Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(1,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(70.8022920069\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 600) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.00000 | 0.269975 | 0.134987 | − | 0.990847i | \(-0.456901\pi\) | ||||
0.134987 | + | 0.990847i | \(0.456901\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.0000 | −0.383742 | −0.191871 | − | 0.981420i | \(-0.561455\pi\) | ||||
−0.191871 | + | 0.981420i | \(0.561455\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.0213346 | −0.0106673 | − | 0.999943i | \(-0.503396\pi\) | ||||
−0.0106673 | + | 0.999943i | \(0.503396\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −46.0000 | −0.656273 | −0.328136 | − | 0.944630i | \(-0.606421\pi\) | ||||
−0.328136 | + | 0.944630i | \(0.606421\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 15.0000 | 0.155870 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −46.0000 | −0.417029 | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208514 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 14.0000 | 0.0896460 | 0.0448230 | − | 0.998995i | \(-0.485728\pi\) | ||||
0.0448230 | + | 0.998995i | \(0.485728\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −133.000 | −0.770565 | −0.385282 | − | 0.922799i | \(-0.625896\pi\) | ||||
−0.385282 | + | 0.922799i | \(0.625896\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −42.0000 | −0.221553 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −258.000 | −1.14635 | −0.573175 | − | 0.819433i | \(-0.694288\pi\) | ||||
−0.573175 | + | 0.819433i | \(0.694288\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.00000 | −0.0123176 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 84.0000 | 0.319966 | 0.159983 | − | 0.987120i | \(-0.448856\pi\) | ||||
0.159983 | + | 0.987120i | \(0.448856\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −167.000 | −0.592262 | −0.296131 | − | 0.955147i | \(-0.595696\pi\) | ||||
−0.296131 | + | 0.955147i | \(0.595696\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 410.000 | 1.27244 | 0.636220 | − | 0.771508i | \(-0.280497\pi\) | ||||
0.636220 | + | 0.771508i | \(0.280497\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −318.000 | −0.927114 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −138.000 | −0.378899 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −456.000 | −1.18182 | −0.590910 | − | 0.806738i | \(-0.701231\pi\) | ||||
−0.590910 | + | 0.806738i | \(0.701231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −57.0000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 194.000 | 0.428079 | 0.214039 | − | 0.976825i | \(-0.431338\pi\) | ||||
0.214039 | + | 0.976825i | \(0.431338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17.0000 | −0.0356824 | −0.0178412 | − | 0.999841i | \(-0.505679\pi\) | ||||
−0.0178412 | + | 0.999841i | \(0.505679\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 45.0000 | 0.0899915 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 653.000 | 1.19070 | 0.595348 | − | 0.803468i | \(-0.297014\pi\) | ||||
0.595348 | + | 0.803468i | \(0.297014\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −138.000 | −0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −828.000 | −1.38402 | −0.692011 | − | 0.721887i | \(-0.743275\pi\) | ||||
−0.692011 | + | 0.721887i | \(0.743275\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −570.000 | −0.913883 | −0.456941 | − | 0.889497i | \(-0.651055\pi\) | ||||
−0.456941 | + | 0.889497i | \(0.651055\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −70.0000 | −0.103601 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 552.000 | 0.786137 | 0.393069 | − | 0.919509i | \(-0.371413\pi\) | ||||
0.393069 | + | 0.919509i | \(0.371413\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 142.000 | 0.187789 | 0.0938947 | − | 0.995582i | \(-0.470068\pi\) | ||||
0.0938947 | + | 0.995582i | \(0.470068\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 42.0000 | 0.0517572 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1104.00 | −1.31487 | −0.657437 | − | 0.753510i | \(-0.728359\pi\) | ||||
−0.657437 | + | 0.753510i | \(0.728359\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.00000 | −0.00575981 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −399.000 | −0.444886 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −841.000 | −0.880316 | −0.440158 | − | 0.897920i | \(-0.645077\pi\) | ||||
−0.440158 | + | 0.897920i | \(0.645077\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −126.000 | −0.127914 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 552.000 | 0.543822 | 0.271911 | − | 0.962322i | \(-0.412344\pi\) | ||||
0.271911 | + | 0.962322i | \(0.412344\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −308.000 | −0.294642 | −0.147321 | − | 0.989089i | \(-0.547065\pi\) | ||||
−0.147321 | + | 0.989089i | \(0.547065\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 984.000 | 0.889036 | 0.444518 | − | 0.895770i | \(-0.353375\pi\) | ||||
0.444518 | + | 0.895770i | \(0.353375\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1843.00 | −1.61952 | −0.809759 | − | 0.586763i | \(-0.800402\pi\) | ||||
−0.809759 | + | 0.586763i | \(0.800402\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −774.000 | −0.661845 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −876.000 | −0.729267 | −0.364633 | − | 0.931151i | \(-0.618806\pi\) | ||||
−0.364633 | + | 0.931151i | \(0.618806\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.00000 | −0.00711154 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −230.000 | −0.177177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1135.00 | −0.852742 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 252.000 | 0.184732 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2376.00 | 1.66013 | 0.830063 | − | 0.557670i | \(-0.188305\pi\) | ||||
0.830063 | + | 0.557670i | \(0.188305\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −501.000 | −0.341943 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1056.00 | −0.704299 | −0.352149 | − | 0.935944i | \(-0.614549\pi\) | ||||
−0.352149 | + | 0.935944i | \(0.614549\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −95.0000 | −0.0619364 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 778.000 | 0.485175 | 0.242588 | − | 0.970129i | \(-0.422004\pi\) | ||||
0.242588 | + | 0.970129i | \(0.422004\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1692.00 | −1.03247 | −0.516236 | − | 0.856446i | \(-0.672667\pi\) | ||||
−0.516236 | + | 0.856446i | \(0.672667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1230.00 | 0.734643 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.0000 | 0.00818698 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −954.000 | −0.535269 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −494.000 | −0.271611 | −0.135806 | − | 0.990736i | \(-0.543362\pi\) | ||||
−0.135806 | + | 0.990736i | \(0.543362\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 841.000 | 0.453242 | 0.226621 | − | 0.973983i | \(-0.427232\pi\) | ||||
0.226621 | + | 0.973983i | \(0.427232\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −414.000 | −0.218758 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.0000 | −0.00965838 | −0.00482919 | − | 0.999988i | \(-0.501537\pi\) | ||||
−0.00482919 | + | 0.999988i | \(0.501537\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1368.00 | −0.682324 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −230.000 | −0.112587 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2261.00 | −1.08647 | −0.543237 | − | 0.839580i | \(-0.682801\pi\) | ||||
−0.543237 | + | 0.839580i | \(0.682801\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2112.00 | 0.978632 | 0.489316 | − | 0.872107i | \(-0.337247\pi\) | ||||
0.489316 | + | 0.872107i | \(0.337247\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2196.00 | −0.999545 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −171.000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −562.000 | −0.246983 | −0.123492 | − | 0.992346i | \(-0.539409\pi\) | ||||
−0.123492 | + | 0.992346i | \(0.539409\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 582.000 | 0.247151 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3718.00 | −1.55249 | −0.776247 | − | 0.630429i | \(-0.782879\pi\) | ||||
−0.776247 | + | 0.630429i | \(0.782879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1639.00 | −0.673071 | −0.336536 | − | 0.941671i | \(-0.609255\pi\) | ||||
−0.336536 | + | 0.941671i | \(0.609255\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −51.0000 | −0.0206012 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 644.000 | 0.251839 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 135.000 | 0.0519566 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2410.00 | −0.912992 | −0.456496 | − | 0.889725i | \(-0.650896\pi\) | ||||
−0.456496 | + | 0.889725i | \(0.650896\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2621.00 | 0.977532 | 0.488766 | − | 0.872415i | \(-0.337447\pi\) | ||||
0.488766 | + | 0.872415i | \(0.337447\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4954.00 | 1.79166 | 0.895832 | − | 0.444392i | \(-0.146580\pi\) | ||||
0.895832 | + | 0.444392i | \(0.146580\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1739.00 | −0.619470 | −0.309735 | − | 0.950823i | \(-0.600240\pi\) | ||||
−0.309735 | + | 0.950823i | \(0.600240\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1959.00 | 0.687449 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 70.0000 | 0.0242022 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −414.000 | −0.139010 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 266.000 | 0.0880364 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4525.00 | 1.47637 | 0.738184 | − | 0.674599i | \(-0.235683\pi\) | ||||
0.738184 | + | 0.674599i | \(0.235683\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2484.00 | −0.799065 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −665.000 | −0.208033 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1710.00 | −0.527631 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 46.0000 | 0.0140013 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3211.00 | −0.964235 | −0.482118 | − | 0.876106i | \(-0.660132\pi\) | ||||
−0.482118 | + | 0.876106i | \(0.660132\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2484.00 | −0.726295 | −0.363147 | − | 0.931732i | \(-0.618298\pi\) | ||||
−0.363147 | + | 0.931732i | \(0.618298\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1847.00 | −0.532983 | −0.266492 | − | 0.963837i | \(-0.585864\pi\) | ||||
−0.266492 | + | 0.963837i | \(0.585864\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −210.000 | −0.0598138 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1020.00 | 0.286792 | 0.143396 | − | 0.989665i | \(-0.454198\pi\) | ||||
0.143396 | + | 0.989665i | \(0.454198\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1656.00 | 0.453877 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1176.00 | −0.318281 | −0.159140 | − | 0.987256i | \(-0.550872\pi\) | ||||
−0.159140 | + | 0.987256i | \(0.550872\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6967.00 | −1.86217 | −0.931087 | − | 0.364797i | \(-0.881138\pi\) | ||||
−0.931087 | + | 0.364797i | \(0.881138\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.0000 | 0.00489450 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 426.000 | 0.108420 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1380.00 | −0.347031 | −0.173516 | − | 0.984831i | \(-0.555513\pi\) | ||||
−0.173516 | + | 0.984831i | \(0.555513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 644.000 | 0.160031 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6924.00 | 1.68057 | 0.840286 | − | 0.542143i | \(-0.182387\pi\) | ||||
0.840286 | + | 0.542143i | \(0.182387\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1290.00 | −0.309485 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 126.000 | 0.0298820 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1884.00 | 0.441720 | 0.220860 | − | 0.975305i | \(-0.429114\pi\) | ||||
0.220860 | + | 0.975305i | \(0.429114\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3312.00 | −0.759143 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3610.00 | 0.818236 | 0.409118 | − | 0.912481i | \(-0.365836\pi\) | ||||
0.409118 | + | 0.912481i | \(0.365836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6072.00 | 1.36106 | 0.680531 | − | 0.732719i | \(-0.261749\pi\) | ||||
0.680531 | + | 0.732719i | \(0.261749\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.0000 | −0.00332543 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2803.00 | 0.608000 | 0.304000 | − | 0.952672i | \(-0.401678\pi\) | ||||
0.304000 | + | 0.952672i | \(0.401678\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1197.00 | −0.256855 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6694.00 | −1.42111 | −0.710553 | − | 0.703644i | \(-0.751555\pi\) | ||||
−0.710553 | + | 0.703644i | \(0.751555\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6481.00 | −1.36133 | −0.680663 | − | 0.732596i | \(-0.738308\pi\) | ||||
−0.680663 | + | 0.732596i | \(0.738308\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 420.000 | 0.0863826 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2797.00 | −0.569306 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2523.00 | −0.508250 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3014.00 | −0.600955 | −0.300477 | − | 0.953789i | \(-0.597146\pi\) | ||||
−0.300477 | + | 0.953789i | \(0.597146\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −378.000 | −0.0738511 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 46.0000 | 0.00889715 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −835.000 | −0.159896 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1656.00 | 0.313976 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5369.00 | −0.998127 | −0.499064 | − | 0.866565i | \(-0.666323\pi\) | ||||
−0.499064 | + | 0.866565i | \(0.666323\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −924.000 | −0.170112 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4846.00 | −0.883574 | −0.441787 | − | 0.897120i | \(-0.645655\pi\) | ||||
−0.441787 | + | 0.897120i | \(0.645655\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 757.000 | 0.136703 | 0.0683517 | − | 0.997661i | \(-0.478226\pi\) | ||||
0.0683517 | + | 0.997661i | \(0.478226\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7632.00 | 1.35223 | 0.676113 | − | 0.736798i | \(-0.263663\pi\) | ||||
0.676113 | + | 0.736798i | \(0.263663\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −196.000 | −0.0344009 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2952.00 | 0.513285 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 874.000 | 0.150559 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5529.00 | −0.935029 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2050.00 | 0.343526 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6780.00 | 1.12587 | 0.562934 | − | 0.826502i | \(-0.309672\pi\) | ||||
0.562934 | + | 0.826502i | \(0.309672\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2322.00 | −0.382117 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7849.00 | −1.26873 | −0.634365 | − | 0.773033i | \(-0.718739\pi\) | ||||
−0.634365 | + | 0.773033i | \(0.718739\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2628.00 | −0.421042 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1862.00 | 0.295698 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3305.00 | −0.520272 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 634.000 | 0.0980833 | 0.0490416 | − | 0.998797i | \(-0.484383\pi\) | ||||
0.0490416 | + | 0.998797i | \(0.484383\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 930.000 | 0.142641 | 0.0713206 | − | 0.997453i | \(-0.477279\pi\) | ||||
0.0713206 | + | 0.997453i | \(0.477279\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.0000 | −0.00410585 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4286.00 | 0.646234 | 0.323117 | − | 0.946359i | \(-0.395269\pi\) | ||||
0.323117 | + | 0.946359i | \(0.395269\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −690.000 | −0.102293 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4236.00 | 0.622751 | 0.311375 | − | 0.950287i | \(-0.399210\pi\) | ||||
0.311375 | + | 0.950287i | \(0.399210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6498.00 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3405.00 | −0.492331 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1451.00 | 0.206380 | 0.103190 | − | 0.994662i | \(-0.467095\pi\) | ||||
0.103190 | + | 0.994662i | \(0.467095\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 756.000 | 0.106655 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2280.00 | −0.319061 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3115.00 | −0.432409 | −0.216205 | − | 0.976348i | \(-0.569368\pi\) | ||||
−0.216205 | + | 0.976348i | \(0.569368\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.0000 | −0.00191256 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1415.00 | 0.191777 | 0.0958887 | − | 0.995392i | \(-0.469431\pi\) | ||||
0.0958887 | + | 0.995392i | \(0.469431\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7128.00 | 0.958474 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −180.000 | −0.0240145 | −0.0120073 | − | 0.999928i | \(-0.503822\pi\) | ||||
−0.0120073 | + | 0.999928i | \(0.503822\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1503.00 | −0.197421 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12372.0 | 1.61256 | 0.806279 | − | 0.591535i | \(-0.201478\pi\) | ||||
0.806279 | + | 0.591535i | \(0.201478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2116.00 | 0.273685 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3168.00 | −0.406627 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5767.00 | −0.729062 | −0.364531 | − | 0.931191i | \(-0.618771\pi\) | ||||
−0.364531 | + | 0.931191i | \(0.618771\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −285.000 | −0.0357590 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3120.00 | −0.388542 | −0.194271 | − | 0.980948i | \(-0.562234\pi\) | ||||
−0.194271 | + | 0.980948i | \(0.562234\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 133.000 | 0.0164397 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3612.00 | 0.439902 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1501.00 | 0.181466 | 0.0907331 | − | 0.995875i | \(-0.471079\pi\) | ||||
0.0907331 | + | 0.995875i | \(0.471079\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2334.00 | 0.280116 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 970.000 | 0.115570 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5076.00 | −0.596098 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9072.00 | 1.05775 | 0.528874 | − | 0.848701i | \(-0.322614\pi\) | ||||
0.528874 | + | 0.848701i | \(0.322614\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7350.00 | 0.850872 | 0.425436 | − | 0.904989i | \(-0.360121\pi\) | ||||
0.425436 | + | 0.904989i | \(0.360121\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3690.00 | 0.424146 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −85.0000 | −0.00963334 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 42.0000 | 0.00472676 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5962.00 | −0.666310 | −0.333155 | − | 0.942872i | \(-0.608113\pi\) | ||||
−0.333155 | + | 0.942872i | \(0.608113\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10093.0 | 1.12018 | 0.560091 | − | 0.828431i | \(-0.310766\pi\) | ||||
0.560091 | + | 0.828431i | \(0.310766\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 874.000 | 0.0956730 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2555.00 | 0.277776 | 0.138888 | − | 0.990308i | \(-0.455647\pi\) | ||||
0.138888 | + | 0.990308i | \(0.455647\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2862.00 | −0.309038 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6240.00 | 0.669236 | 0.334618 | − | 0.942354i | \(-0.391393\pi\) | ||||
0.334618 | + | 0.942354i | \(0.391393\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1482.00 | −0.156815 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3324.00 | 0.349375 | 0.174687 | − | 0.984624i | \(-0.444109\pi\) | ||||
0.174687 | + | 0.984624i | \(0.444109\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1176.00 | −0.122784 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2523.00 | 0.261680 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16774.0 | −1.71697 | −0.858484 | − | 0.512840i | \(-0.828593\pi\) | ||||
−0.858484 | + | 0.512840i | \(0.828593\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1242.00 | −0.126300 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14304.0 | 1.44513 | 0.722564 | − | 0.691304i | \(-0.242964\pi\) | ||||
0.722564 | + | 0.691304i | \(0.242964\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6936.00 | 0.696206 | 0.348103 | − | 0.937456i | \(-0.386826\pi\) | ||||
0.348103 | + | 0.937456i | \(0.386826\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15622.0 | 1.54797 | 0.773983 | − | 0.633207i | \(-0.218262\pi\) | ||||
0.773983 | + | 0.633207i | \(0.218262\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3265.00 | 0.321458 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −57.0000 | −0.00557627 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2338.00 | 0.227276 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4104.00 | −0.393940 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13354.0 | 1.27382 | 0.636910 | − | 0.770938i | \(-0.280212\pi\) | ||||
0.636910 | + | 0.770938i | \(0.280212\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 258.000 | 0.0244569 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −690.000 | −0.0650023 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −461.000 | −0.0428951 | −0.0214475 | − | 0.999770i | \(-0.506827\pi\) | ||||
−0.0214475 | + | 0.999770i | \(0.506827\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6783.00 | −0.627276 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3768.00 | −0.346329 | −0.173164 | − | 0.984893i | \(-0.555399\pi\) | ||||
−0.173164 | + | 0.984893i | \(0.555399\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −644.000 | −0.0588323 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4140.00 | −0.373651 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14317.0 | 1.28440 | 0.642201 | − | 0.766536i | \(-0.278021\pi\) | ||||
0.642201 | + | 0.766536i | \(0.278021\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6336.00 | 0.565013 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9228.00 | 0.818004 | 0.409002 | − | 0.912533i | \(-0.365877\pi\) | ||||
0.409002 | + | 0.912533i | \(0.365877\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6588.00 | −0.577087 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4574.00 | 0.398308 | 0.199154 | − | 0.979968i | \(-0.436181\pi\) | ||||
0.199154 | + | 0.979968i | \(0.436181\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2850.00 | −0.246725 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −513.000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5740.00 | −0.488288 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1686.00 | −0.142596 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8494.00 | −0.714259 | −0.357129 | − | 0.934055i | \(-0.616245\pi\) | ||||
−0.357129 | + | 0.934055i | \(0.616245\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8263.00 | 0.690852 | 0.345426 | − | 0.938446i | \(-0.387734\pi\) | ||||
0.345426 | + | 0.938446i | \(0.387734\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6118.00 | 0.505701 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10051.0 | −0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1746.00 | 0.142693 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −84.0000 | −0.00682635 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11154.0 | −0.896333 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4452.00 | 0.355772 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21157.0 | 1.68135 | 0.840675 | − | 0.541540i | \(-0.182158\pi\) | ||||
0.840675 | + | 0.541540i | \(0.182158\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4917.00 | −0.388598 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4048.00 | −0.316417 | −0.158208 | − | 0.987406i | \(-0.550572\pi\) | ||||
−0.158208 | + | 0.987406i | \(0.550572\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −153.000 | −0.0118941 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −266.000 | −0.0205662 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2760.00 | 0.212237 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6758.00 | 0.514086 | 0.257043 | − | 0.966400i | \(-0.417252\pi\) | ||||
0.257043 | + | 0.966400i | \(0.417252\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 167.000 | 0.0126357 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1932.00 | 0.145399 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24506.0 | 1.83447 | 0.917233 | − | 0.398350i | \(-0.130417\pi\) | ||||
0.917233 | + | 0.398350i | \(0.130417\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 405.000 | 0.0299972 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1430.00 | −0.105358 | −0.0526790 | − | 0.998611i | \(-0.516776\pi\) | ||||
−0.0526790 | + | 0.998611i | \(0.516776\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3691.00 | −0.270514 | −0.135257 | − | 0.990811i | \(-0.543186\pi\) | ||||
−0.135257 | + | 0.990811i | \(0.543186\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7230.00 | −0.527116 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4571.00 | −0.329798 | −0.164899 | − | 0.986310i | \(-0.552730\pi\) | ||||
−0.164899 | + | 0.986310i | \(0.552730\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7863.00 | 0.564378 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 710.000 | 0.0506984 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6384.00 | 0.453513 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14808.0 | 1.04121 | 0.520606 | − | 0.853797i | \(-0.325706\pi\) | ||||
0.520606 | + | 0.853797i | \(0.325706\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2527.00 | 0.176780 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14862.0 | 1.03442 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24588.0 | 1.70271 | 0.851356 | − | 0.524588i | \(-0.175781\pi\) | ||||
0.851356 | + | 0.524588i | \(0.175781\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5217.00 | −0.357651 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27564.0 | 1.88019 | 0.940096 | − | 0.340911i | \(-0.110735\pi\) | ||||
0.940096 | + | 0.340911i | \(0.110735\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10987.0 | 0.745706 | 0.372853 | − | 0.927891i | \(-0.378380\pi\) | ||||
0.372853 | + | 0.927891i | \(0.378380\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5877.00 | 0.396899 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13200.0 | −0.882655 | −0.441327 | − | 0.897346i | \(-0.645492\pi\) | ||||
−0.441327 | + | 0.897346i | \(0.645492\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 210.000 | 0.0139731 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −410.000 | −0.0271470 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21066.0 | −1.38801 | −0.694003 | − | 0.719972i | \(-0.744155\pi\) | ||||
−0.694003 | + | 0.719972i | \(0.744155\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12336.0 | −0.804909 | −0.402454 | − | 0.915440i | \(-0.631843\pi\) | ||||
−0.402454 | + | 0.915440i | \(0.631843\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1441.00 | 0.0935681 | 0.0467841 | − | 0.998905i | \(-0.485103\pi\) | ||||
0.0467841 | + | 0.998905i | \(0.485103\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1242.00 | −0.0802572 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5520.00 | −0.354983 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 798.000 | 0.0508278 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11868.0 | 0.752318 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9839.00 | 0.620736 | 0.310368 | − | 0.950616i | \(-0.399548\pi\) | ||||
0.310368 | + | 0.950616i | \(0.399548\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13575.0 | 0.852382 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 318.000 | 0.0197796 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7452.00 | −0.461340 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21564.0 | −1.32875 | −0.664373 | − | 0.747401i | \(-0.731302\pi\) | ||||
−0.664373 | + | 0.747401i | \(0.731302\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8604.00 | 0.527696 | 0.263848 | − | 0.964564i | \(-0.415008\pi\) | ||||
0.263848 | + | 0.964564i | \(0.415008\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3444.00 | 0.209270 | 0.104635 | − | 0.994511i | \(-0.466633\pi\) | ||||
0.104635 | + | 0.994511i | \(0.466633\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2716.00 | −0.164272 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1995.00 | −0.120108 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3518.00 | 0.210827 | 0.105413 | − | 0.994428i | \(-0.466383\pi\) | ||||
0.105413 | + | 0.994428i | \(0.466383\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5130.00 | −0.304628 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12612.0 | 0.745514 | 0.372757 | − | 0.927929i | \(-0.378412\pi\) | ||||
0.372757 | + | 0.927929i | \(0.378412\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27090.0 | 1.59407 | 0.797034 | − | 0.603935i | \(-0.206401\pi\) | ||||
0.797034 | + | 0.603935i | \(0.206401\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 138.000 | 0.00808367 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −644.000 | −0.0373850 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9633.00 | −0.556701 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 238.000 | 0.0136928 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5442.00 | 0.311699 | 0.155850 | − | 0.987781i | \(-0.450188\pi\) | ||||
0.155850 | + | 0.987781i | \(0.450188\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15226.0 | 0.864376 | 0.432188 | − | 0.901783i | \(-0.357742\pi\) | ||||
0.432188 | + | 0.901783i | \(0.357742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4205.00 | −0.237663 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7452.00 | −0.419326 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −552.000 | −0.0309249 | −0.0154624 | − | 0.999880i | \(-0.504922\pi\) | ||||
−0.0154624 | + | 0.999880i | \(0.504922\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5541.00 | −0.307718 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 456.000 | 0.0252137 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9776.00 | −0.538201 | −0.269100 | − | 0.963112i | \(-0.586726\pi\) | ||||
−0.269100 | + | 0.963112i | \(0.586726\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −630.000 | −0.0345335 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3864.00 | −0.209985 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3060.00 | 0.165579 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13066.0 | 0.703989 | 0.351994 | − | 0.936002i | \(-0.385504\pi\) | ||||
0.351994 | + | 0.936002i | \(0.385504\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4902.00 | 0.262991 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2760.00 | 0.146818 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28985.0 | 1.53534 | 0.767669 | − | 0.640847i | \(-0.221417\pi\) | ||||
0.767669 | + | 0.640847i | \(0.221417\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4968.00 | 0.262046 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6118.00 | 0.321348 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3528.00 | −0.183760 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15722.0 | −0.815482 | −0.407741 | − | 0.913098i | \(-0.633683\pi\) | ||||
−0.407741 | + | 0.913098i | \(0.633683\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1540.00 | −0.0795459 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20901.0 | −1.07513 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32611.0 | −1.66365 | −0.831826 | − | 0.555036i | \(-0.812704\pi\) | ||||
−0.831826 | + | 0.555036i | \(0.812704\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7682.00 | 0.388685 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8358.00 | −0.421159 | −0.210580 | − | 0.977577i | \(-0.567535\pi\) | ||||
−0.210580 | + | 0.977577i | \(0.567535\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9142.00 | −0.456920 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20604.0 | −1.02562 | −0.512808 | − | 0.858503i | \(-0.671395\pi\) | ||||
−0.512808 | + | 0.858503i | \(0.671395\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 57.0000 | 0.00282584 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19476.0 | −0.961649 | −0.480824 | − | 0.876817i | \(-0.659663\pi\) | ||||
−0.480824 | + | 0.876817i | \(0.659663\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1278.00 | 0.0625965 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4920.00 | 0.240017 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3864.00 | −0.187749 | −0.0938744 | − | 0.995584i | \(-0.529925\pi\) | ||||
−0.0938744 | + | 0.995584i | \(0.529925\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4140.00 | −0.200359 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18871.0 | 0.906048 | 0.453024 | − | 0.891498i | \(-0.350345\pi\) | ||||
0.453024 | + | 0.891498i | \(0.350345\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1932.00 | 0.0923941 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36372.0 | −1.73257 | −0.866284 | − | 0.499552i | \(-0.833498\pi\) | ||||
−0.866284 | + | 0.499552i | \(0.833498\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9215.00 | −0.437229 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −194.000 | −0.00913290 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4603.00 | 0.215850 | 0.107925 | − | 0.994159i | \(-0.465579\pi\) | ||||
0.107925 | + | 0.994159i | \(0.465579\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20772.0 | 0.970279 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.0000 | 0.00167507 | 0.000837536 | − | 1.00000i | \(-0.499733\pi\) | ||||
0.000837536 | 1.00000i | \(0.499733\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3870.00 | −0.178681 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1596.00 | −0.0734052 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11592.0 | 0.531107 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 378.000 | 0.0172524 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20281.0 | −0.918602 | −0.459301 | − | 0.888281i | \(-0.651900\pi\) | ||||
−0.459301 | + | 0.888281i | \(0.651900\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5652.00 | 0.255027 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4380.00 | −0.196884 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.0000 | 0.000761271 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37524.0 | 1.66771 | 0.833857 | − | 0.551980i | \(-0.186128\pi\) | ||||
0.833857 | + | 0.551980i | \(0.186128\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18860.0 | −0.835067 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9936.00 | −0.438291 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7980.00 | 0.350695 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10830.0 | 0.472409 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31224.0 | 1.35696 | 0.678478 | − | 0.734621i | \(-0.262640\pi\) | ||||
0.678478 | + | 0.734621i | \(0.262640\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32579.0 | −1.41061 | −0.705304 | − | 0.708905i | \(-0.749190\pi\) | ||||
−0.705304 | + | 0.708905i | \(0.749190\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18216.0 | 0.785809 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3173.00 | 0.135874 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −45.0000 | −0.00191994 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19810.0 | −0.842112 | −0.421056 | − | 0.907035i | \(-0.638340\pi\) | ||||
−0.421056 | + | 0.907035i | \(0.638340\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10273.0 | 0.435108 | 0.217554 | − | 0.976048i | \(-0.430192\pi\) | ||||
0.217554 | + | 0.976048i | \(0.430192\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16656.0 | 0.700346 | 0.350173 | − | 0.936685i | \(-0.386123\pi\) | ||||
0.350173 | + | 0.936685i | \(0.386123\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4790.00 | −0.200680 | −0.100340 | − | 0.994953i | \(-0.531993\pi\) | ||||
−0.100340 | + | 0.994953i | \(0.531993\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8409.00 | 0.351029 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14628.0 | 0.608440 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3591.00 | −0.148295 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7414.00 | −0.305077 | −0.152539 | − | 0.988298i | \(-0.548745\pi\) | ||||
−0.152539 | + | 0.988298i | \(0.548745\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24193.0 | −0.991964 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20082.0 | −0.820475 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5675.00 | −0.230219 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19443.0 | −0.785962 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11868.0 | 0.478061 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30155.0 | −1.21042 | −0.605210 | − | 0.796066i | \(-0.706911\pi\) | ||||
−0.605210 | + | 0.796066i | \(0.706911\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8244.00 | 0.328599 | 0.164300 | − | 0.986410i | \(-0.447464\pi\) | ||||
0.164300 | + | 0.986410i | \(0.447464\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17552.0 | −0.697167 | −0.348584 | − | 0.937278i | \(-0.613337\pi\) | ||||
−0.348584 | + | 0.937278i | \(0.613337\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1260.00 | 0.0498730 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34104.0 | −1.34521 | −0.672604 | − | 0.740003i | \(-0.734824\pi\) | ||||
−0.672604 | + | 0.740003i | \(0.734824\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8391.00 | −0.328689 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7728.00 | −0.301674 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −653.000 | −0.0254031 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7569.00 | −0.293439 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46229.0 | 1.77998 | 0.889990 | − | 0.455980i | \(-0.150711\pi\) | ||||
0.889990 | + | 0.455980i | \(0.150711\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9042.00 | −0.346961 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22440.0 | −0.858142 | −0.429071 | − | 0.903271i | \(-0.641159\pi\) | ||||
−0.429071 | + | 0.903271i | \(0.641159\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17143.0 | −0.653350 | −0.326675 | − | 0.945137i | \(-0.605928\pi\) | ||||
−0.326675 | + | 0.945137i | \(0.605928\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23626.0 | −0.894344 | −0.447172 | − | 0.894448i | \(-0.647569\pi\) | ||||
−0.447172 | + | 0.894448i | \(0.647569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11880.0 | 0.448192 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1134.00 | −0.0426380 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7790.00 | −0.291918 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 138.000 | 0.00513677 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1862.00 | −0.0690781 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20976.0 | 0.775596 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2505.00 | −0.0923158 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11268.0 | −0.412511 | −0.206256 | − | 0.978498i | \(-0.566128\pi\) | ||||
−0.206256 | + | 0.978498i | \(0.566128\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4968.00 | 0.181274 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10046.0 | −0.365355 | −0.182678 | − | 0.983173i | \(-0.558476\pi\) | ||||
−0.182678 | + | 0.983173i | \(0.558476\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1988.00 | −0.0720626 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5280.00 | −0.190143 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15359.0 | −0.551302 | −0.275651 | − | 0.961258i | \(-0.588893\pi\) | ||||
−0.275651 | + | 0.961258i | \(0.588893\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16107.0 | −0.576269 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 828.000 | 0.0295276 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2772.00 | −0.0982141 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39790.0 | −1.40524 | −0.702620 | − | 0.711565i | \(-0.747986\pi\) | ||||
−0.702620 | + | 0.711565i | \(0.747986\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6042.00 | 0.212694 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14538.0 | −0.510132 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17009.0 | 0.593020 | 0.296510 | − | 0.955030i | \(-0.404177\pi\) | ||||
0.296510 | + | 0.955030i | \(0.404177\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2271.00 | 0.0789258 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11674.0 | −0.404422 | −0.202211 | − | 0.979342i | \(-0.564813\pi\) | ||||
−0.202211 | + | 0.979342i | \(0.564813\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3864.00 | −0.133435 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6026.00 | 0.206778 | 0.103389 | − | 0.994641i | \(-0.467031\pi\) | ||||
0.103389 | + | 0.994641i | \(0.467031\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 570.000 | 0.0194973 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22896.0 | 0.780708 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14088.0 | 0.478862 | 0.239431 | − | 0.970913i | \(-0.423039\pi\) | ||||
0.239431 | + | 0.970913i | \(0.423039\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −588.000 | −0.0198614 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3890.00 | 0.130985 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12102.0 | −0.406230 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8856.00 | 0.296345 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11208.0 | −0.372725 | −0.186362 | − | 0.982481i | \(-0.559670\pi\) | ||||
−0.186362 | + | 0.982481i | \(0.559670\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2622.00 | 0.0869255 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26054.0 | 0.861084 | 0.430542 | − | 0.902571i | \(-0.358322\pi\) | ||||
0.430542 | + | 0.902571i | \(0.358322\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8460.00 | −0.278741 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26870.0 | 0.879885 | 0.439942 | − | 0.898026i | \(-0.354999\pi\) | ||||
0.439942 | + | 0.898026i | \(0.354999\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15456.0 | 0.504572 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16587.0 | −0.539839 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23388.0 | −0.758862 | −0.379431 | − | 0.925220i | \(-0.623880\pi\) | ||||
−0.379431 | + | 0.925220i | \(0.623880\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6150.00 | 0.198335 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7682.00 | 0.246990 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17345.0 | −0.555986 | −0.277993 | − | 0.960583i | \(-0.589669\pi\) | ||||
−0.277993 | + | 0.960583i | \(0.589669\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20340.0 | 0.650021 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25998.0 | 0.825842 | 0.412921 | − | 0.910767i | \(-0.364508\pi\) | ||||
0.412921 | + | 0.910767i | \(0.364508\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6966.00 | −0.220615 |
(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 | 1200.4.a.bd.1.1 | 1 | ||
4.3 | odd | 2 | 600.4.a.e.1.1 | ✓ | 1 | ||
5.2 | odd | 4 | 1200.4.f.i.49.1 | 2 | |||
5.3 | odd | 4 | 1200.4.f.i.49.2 | 2 | |||
5.4 | even | 2 | 1200.4.a.g.1.1 | 1 | |||
12.11 | even | 2 | 1800.4.a.m.1.1 | 1 | |||
20.3 | even | 4 | 600.4.f.e.49.1 | 2 | |||
20.7 | even | 4 | 600.4.f.e.49.2 | 2 | |||
20.19 | odd | 2 | 600.4.a.n.1.1 | yes | 1 | ||
60.23 | odd | 4 | 1800.4.f.l.649.2 | 2 | |||
60.47 | odd | 4 | 1800.4.f.l.649.1 | 2 | |||
60.59 | even | 2 | 1800.4.a.v.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.4.a.e.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
600.4.a.n.1.1 | yes | 1 | 20.19 | odd | 2 | ||
600.4.f.e.49.1 | 2 | 20.3 | even | 4 | |||
600.4.f.e.49.2 | 2 | 20.7 | even | 4 | |||
1200.4.a.g.1.1 | 1 | 5.4 | even | 2 | |||
1200.4.a.bd.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1200.4.f.i.49.1 | 2 | 5.2 | odd | 4 | |||
1200.4.f.i.49.2 | 2 | 5.3 | odd | 4 | |||
1800.4.a.m.1.1 | 1 | 12.11 | even | 2 | |||
1800.4.a.v.1.1 | 1 | 60.59 | even | 2 | |||
1800.4.f.l.649.1 | 2 | 60.47 | odd | 4 | |||
1800.4.f.l.649.2 | 2 | 60.23 | odd | 4 |