Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,3,Mod(799,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.799");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.f (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: | \(33.1336001462\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 799.14 | ||
Character | \(\chi\) | \(=\) | 1216.799 |
Dual form | 1216.3.f.b.799.13 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −3.18150 | −1.06050 | −0.530250 | − | 0.847841i | \(-0.677902\pi\) | ||||
−0.530250 | + | 0.847841i | \(0.677902\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.95407i | − 0.590813i | −0.955372 | − | 0.295407i | \(-0.904545\pi\) | ||||
0.955372 | − | 0.295407i | \(-0.0954551\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.327266i | − 0.0467523i | −0.999727 | − | 0.0233762i | \(-0.992558\pi\) | ||||
0.999727 | − | 0.0233762i | \(-0.00744154\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.12196 | 0.124662 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19.0176 | −1.72888 | −0.864438 | − | 0.502739i | \(-0.832326\pi\) | ||||
−0.864438 | + | 0.502739i | \(0.832326\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 25.3639i | 1.95107i | 0.219841 | + | 0.975536i | \(0.429446\pi\) | ||||
−0.219841 | + | 0.975536i | \(0.570554\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.39837i | 0.626558i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 13.2615 | 0.780086 | 0.390043 | − | 0.920797i | \(-0.372460\pi\) | ||||
0.390043 | + | 0.920797i | \(0.372460\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35890 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.04120i | 0.0495809i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.08382i | 0.0906009i | 0.998973 | + | 0.0453005i | \(0.0144245\pi\) | ||||
−0.998973 | + | 0.0453005i | \(0.985575\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 16.2735 | 0.650940 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 25.0640 | 0.928297 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 18.2270i | − 0.628517i | −0.949337 | − | 0.314259i | \(-0.898244\pi\) | ||||
0.949337 | − | 0.314259i | \(-0.101756\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 21.5738i | − 0.695930i | −0.937507 | − | 0.347965i | \(-0.886873\pi\) | ||||
0.937507 | − | 0.347965i | \(-0.113127\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 60.5047 | 1.83347 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.966767 | −0.0276219 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 62.8483i | 1.69860i | 0.527909 | + | 0.849301i | \(0.322976\pi\) | ||||
−0.527909 | + | 0.849301i | \(0.677024\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 80.6954i | − 2.06911i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −56.7625 | −1.38445 | −0.692226 | − | 0.721681i | \(-0.743370\pi\) | ||||
−0.692226 | + | 0.721681i | \(0.743370\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −13.8389 | −0.321835 | −0.160917 | − | 0.986968i | \(-0.551445\pi\) | ||||
−0.160917 | + | 0.986968i | \(0.551445\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 3.31433i | − 0.0736519i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 31.3493i | 0.667006i | 0.942749 | + | 0.333503i | \(0.108231\pi\) | ||||
−0.942749 | + | 0.333503i | \(0.891769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.8929 | 0.997814 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −42.1914 | −0.827281 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 94.5917i | − 1.78475i | −0.451296 | − | 0.892374i | \(-0.649038\pi\) | ||||
0.451296 | − | 0.892374i | \(-0.350962\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 56.1794i | 1.02144i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.8678 | −0.243296 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −105.050 | −1.78052 | −0.890258 | − | 0.455456i | \(-0.849476\pi\) | ||||
−0.890258 | + | 0.455456i | \(0.849476\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 6.22105i | − 0.101984i | −0.998699 | − | 0.0509922i | \(-0.983762\pi\) | ||||
0.998699 | − | 0.0509922i | \(-0.0162384\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 0.367178i | − 0.00582823i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 74.9267 | 1.15272 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −98.8837 | −1.47588 | −0.737938 | − | 0.674868i | \(-0.764200\pi\) | ||||
−0.737938 | + | 0.674868i | \(0.764200\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 6.62968i | − 0.0960824i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 43.1075i | − 0.607148i | −0.952808 | − | 0.303574i | \(-0.901820\pi\) | ||||
0.952808 | − | 0.303574i | \(-0.0981800\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 71.2332 | 0.975798 | 0.487899 | − | 0.872900i | \(-0.337763\pi\) | ||||
0.487899 | + | 0.872900i | \(0.337763\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −51.7741 | −0.690322 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.22383i | 0.0808290i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 130.530i | − 1.65227i | −0.563469 | − | 0.826137i | \(-0.690534\pi\) | ||||
0.563469 | − | 0.826137i | \(-0.309466\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −89.8388 | −1.10912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 78.7228 | 0.948467 | 0.474234 | − | 0.880399i | \(-0.342725\pi\) | ||||
0.474234 | + | 0.880399i | \(0.342725\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 39.1752i | − 0.460885i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 57.9893i | 0.666543i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 78.2993 | 0.879768 | 0.439884 | − | 0.898055i | \(-0.355020\pi\) | ||||
0.439884 | + | 0.898055i | \(0.355020\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.30076 | 0.0912171 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 68.6372i | 0.738035i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 12.8765i | − 0.135542i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 102.505 | 1.05676 | 0.528379 | − | 0.849009i | \(-0.322800\pi\) | ||||
0.528379 | + | 0.849009i | \(0.322800\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −21.3370 | −0.215525 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 150.928i | − 1.49434i | −0.664636 | − | 0.747168i | \(-0.731413\pi\) | ||||
0.664636 | − | 0.747168i | \(-0.268587\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 23.3527i | 0.226726i | 0.993554 | + | 0.113363i | \(0.0361623\pi\) | ||||
−0.993554 | + | 0.113363i | \(0.963838\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.07577 | 0.0292930 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 47.3004 | 0.442059 | 0.221030 | − | 0.975267i | \(-0.429058\pi\) | ||||
0.221030 | + | 0.975267i | \(0.429058\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 118.475i | − 1.08692i | −0.839434 | − | 0.543462i | \(-0.817113\pi\) | ||||
0.839434 | − | 0.543462i | \(-0.182887\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 199.952i | − 1.80137i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −136.749 | −1.21017 | −0.605083 | − | 0.796162i | \(-0.706860\pi\) | ||||
−0.605083 | + | 0.796162i | \(0.706860\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.15575 | 0.0535282 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 28.4572i | 0.243224i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 4.34003i | − 0.0364708i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 240.671 | 1.98901 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 180.590 | 1.46821 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 121.925i | − 0.975397i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 218.714i | − 1.72216i | −0.508471 | − | 0.861079i | \(-0.669789\pi\) | ||||
0.508471 | − | 0.861079i | \(-0.330211\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 44.0285 | 0.341306 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 38.8083 | 0.296246 | 0.148123 | − | 0.988969i | \(-0.452677\pi\) | ||||
0.148123 | + | 0.988969i | \(0.452677\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.42652i | − 0.0107257i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 74.0408i | − 0.548450i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −32.1959 | −0.235006 | −0.117503 | − | 0.993073i | \(-0.537489\pi\) | ||||
−0.117503 | + | 0.993073i | \(0.537489\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 86.9066 | 0.625227 | 0.312614 | − | 0.949880i | \(-0.398795\pi\) | ||||
0.312614 | + | 0.949880i | \(0.398795\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 99.7379i | − 0.707361i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 482.362i | − 3.37316i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −53.8438 | −0.371336 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −155.553 | −1.05818 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 207.360i | − 1.39168i | −0.718198 | − | 0.695839i | \(-0.755033\pi\) | ||||
0.718198 | − | 0.695839i | \(-0.244967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 115.148i | 0.762569i | 0.924458 | + | 0.381285i | \(0.124518\pi\) | ||||
−0.924458 | + | 0.381285i | \(0.875482\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.8788 | 0.0972469 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −63.7306 | −0.411165 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 181.120i | 1.15363i | 0.816875 | + | 0.576815i | \(0.195705\pi\) | ||||
−0.816875 | + | 0.576815i | \(0.804295\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 300.944i | 1.89273i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.681965 | 0.00423580 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 265.772 | 1.63050 | 0.815252 | − | 0.579106i | \(-0.196598\pi\) | ||||
0.815252 | + | 0.579106i | \(0.196598\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 178.735i | − 1.08324i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 160.259i | 0.959632i | 0.877369 | + | 0.479816i | \(0.159297\pi\) | ||||
−0.877369 | + | 0.479816i | \(0.840703\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −474.329 | −2.80668 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.89049 | 0.0285994 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 52.5124i | 0.303540i | 0.988416 | + | 0.151770i | \(0.0484973\pi\) | ||||
−0.988416 | + | 0.151770i | \(0.951503\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 5.32576i | − 0.0304329i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 334.218 | 1.88824 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −199.981 | −1.11721 | −0.558607 | − | 0.829432i | \(-0.688664\pi\) | ||||
−0.558607 | + | 0.829432i | \(0.688664\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 51.9372i | 0.286946i | 0.989654 | + | 0.143473i | \(0.0458270\pi\) | ||||
−0.989654 | + | 0.143473i | \(0.954173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.7923i | 0.108154i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 185.658 | 1.00356 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −252.202 | −1.34867 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 8.20261i | − 0.0434000i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 134.633i | − 0.704883i | −0.935834 | − | 0.352441i | \(-0.885352\pi\) | ||||
0.935834 | − | 0.352441i | \(-0.114648\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.63560 | 0.0136560 | 0.00682798 | − | 0.999977i | \(-0.497827\pi\) | ||||
0.00682798 | + | 0.999977i | \(0.497827\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −238.380 | −1.22246 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 32.7230i | − 0.166106i | −0.996545 | − | 0.0830532i | \(-0.973533\pi\) | ||||
0.996545 | − | 0.0830532i | \(-0.0264671\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 48.0423i | − 0.241418i | −0.992688 | − | 0.120709i | \(-0.961483\pi\) | ||||
0.992688 | − | 0.120709i | \(-0.0385169\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 314.599 | 1.56517 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.96508 | −0.0293847 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 167.680i | 0.817953i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.33796i | 0.0112945i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −82.8960 | −0.396631 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 320.373 | 1.51835 | 0.759177 | − | 0.650884i | \(-0.225602\pi\) | ||||
0.759177 | + | 0.650884i | \(0.225602\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 137.147i | 0.643881i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 40.8810i | 0.190144i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.06039 | −0.0325364 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −226.629 | −1.03483 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 336.363i | 1.52200i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 55.9638i | − 0.250959i | −0.992096 | − | 0.125479i | \(-0.959953\pi\) | ||||
0.992096 | − | 0.125479i | \(-0.0400469\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 18.2581 | 0.0811473 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 242.543 | 1.06847 | 0.534235 | − | 0.845336i | \(-0.320600\pi\) | ||||
0.534235 | + | 0.845336i | \(0.320600\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 179.312i | − 0.783022i | −0.920173 | − | 0.391511i | \(-0.871952\pi\) | ||||
0.920173 | − | 0.391511i | \(-0.128048\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 19.8011i | − 0.0857192i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 212.631 | 0.912581 | 0.456291 | − | 0.889831i | \(-0.349178\pi\) | ||||
0.456291 | + | 0.889831i | \(0.349178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 92.6079 | 0.394076 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 415.280i | 1.75224i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 287.776i | 1.20408i | 0.798465 | + | 0.602042i | \(0.205646\pi\) | ||||
−0.798465 | + | 0.602042i | \(0.794354\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.3514 | −0.0595494 | −0.0297747 | − | 0.999557i | \(-0.509479\pi\) | ||||
−0.0297747 | + | 0.999557i | \(0.509479\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 60.2463 | 0.247927 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 144.433i | − 0.589522i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 110.559i | 0.447607i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −250.457 | −1.00585 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 134.282 | 0.534987 | 0.267493 | − | 0.963560i | \(-0.413805\pi\) | ||||
0.267493 | + | 0.963560i | \(0.413805\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 39.6294i | − 0.156638i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 124.636i | 0.488769i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 53.9448 | 0.209902 | 0.104951 | − | 0.994477i | \(-0.466531\pi\) | ||||
0.104951 | + | 0.994477i | \(0.466531\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.5681 | 0.0794136 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 20.4499i | − 0.0783521i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 239.810i | − 0.911823i | −0.890025 | − | 0.455912i | \(-0.849313\pi\) | ||||
0.890025 | − | 0.455912i | \(-0.150687\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −279.430 | −1.05445 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −249.110 | −0.932994 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 156.402i | 0.581420i | 0.956811 | + | 0.290710i | \(0.0938915\pi\) | ||||
−0.956811 | + | 0.290710i | \(0.906109\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 147.578i | − 0.544569i | −0.962217 | − | 0.272284i | \(-0.912221\pi\) | ||||
0.962217 | − | 0.272284i | \(-0.0877791\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −26.4089 | −0.0967358 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −309.483 | −1.12539 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 462.232i | − 1.66871i | −0.551230 | − | 0.834353i | \(-0.685841\pi\) | ||||
0.551230 | − | 0.834353i | \(-0.314159\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 24.2049i | − 0.0867559i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 245.672 | 0.874278 | 0.437139 | − | 0.899394i | \(-0.355992\pi\) | ||||
0.437139 | + | 0.899394i | \(0.355992\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 186.202 | 0.657956 | 0.328978 | − | 0.944338i | \(-0.393296\pi\) | ||||
0.328978 | + | 0.944338i | \(0.393296\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 40.9665i | 0.143742i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.5765i | 0.0647264i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −113.134 | −0.391466 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −326.121 | −1.12069 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 48.2216i | 0.164579i | 0.996608 | + | 0.0822894i | \(0.0262232\pi\) | ||||
−0.996608 | + | 0.0822894i | \(0.973777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 310.326i | 1.05195i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −476.658 | −1.60491 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −52.8539 | −0.176769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.52900i | 0.0150465i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 480.177i | 1.58474i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.3774 | −0.0602537 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −389.254 | −1.26793 | −0.633964 | − | 0.773362i | \(-0.718573\pi\) | ||||
−0.633964 | + | 0.773362i | \(0.718573\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 74.2968i | − 0.240443i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 178.649i | − 0.574432i | −0.957866 | − | 0.287216i | \(-0.907270\pi\) | ||||
0.957866 | − | 0.287216i | \(-0.0927298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −278.244 | −0.888958 | −0.444479 | − | 0.895789i | \(-0.646611\pi\) | ||||
−0.444479 | + | 0.895789i | \(0.646611\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.08467 | −0.00344340 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 133.094i | 0.419855i | 0.977717 | + | 0.209928i | \(0.0673228\pi\) | ||||
−0.977717 | + | 0.209928i | \(0.932677\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 346.635i | 1.08663i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −150.486 | −0.468804 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 57.8053 | 0.178964 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 412.760i | 1.27003i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 376.928i | 1.15268i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.2596 | 0.0311841 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 347.507 | 1.04987 | 0.524934 | − | 0.851143i | \(-0.324090\pi\) | ||||
0.524934 | + | 0.851143i | \(0.324090\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 70.5130i | 0.211751i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 292.109i | 0.871967i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.3718 | 0.104961 | 0.0524805 | − | 0.998622i | \(-0.483287\pi\) | ||||
0.0524805 | + | 0.998622i | \(0.483287\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 435.067 | 1.28338 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 410.284i | 1.20318i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 32.0370i | − 0.0934025i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −19.5845 | −0.0567667 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 439.041 | 1.26525 | 0.632623 | − | 0.774460i | \(-0.281978\pi\) | ||||
0.632623 | + | 0.774460i | \(0.281978\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 266.762i | − 0.764360i | −0.924088 | − | 0.382180i | \(-0.875173\pi\) | ||||
0.924088 | − | 0.382180i | \(-0.124827\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 635.722i | 1.81117i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −307.704 | −0.871683 | −0.435842 | − | 0.900023i | \(-0.643549\pi\) | ||||
−0.435842 | + | 0.900023i | \(0.643549\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −127.342 | −0.358711 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.8078i | 0.0386773i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 135.734i | 0.378088i | 0.981969 | + | 0.189044i | \(0.0605389\pi\) | ||||
−0.981969 | + | 0.189044i | \(0.939461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −765.694 | −2.10935 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 210.428i | − 0.576514i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 133.270i | − 0.363134i | −0.983379 | − | 0.181567i | \(-0.941883\pi\) | ||||
0.983379 | − | 0.181567i | \(-0.0581169\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −63.6851 | −0.172588 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −30.9567 | −0.0834411 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 225.178i | − 0.603693i | −0.953356 | − | 0.301847i | \(-0.902397\pi\) | ||||
0.953356 | − | 0.301847i | \(-0.0976031\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 387.904i | 1.03441i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 462.308 | 1.22628 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 404.256 | 1.06664 | 0.533320 | − | 0.845914i | \(-0.320944\pi\) | ||||
0.533320 | + | 0.845914i | \(0.320944\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 695.839i | 1.82635i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 467.071i | − 1.21951i | −0.792591 | − | 0.609753i | \(-0.791269\pi\) | ||||
0.792591 | − | 0.609753i | \(-0.208731\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.3856 | 0.0477548 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.5266 | −0.0401205 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 176.361i | − 0.453371i | −0.973968 | − | 0.226685i | \(-0.927211\pi\) | ||||
0.973968 | − | 0.226685i | \(-0.0727889\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.6345i | 0.0706765i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −123.469 | −0.314170 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −385.593 | −0.976186 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 535.118i | 1.34790i | 0.738775 | + | 0.673952i | \(0.235405\pi\) | ||||
−0.738775 | + | 0.673952i | \(0.764595\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.53848i | 0.0113746i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −438.547 | −1.09363 | −0.546817 | − | 0.837252i | \(-0.684161\pi\) | ||||
−0.546817 | + | 0.837252i | \(0.684161\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 547.197 | 1.35781 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 265.390i | 0.655284i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1195.23i | − 2.93667i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 319.560 | 0.781321 | 0.390661 | − | 0.920535i | \(-0.372247\pi\) | ||||
0.390661 | + | 0.920535i | \(0.372247\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 102.431 | 0.249224 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 34.3795i | 0.0832433i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 232.552i | − 0.560367i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −276.494 | −0.663054 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 493.329 | 1.17740 | 0.588698 | − | 0.808353i | \(-0.299641\pi\) | ||||
0.588698 | + | 0.808353i | \(0.299641\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 509.419i | − 1.21002i | −0.796217 | − | 0.605011i | \(-0.793169\pi\) | ||||
0.796217 | − | 0.605011i | \(-0.206831\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 35.1725i | 0.0831502i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 215.810 | 0.507789 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.03594 | −0.00476801 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1534.64i | 3.57724i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 676.765i | 1.57022i | 0.619355 | + | 0.785111i | \(0.287394\pi\) | ||||
−0.619355 | + | 0.785111i | \(0.712606\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −379.072 | −0.875455 | −0.437728 | − | 0.899108i | \(-0.644217\pi\) | ||||
−0.437728 | + | 0.899108i | \(0.644217\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 171.304 | 0.393803 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.08317i | 0.0207853i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 271.578i | 0.618628i | 0.950960 | + | 0.309314i | \(0.100099\pi\) | ||||
−0.950960 | + | 0.309314i | \(0.899901\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 54.8557 | 0.124389 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 758.996 | 1.71331 | 0.856655 | − | 0.515890i | \(-0.172539\pi\) | ||||
0.856655 | + | 0.515890i | \(0.172539\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 231.301i | − 0.519779i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 659.716i | 1.47588i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −68.6412 | −0.152876 | −0.0764379 | − | 0.997074i | \(-0.524355\pi\) | ||||
−0.0764379 | + | 0.997074i | \(0.524355\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1079.49 | 2.39355 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 366.343i | − 0.808705i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 24.5210i | − 0.0538923i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −333.056 | −0.728787 | −0.364394 | − | 0.931245i | \(-0.618724\pi\) | ||||
−0.364394 | + | 0.931245i | \(0.618724\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 332.385 | 0.724151 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 863.541i | − 1.87319i | −0.350413 | − | 0.936595i | \(-0.613959\pi\) | ||||
0.350413 | − | 0.936595i | \(-0.386041\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 295.481i | − 0.638187i | −0.947723 | − | 0.319094i | \(-0.896622\pi\) | ||||
0.947723 | − | 0.319094i | \(-0.103378\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 202.759 | 0.436041 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −633.073 | −1.35562 | −0.677808 | − | 0.735239i | \(-0.737070\pi\) | ||||
−0.677808 | + | 0.735239i | \(0.737070\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.3613i | 0.0690007i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 576.233i | − 1.22343i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 263.183 | 0.556413 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 70.9345 | 0.149336 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 106.128i | − 0.222490i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 109.004i | 0.227566i | 0.993506 | + | 0.113783i | \(0.0362969\pi\) | ||||
−0.993506 | + | 0.113783i | \(0.963703\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1594.08 | −3.31409 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.16967 | −0.00449207 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 302.808i | − 0.624347i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 250.022i | 0.513392i | 0.966492 | + | 0.256696i | \(0.0826339\pi\) | ||||
−0.966492 | + | 0.256696i | \(0.917366\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −845.555 | −1.72915 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −113.285 | −0.230724 | −0.115362 | − | 0.993324i | \(-0.536803\pi\) | ||||
−0.115362 | + | 0.993324i | \(0.536803\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 241.717i | − 0.490297i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 63.0308i | 0.127335i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.1076 | −0.0283856 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −588.287 | −1.17893 | −0.589466 | − | 0.807793i | \(-0.700662\pi\) | ||||
−0.589466 | + | 0.807793i | \(0.700662\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 509.863i | − 1.01769i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 419.065i | 0.833132i | 0.909105 | + | 0.416566i | \(0.136767\pi\) | ||||
−0.909105 | + | 0.416566i | \(0.863233\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −445.851 | −0.882873 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1509.08 | 2.97649 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 438.284i | 0.861069i | 0.902574 | + | 0.430535i | \(0.141675\pi\) | ||||
−0.902574 | + | 0.430535i | \(0.858325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 23.3122i | − 0.0456208i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 109.252 | 0.212966 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 68.9856 | 0.133953 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 596.190i | − 1.15317i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 167.068i | − 0.321904i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −516.120 | −0.990633 | −0.495316 | − | 0.868713i | \(-0.664948\pi\) | ||||
−0.495316 | + | 0.868713i | \(0.664948\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.1871 | 0.0634552 | 0.0317276 | − | 0.999497i | \(-0.489899\pi\) | ||||
0.0317276 | + | 0.999497i | \(0.489899\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.9439i | 0.0322742i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 286.101i | − 0.542885i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 524.658 | 0.991791 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −117.862 | −0.221962 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1439.72i | − 2.70117i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 139.728i | − 0.261175i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 636.241 | 1.18481 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −929.827 | −1.72510 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 706.200i | 1.30536i | 0.757633 | + | 0.652680i | \(0.226356\pi\) | ||||
−0.757633 | + | 0.652680i | \(0.773644\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 165.238i | − 0.304306i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −349.982 | −0.642169 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.1572 | −0.0606165 | −0.0303082 | − | 0.999541i | \(-0.509649\pi\) | ||||
−0.0303082 | + | 0.999541i | \(0.509649\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 6.97974i | − 0.0127136i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 79.4497i | − 0.144192i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −42.7180 | −0.0772477 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −590.671 | −1.06427 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 192.697i | 0.345955i | 0.984926 | + | 0.172978i | \(0.0553388\pi\) | ||||
−0.984926 | + | 0.172978i | \(0.944661\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 351.009i | − 0.627923i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 802.380 | 1.43027 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 740.912 | 1.31601 | 0.658004 | − | 0.753014i | \(-0.271401\pi\) | ||||
0.658004 | + | 0.753014i | \(0.271401\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 403.965i | 0.714983i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 29.4012i | 0.0518540i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −152.452 | −0.267929 | −0.133965 | − | 0.990986i | \(-0.542771\pi\) | ||||
−0.133965 | + | 0.990986i | \(0.542771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −244.246 | −0.427751 | −0.213876 | − | 0.976861i | \(-0.568609\pi\) | ||||
−0.213876 | + | 0.976861i | \(0.568609\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 428.334i | 0.747529i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33.9110i | 0.0589757i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 731.465 | 1.26770 | 0.633852 | − | 0.773455i | \(-0.281473\pi\) | ||||
0.633852 | + | 0.773455i | \(0.281473\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.38516 | −0.0144821 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 25.7633i | − 0.0443430i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1798.91i | 3.08561i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 84.0645 | 0.143700 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −239.530 | −0.408058 | −0.204029 | − | 0.978965i | \(-0.565404\pi\) | ||||
−0.204029 | + | 0.978965i | \(0.565404\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 94.0382i | − 0.159657i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 104.108i | 0.176156i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 720.684 | 1.21532 | 0.607659 | − | 0.794198i | \(-0.292109\pi\) | ||||
0.607659 | + | 0.794198i | \(0.292109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.8207 | −0.0215474 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 152.847i | 0.256024i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.6100i | 0.0377462i | 0.999822 | + | 0.0188731i | \(0.00600785\pi\) | ||||
−0.999822 | + | 0.0188731i | \(0.993992\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 346.941 | 0.577272 | 0.288636 | − | 0.957439i | \(-0.406798\pi\) | ||||
0.288636 | + | 0.957439i | \(0.406798\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −110.943 | −0.183985 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 710.957i | − 1.17514i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 496.637i | 0.818183i | 0.912493 | + | 0.409092i | \(0.134154\pi\) | ||||
−0.912493 | + | 0.409092i | \(0.865846\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.9779 | 0.0311624 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −795.141 | −1.30138 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 534.048i | 0.871204i | 0.900139 | + | 0.435602i | \(0.143465\pi\) | ||||
−0.900139 | + | 0.435602i | \(0.856535\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 533.475i | − 0.867440i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −765.679 | −1.24097 | −0.620485 | − | 0.784218i | \(-0.713064\pi\) | ||||
−0.620485 | + | 0.784218i | \(0.713064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.8187 | 0.0724050 | 0.0362025 | − | 0.999344i | \(-0.488474\pi\) | ||||
0.0362025 | + | 0.999344i | \(0.488474\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 52.2289i | 0.0841046i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 25.6247i | − 0.0411312i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 46.6637 | 0.0746619 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 263.734 | 0.420628 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 833.460i | 1.32505i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 396.162i | − 0.627832i | −0.949451 | − | 0.313916i | \(-0.898359\pi\) | ||||
0.949451 | − | 0.313916i | \(-0.101641\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1019.27 | −1.61022 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −646.096 | −1.01747 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1240.12i | 1.94681i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 48.3647i | − 0.0756882i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −524.768 | −0.818671 | −0.409335 | − | 0.912384i | \(-0.634239\pi\) | ||||
−0.409335 | + | 0.912384i | \(0.634239\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −194.356 | −0.302265 | −0.151132 | − | 0.988514i | \(-0.548292\pi\) | ||||
−0.151132 | + | 0.988514i | \(0.548292\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 130.063i | − 0.201648i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 660.834i | − 1.02138i | −0.859764 | − | 0.510691i | \(-0.829390\pi\) | ||||
0.859764 | − | 0.510691i | \(-0.170610\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1997.81 | 3.07829 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.4626 | 0.0345048 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 149.332i | 0.228686i | 0.993441 | + | 0.114343i | \(0.0364763\pi\) | ||||
−0.993441 | + | 0.114343i | \(0.963524\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 114.642i | − 0.175026i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 79.9206 | 0.121645 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −429.902 | −0.652355 | −0.326178 | − | 0.945308i | \(-0.605761\pi\) | ||||
−0.326178 | + | 0.945308i | \(0.605761\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 112.440i | 0.170106i | 0.996376 | + | 0.0850528i | \(0.0271059\pi\) | ||||
−0.996376 | + | 0.0850528i | \(0.972894\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 1070.14i | − 1.61409i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.21404 | −0.00633690 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 37.9818 | 0.0569443 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 178.049i | 0.266142i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 118.310i | 0.176318i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −320.778 | −0.476639 | −0.238319 | − | 0.971187i | \(-0.576596\pi\) | ||||
−0.238319 | + | 0.971187i | \(0.576596\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 407.879 | 0.604265 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 546.257i | − 0.806878i | −0.915006 | − | 0.403439i | \(-0.867815\pi\) | ||||
0.915006 | − | 0.403439i | \(-0.132185\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 33.5466i | − 0.0494059i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −771.650 | −1.13311 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 924.923 | 1.35421 | 0.677103 | − | 0.735888i | \(-0.263235\pi\) | ||||
0.677103 | + | 0.735888i | \(0.263235\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 95.1088i | 0.138845i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 570.482i | 0.830396i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2399.22 | 3.48217 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −362.238 | −0.524224 | −0.262112 | − | 0.965038i | \(-0.584419\pi\) | ||||
−0.262112 | + | 0.965038i | \(0.584419\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.98287i | 0.0100763i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 256.728i | − 0.369393i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −752.754 | −1.07999 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −676.487 | −0.967793 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1023.52i | − 1.46008i | −0.683403 | − | 0.730042i | \(-0.739501\pi\) | ||||
0.683403 | − | 0.730042i | \(-0.260499\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 273.949i | 0.389686i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −294.632 | −0.417918 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −49.3936 | −0.0698637 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 526.649i | 0.742805i | 0.928472 | + | 0.371403i | \(0.121123\pi\) | ||||
−0.928472 | + | 0.371403i | \(0.878877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 146.449i | − 0.205976i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 44.9560 | 0.0630519 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1424.93 | −1.99291 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 915.560i | − 1.27693i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 67.2606i | 0.0935474i | 0.998906 | + | 0.0467737i | \(0.0148940\pi\) | ||||
−0.998906 | + | 0.0467737i | \(0.985106\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.64257 | 0.0106000 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 45.6590 | 0.0631521 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 296.617i | − 0.409127i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 614.959i | − 0.845886i | −0.906156 | − | 0.422943i | \(-0.860997\pi\) | ||||
0.906156 | − | 0.422943i | \(-0.139003\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 616.876 | 0.846194 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −183.524 | −0.251059 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 82.7464i | − 0.112887i | −0.998406 | − | 0.0564437i | \(-0.982024\pi\) | ||||
0.998406 | − | 0.0564437i | \(-0.0179761\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 459.514i | 0.625188i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1880.53 | 2.55161 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −504.689 | −0.682935 | −0.341468 | − | 0.939894i | \(-0.610924\pi\) | ||||
−0.341468 | + | 0.939894i | \(0.610924\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 351.743i | − 0.474687i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 166.827i | 0.224531i | 0.993678 | + | 0.112266i | \(0.0358107\pi\) | ||||
−0.993678 | + | 0.112266i | \(0.964189\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −612.555 | −0.822222 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 88.3235 | 0.118238 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 15.4798i | − 0.0206673i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1275.98i | 1.69905i | 0.527551 | + | 0.849524i | \(0.323111\pi\) | ||||
−0.527551 | + | 0.849524i | \(0.676889\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −427.217 | −0.567354 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 340.155 | 0.450536 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1275.37i | − 1.68477i | −0.538878 | − | 0.842384i | \(-0.681151\pi\) | ||||
0.538878 | − | 0.842384i | \(-0.318849\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 126.081i | 0.166115i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 734.573 | 0.965274 | 0.482637 | − | 0.875821i | \(-0.339679\pi\) | ||||
0.482637 | + | 0.875821i | \(0.339679\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.7728 | −0.0508162 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 43.9529i | − 0.0574548i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 2664.49i | − 3.47392i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −589.509 | −0.766591 | −0.383296 | − | 0.923626i | \(-0.625211\pi\) | ||||
−0.383296 | + | 0.923626i | \(0.625211\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −171.625 | −0.222601 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 253.428i | − 0.327850i | −0.986473 | − | 0.163925i | \(-0.947585\pi\) | ||||
0.986473 | − | 0.163925i | \(-0.0524154\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 351.082i | − 0.453009i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −65.4375 | −0.0842182 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −247.422 | −0.317615 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 819.803i | 1.04968i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 456.842i | − 0.583451i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 535.040 | 0.681580 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −617.729 | −0.784917 | −0.392458 | − | 0.919770i | \(-0.628375\pi\) | ||||
−0.392458 | + | 0.919770i | \(0.628375\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 762.955i | 0.966989i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44.7533i | 0.0565781i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 157.790 | 0.198979 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 889.007 | 1.11825 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1329.45i | − 1.66807i | −0.551709 | − | 0.834036i | \(-0.686024\pi\) | ||||
0.551709 | − | 0.834036i | \(-0.313976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 415.737i | 0.520322i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 87.8484 | 0.109673 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1354.69 | −1.68703 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.01457i | − 0.00250257i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 497.593i | − 0.616596i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −325.542 | −0.402401 | −0.201200 | − | 0.979550i | \(-0.564484\pi\) | ||||
−0.201200 | + | 0.979550i | \(0.564484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1092.05 | 1.34655 | 0.673273 | − | 0.739394i | \(-0.264888\pi\) | ||||
0.673273 | + | 0.739394i | \(0.264888\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 469.520i | 0.577515i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 785.109i | − 0.963324i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −60.3224 | −0.0738340 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.31309 | 0.0113713 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 125.979i | 0.153446i | 0.997052 | + | 0.0767231i | \(0.0244458\pi\) | ||||
−0.997052 | + | 0.0767231i | \(0.975554\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1254.58i | 1.52440i | 0.647342 | + | 0.762199i | \(0.275880\pi\) | ||||
−0.647342 | + | 0.762199i | \(0.724120\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 984.622 | 1.19348 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −939.804 | −1.13640 | −0.568201 | − | 0.822890i | \(-0.692360\pi\) | ||||
−0.568201 | + | 0.822890i | \(0.692360\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1389.36i | 1.67595i | 0.545711 | + | 0.837974i | \(0.316260\pi\) | ||||
−0.545711 | + | 0.837974i | \(0.683740\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1470.59i | 1.76966i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 648.391 | 0.778381 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 473.414 | 0.566963 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 540.727i | − 0.646030i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1006.46i | − 1.19959i | −0.800152 | − | 0.599797i | \(-0.795248\pi\) | ||||
0.800152 | − | 0.599797i | \(-0.204752\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 508.776 | 0.604966 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −781.607 | −0.927173 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1401.20i | 1.65822i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 78.7634i | − 0.0929910i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −592.401 | −0.697763 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −130.965 | −0.153895 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1042.56i | − 1.22223i | −0.791544 | − | 0.611113i | \(-0.790722\pi\) | ||||
0.791544 | − | 0.611113i | \(-0.209278\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 14.4468i | − 0.0168969i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1604.77 | 1.87255 | 0.936274 | − | 0.351271i | \(-0.114250\pi\) | ||||
0.936274 | + | 0.351271i | \(0.114250\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 288.343 | 0.335673 | 0.167836 | − | 0.985815i | \(-0.446322\pi\) | ||||
0.167836 | + | 0.985815i | \(0.446322\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 59.1011i | − 0.0686424i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1330.02i | − 1.54116i | −0.637344 | − | 0.770579i | \(-0.719967\pi\) | ||||
0.637344 | − | 0.770579i | \(-0.280033\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 155.125 | 0.179335 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 359.935 | 0.415150 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2482.37i | 2.85658i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 2508.08i | − 2.87954i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 115.007 | 0.131737 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −39.9018 | −0.0456021 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1091.50i | − 1.24459i | −0.782783 | − | 0.622294i | \(-0.786201\pi\) | ||||
0.782783 | − | 0.622294i | \(-0.213799\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 153.417i | − 0.174536i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1084.33 | 1.23080 | 0.615398 | − | 0.788216i | \(-0.288995\pi\) | ||||
0.615398 | + | 0.788216i | \(0.288995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −698.592 | −0.791158 | −0.395579 | − | 0.918432i | \(-0.629456\pi\) | ||||
−0.395579 | + | 0.918432i | \(0.629456\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 987.303i | − 1.11560i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1094.01i | − 1.23338i | −0.787205 | − | 0.616691i | \(-0.788473\pi\) | ||||
0.787205 | − | 0.616691i | \(-0.211527\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −71.5778 | −0.0805149 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1708.52 | 1.91753 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 136.648i | 0.153022i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 590.758i | 0.660065i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 168.155 | 0.187464 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −393.226 | −0.437404 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1254.42i | − 1.39226i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 14.4090i | − 0.0159569i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 153.426 | 0.169531 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1342.65 | −1.48032 | −0.740161 | − | 0.672430i | \(-0.765251\pi\) | ||||
−0.740161 | + | 0.672430i | \(0.765251\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 169.334i | − 0.186287i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 147.927i | − 0.162379i | −0.996699 | − | 0.0811894i | \(-0.974128\pi\) | ||||
0.996699 | − | 0.0811894i | \(-0.0258719\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1497.12 | −1.63978 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 58.4677 | 0.0638991 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 12.7006i | − 0.0138502i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1550.70i | 1.68738i | 0.536829 | + | 0.843691i | \(0.319622\pi\) | ||||
−0.536829 | + | 0.843691i | \(0.680378\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1238.41 | 1.34464 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1093.38 | 1.18459 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1022.76i | 1.10569i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.2008i | 0.0282640i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −511.095 | −0.550156 | −0.275078 | − | 0.961422i | \(-0.588704\pi\) | ||||
−0.275078 | + | 0.961422i | \(0.588704\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 213.119 | 0.228914 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 568.371i | 0.609186i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 745.020i | 0.796813i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 517.012 | 0.551774 | 0.275887 | − | 0.961190i | \(-0.411028\pi\) | ||||
0.275887 | + | 0.961190i | \(0.411028\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 885.233 | 0.942741 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 677.774i | − 0.720270i | −0.932900 | − | 0.360135i | \(-0.882731\pi\) | ||||
0.932900 | − | 0.360135i | \(-0.117269\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 118.283i | − 0.125433i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −24.2310 | −0.0256413 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1131.47 | 1.19479 | 0.597397 | − | 0.801946i | \(-0.296202\pi\) | ||||
0.597397 | + | 0.801946i | \(0.296202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1806.75i | 1.90385i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 423.439i | − 0.445257i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −401.743 | −0.421556 | −0.210778 | − | 0.977534i | \(-0.567600\pi\) | ||||
−0.210778 | + | 0.977534i | \(0.567600\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −397.714 | −0.416454 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1102.82i | − 1.15237i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.5366i | 0.0109871i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 495.569 | 0.515681 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 53.0689 | 0.0551079 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 7.78573i | − 0.00806812i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 161.040i | 0.166536i | 0.996527 | + | 0.0832679i | \(0.0265357\pi\) | ||||
−0.996527 | + | 0.0832679i | \(0.973464\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −183.908 | −0.189791 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1592.36 | −1.63992 | −0.819960 | − | 0.572420i | \(-0.806005\pi\) | ||||
−0.819960 | + | 0.572420i | \(0.806005\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 28.4416i | − 0.0292308i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 1313.20i | − 1.34687i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 371.849 | 0.380603 | 0.190301 | − | 0.981726i | \(-0.439054\pi\) | ||||
0.190301 | + | 0.981726i | \(0.439054\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1489.07 | −1.52101 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 132.923i | − 0.135498i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 280.721i | 0.285575i | 0.989753 | + | 0.142788i | \(0.0456066\pi\) | ||||
−0.989753 | + | 0.142788i | \(0.954393\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −96.6658 | −0.0981379 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −32.6408 | −0.0330708 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 28.8378i | − 0.0291585i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 992.938i | − 1.00196i | −0.865460 | − | 0.500978i | \(-0.832974\pi\) | ||||
0.865460 | − | 0.500978i | \(-0.167026\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1105.59 | −1.11339 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −141.920 | −0.142633 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1144.50i | − 1.14795i | −0.818874 | − | 0.573974i | \(-0.805401\pi\) | ||||
0.818874 | − | 0.573974i | \(-0.194599\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1575.23i | 1.57681i |
(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 | 1216.3.f.b.799.14 | yes | 48 | |
4.3 | odd | 2 | inner | 1216.3.f.b.799.36 | yes | 48 | |
8.3 | odd | 2 | inner | 1216.3.f.b.799.13 | ✓ | 48 | |
8.5 | even | 2 | inner | 1216.3.f.b.799.35 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.3.f.b.799.13 | ✓ | 48 | 8.3 | odd | 2 | inner | |
1216.3.f.b.799.14 | yes | 48 | 1.1 | even | 1 | trivial | |
1216.3.f.b.799.35 | yes | 48 | 8.5 | even | 2 | inner | |
1216.3.f.b.799.36 | yes | 48 | 4.3 | odd | 2 | inner |