Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(1711,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1711");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.m (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: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 2 x^{10} - 28 x^{9} - 400 x^{8} - 520 x^{7} + 17067 x^{6} - 3250 x^{5} - 195494 x^{4} + 302996 x^{3} + 602332 x^{2} - 2263536 x + 2052928 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 912) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1711.9 | ||
Root | \(1.30395 + 1.41343i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1711 |
Dual form | 2736.3.m.e.1711.10 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.08630 | 1.21726 | 0.608630 | − | 0.793454i | \(-0.291719\pi\) | ||||
0.608630 | + | 0.793454i | \(0.291719\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 8.85163i | − 1.26452i | −0.774757 | − | 0.632259i | \(-0.782128\pi\) | ||||
0.774757 | − | 0.632259i | \(-0.217872\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.64046i | 0.603678i | 0.953359 | + | 0.301839i | \(0.0976005\pi\) | ||||
−0.953359 | + | 0.301839i | \(0.902399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.95680 | −0.227446 | −0.113723 | − | 0.993512i | \(-0.536278\pi\) | ||||
−0.113723 | + | 0.993512i | \(0.536278\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −21.7835 | −1.28138 | −0.640691 | − | 0.767799i | \(-0.721352\pi\) | ||||
−0.640691 | + | 0.767799i | \(0.721352\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.35890i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 30.4779i | − 1.32513i | −0.749006 | − | 0.662563i | \(-0.769469\pi\) | ||||
0.749006 | − | 0.662563i | \(-0.230531\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.0431 | 0.481724 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17.0059 | 0.586410 | 0.293205 | − | 0.956050i | \(-0.405278\pi\) | ||||
0.293205 | + | 0.956050i | \(0.405278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 58.0298i | 1.87193i | 0.352094 | + | 0.935965i | \(0.385470\pi\) | ||||
−0.352094 | + | 0.935965i | \(0.614530\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 53.8737i | − 1.53925i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −44.3601 | −1.19892 | −0.599461 | − | 0.800404i | \(-0.704618\pi\) | ||||
−0.599461 | + | 0.800404i | \(0.704618\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.33039 | 0.130009 | 0.0650047 | − | 0.997885i | \(-0.479294\pi\) | ||||
0.0650047 | + | 0.997885i | \(0.479294\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 50.1443i | − 1.16615i | −0.812419 | − | 0.583074i | \(-0.801850\pi\) | ||||
0.812419 | − | 0.583074i | \(-0.198150\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 74.0431i | − 1.57538i | −0.616069 | − | 0.787692i | \(-0.711276\pi\) | ||||
0.616069 | − | 0.787692i | \(-0.288724\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −29.3513 | −0.599005 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −51.5148 | −0.971977 | −0.485988 | − | 0.873965i | \(-0.661540\pi\) | ||||
−0.485988 | + | 0.873965i | \(0.661540\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 40.4159i | 0.734834i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 18.5370i | − 0.314187i | −0.987584 | − | 0.157093i | \(-0.949788\pi\) | ||||
0.987584 | − | 0.157093i | \(-0.0502124\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −100.168 | −1.64210 | −0.821048 | − | 0.570859i | \(-0.806610\pi\) | ||||
−0.821048 | + | 0.570859i | \(0.806610\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −17.9960 | −0.276861 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 31.1882i | − 0.465495i | −0.972537 | − | 0.232747i | \(-0.925228\pi\) | ||||
0.972537 | − | 0.232747i | \(-0.0747715\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 74.3566i | − 1.04728i | −0.851941 | − | 0.523638i | \(-0.824574\pi\) | ||||
0.851941 | − | 0.523638i | \(-0.175426\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −50.4741 | −0.691426 | −0.345713 | − | 0.938340i | \(-0.612363\pi\) | ||||
−0.345713 | + | 0.938340i | \(0.612363\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 58.7789 | 0.763362 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.81405i | 0.0862538i | 0.999070 | + | 0.0431269i | \(0.0137320\pi\) | ||||
−0.999070 | + | 0.0431269i | \(0.986268\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 25.6400i | − 0.308916i | −0.987999 | − | 0.154458i | \(-0.950637\pi\) | ||||
0.987999 | − | 0.154458i | \(-0.0493632\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −132.581 | −1.55978 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.61427 | −0.0406098 | −0.0203049 | − | 0.999794i | \(-0.506464\pi\) | ||||
−0.0203049 | + | 0.999794i | \(0.506464\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 26.1725i | 0.287610i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 26.5296i | − 0.279259i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 140.421 | 1.44764 | 0.723819 | − | 0.689990i | \(-0.242385\pi\) | ||||
0.723819 | + | 0.689990i | \(0.242385\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −71.3972 | −0.706903 | −0.353451 | − | 0.935453i | \(-0.614992\pi\) | ||||
−0.353451 | + | 0.935453i | \(0.614992\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 102.721i | 0.997295i | 0.866805 | + | 0.498647i | \(0.166170\pi\) | ||||
−0.866805 | + | 0.498647i | \(0.833830\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 64.9271i | − 0.606796i | −0.952864 | − | 0.303398i | \(-0.901879\pi\) | ||||
0.952864 | − | 0.303398i | \(-0.0981211\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −115.572 | −1.06029 | −0.530145 | − | 0.847907i | \(-0.677863\pi\) | ||||
−0.530145 | + | 0.847907i | \(0.677863\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 217.263 | 1.92268 | 0.961339 | − | 0.275366i | \(-0.0887991\pi\) | ||||
0.961339 | + | 0.275366i | \(0.0887991\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 185.498i | − 1.61302i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 192.819i | 1.62033i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 76.9043 | 0.635573 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −78.8596 | −0.630877 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.3029i | 0.136243i | 0.997677 | + | 0.0681217i | \(0.0217006\pi\) | ||||
−0.997677 | + | 0.0681217i | \(0.978299\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 72.8478i | − 0.556090i | −0.960568 | − | 0.278045i | \(-0.910314\pi\) | ||||
0.960568 | − | 0.278045i | \(-0.0896864\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −38.5833 | −0.290100 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −166.375 | −1.21441 | −0.607207 | − | 0.794544i | \(-0.707710\pi\) | ||||
−0.607207 | + | 0.794544i | \(0.707710\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 197.109i | 1.41805i | 0.705184 | + | 0.709024i | \(0.250864\pi\) | ||||
−0.705184 | + | 0.709024i | \(0.749136\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 19.6345i | − 0.137304i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 103.503 | 0.713814 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −240.667 | −1.61522 | −0.807608 | − | 0.589720i | \(-0.799238\pi\) | ||||
−0.807608 | + | 0.589720i | \(0.799238\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 123.722i | 0.819354i | 0.912231 | + | 0.409677i | \(0.134359\pi\) | ||||
−0.912231 | + | 0.409677i | \(0.865641\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 353.187i | 2.27863i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 114.012 | 0.726194 | 0.363097 | − | 0.931751i | \(-0.381719\pi\) | ||||
0.363097 | + | 0.931751i | \(0.381719\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −269.779 | −1.67565 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 227.685i | 1.39684i | 0.715689 | + | 0.698419i | \(0.246113\pi\) | ||||
−0.715689 | + | 0.698419i | \(0.753887\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 96.0499i | − 0.575149i | −0.957758 | − | 0.287575i | \(-0.907151\pi\) | ||||
0.957758 | − | 0.287575i | \(-0.0928489\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −160.257 | −0.948268 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 277.388 | 1.60340 | 0.801698 | − | 0.597729i | \(-0.203930\pi\) | ||||
0.801698 | + | 0.597729i | \(0.203930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 106.601i | − 0.609149i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 103.569i | − 0.578600i | −0.957239 | − | 0.289300i | \(-0.906578\pi\) | ||||
0.957239 | − | 0.289300i | \(-0.0934225\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −126.631 | −0.699621 | −0.349810 | − | 0.936821i | \(-0.613754\pi\) | ||||
−0.349810 | + | 0.936821i | \(0.613754\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −269.989 | −1.45940 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 144.652i | − 0.773542i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 118.419i | − 0.619997i | −0.950737 | − | 0.309998i | \(-0.899672\pi\) | ||||
0.950737 | − | 0.309998i | \(-0.100328\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −179.569 | −0.930412 | −0.465206 | − | 0.885203i | \(-0.654020\pi\) | ||||
−0.465206 | + | 0.885203i | \(0.654020\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −185.985 | −0.944088 | −0.472044 | − | 0.881575i | \(-0.656484\pi\) | ||||
−0.472044 | + | 0.881575i | \(0.656484\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 11.9251i | − 0.0599251i | −0.999551 | − | 0.0299625i | \(-0.990461\pi\) | ||||
0.999551 | − | 0.0299625i | \(-0.00953880\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 150.530i | − 0.741526i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 32.4423 | 0.158255 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.9451 | 0.138493 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 54.6535i | − 0.259021i | −0.991578 | − | 0.129511i | \(-0.958659\pi\) | ||||
0.991578 | − | 0.129511i | \(-0.0413406\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 305.194i | − 1.41951i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 513.658 | 2.36709 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 64.4094 | 0.291445 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 125.844i | − 0.564321i | −0.959367 | − | 0.282161i | \(-0.908949\pi\) | ||||
0.959367 | − | 0.282161i | \(-0.0910511\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 372.784i | − 1.64222i | −0.570769 | − | 0.821110i | \(-0.693355\pi\) | ||||
0.570769 | − | 0.821110i | \(-0.306645\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.2915 | −0.0624082 | −0.0312041 | − | 0.999513i | \(-0.509934\pi\) | ||||
−0.0312041 | + | 0.999513i | \(0.509934\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.2964 | −0.0828170 | −0.0414085 | − | 0.999142i | \(-0.513184\pi\) | ||||
−0.0414085 | + | 0.999142i | \(0.513184\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 450.649i | − 1.91765i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 147.097i | 0.615470i | 0.951472 | + | 0.307735i | \(0.0995710\pi\) | ||||
−0.951472 | + | 0.307735i | \(0.900429\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −210.083 | −0.871713 | −0.435857 | − | 0.900016i | \(-0.643555\pi\) | ||||
−0.435857 | + | 0.900016i | \(0.643555\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −178.641 | −0.729146 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.8884i | 0.0521797i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 53.6081i | 0.213578i | 0.994282 | + | 0.106789i | \(0.0340570\pi\) | ||||
−0.994282 | + | 0.106789i | \(0.965943\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 202.387 | 0.799950 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 346.789 | 1.34937 | 0.674686 | − | 0.738105i | \(-0.264279\pi\) | ||||
0.674686 | + | 0.738105i | \(0.264279\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 392.659i | 1.51606i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 355.183i | 1.35050i | 0.737587 | + | 0.675252i | \(0.235965\pi\) | ||||
−0.737587 | + | 0.675252i | \(0.764035\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −313.535 | −1.18315 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 41.7600 | 0.155242 | 0.0776209 | − | 0.996983i | \(-0.475268\pi\) | ||||
0.0776209 | + | 0.996983i | \(0.475268\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 433.198i | − 1.59852i | −0.600987 | − | 0.799259i | \(-0.705226\pi\) | ||||
0.600987 | − | 0.799259i | \(-0.294774\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 79.9717i | 0.290806i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 380.398 | 1.37328 | 0.686640 | − | 0.726998i | \(-0.259085\pi\) | ||||
0.686640 | + | 0.726998i | \(0.259085\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −185.121 | −0.658792 | −0.329396 | − | 0.944192i | \(-0.606845\pi\) | ||||
−0.329396 | + | 0.944192i | \(0.606845\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 397.379i | − 1.40417i | −0.712096 | − | 0.702083i | \(-0.752254\pi\) | ||||
0.712096 | − | 0.702083i | \(-0.247746\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 47.1826i | − 0.164399i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 185.520 | 0.641939 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −489.006 | −1.66896 | −0.834480 | − | 0.551037i | \(-0.814232\pi\) | ||||
−0.834480 | + | 0.551037i | \(0.814232\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 112.822i | − 0.382447i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 90.1170i | 0.301395i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −443.859 | −1.47461 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −609.652 | −1.99886 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 93.4725i | 0.304471i | 0.988344 | + | 0.152235i | \(0.0486471\pi\) | ||||
−0.988344 | + | 0.152235i | \(0.951353\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 214.371i | − 0.689294i | −0.938732 | − | 0.344647i | \(-0.887999\pi\) | ||||
0.938732 | − | 0.344647i | \(-0.112001\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 148.994 | 0.476020 | 0.238010 | − | 0.971263i | \(-0.423505\pi\) | ||||
0.238010 | + | 0.971263i | \(0.423505\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 490.937 | 1.54870 | 0.774349 | − | 0.632759i | \(-0.218077\pi\) | ||||
0.774349 | + | 0.632759i | \(0.218077\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 112.927i | 0.354003i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 94.9520i | 0.293969i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −35.6090 | −0.109566 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −655.401 | −1.99210 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 489.131i | − 1.47774i | −0.673850 | − | 0.738868i | \(-0.735361\pi\) | ||||
0.673850 | − | 0.738868i | \(-0.264639\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 189.821i | − 0.566629i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.82451 | 0.0113487 | 0.00567435 | − | 0.999984i | \(-0.498194\pi\) | ||||
0.00567435 | + | 0.999984i | \(0.498194\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −385.345 | −1.13004 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 173.923i | − 0.507065i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 151.748i | 0.437314i | 0.975802 | + | 0.218657i | \(0.0701676\pi\) | ||||
−0.975802 | + | 0.218657i | \(0.929832\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.2852 | 0.0352011 | 0.0176005 | − | 0.999845i | \(-0.494397\pi\) | ||||
0.0176005 | + | 0.999845i | \(0.494397\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.69743 | 0.0104743 | 0.00523716 | − | 0.999986i | \(-0.498333\pi\) | ||||
0.00523716 | + | 0.999986i | \(0.498333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 452.557i | − 1.27481i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 109.483i | 0.304966i | 0.988306 | + | 0.152483i | \(0.0487270\pi\) | ||||
−0.988306 | + | 0.152483i | \(0.951273\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −307.201 | −0.841646 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 611.742i | − 1.66687i | −0.552615 | − | 0.833436i | \(-0.686370\pi\) | ||||
0.552615 | − | 0.833436i | \(-0.313630\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 455.989i | 1.22908i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −670.407 | −1.79734 | −0.898669 | − | 0.438628i | \(-0.855465\pi\) | ||||
−0.898669 | + | 0.438628i | \(0.855465\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −50.2830 | −0.133377 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 187.724i | − 0.495315i | −0.968848 | − | 0.247658i | \(-0.920339\pi\) | ||||
0.968848 | − | 0.247658i | \(-0.0796608\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 190.583i | − 0.497605i | −0.968554 | − | 0.248803i | \(-0.919963\pi\) | ||||
0.968554 | − | 0.248803i | \(-0.0800370\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 357.746 | 0.929211 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 584.136 | 1.50164 | 0.750818 | − | 0.660510i | \(-0.229660\pi\) | ||||
0.750818 | + | 0.660510i | \(0.229660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 663.915i | 1.69799i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 41.4724i | 0.104993i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −571.136 | −1.43863 | −0.719315 | − | 0.694684i | \(-0.755544\pi\) | ||||
−0.719315 | + | 0.694684i | \(0.755544\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −56.0922 | −0.139881 | −0.0699404 | − | 0.997551i | \(-0.522281\pi\) | ||||
−0.0699404 | + | 0.997551i | \(0.522281\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 171.582i | − 0.425763i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 294.572i | − 0.723763i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −136.122 | −0.332816 | −0.166408 | − | 0.986057i | \(-0.553217\pi\) | ||||
−0.166408 | + | 0.986057i | \(0.553217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −164.083 | −0.397295 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 156.053i | − 0.376032i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 235.462i | 0.561962i | 0.959713 | + | 0.280981i | \(0.0906598\pi\) | ||||
−0.959713 | + | 0.280981i | \(0.909340\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −568.408 | −1.35014 | −0.675068 | − | 0.737755i | \(-0.735886\pi\) | ||||
−0.675068 | + | 0.737755i | \(0.735886\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −262.341 | −0.617272 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 886.649i | 2.07646i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 40.3202i | − 0.0935504i | −0.998905 | − | 0.0467752i | \(-0.985106\pi\) | ||||
0.998905 | − | 0.0467752i | \(-0.0148944\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 122.057 | 0.281887 | 0.140943 | − | 0.990018i | \(-0.454986\pi\) | ||||
0.140943 | + | 0.990018i | \(0.454986\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −132.850 | −0.304005 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 701.020i | − 1.59686i | −0.602090 | − | 0.798428i | \(-0.705665\pi\) | ||||
0.602090 | − | 0.798428i | \(-0.294335\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 693.845i | − 1.56624i | −0.621870 | − | 0.783120i | \(-0.713627\pi\) | ||||
0.621870 | − | 0.783120i | \(-0.286373\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.9976 | −0.0494327 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −383.490 | −0.854098 | −0.427049 | − | 0.904228i | \(-0.640447\pi\) | ||||
−0.427049 | + | 0.904228i | \(0.640447\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.3962i | 0.0784838i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 159.294i | 0.350096i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −191.679 | −0.419429 | −0.209715 | − | 0.977763i | \(-0.567253\pi\) | ||||
−0.209715 | + | 0.977763i | \(0.567253\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 674.072 | 1.46220 | 0.731098 | − | 0.682272i | \(-0.239008\pi\) | ||||
0.731098 | + | 0.682272i | \(0.239008\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 439.695i | 0.949666i | 0.880076 | + | 0.474833i | \(0.157491\pi\) | ||||
−0.880076 | + | 0.474833i | \(0.842509\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 221.787i | 0.474920i | 0.971397 | + | 0.237460i | \(0.0763148\pi\) | ||||
−0.971397 | + | 0.237460i | \(0.923685\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −276.066 | −0.588627 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 332.981 | 0.703978 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 52.4947i | − 0.110515i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 226.990i | 0.473882i | 0.971524 | + | 0.236941i | \(0.0761449\pi\) | ||||
−0.971524 | + | 0.236941i | \(0.923855\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 131.164 | 0.272690 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 854.644 | 1.76215 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 801.415i | 1.64562i | 0.568319 | + | 0.822808i | \(0.307594\pi\) | ||||
−0.568319 | + | 0.822808i | \(0.692406\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 64.6780i | − 0.131727i | −0.997829 | − | 0.0658635i | \(-0.979020\pi\) | ||||
0.997829 | − | 0.0658635i | \(-0.0209802\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −370.448 | −0.751415 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −658.177 | −1.32430 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 183.365i | 0.367465i | 0.982976 | + | 0.183732i | \(0.0588180\pi\) | ||||
−0.982976 | + | 0.183732i | \(0.941182\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 587.722i | 1.16843i | 0.811598 | + | 0.584217i | \(0.198598\pi\) | ||||
−0.811598 | + | 0.584217i | \(0.801402\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −434.545 | −0.860485 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 152.232 | 0.299080 | 0.149540 | − | 0.988756i | \(-0.452221\pi\) | ||||
0.149540 | + | 0.988756i | \(0.452221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 446.778i | 0.874321i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 625.193i | 1.21397i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 491.680 | 0.951025 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −705.378 | −1.35389 | −0.676946 | − | 0.736032i | \(-0.736697\pi\) | ||||
−0.676946 | + | 0.736032i | \(0.736697\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 579.461i | 1.10796i | 0.832531 | + | 0.553978i | \(0.186891\pi\) | ||||
−0.832531 | + | 0.553978i | \(0.813109\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1264.09i | − 2.39866i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −399.902 | −0.755959 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.7609 | −0.0295701 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 395.166i | − 0.738629i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 194.906i | − 0.361607i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 275.470 | 0.509187 | 0.254593 | − | 0.967048i | \(-0.418058\pi\) | ||||
0.254593 | + | 0.967048i | \(0.418058\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −703.405 | −1.29065 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 920.704i | 1.68319i | 0.540111 | + | 0.841594i | \(0.318382\pi\) | ||||
−0.540111 | + | 0.841594i | \(0.681618\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 74.1269i | − 0.134532i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 60.3154 | 0.109069 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 154.313 | 0.277043 | 0.138522 | − | 0.990359i | \(-0.455765\pi\) | ||||
0.138522 | + | 0.990359i | \(0.455765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 148.267i | 0.265235i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 317.068i | 0.563176i | 0.959535 | + | 0.281588i | \(0.0908611\pi\) | ||||
−0.959535 | + | 0.281588i | \(0.909139\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1322.33 | 2.34040 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 420.374 | 0.738794 | 0.369397 | − | 0.929272i | \(-0.379564\pi\) | ||||
0.369397 | + | 0.929272i | \(0.379564\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 426.174i | 0.746364i | 0.927758 | + | 0.373182i | \(0.121733\pi\) | ||||
−0.927758 | + | 0.373182i | \(0.878267\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 367.048i | − 0.638345i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 865.702 | 1.50035 | 0.750175 | − | 0.661239i | \(-0.229969\pi\) | ||||
0.750175 | + | 0.661239i | \(0.229969\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −226.956 | −0.390630 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 342.082i | − 0.586761i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 327.570i | − 0.558041i | −0.960285 | − | 0.279021i | \(-0.909990\pi\) | ||||
0.960285 | − | 0.279021i | \(-0.0900098\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 252.946 | 0.429450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 250.431 | 0.422312 | 0.211156 | − | 0.977452i | \(-0.432277\pi\) | ||||
0.211156 | + | 0.977452i | \(0.432277\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1173.56i | 1.97236i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 369.741i | − 0.617264i | −0.951182 | − | 0.308632i | \(-0.900129\pi\) | ||||
0.951182 | − | 0.308632i | \(-0.0998711\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1109.33 | 1.84581 | 0.922903 | − | 0.385034i | \(-0.125810\pi\) | ||||
0.922903 | + | 0.385034i | \(0.125810\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 468.063 | 0.773658 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1103.84i | − 1.81852i | −0.416228 | − | 0.909260i | \(-0.636648\pi\) | ||||
0.416228 | − | 0.909260i | \(-0.363352\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 218.930i | 0.358315i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 808.834 | 1.31947 | 0.659734 | − | 0.751499i | \(-0.270669\pi\) | ||||
0.659734 | + | 0.751499i | \(0.270669\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 681.933 | 1.10524 | 0.552620 | − | 0.833433i | \(-0.313628\pi\) | ||||
0.552620 | + | 0.833433i | \(0.313628\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 203.788i | − 0.329222i | −0.986359 | − | 0.164611i | \(-0.947363\pi\) | ||||
0.986359 | − | 0.164611i | \(-0.0526368\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31.9922i | 0.0513518i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −781.041 | −1.24967 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 966.318 | 1.53628 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 51.4201i | − 0.0814899i | −0.999170 | − | 0.0407449i | \(-0.987027\pi\) | ||||
0.999170 | − | 0.0407449i | \(-0.0129731\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 105.311i | 0.165844i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 86.7858 | 0.136241 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 652.952 | 1.01865 | 0.509323 | − | 0.860576i | \(-0.329896\pi\) | ||||
0.509323 | + | 0.860576i | \(0.329896\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 620.192i | 0.964529i | 0.876026 | + | 0.482264i | \(0.160186\pi\) | ||||
−0.876026 | + | 0.482264i | \(0.839814\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 510.756i | − 0.789421i | −0.918805 | − | 0.394711i | \(-0.870845\pi\) | ||||
0.918805 | − | 0.394711i | \(-0.129155\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 123.094 | 0.189668 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1227.41 | 1.87964 | 0.939821 | − | 0.341666i | \(-0.110991\pi\) | ||||
0.939821 | + | 0.341666i | \(0.110991\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 443.374i | − 0.676906i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 335.934i | − 0.509763i | −0.966972 | − | 0.254881i | \(-0.917964\pi\) | ||||
0.966972 | − | 0.254881i | \(-0.0820364\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 170.169 | 0.257442 | 0.128721 | − | 0.991681i | \(-0.458913\pi\) | ||||
0.128721 | + | 0.991681i | \(0.458913\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −234.830 | −0.353128 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 518.304i | − 0.777067i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 665.161i | − 0.991298i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −738.836 | −1.09782 | −0.548912 | − | 0.835880i | \(-0.684958\pi\) | ||||
−0.548912 | + | 0.835880i | \(0.684958\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −443.165 | −0.654601 | −0.327300 | − | 0.944920i | \(-0.606139\pi\) | ||||
−0.327300 | + | 0.944920i | \(0.606139\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1242.95i | − 1.83056i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 335.857i | − 0.491738i | −0.969303 | − | 0.245869i | \(-0.920927\pi\) | ||||
0.969303 | − | 0.245869i | \(-0.0790734\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1012.61 | −1.47826 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 152.319 | 0.221072 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 818.494i | 1.18451i | 0.805752 | + | 0.592254i | \(0.201762\pi\) | ||||
−0.805752 | + | 0.592254i | \(0.798238\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1199.66i | 1.72613i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −116.114 | −0.166592 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 601.994 | 0.858765 | 0.429383 | − | 0.903123i | \(-0.358731\pi\) | ||||
0.429383 | + | 0.903123i | \(0.358731\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 193.361i | 0.275052i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 631.981i | 0.893891i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 720.442 | 1.01614 | 0.508069 | − | 0.861316i | \(-0.330359\pi\) | ||||
0.508069 | + | 0.861316i | \(0.330359\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1768.63 | 2.48054 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 119.502i | − 0.167135i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1106.86i | − 1.53944i | −0.638379 | − | 0.769722i | \(-0.720395\pi\) | ||||
0.638379 | − | 0.769722i | \(-0.279605\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 909.251 | 1.26110 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 204.804 | 0.282488 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 108.860i | 0.149739i | 0.997193 | + | 0.0748696i | \(0.0238541\pi\) | ||||
−0.997193 | + | 0.0748696i | \(0.976146\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1092.32i | 1.49428i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1251.06 | −1.70677 | −0.853385 | − | 0.521280i | \(-0.825455\pi\) | ||||
−0.853385 | + | 0.521280i | \(0.825455\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 207.104 | 0.281009 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 246.376i | − 0.333391i | −0.986008 | − | 0.166696i | \(-0.946690\pi\) | ||||
0.986008 | − | 0.166696i | \(-0.0533098\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 160.506i | − 0.216024i | −0.994150 | − | 0.108012i | \(-0.965551\pi\) | ||||
0.994150 | − | 0.108012i | \(-0.0344486\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1464.77 | −1.96614 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −574.711 | −0.767304 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 774.408i | 1.03117i | 0.856839 | + | 0.515584i | \(0.172425\pi\) | ||||
−0.856839 | + | 0.515584i | \(0.827575\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 753.012i | 0.997367i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −159.858 | −0.211174 | −0.105587 | − | 0.994410i | \(-0.533672\pi\) | ||||
−0.105587 | + | 0.994410i | \(0.533672\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −66.4269 | −0.0872889 | −0.0436445 | − | 0.999047i | \(-0.513897\pi\) | ||||
−0.0436445 | + | 0.999047i | \(0.513897\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1023.00i | 1.34076i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 54.8102i | 0.0714605i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1469.57 | 1.91102 | 0.955509 | − | 0.294960i | \(-0.0953064\pi\) | ||||
0.955509 | + | 0.294960i | \(0.0953064\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −255.482 | −0.330508 | −0.165254 | − | 0.986251i | \(-0.552844\pi\) | ||||
−0.165254 | + | 0.986251i | \(0.552844\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 698.859i | 0.901754i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 23.2346i | − 0.0298262i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 493.762 | 0.632218 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 693.915 | 0.883968 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 640.558i | 0.813923i | 0.913445 | + | 0.406962i | \(0.133412\pi\) | ||||
−0.913445 | + | 0.406962i | \(0.866588\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 1923.13i | − 2.43126i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 296.176 | 0.373488 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 780.994 | 0.979917 | 0.489959 | − | 0.871746i | \(-0.337012\pi\) | ||||
0.489959 | + | 0.871746i | \(0.337012\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1612.92i | 2.01867i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 335.171i | − 0.417399i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1641.96 | −2.03970 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1091.04 | 1.34862 | 0.674312 | − | 0.738446i | \(-0.264440\pi\) | ||||
0.674312 | + | 0.738446i | \(0.264440\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 587.805i | 0.724790i | 0.932025 | + | 0.362395i | \(0.118041\pi\) | ||||
−0.932025 | + | 0.362395i | \(0.881959\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1385.76i | 1.70032i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −218.574 | −0.267532 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −397.797 | −0.484527 | −0.242264 | − | 0.970210i | \(-0.577890\pi\) | ||||
−0.242264 | + | 0.970210i | \(0.577890\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 772.958i | − 0.939195i | −0.882880 | − | 0.469598i | \(-0.844399\pi\) | ||||
0.882880 | − | 0.469598i | \(-0.155601\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 604.655i | 0.731143i | 0.930783 | + | 0.365572i | \(0.119126\pi\) | ||||
−0.930783 | + | 0.365572i | \(0.880874\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 391.614 | 0.472393 | 0.236197 | − | 0.971705i | \(-0.424099\pi\) | ||||
0.236197 | + | 0.971705i | \(0.424099\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 639.373 | 0.767555 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 584.589i | − 0.700106i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1446.75i | − 1.72437i | −0.506590 | − | 0.862187i | \(-0.669094\pi\) | ||||
0.506590 | − | 0.862187i | \(-0.330906\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −551.800 | −0.656123 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −975.375 | −1.15429 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 680.728i | − 0.803693i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1352.00i | 1.58872i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 77.7668 | 0.0911686 | 0.0455843 | − | 0.998960i | \(-0.485485\pi\) | ||||
0.0455843 | + | 0.998960i | \(0.485485\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1213.91 | 1.41646 | 0.708230 | − | 0.705981i | \(-0.249494\pi\) | ||||
0.708230 | + | 0.705981i | \(0.249494\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1427.11i | − 1.66136i | −0.556751 | − | 0.830679i | \(-0.687952\pi\) | ||||
0.556751 | − | 0.830679i | \(-0.312048\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1371.18i | − 1.58885i | −0.607362 | − | 0.794425i | \(-0.707772\pi\) | ||||
0.607362 | − | 0.794425i | \(-0.292228\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1688.27 | 1.95175 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −45.2484 | −0.0520695 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 92.2171i | 0.105875i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 698.036i | 0.797755i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1329.39 | 1.51584 | 0.757920 | − | 0.652348i | \(-0.226216\pi\) | ||||
0.757920 | + | 0.652348i | \(0.226216\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 887.373 | 1.00723 | 0.503617 | − | 0.863927i | \(-0.332002\pi\) | ||||
0.503617 | + | 0.863927i | \(0.332002\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1238.75i | 1.40288i | 0.712726 | + | 0.701442i | \(0.247460\pi\) | ||||
−0.712726 | + | 0.701442i | \(0.752540\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 717.716i | 0.809150i | 0.914505 | + | 0.404575i | \(0.132581\pi\) | ||||
−0.914505 | + | 0.404575i | \(0.867419\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 153.159 | 0.172282 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −322.746 | −0.361418 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 630.355i | − 0.704307i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 986.848i | 1.09772i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1122.17 | 1.24547 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −770.717 | −0.851621 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 484.018i | − 0.533647i | −0.963745 | − | 0.266824i | \(-0.914026\pi\) | ||||
0.963745 | − | 0.266824i | \(-0.0859741\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1391.42i | 1.52736i | 0.645595 | + | 0.763680i | \(0.276609\pi\) | ||||
−0.645595 | + | 0.763680i | \(0.723391\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 170.262 | 0.186486 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −644.821 | −0.703186 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 50.4361i | − 0.0548815i | −0.999623 | − | 0.0274407i | \(-0.991264\pi\) | ||||
0.999623 | − | 0.0274407i | \(-0.00873576\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 219.857i | 0.238199i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −534.233 | −0.577550 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −783.700 | −0.843595 | −0.421798 | − | 0.906690i | \(-0.638601\pi\) | ||||
−0.421798 | + | 0.906690i | \(0.638601\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 127.939i | 0.137421i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 880.398i | − 0.941603i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.8290 | −0.0542465 | −0.0271233 | − | 0.999632i | \(-0.508635\pi\) | ||||
−0.0271233 | + | 0.999632i | \(0.508635\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1572.18 | −1.67076 | −0.835380 | − | 0.549673i | \(-0.814752\pi\) | ||||
−0.835380 | + | 0.549673i | \(0.814752\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 162.459i | − 0.172279i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 81.5277i | 0.0860905i | 0.999073 | + | 0.0430453i | \(0.0137060\pi\) | ||||
−0.999073 | + | 0.0430453i | \(0.986294\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 149.242 | 0.157262 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1153.28 | 1.21016 | 0.605079 | − | 0.796165i | \(-0.293141\pi\) | ||||
0.605079 | + | 0.796165i | \(0.293141\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 720.736i | − 0.754698i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1472.69i | 1.53565i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2406.46 | −2.50412 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1092.91 | −1.13255 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 889.643i | − 0.920003i | −0.887918 | − | 0.460001i | \(-0.847849\pi\) | ||||
0.887918 | − | 0.460001i | \(-0.152151\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1664.80i | 1.71452i | 0.514882 | + | 0.857261i | \(0.327836\pi\) | ||||
−0.514882 | + | 0.857261i | \(0.672164\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1744.73 | 1.79315 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1362.00 | 1.39406 | 0.697030 | − | 0.717042i | \(-0.254504\pi\) | ||||
0.697030 | + | 0.717042i | \(0.254504\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 24.0004i | − 0.0245152i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1173.24i | − 1.19353i | −0.802415 | − | 0.596766i | \(-0.796452\pi\) | ||||
0.802415 | − | 0.596766i | \(-0.203548\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1131.96 | −1.14920 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1528.29 | −1.54529 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 797.134i | 0.804373i | 0.915558 | + | 0.402186i | \(0.131750\pi\) | ||||
−0.915558 | + | 0.402186i | \(0.868250\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 72.5797i | − 0.0729444i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1534.22 | −1.53884 | −0.769419 | − | 0.638744i | \(-0.779454\pi\) | ||||
−0.769419 | + | 0.638744i | \(0.779454\pi\) | |||||||
\(998\) | 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 | 2736.3.m.e.1711.9 | 12 | ||
3.2 | odd | 2 | 912.3.m.b.799.8 | yes | 12 | ||
4.3 | odd | 2 | inner | 2736.3.m.e.1711.10 | 12 | ||
12.11 | even | 2 | 912.3.m.b.799.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.3.m.b.799.2 | ✓ | 12 | 12.11 | even | 2 | ||
912.3.m.b.799.8 | yes | 12 | 3.2 | odd | 2 | ||
2736.3.m.e.1711.9 | 12 | 1.1 | even | 1 | trivial | ||
2736.3.m.e.1711.10 | 12 | 4.3 | odd | 2 | inner |