0.990406 | − | 0.138187i | \(-0.0441273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6889.53 | −0.614374 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14985.9 | −1.32840 | −0.664201 | − | 0.747554i | \(-0.731228\pi\) | ||||
−0.664201 | + | 0.747554i | \(0.731228\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5471.33 | −0.482121 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10509.5 | −0.920599 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 5360.33i | − | 0.466783i | −0.972383 | − | 0.233392i | \(-0.925018\pi\) | ||
0.972383 | − | 0.233392i | \(-0.0749824\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1167.24 | + | 243.088i | −0.101048 | + | 0.0210442i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2403.81 | 0.206883 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2699.26i | 0.230959i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 389.216i | 0.0331097i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4458.44i | 0.377079i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 4858.45i | − | 0.408546i | −0.978914 | − | 0.204273i | \(-0.934517\pi\) | ||
0.978914 | − | 0.204273i | \(-0.0654831\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11679.7 | −0.976517 | −0.488259 | − | 0.872699i | \(-0.662368\pi\) | ||||
−0.488259 | + | 0.872699i | \(0.662368\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1038.25 | − | 4985.37i | −0.0863102 | − | 0.414437i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1102.43i | − | 0.0911246i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12076.0 | 0.992523 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4915.85 | 0.401751 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25779.4 | −2.09499 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1603.36 | −0.129569 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3495.46i | 0.280894i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1990.80 | + | 4572.32i | 0.159090 | + | 0.365387i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22704.0 | 1.80429 | 0.902147 | − | 0.431429i | \(-0.141991\pi\) | ||||
0.902147 | + | 0.431429i | \(0.141991\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4871.87i | 0.385031i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 7077.18i | − | 0.556245i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9236.63i | 0.721992i | 0.932567 | + | 0.360996i | \(0.117563\pi\) | ||||
−0.932567 | + | 0.360996i | \(0.882437\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 7340.09i | − | 0.570615i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23084.4 | −1.78481 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2388.65 | − | 497.458i | 0.183681 | − | 0.0382533i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 3411.68i | − | 0.260933i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2287.70 | −0.174027 | −0.0870136 | − | 0.996207i | \(-0.527732\pi\) | ||||
−0.0870136 | + | 0.996207i | \(0.527732\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40407.2 | −3.05732 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3557.81 | 0.267756 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15794.1 | −1.18231 | −0.591157 | − | 0.806556i | \(-0.701329\pi\) | ||||
−0.591157 | + | 0.806556i | \(0.701329\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11509.8i | 0.857027i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −305.856 | − | 1468.63i | −0.0226538 | − | 0.108777i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19977.7 | −1.47189 | −0.735947 | − | 0.677039i | \(-0.763263\pi\) | ||||
−0.735947 | + | 0.677039i | \(0.763263\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20104.0i | 1.47342i | 0.676207 | + | 0.736711i | \(0.263622\pi\) | ||||
−0.676207 | + | 0.736711i | \(0.736378\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 4844.10i | − | 0.353168i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 874.211i | 0.0634037i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14026.0i | 1.01198i | 0.862540 | + | 0.505990i | \(0.168873\pi\) | ||||
−0.862540 | + | 0.505990i | \(0.831127\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5992.74 | −0.430138 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3104.18 | − | 14905.4i | −0.221658 | − | 1.06434i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 9765.88i | − | 0.693759i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3923.85 | 0.277318 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27143.4 | 1.90857 | 0.954283 | − | 0.298904i | \(-0.0966211\pi\) | ||||
0.954283 | + | 0.298904i | \(0.0966211\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1203.27 | −0.0841766 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4724.93 | −0.328862 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6180.97i | 0.428030i | 0.976830 | + | 0.214015i | \(0.0686542\pi\) | ||||
−0.976830 | + | 0.214015i | \(0.931346\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1778.61 | − | 8540.38i | −0.122548 | − | 0.588439i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11984.5 | 0.821596 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11988.1i | 0.817730i | 0.912595 | + | 0.408865i | \(0.134075\pi\) | ||||
−0.912595 | + | 0.408865i | \(0.865925\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 27089.7i | − | 1.83862i | −0.393534 | − | 0.919310i | \(-0.628748\pi\) | ||
0.393534 | − | 0.919310i | \(-0.371252\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 5446.36i | − | 0.367815i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 6465.38i | − | 0.434471i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1352.56 | −0.0904425 | −0.0452212 | − | 0.998977i | \(-0.514399\pi\) | ||||
−0.0452212 | + | 0.998977i | \(0.514399\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2937.21 | + | 14103.6i | 0.195438 | + | 0.938437i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 2021.14i | − | 0.133824i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13838.7 | 0.911808 | 0.455904 | − | 0.890029i | \(-0.349316\pi\) | ||||
0.455904 | + | 0.890029i | \(0.349316\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5915.28 | 0.387849 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14746.5 | −0.962191 | −0.481096 | − | 0.876668i | \(-0.659761\pi\) | ||||
−0.481096 | + | 0.876668i | \(0.659761\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1773.86 | −0.115182 | −0.0575909 | − | 0.998340i | \(-0.518342\pi\) | ||||
−0.0575909 | + | 0.998340i | \(0.518342\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 257.532i | 0.0166416i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13365.8 | − | 2783.55i | 0.859534 | − | 0.179006i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4232.01 | 0.270849 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 3883.26i | − | 0.247340i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16063.6i | 1.01828i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 16563.6i | − | 1.04499i | −0.852643 | − | 0.522494i | \(-0.825002\pi\) | ||
0.852643 | − | 0.522494i | \(-0.174998\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 2426.30i | − | 0.152349i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11392.4 | 0.711959 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10337.9 | − | 23743.4i | −0.643019 | − | 1.47684i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 2591.20i | − | 0.160417i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22907.9 | −1.41156 | −0.705779 | − | 0.708432i | \(-0.749403\pi\) | ||||
−0.705779 | + | 0.708432i | \(0.749403\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2919.92 | −0.179083 | −0.0895414 | − | 0.995983i | \(-0.528540\pi\) | ||||
−0.0895414 | + | 0.995983i | \(0.528540\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9271.75 | 0.566008 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23638.1 | −1.43634 | −0.718169 | − | 0.695868i | \(-0.755020\pi\) | ||||
−0.718169 | + | 0.695868i | \(0.755020\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7941.35i | − | 0.480316i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 153.102 | + | 735.151i | 0.00921741 | + | 0.0442594i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3983.07 | −0.238698 | −0.119349 | − | 0.992852i | \(-0.538081\pi\) | ||||
−0.119349 | + | 0.992852i | \(0.538081\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 13002.8i | − | 0.775666i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 579.394i | − | 0.0344053i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 13889.1i | − | 0.821004i | −0.911860 | − | 0.410502i | \(-0.865354\pi\) | ||
0.911860 | − | 0.410502i | \(-0.134646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 11415.7i | − | 0.671736i | −0.941909 | − | 0.335868i | \(-0.890970\pi\) | ||
0.941909 | − | 0.335868i | \(-0.109030\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18475.2 | −1.08223 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9321.58 | + | 1941.30i | −0.543572 | + | 0.113204i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2473.15i | − | 0.143569i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15309.7 | 0.884765 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11857.6 | −0.682203 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10799.6 | 0.618567 | 0.309284 | − | 0.950970i | \(-0.399911\pi\) | ||||
0.309284 | + | 0.950970i | \(0.399911\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2474.64 | 0.141110 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11603.5i | 0.658730i | 0.944203 | + | 0.329365i | \(0.106835\pi\) | ||||
−0.944203 | + | 0.329365i | \(0.893165\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6324.46 | + | 1317.13i | −0.357453 | + | 0.0744428i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7603.90 | 0.427874 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 18698.8i | − | 1.04757i | −0.851851 | − | 0.523784i | \(-0.824520\pi\) | ||
0.851851 | − | 0.523784i | \(-0.175480\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6846.57i | − | 0.381889i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6969.46i | 0.387047i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 50712.7i | 2.80406i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7549.67 | −0.415634 | −0.207817 | − | 0.978168i | \(-0.566636\pi\) | ||||
−0.207817 | + | 0.978168i | \(0.566636\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2372.51 | + | 494.097i | −0.130049 | + | 0.0270840i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 15000.4i | − | 0.818699i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27851.7 | −1.51357 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3817.38 | −0.206562 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6127.34 | −0.330138 | −0.165069 | − | 0.986282i | \(-0.552785\pi\) | ||||
−0.165069 | + | 0.986282i | \(0.552785\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17533.0 | 0.940641 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 463.767i | 0.0247751i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17178.9 | + | 3577.65i | −0.913829 | + | 0.190313i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3209.29 | −0.169996 | −0.0849981 | − | 0.996381i | \(-0.527088\pi\) | ||||
−0.0849981 | + | 0.996381i | \(0.527088\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1185.68i | 0.0625407i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 128.913i | − | 0.00677113i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 6338.82i | − | 0.331550i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 936.910i | 0.0487999i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5415.53 | −0.280897 | −0.140449 | − | 0.990088i | \(-0.544854\pi\) | ||||
−0.140449 | + | 0.990088i | \(0.544854\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1765.02 | + | 8475.14i | 0.0911691 | + | 0.437768i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 3272.20i | − | 0.168319i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23764.6 | −1.21737 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12165.9 | −0.620643 | −0.310322 | − | 0.950632i | \(-0.600437\pi\) | ||||
−0.310322 | + | 0.950632i | \(0.600437\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −43655.4 | −2.20883 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 7503.91i | − | 0.378122i | −0.981965 | − | 0.189061i | \(-0.939456\pi\) | ||
0.981965 | − | 0.189061i | \(-0.0605444\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2372.12 | + | 5448.10i | 0.119043 | + | 0.273410i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8798.36 | −0.439745 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25591.6i | 1.27389i | 0.770910 | + | 0.636944i | \(0.219802\pi\) | ||||
−0.770910 | + | 0.636944i | \(0.780198\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20165.1i | 0.999710i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13474.7i | − | 0.665328i | −0.943045 | − | 0.332664i | \(-0.892053\pi\) | ||
0.943045 | − | 0.332664i | \(-0.107947\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8345.54i | 0.410412i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7398.74 | 0.362391 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5034.22 | + | 1048.42i | −0.245589 | + | 0.0511462i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6265.52i | 0.304437i | 0.988347 | + | 0.152219i | \(0.0486418\pi\) | ||||
−0.988347 | + | 0.152219i | \(0.951358\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12962.7 | −0.627342 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10834.1 | 0.522241 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12600.0 | −0.604960 | −0.302480 | − | 0.953156i | \(-0.597815\pi\) | ||||
−0.302480 | + | 0.953156i | \(0.597815\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 416.033 | 0.0198960 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 14110.8i | − | 0.672163i | −0.941833 | − | 0.336082i | \(-0.890898\pi\) | ||
0.941833 | − | 0.336082i | \(-0.109102\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4627.71 | − | 22220.9i | −0.219573 | − | 1.05433i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4239.28 | 0.200355 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 41238.2i | 1.94136i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 18732.3i | − | 0.878419i | −0.898385 | − | 0.439210i | \(-0.855259\pi\) | ||
0.898385 | − | 0.439210i | \(-0.144741\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 416.939i | 0.0194756i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17750.9i | 0.825943i | 0.910744 | + | 0.412972i | \(0.135509\pi\) | ||||
−0.910744 | + | 0.412972i | \(0.864491\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1238.73 | −0.0574148 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2230.86 | − | 10712.0i | −0.103001 | − | 0.494581i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30399.4i | 1.39817i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4185.98 | −0.191788 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7000.78 | −0.319524 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2143.18 | 0.0974438 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12685.4 | −0.574567 | −0.287283 | − | 0.957846i | \(-0.592752\pi\) | ||||
−0.287283 | + | 0.957846i | \(0.592752\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20346.3i | 0.918059i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7526.15 | + | 36138.4i | 0.338305 | + | 1.62444i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 61574.8 | 2.75736 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 11636.4i | − | 0.519122i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 21163.9i | − | 0.940608i | −0.882505 | − | 0.470304i | \(-0.844144\pi\) | ||
0.882505 | − | 0.470304i | \(-0.155856\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2183.62i | − | 0.0966843i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6634.53i | 0.292659i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −935.987 | −0.0411336 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −207.982 | − | 998.668i | −0.00910608 | − | 0.0437248i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 16817.5i | − | 0.733585i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18524.3 | −0.805042 | −0.402521 | − | 0.915411i | \(-0.631866\pi\) | ||||
−0.402521 | + | 0.915411i | \(0.631866\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9847.07 | −0.426359 | −0.213180 | − | 0.977013i | \(-0.568382\pi\) | ||||
−0.213180 | + | 0.977013i | \(0.568382\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2243.63 | −0.0967865 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4423.88 | −0.190137 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 47648.7i | 2.04041i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12320.1 | − | 2565.77i | 0.525640 | − | 0.109469i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29068.7 | 1.23570 | 0.617848 | − | 0.786298i | \(-0.288005\pi\) | ||||
0.617848 | + | 0.786298i | \(0.288005\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 39075.4i | − | 1.65502i | −0.561450 | − | 0.827511i | \(-0.689756\pi\) | ||
0.561450 | − | 0.827511i | \(-0.310244\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 3997.68i | − | 0.168705i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 2846.21i | − | 0.119677i | −0.998208 | − | 0.0598383i | \(-0.980941\pi\) | ||
0.998208 | − | 0.0598383i | \(-0.0190585\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1936.00i | 0.0811099i | 0.999177 | + | 0.0405550i | \(0.0129126\pi\) | ||||
−0.999177 | + | 0.0405550i | \(0.987087\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16810.3 | 0.701737 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11169.0 | − | 25652.0i | −0.464563 | − | 1.06697i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13261.6i | 0.549623i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −364.915 | −0.0150697 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17052.5 | −0.701690 | −0.350845 | − | 0.936434i | \(-0.614106\pi\) | ||||
−0.350845 | + | 0.936434i | \(0.614106\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42841.3 | 1.75658 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5863.69 | 0.239568 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20229.6i | 0.823573i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4227.66 | − | 20300.0i | −0.171504 | − | 0.823513i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15034.7 | −0.607761 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1878.40i | 0.0756648i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24807.3i | 0.995764i | 0.867245 | + | 0.497882i | \(0.165889\pi\) | ||||
−0.867245 | + | 0.497882i | \(0.834111\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 4627.06i | − | 0.185078i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 35069.3i | − | 1.39784i | −0.715202 | − | 0.698918i | \(-0.753665\pi\) | ||
0.715202 | − | 0.698918i | \(-0.246335\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42164.9 | 1.67479 | 0.837397 | − | 0.546596i | \(-0.184077\pi\) | ||||
0.837397 | + | 0.546596i | \(0.184077\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18572.8 | − | 3867.95i | 0.735144 | − | 0.153100i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 25133.2i | − | 0.991360i | −0.868505 | − | 0.495680i | \(-0.834919\pi\) | ||
0.868505 | − | 0.495680i | \(-0.165081\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8581.98 | 0.337337 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5221.35 | −0.204529 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1915.42 | 0.0747710 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45688.5 | 1.77738 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3139.34i | − | 0.121707i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22684.0 | + | 4724.14i | −0.876409 | + | 0.182520i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47942.9 | −1.84597 | −0.922985 | − | 0.384835i | \(-0.874258\pi\) | ||||
−0.922985 | + | 0.384835i | \(0.874258\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24759.2i | 0.950064i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 40982.4i | − | 1.56723i | −0.621244 | − | 0.783617i | \(-0.713373\pi\) | ||
0.621244 | − | 0.783617i | \(-0.286627\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23832.4i | 0.908295i | 0.890927 | + | 0.454147i | \(0.150056\pi\) | ||||
−0.890927 | + | 0.454147i | \(0.849944\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 9462.44i | − | 0.359408i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33825.6 | 1.28044 | 0.640220 | − | 0.768191i | \(-0.278843\pi\) | ||||
0.640220 | + | 0.768191i | \(0.278843\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35769.8 | − | 7449.39i | 1.34947 | − | 0.281040i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1177.67i | − | 0.0442799i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2383.36 | −0.0893124 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6728.36 | 0.251290 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2160.39 | −0.0804163 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3504.37 | 0.130008 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54789.4i | 2.02586i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 29111.4 | − | 6062.72i | 1.07283 | − | 0.223427i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9377.79 | 0.344451 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 43691.4i | − | 1.59950i | −0.600330 | − | 0.799752i | \(-0.704964\pi\) | ||
0.600330 | − | 0.799752i | \(-0.295036\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 8527.26i | − | 0.311145i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16717.9i | 0.608001i | 0.952672 | + | 0.304000i | \(0.0983224\pi\) | ||||
−0.952672 | + | 0.304000i | \(0.901678\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 11952.4i | − | 0.433259i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14128.8 | −0.510475 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8502.41 | − | 40826.1i | −0.306188 | − | 1.47023i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 7962.36i | − | 0.285804i | −0.989737 | − | 0.142902i | \(-0.954357\pi\) | ||
0.989737 | − | 0.142902i | \(-0.0456434\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31662.3 | 1.13280 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21737.1 | 0.775175 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18049.7 | 0.641588 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4206.90 | −0.149054 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24057.0i | 0.849606i | 0.905286 | + | 0.424803i | \(0.139657\pi\) | ||||
−0.905286 | + | 0.424803i | \(0.860343\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27998.5 | + | 12190.6i | −0.985621 | + | 0.429142i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29270.9 | 1.02710 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 6848.38i | − | 0.239536i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 42305.5i | − | 1.47498i | −0.675356 | − | 0.737492i | \(-0.736010\pi\) | ||
0.675356 | − | 0.737492i | \(-0.263990\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 25991.2i | − | 0.903293i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 43425.7i | − | 1.50440i | −0.658936 | − | 0.752199i | \(-0.728993\pi\) | ||
0.658936 | − | 0.752199i | \(-0.271007\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3256.84 | −0.112468 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2826.94 | + | 588.737i | −0.0973127 | + | 0.0202663i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 40700.2i | − | 1.39660i | −0.715806 | − | 0.698299i | \(-0.753941\pi\) | ||
0.715806 | − | 0.698299i | \(-0.246059\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4860.44 | 0.166255 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29055.5 | −0.990735 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 335.224 | 0.0113945 | 0.00569726 | − | 0.999984i | \(-0.498186\pi\) | ||||
0.00569726 | + | 0.999984i | \(0.498186\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9324.33 | −0.315946 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11309.5i | 0.382010i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4476.91 | − | 21496.8i | −0.150748 | − | 0.723847i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29608.3 | −0.993868 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 2498.89i | − | 0.0836195i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11535.3i | 0.384804i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23773.5i | 0.790595i | 0.918553 | + | 0.395298i | \(0.129359\pi\) | ||||
−0.918553 | + | 0.395298i | \(0.870641\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21786.2i | 0.722263i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30129.6 | −0.995781 | −0.497891 | − | 0.867240i | \(-0.665892\pi\) | ||||
−0.497891 | + | 0.867240i | \(0.665892\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9808.60 | − | 47098.1i | −0.323175 | − | 1.55179i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20759.3i | 0.681878i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2562.41 | −0.0839086 | −0.0419543 | − | 0.999120i | \(-0.513358\pi\) | ||||
−0.0419543 | + | 0.999120i | \(0.513358\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10717.8 | 0.349890 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11030.0 | 0.358983 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50346.8 | 1.63358 | 0.816792 | − | 0.576932i | \(-0.195750\pi\) | ||||
0.816792 | + | 0.576932i | \(0.195750\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9094.94i | 0.294202i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 303.253 | + | 1456.13i | 0.00977979 | + | 0.0469597i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5104.84 | −0.164130 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 6553.24i | − | 0.210061i | −0.994469 | − | 0.105031i | \(-0.966506\pi\) | ||
0.994469 | − | 0.105031i | \(-0.0334941\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 30403.1i | − | 0.971614i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 23068.8i | − | 0.735004i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34220.3i | 1.08703i | 0.839400 | + | 0.543514i | \(0.182907\pi\) | ||||
−0.839400 | + | 0.543514i | \(0.817093\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5317.22 | 0.168398 |
(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.b.j.895.9 | 24 | ||
4.3 | odd | 2 | 1344.4.b.i.895.9 | 24 | |||
7.6 | odd | 2 | 1344.4.b.i.895.16 | 24 | |||
8.3 | odd | 2 | 672.4.b.b.223.16 | yes | 24 | ||
8.5 | even | 2 | 672.4.b.a.223.16 | yes | 24 | ||
28.27 | even | 2 | inner | 1344.4.b.j.895.16 | 24 | ||
56.13 | odd | 2 | 672.4.b.b.223.9 | yes | 24 | ||
56.27 | even | 2 | 672.4.b.a.223.9 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.b.a.223.9 | ✓ | 24 | 56.27 | even | 2 | ||
672.4.b.a.223.16 | yes | 24 | 8.5 | even | 2 | ||
672.4.b.b.223.9 | yes | 24 | 56.13 | odd | 2 | ||
672.4.b.b.223.16 | yes | 24 | 8.3 | odd | 2 | ||
1344.4.b.i.895.9 | 24 | 4.3 | odd | 2 | |||
1344.4.b.i.895.16 | 24 | 7.6 | odd | 2 | |||
1344.4.b.j.895.9 | 24 | 1.1 | even | 1 | trivial | ||
1344.4.b.j.895.16 | 24 | 28.27 | even | 2 | inner |