Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(809,1620)]
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, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.809");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 809.18 | ||
Character | \(\chi\) | \(=\) | 1620.809 |
Dual form | 1620.3.b.b.809.17 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.98582 | + | 4.58874i | 0.397164 | + | 0.917748i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.667924i | 0.0954177i | 0.998861 | + | 0.0477088i | \(0.0151920\pi\) | ||||
−0.998861 | + | 0.0477088i | \(0.984808\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.4601i | 1.76910i | 0.466447 | + | 0.884549i | \(0.345534\pi\) | ||||
−0.466447 | + | 0.884549i | \(0.654466\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 20.0501i | − | 1.54232i | −0.636644 | − | 0.771158i | \(-0.719678\pi\) | ||
0.636644 | − | 0.771158i | \(-0.280322\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −16.3370 | −0.960998 | −0.480499 | − | 0.876995i | \(-0.659544\pi\) | ||||
−0.480499 | + | 0.876995i | \(0.659544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.43805 | 0.128319 | 0.0641593 | − | 0.997940i | \(-0.479563\pi\) | ||||
0.0641593 | + | 0.997940i | \(0.479563\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −34.3714 | −1.49441 | −0.747203 | − | 0.664595i | \(-0.768604\pi\) | ||||
−0.747203 | + | 0.664595i | \(0.768604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −17.1130 | + | 18.2248i | −0.684521 | + | 0.728993i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.73648i | 0.197810i | 0.995097 | + | 0.0989048i | \(0.0315339\pi\) | ||||
−0.995097 | + | 0.0989048i | \(0.968466\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −26.8521 | −0.866198 | −0.433099 | − | 0.901346i | \(-0.642580\pi\) | ||||
−0.433099 | + | 0.901346i | \(0.642580\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.06493 | + | 1.32638i | −0.0875694 | + | 0.0378965i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 11.3929i | − | 0.307916i | −0.988077 | − | 0.153958i | \(-0.950798\pi\) | ||
0.988077 | − | 0.153958i | \(-0.0492021\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 29.2502i | − | 0.713419i | −0.934215 | − | 0.356709i | \(-0.883899\pi\) | ||
0.934215 | − | 0.356709i | \(-0.116101\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 34.1247i | 0.793598i | 0.917906 | + | 0.396799i | \(0.129879\pi\) | ||||
−0.917906 | + | 0.396799i | \(0.870121\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 67.9986 | 1.44678 | 0.723389 | − | 0.690440i | \(-0.242583\pi\) | ||||
0.723389 | + | 0.690440i | \(0.242583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.5539 | 0.990895 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −37.0720 | −0.699471 | −0.349736 | − | 0.936848i | \(-0.613729\pi\) | ||||
−0.349736 | + | 0.936848i | \(0.613729\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −89.2972 | + | 38.6442i | −1.62359 | + | 0.702622i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 19.0295i | 0.322533i | 0.986911 | + | 0.161267i | \(0.0515579\pi\) | ||||
−0.986911 | + | 0.161267i | \(0.948442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −113.562 | −1.86168 | −0.930839 | − | 0.365430i | \(-0.880922\pi\) | ||||
−0.930839 | + | 0.365430i | \(0.880922\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 92.0047 | − | 39.8159i | 1.41546 | − | 0.612553i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 106.718i | − | 1.59280i | −0.604769 | − | 0.796401i | \(-0.706735\pi\) | ||
0.604769 | − | 0.796401i | \(-0.293265\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 37.0887i | − | 0.522376i | −0.965288 | − | 0.261188i | \(-0.915886\pi\) | ||
0.965288 | − | 0.261188i | \(-0.0841142\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 115.846i | − | 1.58694i | −0.608612 | − | 0.793468i | \(-0.708273\pi\) | ||
0.608612 | − | 0.793468i | \(-0.291727\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.9979 | −0.168803 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.7659 | 0.212226 | 0.106113 | − | 0.994354i | \(-0.466159\pi\) | ||||
0.106113 | + | 0.994354i | \(0.466159\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −90.4200 | −1.08940 | −0.544699 | − | 0.838632i | \(-0.683356\pi\) | ||||
−0.544699 | + | 0.838632i | \(0.683356\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −32.4423 | − | 74.9660i | −0.381674 | − | 0.881954i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 28.0932i | 0.315654i | 0.987467 | + | 0.157827i | \(0.0504488\pi\) | ||||
−0.987467 | + | 0.157827i | \(0.949551\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.3919 | 0.147164 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.84154 | + | 11.1876i | 0.0509636 | + | 0.117764i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.42958i | − | 0.0972121i | −0.998818 | − | 0.0486061i | \(-0.984522\pi\) | ||
0.998818 | − | 0.0486061i | \(-0.0154779\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 93.7242i | 0.927962i | 0.885845 | + | 0.463981i | \(0.153579\pi\) | ||||
−0.885845 | + | 0.463981i | \(0.846421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 101.748i | 0.987846i | 0.869506 | + | 0.493923i | \(0.164438\pi\) | ||||
−0.869506 | + | 0.493923i | \(0.835562\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 48.7944 | 0.456022 | 0.228011 | − | 0.973659i | \(-0.426778\pi\) | ||||
0.228011 | + | 0.973659i | \(0.426778\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −78.0486 | −0.716042 | −0.358021 | − | 0.933713i | \(-0.616548\pi\) | ||||
−0.358021 | + | 0.933713i | \(0.616548\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 57.6078 | 0.509804 | 0.254902 | − | 0.966967i | \(-0.417957\pi\) | ||||
0.254902 | + | 0.966967i | \(0.417957\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −68.2554 | − | 157.721i | −0.593525 | − | 1.37149i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 10.9118i | − | 0.0916962i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −257.695 | −2.12971 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −117.612 | − | 42.3360i | −0.940899 | − | 0.338688i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 78.7342i | 0.619954i | 0.950744 | + | 0.309977i | \(0.100321\pi\) | ||||
−0.950744 | + | 0.309977i | \(0.899679\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 136.725i | − | 1.04370i | −0.853036 | − | 0.521852i | \(-0.825241\pi\) | ||
0.853036 | − | 0.521852i | \(-0.174759\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.62843i | 0.0122439i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −62.2123 | −0.454105 | −0.227052 | − | 0.973883i | \(-0.572909\pi\) | ||||
−0.227052 | + | 0.973883i | \(0.572909\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −171.778 | −1.23581 | −0.617907 | − | 0.786251i | \(-0.712019\pi\) | ||||
−0.617907 | + | 0.786251i | \(0.712019\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 390.177 | 2.72851 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.3232 | + | 11.3916i | −0.181539 | + | 0.0785629i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 99.7497i | 0.669461i | 0.942314 | + | 0.334731i | \(0.108645\pi\) | ||||
−0.942314 | + | 0.334731i | \(0.891355\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 47.7638 | 0.316316 | 0.158158 | − | 0.987414i | \(-0.449444\pi\) | ||||
0.158158 | + | 0.987414i | \(0.449444\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −53.3235 | − | 123.217i | −0.344023 | − | 0.794951i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 153.095i | 0.975127i | 0.873088 | + | 0.487563i | \(0.162114\pi\) | ||||
−0.873088 | + | 0.487563i | \(0.837886\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 22.9575i | − | 0.142593i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 162.445i | − | 0.996595i | −0.867006 | − | 0.498298i | \(-0.833959\pi\) | ||
0.867006 | − | 0.498298i | \(-0.166041\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 131.441 | 0.787074 | 0.393537 | − | 0.919309i | \(-0.371251\pi\) | ||||
0.393537 | + | 0.919309i | \(0.371251\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −233.007 | −1.37874 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −221.466 | −1.28015 | −0.640075 | − | 0.768312i | \(-0.721097\pi\) | ||||
−0.640075 | + | 0.768312i | \(0.721097\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.1728 | − | 11.4302i | −0.0695588 | − | 0.0653154i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 68.5428i | 0.382921i | 0.981500 | + | 0.191460i | \(0.0613223\pi\) | ||||
−0.981500 | + | 0.191460i | \(0.938678\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −197.707 | −1.09230 | −0.546152 | − | 0.837686i | \(-0.683908\pi\) | ||||
−0.546152 | + | 0.837686i | \(0.683908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 52.2790 | − | 22.6243i | 0.282589 | − | 0.122293i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 317.919i | − | 1.70010i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 269.998i | − | 1.41360i | −0.707412 | − | 0.706802i | \(-0.750137\pi\) | ||
0.707412 | − | 0.706802i | \(-0.249863\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 51.6976i | 0.267863i | 0.990991 | + | 0.133932i | \(0.0427603\pi\) | ||||
−0.990991 | + | 0.133932i | \(0.957240\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −293.145 | −1.48805 | −0.744024 | − | 0.668153i | \(-0.767085\pi\) | ||||
−0.744024 | + | 0.668153i | \(0.767085\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −216.611 | −1.08850 | −0.544248 | − | 0.838924i | \(-0.683185\pi\) | ||||
−0.544248 | + | 0.838924i | \(0.683185\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.83153 | −0.0188745 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 134.221 | − | 58.0856i | 0.654738 | − | 0.283344i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 47.4447i | 0.227008i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 278.581 | 1.32029 | 0.660144 | − | 0.751139i | \(-0.270495\pi\) | ||||
0.660144 | + | 0.751139i | \(0.270495\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −156.589 | + | 67.7656i | −0.728323 | + | 0.315189i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 17.9352i | − | 0.0826506i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 327.558i | 1.48216i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 84.4757i | − | 0.378815i | −0.981899 | − | 0.189407i | \(-0.939343\pi\) | ||
0.981899 | − | 0.189407i | \(-0.0606567\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.9286 | −0.109818 | −0.0549089 | − | 0.998491i | \(-0.517487\pi\) | ||||
−0.0549089 | + | 0.998491i | \(0.517487\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −265.181 | −1.15800 | −0.578998 | − | 0.815329i | \(-0.696556\pi\) | ||||
−0.578998 | + | 0.815329i | \(0.696556\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 290.507 | 1.24681 | 0.623405 | − | 0.781899i | \(-0.285749\pi\) | ||||
0.623405 | + | 0.781899i | \(0.285749\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 135.033 | + | 312.028i | 0.574609 | + | 1.32778i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 106.849i | 0.447069i | 0.974696 | + | 0.223534i | \(0.0717595\pi\) | ||||
−0.974696 | + | 0.223534i | \(0.928241\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −125.991 | −0.522782 | −0.261391 | − | 0.965233i | \(-0.584181\pi\) | ||||
−0.261391 | + | 0.965233i | \(0.584181\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 96.4193 | + | 222.801i | 0.393548 | + | 0.909392i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 48.8832i | − | 0.197908i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 201.781i | 0.803908i | 0.915660 | + | 0.401954i | \(0.131669\pi\) | ||||
−0.915660 | + | 0.401954i | \(0.868331\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 668.869i | − | 2.64375i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −250.865 | −0.976128 | −0.488064 | − | 0.872808i | \(-0.662297\pi\) | ||||
−0.488064 | + | 0.872808i | \(0.662297\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.60959 | 0.0293807 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −358.139 | −1.36175 | −0.680873 | − | 0.732401i | \(-0.738400\pi\) | ||||
−0.680873 | + | 0.732401i | \(0.738400\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −73.6183 | − | 170.114i | −0.277805 | − | 0.641938i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 366.978i | 1.36423i | 0.731245 | + | 0.682115i | \(0.238940\pi\) | ||||
−0.731245 | + | 0.682115i | \(0.761060\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.74235 | 0.0285695 | 0.0142848 | − | 0.999898i | \(-0.495453\pi\) | ||||
0.0142848 | + | 0.999898i | \(0.495453\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −354.657 | − | 333.021i | −1.28966 | − | 1.21099i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 101.934i | 0.367994i | 0.982927 | + | 0.183997i | \(0.0589036\pi\) | ||||
−0.982927 | + | 0.183997i | \(0.941096\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 181.599i | − | 0.646260i | −0.946355 | − | 0.323130i | \(-0.895265\pi\) | ||
0.946355 | − | 0.323130i | \(-0.104735\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 267.926i | 0.946736i | 0.880865 | + | 0.473368i | \(0.156962\pi\) | ||||
−0.880865 | + | 0.473368i | \(0.843038\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.5369 | 0.0680728 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −22.1036 | −0.0764830 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 269.238 | 0.918900 | 0.459450 | − | 0.888204i | \(-0.348047\pi\) | ||||
0.459450 | + | 0.888204i | \(0.348047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −87.3212 | + | 37.7891i | −0.296004 | + | 0.128099i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 689.149i | 2.30485i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.7927 | −0.0757233 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −225.514 | − | 521.108i | −0.739392 | − | 1.70855i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 409.604i | 1.33422i | 0.744961 | + | 0.667108i | \(0.232468\pi\) | ||||
−0.744961 | + | 0.667108i | \(0.767532\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 24.1223i | − | 0.0775637i | −0.999248 | − | 0.0387819i | \(-0.987652\pi\) | ||
0.999248 | − | 0.0387819i | \(-0.0123477\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 435.203i | 1.39042i | 0.718805 | + | 0.695212i | \(0.244690\pi\) | ||||
−0.718805 | + | 0.695212i | \(0.755310\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 392.849 | 1.23927 | 0.619636 | − | 0.784890i | \(-0.287280\pi\) | ||||
0.619636 | + | 0.784890i | \(0.287280\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −111.632 | −0.349945 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −39.8304 | −0.123314 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 365.410 | + | 343.118i | 1.12434 | + | 1.05575i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 45.4179i | 0.138048i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 380.480 | 1.14949 | 0.574743 | − | 0.818334i | \(-0.305102\pi\) | ||||
0.574743 | + | 0.818334i | \(0.305102\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 489.699 | − | 211.922i | 1.46179 | − | 0.632604i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 636.992i | − | 1.89018i | −0.326804 | − | 0.945092i | \(-0.605972\pi\) | ||
0.326804 | − | 0.945092i | \(-0.394028\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 522.545i | − | 1.53239i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 65.1586i | 0.189967i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 105.078 | 0.302819 | 0.151410 | − | 0.988471i | \(-0.451619\pi\) | ||||
0.151410 | + | 0.988471i | \(0.451619\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −346.448 | −0.992688 | −0.496344 | − | 0.868126i | \(-0.665325\pi\) | ||||
−0.496344 | + | 0.868126i | \(0.665325\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 214.861 | 0.608671 | 0.304335 | − | 0.952565i | \(-0.401566\pi\) | ||||
0.304335 | + | 0.952565i | \(0.401566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 170.190 | − | 73.6515i | 0.479409 | − | 0.207469i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 221.170i | − | 0.616073i | −0.951375 | − | 0.308037i | \(-0.900328\pi\) | ||
0.951375 | − | 0.308037i | \(-0.0996719\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −355.056 | −0.983534 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 531.588 | − | 230.050i | 1.45641 | − | 0.630274i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 463.766i | 1.26367i | 0.775103 | + | 0.631834i | \(0.217698\pi\) | ||||
−0.775103 | + | 0.631834i | \(0.782302\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 24.7613i | − | 0.0667419i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 61.9988i | − | 0.166217i | −0.996541 | − | 0.0831083i | \(-0.973515\pi\) | ||
0.996541 | − | 0.0831083i | \(-0.0264847\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 115.017 | 0.305085 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 560.650 | 1.47929 | 0.739644 | − | 0.672998i | \(-0.234994\pi\) | ||||
0.739644 | + | 0.672998i | \(0.234994\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −499.720 | −1.30475 | −0.652377 | − | 0.757895i | \(-0.726228\pi\) | ||||
−0.652377 | + | 0.757895i | \(0.726228\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −25.8114 | − | 59.6437i | −0.0670426 | − | 0.154919i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 100.320i | − | 0.257892i | −0.991652 | − | 0.128946i | \(-0.958841\pi\) | ||
0.991652 | − | 0.128946i | \(-0.0411595\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 561.524 | 1.43612 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.2940 | + | 76.9342i | 0.0842886 | + | 0.194770i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 467.421i | − | 1.17738i | −0.808357 | − | 0.588692i | \(-0.799643\pi\) | ||
0.808357 | − | 0.588692i | \(-0.200357\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 735.269i | − | 1.83359i | −0.399361 | − | 0.916794i | \(-0.630768\pi\) | ||
0.399361 | − | 0.916794i | \(-0.369232\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 538.388i | 1.33595i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 221.707 | 0.544734 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 766.716 | 1.87461 | 0.937306 | − | 0.348509i | \(-0.113312\pi\) | ||||
0.937306 | + | 0.348509i | \(0.113312\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.7102 | −0.0307754 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −179.558 | − | 414.914i | −0.432670 | − | 0.999792i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 388.690i | 0.927662i | 0.885924 | + | 0.463831i | \(0.153526\pi\) | ||||
−0.885924 | + | 0.463831i | \(0.846474\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −133.546 | −0.317211 | −0.158605 | − | 0.987342i | \(-0.550700\pi\) | ||||
−0.158605 | + | 0.987342i | \(0.550700\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 279.575 | − | 297.738i | 0.657823 | − | 0.700561i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 75.8510i | − | 0.177637i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4.42143i | − | 0.0102585i | −0.999987 | − | 0.00512927i | \(-0.998367\pi\) | ||
0.999987 | − | 0.00512927i | \(-0.00163270\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 503.803i | 1.16352i | 0.813361 | + | 0.581759i | \(0.197635\pi\) | ||||
−0.813361 | + | 0.581759i | \(0.802365\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −83.7992 | −0.191760 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 797.121 | 1.81577 | 0.907883 | − | 0.419223i | \(-0.137698\pi\) | ||||
0.907883 | + | 0.419223i | \(0.137698\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 51.1612 | 0.115488 | 0.0577440 | − | 0.998331i | \(-0.481609\pi\) | ||||
0.0577440 | + | 0.998331i | \(0.481609\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −128.912 | + | 55.7880i | −0.289691 | + | 0.125366i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 410.343i | 0.913904i | 0.889491 | + | 0.456952i | \(0.151059\pi\) | ||||
−0.889491 | + | 0.456952i | \(0.848941\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 569.211 | 1.26211 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26.5940 | + | 61.4521i | 0.0584484 | + | 0.135060i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 590.003i | − | 1.29104i | −0.763745 | − | 0.645518i | \(-0.776642\pi\) | ||
0.763745 | − | 0.645518i | \(-0.223358\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 165.283i | − | 0.358530i | −0.983801 | − | 0.179265i | \(-0.942628\pi\) | ||
0.983801 | − | 0.179265i | \(-0.0573720\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.37297i | − | 0.00728502i | −0.999993 | − | 0.00364251i | \(-0.998841\pi\) | ||
0.999993 | − | 0.00364251i | \(-0.00115945\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −553.128 | −1.18443 | −0.592214 | − | 0.805781i | \(-0.701746\pi\) | ||||
−0.592214 | + | 0.805781i | \(0.701746\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 71.2793 | 0.151981 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −664.070 | −1.40395 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −41.7225 | + | 44.4331i | −0.0878368 | + | 0.0935434i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 305.218i | 0.637199i | 0.947889 | + | 0.318600i | \(0.103213\pi\) | ||||
−0.947889 | + | 0.318600i | \(0.896787\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −228.429 | −0.474904 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 43.2699 | − | 18.7254i | 0.0892162 | − | 0.0386092i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 263.256i | 0.540566i | 0.962781 | + | 0.270283i | \(0.0871173\pi\) | ||||
−0.962781 | + | 0.270283i | \(0.912883\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 546.341i | 1.11271i | 0.830945 | + | 0.556355i | \(0.187801\pi\) | ||||
−0.830945 | + | 0.556355i | \(0.812199\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 93.7166i | − | 0.190095i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.7724 | 0.0498439 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 651.657 | 1.30593 | 0.652963 | − | 0.757390i | \(-0.273526\pi\) | ||||
0.652963 | + | 0.757390i | \(0.273526\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −188.144 | −0.374045 | −0.187022 | − | 0.982356i | \(-0.559884\pi\) | ||||
−0.187022 | + | 0.982356i | \(0.559884\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −430.076 | + | 186.119i | −0.851635 | + | 0.368553i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 233.722i | 0.459178i | 0.973288 | + | 0.229589i | \(0.0737382\pi\) | ||||
−0.973288 | + | 0.229589i | \(0.926262\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 77.3765 | 0.151422 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −466.896 | + | 202.054i | −0.906594 | + | 0.392337i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1323.26i | 2.55949i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 455.570i | 0.874415i | 0.899361 | + | 0.437207i | \(0.144032\pi\) | ||||
−0.899361 | + | 0.437207i | \(0.855968\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 176.002i | − | 0.336523i | −0.985742 | − | 0.168261i | \(-0.946185\pi\) | ||
0.985742 | − | 0.168261i | \(-0.0538153\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 438.682 | 0.832414 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 652.390 | 1.23325 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −586.469 | −1.10032 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 96.8969 | + | 223.905i | 0.181116 | + | 0.418513i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 944.862i | 1.75299i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 409.786 | 0.757461 | 0.378730 | − | 0.925507i | \(-0.376361\pi\) | ||||
0.378730 | + | 0.925507i | \(0.376361\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −154.991 | − | 358.145i | −0.284386 | − | 0.657146i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 959.956i | 1.75495i | 0.479626 | + | 0.877473i | \(0.340772\pi\) | ||||
−0.479626 | + | 0.877473i | \(0.659228\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.9858i | 0.0253827i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.1983i | 0.0202501i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 813.070 | 1.45973 | 0.729865 | − | 0.683591i | \(-0.239583\pi\) | ||||
0.729865 | + | 0.683591i | \(0.239583\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 684.204 | 1.22398 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 720.361 | 1.27950 | 0.639752 | − | 0.768581i | \(-0.279037\pi\) | ||||
0.639752 | + | 0.768581i | \(0.279037\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 114.399 | + | 264.347i | 0.202476 | + | 0.467871i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 741.140i | 1.30253i | 0.758850 | + | 0.651265i | \(0.225761\pi\) | ||||
−0.758850 | + | 0.651265i | \(0.774239\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −139.808 | −0.244847 | −0.122424 | − | 0.992478i | \(-0.539067\pi\) | ||||
−0.122424 | + | 0.992478i | \(0.539067\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 588.198 | − | 626.412i | 1.02295 | − | 1.08941i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 696.659i | 1.20738i | 0.797219 | + | 0.603690i | \(0.206304\pi\) | ||||
−0.797219 | + | 0.603690i | \(0.793696\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 60.3937i | − | 0.103948i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 721.424i | − | 1.23743i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −514.225 | −0.876022 | −0.438011 | − | 0.898970i | \(-0.644317\pi\) | ||||
−0.438011 | + | 0.898970i | \(0.644317\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −65.4670 | −0.111149 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −319.924 | −0.539501 | −0.269751 | − | 0.962930i | \(-0.586941\pi\) | ||||
−0.269751 | + | 0.962930i | \(0.586941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 50.0716 | − | 21.6690i | 0.0841540 | − | 0.0364184i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1003.57i | 1.67542i | 0.546118 | + | 0.837709i | \(0.316105\pi\) | ||||
−0.546118 | + | 0.837709i | \(0.683895\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −83.3311 | −0.138654 | −0.0693271 | − | 0.997594i | \(-0.522085\pi\) | ||||
−0.0693271 | + | 0.997594i | \(0.522085\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −511.736 | − | 1182.49i | −0.845844 | − | 1.95454i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 50.6944i | − | 0.0835163i | −0.999128 | − | 0.0417581i | \(-0.986704\pi\) | ||
0.999128 | − | 0.0417581i | \(-0.0132959\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1363.38i | − | 2.23139i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 262.022i | 0.427442i | 0.976895 | + | 0.213721i | \(0.0685584\pi\) | ||||
−0.976895 | + | 0.213721i | \(0.931442\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −342.435 | −0.555001 | −0.277500 | − | 0.960726i | \(-0.589506\pi\) | ||||
−0.277500 | + | 0.960726i | \(0.589506\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 545.803 | 0.881749 | 0.440875 | − | 0.897569i | \(-0.354668\pi\) | ||||
0.440875 | + | 0.897569i | \(0.354668\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.7641 | −0.0301190 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −39.2883 | − | 623.764i | −0.0628613 | − | 0.998022i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 186.125i | 0.295907i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 906.405 | 1.43646 | 0.718229 | − | 0.695807i | \(-0.244953\pi\) | ||||
0.718229 | + | 0.695807i | \(0.244953\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −361.290 | + | 156.352i | −0.568961 | + | 0.246224i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 973.510i | − | 1.52827i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 809.751i | 1.26326i | 0.775269 | + | 0.631631i | \(0.217614\pi\) | ||||
−0.775269 | + | 0.631631i | \(0.782386\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 425.314i | 0.661453i | 0.943727 | + | 0.330726i | \(0.107294\pi\) | ||||
−0.943727 | + | 0.330726i | \(0.892706\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −782.663 | −1.20968 | −0.604840 | − | 0.796347i | \(-0.706763\pi\) | ||||
−0.604840 | + | 0.796347i | \(0.706763\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −370.315 | −0.570593 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1028.32 | 1.57477 | 0.787385 | − | 0.616462i | \(-0.211434\pi\) | ||||
0.787385 | + | 0.616462i | \(0.211434\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 627.397 | − | 271.512i | 0.957857 | − | 0.414522i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 266.180i | − | 0.403916i | −0.979394 | − | 0.201958i | \(-0.935270\pi\) | ||
0.979394 | − | 0.201958i | \(-0.0647304\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −509.305 | −0.770507 | −0.385254 | − | 0.922811i | \(-0.625886\pi\) | ||||
−0.385254 | + | 0.922811i | \(0.625886\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.47246 | + | 3.23378i | −0.0112368 | + | 0.00486283i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 197.171i | − | 0.295608i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2209.93i | − | 3.29349i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 796.227i | − | 1.18310i | −0.806268 | − | 0.591551i | \(-0.798516\pi\) | ||
0.806268 | − | 0.591551i | \(-0.201484\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1264.05 | −1.86713 | −0.933565 | − | 0.358408i | \(-0.883320\pi\) | ||||
−0.933565 | + | 0.358408i | \(0.883320\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.29824 | 0.00927576 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 262.103 | 0.383753 | 0.191876 | − | 0.981419i | \(-0.438543\pi\) | ||||
0.191876 | + | 0.981419i | \(0.438543\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −123.543 | − | 285.476i | −0.180354 | − | 0.416753i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 743.297i | 1.07881i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 751.634 | 1.08775 | 0.543874 | − | 0.839167i | \(-0.316957\pi\) | ||||
0.543874 | + | 0.839167i | \(0.316957\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −341.120 | − | 788.245i | −0.490821 | − | 1.13416i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 477.859i | 0.685594i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 620.953i | 0.885810i | 0.896569 | + | 0.442905i | \(0.146052\pi\) | ||||
−0.896569 | + | 0.442905i | \(0.853948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 27.7765i | − | 0.0395114i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −62.6006 | −0.0885440 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −403.710 | −0.569408 | −0.284704 | − | 0.958615i | \(-0.591895\pi\) | ||||
−0.284704 | + | 0.958615i | \(0.591895\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 922.945 | 1.29445 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 774.821 | + | 1790.42i | 1.08367 | + | 2.50408i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 316.833i | 0.440658i | 0.975426 | + | 0.220329i | \(0.0707132\pi\) | ||||
−0.975426 | + | 0.220329i | \(0.929287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −67.9600 | −0.0942580 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −104.546 | − | 98.1685i | −0.144202 | − | 0.135405i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 557.477i | 0.766818i | 0.923579 | + | 0.383409i | \(0.125250\pi\) | ||||
−0.923579 | + | 0.383409i | \(0.874750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 557.494i | − | 0.762646i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 446.752i | − | 0.609485i | −0.952435 | − | 0.304742i | \(-0.901430\pi\) | ||
0.952435 | − | 0.304742i | \(-0.0985704\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2076.73 | 2.81782 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 209.090 | 0.282937 | 0.141468 | − | 0.989943i | \(-0.454818\pi\) | ||||
0.141468 | + | 0.989943i | \(0.454818\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.5445 | 0.0612981 | 0.0306490 | − | 0.999530i | \(-0.490243\pi\) | ||||
0.0306490 | + | 0.999530i | \(0.490243\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −457.725 | + | 198.085i | −0.614396 | + | 0.265886i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.5909i | 0.0435126i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.3154 | 0.0230564 | 0.0115282 | − | 0.999934i | \(-0.496330\pi\) | ||||
0.0115282 | + | 0.999934i | \(0.496330\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 94.8503 | + | 219.175i | 0.125629 | + | 0.290298i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1269.99i | − | 1.67767i | −0.544388 | − | 0.838834i | \(-0.683238\pi\) | ||
0.544388 | − | 0.838834i | \(-0.316762\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1152.17i | 1.51402i | 0.653403 | + | 0.757010i | \(0.273341\pi\) | ||||
−0.653403 | + | 0.757010i | \(0.726659\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 52.1305i | − | 0.0683231i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 381.543 | 0.497448 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −506.118 | −0.658151 | −0.329076 | − | 0.944304i | \(-0.606737\pi\) | ||||
−0.329076 | + | 0.944304i | \(0.606737\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −374.490 | −0.484463 | −0.242232 | − | 0.970218i | \(-0.577879\pi\) | ||||
−0.242232 | + | 0.970218i | \(0.577879\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 459.521 | − | 489.375i | 0.592931 | − | 0.631452i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 71.3135i | − | 0.0915449i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 721.749 | 0.924134 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −702.512 | + | 304.019i | −0.894920 | + | 0.387285i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 856.557i | − | 1.08838i | −0.838961 | − | 0.544191i | \(-0.816837\pi\) | ||
0.838961 | − | 0.544191i | \(-0.183163\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.4776i | 0.0486443i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2276.94i | 2.87129i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −229.964 | −0.288536 | −0.144268 | − | 0.989539i | \(-0.546083\pi\) | ||||
−0.144268 | + | 0.989539i | \(0.546083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1110.89 | −1.39035 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2254.38 | 2.80745 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 105.346 | − | 45.5894i | 0.130864 | − | 0.0566328i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1140.95i | 1.41032i | 0.709046 | + | 0.705162i | \(0.249126\pi\) | ||||
−0.709046 | + | 0.705162i | \(0.750874\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −853.740 | −1.05270 | −0.526350 | − | 0.850268i | \(-0.676440\pi\) | ||||
−0.526350 | + | 0.850268i | \(0.676440\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 745.418 | − | 322.587i | 0.914623 | − | 0.395812i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 83.1979i | 0.101833i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 733.845i | − | 0.893843i | −0.894573 | − | 0.446921i | \(-0.852520\pi\) | ||
0.894573 | − | 0.446921i | \(-0.147480\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 334.806i | − | 0.406811i | −0.979095 | − | 0.203406i | \(-0.934799\pi\) | ||
0.979095 | − | 0.203406i | \(-0.0652010\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1023.56 | −1.23768 | −0.618840 | − | 0.785517i | \(-0.712397\pi\) | ||||
−0.618840 | + | 0.785517i | \(0.712397\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1381.98 | −1.66705 | −0.833525 | − | 0.552482i | \(-0.813681\pi\) | ||||
−0.833525 | + | 0.552482i | \(0.813681\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −793.223 | −0.952248 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 261.019 | + | 603.150i | 0.312597 | + | 0.722335i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1213.98i | 1.44693i | 0.690358 | + | 0.723467i | \(0.257453\pi\) | ||||
−0.690358 | + | 0.723467i | \(0.742547\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 808.093 | 0.960871 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −462.710 | − | 1069.21i | −0.547585 | − | 1.26533i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 172.120i | − | 0.203212i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 391.589i | 0.460152i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 100.817i | 0.118192i | 0.998252 | + | 0.0590958i | \(0.0188217\pi\) | ||||
−0.998252 | + | 0.0590958i | \(0.981178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 137.768 | 0.160756 | 0.0803780 | − | 0.996764i | \(-0.474387\pi\) | ||||
0.0803780 | + | 0.996764i | \(0.474387\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 387.465 | 0.451065 | 0.225532 | − | 0.974236i | \(-0.427588\pi\) | ||||
0.225532 | + | 0.974236i | \(0.427588\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1033.60 | −1.19768 | −0.598841 | − | 0.800868i | \(-0.704372\pi\) | ||||
−0.598841 | + | 0.800868i | \(0.704372\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −439.792 | − | 1016.25i | −0.508430 | − | 1.17486i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 326.265i | 0.375449i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2139.70 | −2.45660 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.2772 | − | 78.5561i | 0.0323168 | − | 0.0897784i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 257.248i | 0.293327i | 0.989186 | + | 0.146663i | \(0.0468534\pi\) | ||||
−0.989186 | + | 0.146663i | \(0.953147\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 861.458i | − | 0.977819i | −0.872335 | − | 0.488909i | \(-0.837395\pi\) | ||
0.872335 | − | 0.488909i | \(-0.162605\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1059.68i | 1.20009i | 0.799967 | + | 0.600045i | \(0.204850\pi\) | ||||
−0.799967 | + | 0.600045i | \(0.795150\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1292.44 | 1.45709 | 0.728546 | − | 0.684997i | \(-0.240197\pi\) | ||||
0.728546 | + | 0.684997i | \(0.240197\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −52.5884 | −0.0591546 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 165.784 | 0.185649 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −314.525 | + | 136.114i | −0.351424 | + | 0.152082i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 154.037i | − | 0.171342i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 605.643 | 0.672190 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −392.611 | − | 907.227i | −0.433824 | − | 1.00246i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 304.430i | 0.335645i | 0.985817 | + | 0.167823i | \(0.0536736\pi\) | ||||
−0.985817 | + | 0.167823i | \(0.946326\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 253.095i | − | 0.277822i | −0.990305 | − | 0.138911i | \(-0.955640\pi\) | ||
0.990305 | − | 0.138911i | \(-0.0443601\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1759.58i | − | 1.92725i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 91.3221 | 0.0995879 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −782.852 | −0.851852 | −0.425926 | − | 0.904758i | \(-0.640052\pi\) | ||||
−0.425926 | + | 0.904758i | \(0.640052\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −743.632 | −0.805668 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 207.634 | + | 194.967i | 0.224469 | + | 0.210775i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 253.182i | 0.272532i | 0.990672 | + | 0.136266i | \(0.0435102\pi\) | ||||
−0.990672 | + | 0.136266i | \(0.956490\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 118.377 | 0.127150 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1458.85 | − | 631.329i | 1.56026 | − | 0.675219i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 578.052i | − | 0.616918i | −0.951238 | − | 0.308459i | \(-0.900187\pi\) | ||
0.951238 | − | 0.308459i | \(-0.0998133\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 768.963i | − | 0.817176i | −0.912719 | − | 0.408588i | \(-0.866021\pi\) | ||
0.912719 | − | 0.408588i | \(-0.133979\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1005.37i | 1.06614i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.3925 | 0.0247016 | 0.0123508 | − | 0.999924i | \(-0.496069\pi\) | ||||
0.0123508 | + | 0.999924i | \(0.496069\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2322.73 | −2.44756 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1230.20 | −1.29087 | −0.645437 | − | 0.763814i | \(-0.723325\pi\) | ||||
−0.645437 | + | 0.763814i | \(0.723325\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1238.95 | − | 536.168i | 1.29733 | − | 0.561433i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 41.5531i | − | 0.0433296i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −239.963 | −0.249701 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −237.227 | + | 102.662i | −0.245831 | + | 0.106386i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1023.85i | − | 1.05879i | −0.848375 | − | 0.529396i | \(-0.822419\pi\) | ||
0.848375 | − | 0.529396i | \(-0.177581\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 180.852i | − | 0.186253i | −0.995654 | − | 0.0931267i | \(-0.970314\pi\) | ||
0.995654 | − | 0.0931267i | \(-0.0296862\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 114.735i | − | 0.117918i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1738.78 | −1.77971 | −0.889856 | − | 0.456242i | \(-0.849195\pi\) | ||||
−0.889856 | + | 0.456242i | \(0.849195\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −546.696 | −0.558423 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 693.798 | 0.705796 | 0.352898 | − | 0.935662i | \(-0.385196\pi\) | ||||
0.352898 | + | 0.935662i | \(0.385196\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −582.134 | − | 1345.17i | −0.590999 | − | 1.36565i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1172.91i | − | 1.18596i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −587.142 | −0.592474 | −0.296237 | − | 0.955114i | \(-0.595732\pi\) | ||||
−0.296237 | + | 0.955114i | \(0.595732\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −430.150 | − | 993.970i | −0.432312 | − | 0.998965i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.24185i | 0.00425462i | 0.999998 | + | 0.00212731i | \(0.000677144\pi\) | ||||
−0.999998 | + | 0.00212731i | \(0.999323\pi\) | |||||||
\(998\) | 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 | 1620.3.b.b.809.18 | 24 | ||
3.2 | odd | 2 | inner | 1620.3.b.b.809.7 | 24 | ||
5.4 | even | 2 | inner | 1620.3.b.b.809.8 | 24 | ||
9.2 | odd | 6 | 540.3.t.a.449.12 | 24 | |||
9.4 | even | 3 | 540.3.t.a.89.8 | 24 | |||
9.5 | odd | 6 | 180.3.t.a.29.11 | yes | 24 | ||
9.7 | even | 3 | 180.3.t.a.149.2 | yes | 24 | ||
15.14 | odd | 2 | inner | 1620.3.b.b.809.17 | 24 | ||
45.2 | even | 12 | 2700.3.p.f.2501.7 | 24 | |||
45.4 | even | 6 | 540.3.t.a.89.12 | 24 | |||
45.7 | odd | 12 | 900.3.p.f.401.8 | 24 | |||
45.13 | odd | 12 | 2700.3.p.f.1601.6 | 24 | |||
45.14 | odd | 6 | 180.3.t.a.29.2 | ✓ | 24 | ||
45.22 | odd | 12 | 2700.3.p.f.1601.7 | 24 | |||
45.23 | even | 12 | 900.3.p.f.101.5 | 24 | |||
45.29 | odd | 6 | 540.3.t.a.449.8 | 24 | |||
45.32 | even | 12 | 900.3.p.f.101.8 | 24 | |||
45.34 | even | 6 | 180.3.t.a.149.11 | yes | 24 | ||
45.38 | even | 12 | 2700.3.p.f.2501.6 | 24 | |||
45.43 | odd | 12 | 900.3.p.f.401.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.t.a.29.2 | ✓ | 24 | 45.14 | odd | 6 | ||
180.3.t.a.29.11 | yes | 24 | 9.5 | odd | 6 | ||
180.3.t.a.149.2 | yes | 24 | 9.7 | even | 3 | ||
180.3.t.a.149.11 | yes | 24 | 45.34 | even | 6 | ||
540.3.t.a.89.8 | 24 | 9.4 | even | 3 | |||
540.3.t.a.89.12 | 24 | 45.4 | even | 6 | |||
540.3.t.a.449.8 | 24 | 45.29 | odd | 6 | |||
540.3.t.a.449.12 | 24 | 9.2 | odd | 6 | |||
900.3.p.f.101.5 | 24 | 45.23 | even | 12 | |||
900.3.p.f.101.8 | 24 | 45.32 | even | 12 | |||
900.3.p.f.401.5 | 24 | 45.43 | odd | 12 | |||
900.3.p.f.401.8 | 24 | 45.7 | odd | 12 | |||
1620.3.b.b.809.7 | 24 | 3.2 | odd | 2 | inner | ||
1620.3.b.b.809.8 | 24 | 5.4 | even | 2 | inner | ||
1620.3.b.b.809.17 | 24 | 15.14 | odd | 2 | inner | ||
1620.3.b.b.809.18 | 24 | 1.1 | even | 1 | trivial | ||
2700.3.p.f.1601.6 | 24 | 45.13 | odd | 12 | |||
2700.3.p.f.1601.7 | 24 | 45.22 | odd | 12 | |||
2700.3.p.f.2501.6 | 24 | 45.38 | even | 12 | |||
2700.3.p.f.2501.7 | 24 | 45.2 | even | 12 |