Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(49,1200)]
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, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(70.8022920069\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 600) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.49 |
Dual form | 1200.4.f.i.49.1 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 5.00000i | − 0.269975i | −0.990847 | − | 0.134987i | \(-0.956901\pi\) | ||||
0.990847 | − | 0.134987i | \(-0.0430994\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | − 1.00000i | − 0.0213346i | −0.999943 | − | 0.0106673i | \(-0.996604\pi\) | ||||
0.999943 | − | 0.0106673i | \(-0.00339558\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 46.0000i | 0.656273i | 0.944630 | + | 0.328136i | \(0.106421\pi\) | ||||
−0.944630 | + | 0.328136i | \(0.893579\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.0000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 15.0000 | 0.155870 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 46.0000i | − 0.417029i | −0.978019 | − | 0.208514i | \(-0.933137\pi\) | ||||
0.978019 | − | 0.208514i | \(-0.0668628\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −14.0000 | −0.0896460 | −0.0448230 | − | 0.998995i | \(-0.514272\pi\) | ||||
−0.0448230 | + | 0.998995i | \(0.514272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −133.000 | −0.770565 | −0.385282 | − | 0.922799i | \(-0.625896\pi\) | ||||
−0.385282 | + | 0.922799i | \(0.625896\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 42.0000i | − 0.221553i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 258.000i | 1.14635i | 0.819433 | + | 0.573175i | \(0.194288\pi\) | ||||
−0.819433 | + | 0.573175i | \(0.805712\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | − 167.000i | − 0.592262i | −0.955147 | − | 0.296131i | \(-0.904304\pi\) | ||||
0.955147 | − | 0.296131i | \(-0.0956965\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 410.000i | − 1.27244i | −0.771508 | − | 0.636220i | \(-0.780497\pi\) | ||||
0.771508 | − | 0.636220i | \(-0.219503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 318.000 | 0.927114 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −138.000 | −0.378899 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 456.000i | − 1.18182i | −0.806738 | − | 0.590910i | \(-0.798769\pi\) | ||||
0.806738 | − | 0.590910i | \(-0.201231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 57.0000i | 0.132453i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −194.000 | −0.428079 | −0.214039 | − | 0.976825i | \(-0.568662\pi\) | ||||
−0.214039 | + | 0.976825i | \(0.568662\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17.0000 | −0.0356824 | −0.0178412 | − | 0.999841i | \(-0.505679\pi\) | ||||
−0.0178412 | + | 0.999841i | \(0.505679\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 45.0000i | 0.0899915i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 653.000i | − 1.19070i | −0.803468 | − | 0.595348i | \(-0.797014\pi\) | ||||
0.803468 | − | 0.595348i | \(-0.202986\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | − 570.000i | − 0.913883i | −0.889497 | − | 0.456941i | \(-0.848945\pi\) | ||||
0.889497 | − | 0.456941i | \(-0.151055\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 70.0000i | 0.103601i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −552.000 | −0.786137 | −0.393069 | − | 0.919509i | \(-0.628587\pi\) | ||||
−0.393069 | + | 0.919509i | \(0.628587\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 142.000i | 0.187789i | 0.995582 | + | 0.0938947i | \(0.0299317\pi\) | ||||
−0.995582 | + | 0.0938947i | \(0.970068\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 42.0000i | − 0.0517572i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1104.00 | 1.31487 | 0.657437 | − | 0.753510i | \(-0.271641\pi\) | ||||
0.657437 | + | 0.753510i | \(0.271641\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.00000 | −0.00575981 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 399.000i | − 0.444886i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 841.000i | 0.880316i | 0.897920 | + | 0.440158i | \(0.145077\pi\) | ||||
−0.897920 | + | 0.440158i | \(0.854923\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | − 308.000i | − 0.294642i | −0.989089 | − | 0.147321i | \(-0.952935\pi\) | ||||
0.989089 | − | 0.147321i | \(-0.0470651\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 984.000i | − 0.889036i | −0.895770 | − | 0.444518i | \(-0.853375\pi\) | ||||
0.895770 | − | 0.444518i | \(-0.146625\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1843.00 | 1.61952 | 0.809759 | − | 0.586763i | \(-0.199598\pi\) | ||||
0.809759 | + | 0.586763i | \(0.199598\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −774.000 | −0.661845 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 876.000i | − 0.729267i | −0.931151 | − | 0.364633i | \(-0.881194\pi\) | ||||
0.931151 | − | 0.364633i | \(-0.118806\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.00000i | 0.00711154i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 230.000 | 0.177177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1135.00 | −0.852742 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 252.000i | 0.184732i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2376.00i | − 1.66013i | −0.557670 | − | 0.830063i | \(-0.688305\pi\) | ||||
0.557670 | − | 0.830063i | \(-0.311695\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | − 95.0000i | − 0.0619364i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 778.000i | − 0.485175i | −0.970129 | − | 0.242588i | \(-0.922004\pi\) | ||||
0.970129 | − | 0.242588i | \(-0.0779962\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1692.00 | 1.03247 | 0.516236 | − | 0.856446i | \(-0.327333\pi\) | ||||
0.516236 | + | 0.856446i | \(0.327333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1230.00 | 0.734643 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.0000i | 0.00818698i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 954.000i | 0.535269i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 494.000 | 0.271611 | 0.135806 | − | 0.990736i | \(-0.456638\pi\) | ||||
0.135806 | + | 0.990736i | \(0.456638\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 841.000 | 0.453242 | 0.226621 | − | 0.973983i | \(-0.427232\pi\) | ||||
0.226621 | + | 0.973983i | \(0.427232\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 414.000i | − 0.218758i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.0000i | 0.00965838i | 0.999988 | + | 0.00482919i | \(0.00153718\pi\) | ||||
−0.999988 | + | 0.00482919i | \(0.998463\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1368.00 | 0.682324 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −230.000 | −0.112587 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2261.00i | − 1.08647i | −0.839580 | − | 0.543237i | \(-0.817199\pi\) | ||||
0.839580 | − | 0.543237i | \(-0.182801\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 2112.00i | − 0.978632i | −0.872107 | − | 0.489316i | \(-0.837247\pi\) | ||||
0.872107 | − | 0.489316i | \(-0.162753\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2196.00 | 0.999545 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −171.000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 562.000i | − 0.246983i | −0.992346 | − | 0.123492i | \(-0.960591\pi\) | ||||
0.992346 | − | 0.123492i | \(-0.0394092\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 582.000i | − 0.247151i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3718.00 | 1.55249 | 0.776247 | − | 0.630429i | \(-0.217121\pi\) | ||||
0.776247 | + | 0.630429i | \(0.217121\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1639.00 | −0.673071 | −0.336536 | − | 0.941671i | \(-0.609255\pi\) | ||||
−0.336536 | + | 0.941671i | \(0.609255\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 51.0000i | − 0.0206012i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 644.000i | − 0.251839i | ||||||||
\(188\) | 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 | ||||||||
\(193\) | 2621.00i | 0.977532i | 0.872415 | + | 0.488766i | \(0.162553\pi\) | ||||
−0.872415 | + | 0.488766i | \(0.837447\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4954.00i | − 1.79166i | −0.444392 | − | 0.895832i | \(-0.646580\pi\) | ||||
0.444392 | − | 0.895832i | \(-0.353420\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1739.00 | 0.619470 | 0.309735 | − | 0.950823i | \(-0.399760\pi\) | ||||
0.309735 | + | 0.950823i | \(0.399760\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1959.00 | 0.687449 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 70.0000i | 0.0242022i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 414.000i | 0.139010i | ||||||||
\(208\) | 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 | ||||||||
\(213\) | − 2484.00i | − 0.799065i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 665.000i | 0.208033i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1710.00 | 0.527631 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 46.0000 | 0.0140013 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3211.00i | − 0.964235i | −0.876106 | − | 0.482118i | \(-0.839868\pi\) | ||||
0.876106 | − | 0.482118i | \(-0.160132\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2484.00i | 0.726295i | 0.931732 | + | 0.363147i | \(0.118298\pi\) | ||||
−0.931732 | + | 0.363147i | \(0.881702\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1847.00 | 0.532983 | 0.266492 | − | 0.963837i | \(-0.414136\pi\) | ||||
0.266492 | + | 0.963837i | \(0.414136\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −210.000 | −0.0598138 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1020.00i | 0.286792i | 0.989665 | + | 0.143396i | \(0.0458022\pi\) | ||||
−0.989665 | + | 0.143396i | \(0.954198\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1656.00i | − 0.453877i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1176.00 | 0.318281 | 0.159140 | − | 0.987256i | \(-0.449128\pi\) | ||||
0.159140 | + | 0.987256i | \(0.449128\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6967.00 | −1.86217 | −0.931087 | − | 0.364797i | \(-0.881138\pi\) | ||||
−0.931087 | + | 0.364797i | \(0.881138\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 19.0000i | − 0.00489450i | ||||||||
\(248\) | 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 | ||||||||
\(253\) | 644.000i | 0.160031i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 6924.00i | − 1.68057i | −0.542143 | − | 0.840286i | \(-0.682387\pi\) | ||||
0.542143 | − | 0.840286i | \(-0.317613\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1290.00 | 0.309485 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 126.000 | 0.0298820 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1884.00i | 0.441720i | 0.975305 | + | 0.220860i | \(0.0708864\pi\) | ||||
−0.975305 | + | 0.220860i | \(0.929114\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3312.00i | 0.759143i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3610.00 | −0.818236 | −0.409118 | − | 0.912481i | \(-0.634164\pi\) | ||||
−0.409118 | + | 0.912481i | \(0.634164\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6072.00 | 1.36106 | 0.680531 | − | 0.732719i | \(-0.261749\pi\) | ||||
0.680531 | + | 0.732719i | \(0.261749\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 15.0000i | − 0.00332543i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2803.00i | − 0.608000i | −0.952672 | − | 0.304000i | \(-0.901678\pi\) | ||||
0.952672 | − | 0.304000i | \(-0.0983223\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | − 6481.00i | − 1.36133i | −0.732596 | − | 0.680663i | \(-0.761692\pi\) | ||||
0.732596 | − | 0.680663i | \(-0.238308\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 420.000i | − 0.0863826i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2797.00 | 0.569306 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2523.00 | −0.508250 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3014.00i | − 0.600955i | −0.953789 | − | 0.300477i | \(-0.902854\pi\) | ||||
0.953789 | − | 0.300477i | \(-0.0971460\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 378.000i | 0.0738511i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −46.0000 | −0.00889715 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −835.000 | −0.159896 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1656.00i | 0.313976i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5369.00i | 0.998127i | 0.866565 | + | 0.499064i | \(0.166323\pi\) | ||||
−0.866565 | + | 0.499064i | \(0.833677\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 757.000i | 0.136703i | 0.997661 | + | 0.0683517i | \(0.0217740\pi\) | ||||
−0.997661 | + | 0.0683517i | \(0.978226\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 7632.00i | − 1.35223i | −0.736798 | − | 0.676113i | \(-0.763663\pi\) | ||||
0.736798 | − | 0.676113i | \(-0.236337\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 196.000 | 0.0344009 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2952.00 | 0.513285 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 874.000i | 0.150559i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5529.00i | 0.935029i | ||||||||
\(328\) | 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 | ||||||||
\(333\) | − 2322.00i | − 0.382117i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7849.00i | 1.26873i | 0.773033 | + | 0.634365i | \(0.218739\pi\) | ||||
−0.773033 | + | 0.634365i | \(0.781261\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2628.00 | 0.421042 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1862.00 | 0.295698 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 3305.00i | − 0.520272i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 634.000i | − 0.0980833i | −0.998797 | − | 0.0490416i | \(-0.984383\pi\) | ||||
0.998797 | − | 0.0490416i | \(-0.0156167\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −930.000 | −0.142641 | −0.0713206 | − | 0.997453i | \(-0.522721\pi\) | ||||
−0.0713206 | + | 0.997453i | \(0.522721\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.0000 | −0.00410585 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4286.00i | 0.646234i | 0.946359 | + | 0.323117i | \(0.104731\pi\) | ||||
−0.946359 | + | 0.323117i | \(0.895269\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 690.000i | 0.102293i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4236.00 | −0.622751 | −0.311375 | − | 0.950287i | \(-0.600790\pi\) | ||||
−0.311375 | + | 0.950287i | \(0.600790\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6498.00 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3405.00i | − 0.492331i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1451.00i | − 0.206380i | −0.994662 | − | 0.103190i | \(-0.967095\pi\) | ||||
0.994662 | − | 0.103190i | \(-0.0329050\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −756.000 | −0.106655 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2280.00 | −0.319061 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 3115.00i | − 0.432409i | −0.976348 | − | 0.216205i | \(-0.930632\pi\) | ||||
0.976348 | − | 0.216205i | \(-0.0693678\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.0000i | 0.00191256i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1415.00 | −0.191777 | −0.0958887 | − | 0.995392i | \(-0.530569\pi\) | ||||
−0.0958887 | + | 0.995392i | \(0.530569\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7128.00 | 0.958474 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 180.000i | − 0.0240145i | −0.999928 | − | 0.0120073i | \(-0.996178\pi\) | ||||
0.999928 | − | 0.0120073i | \(-0.00382213\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1503.00i | 0.197421i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12372.0 | −1.61256 | −0.806279 | − | 0.591535i | \(-0.798522\pi\) | ||||
−0.806279 | + | 0.591535i | \(0.798522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2116.00 | 0.273685 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 3168.00i | − 0.406627i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5767.00i | 0.729062i | 0.931191 | + | 0.364531i | \(0.118771\pi\) | ||||
−0.931191 | + | 0.364531i | \(0.881229\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 133.000i | 0.0164397i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 3612.00i | − 0.439902i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1501.00 | −0.181466 | −0.0907331 | − | 0.995875i | \(-0.528921\pi\) | ||||
−0.0907331 | + | 0.995875i | \(0.528921\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2334.00 | 0.280116 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 970.000i | 0.115570i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5076.00i | 0.596098i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9072.00 | −1.05775 | −0.528874 | − | 0.848701i | \(-0.677386\pi\) | ||||
−0.528874 | + | 0.848701i | \(0.677386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7350.00 | 0.850872 | 0.425436 | − | 0.904989i | \(-0.360121\pi\) | ||||
0.425436 | + | 0.904989i | \(0.360121\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3690.00i | 0.424146i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 85.0000i | 0.00963334i | ||||||||
\(428\) | 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 | ||||||||
\(433\) | 10093.0i | 1.12018i | 0.828431 | + | 0.560091i | \(0.189234\pi\) | ||||
−0.828431 | + | 0.560091i | \(0.810766\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 874.000i | − 0.0956730i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2555.00 | −0.277776 | −0.138888 | − | 0.990308i | \(-0.544353\pi\) | ||||
−0.138888 | + | 0.990308i | \(0.544353\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2862.00 | −0.309038 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6240.00i | 0.669236i | 0.942354 | + | 0.334618i | \(0.108607\pi\) | ||||
−0.942354 | + | 0.334618i | \(0.891393\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1482.00i | 0.156815i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3324.00 | −0.349375 | −0.174687 | − | 0.984624i | \(-0.555891\pi\) | ||||
−0.174687 | + | 0.984624i | \(0.555891\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1176.00 | −0.122784 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2523.00i | 0.261680i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16774.0i | 1.71697i | 0.512840 | + | 0.858484i | \(0.328593\pi\) | ||||
−0.512840 | + | 0.858484i | \(0.671407\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 6936.00i | 0.696206i | 0.937456 | + | 0.348103i | \(0.113174\pi\) | ||||
−0.937456 | + | 0.348103i | \(0.886826\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 15622.0i | − 1.54797i | −0.633207 | − | 0.773983i | \(-0.718262\pi\) | ||||
0.633207 | − | 0.773983i | \(-0.281738\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3265.00 | −0.321458 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −57.0000 | −0.00557627 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2338.00i | 0.227276i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4104.00i | 0.393940i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13354.0 | −1.27382 | −0.636910 | − | 0.770938i | \(-0.719788\pi\) | ||||
−0.636910 | + | 0.770938i | \(0.719788\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 258.000 | 0.0244569 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 690.000i | − 0.0650023i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 461.000i | 0.0428951i | 0.999770 | + | 0.0214475i | \(0.00682749\pi\) | ||||
−0.999770 | + | 0.0214475i | \(0.993173\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | − 644.000i | − 0.0588323i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4140.00i | 0.373651i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14317.0 | −1.28440 | −0.642201 | − | 0.766536i | \(-0.721979\pi\) | ||||
−0.642201 | + | 0.766536i | \(0.721979\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6336.00 | 0.565013 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9228.00i | 0.818004i | 0.912533 | + | 0.409002i | \(0.134123\pi\) | ||||
−0.912533 | + | 0.409002i | \(0.865877\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6588.00i | 0.577087i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4574.00 | −0.398308 | −0.199154 | − | 0.979968i | \(-0.563819\pi\) | ||||
−0.199154 | + | 0.979968i | \(0.563819\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2850.00 | −0.246725 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 513.000i | − 0.0441511i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5740.00i | 0.488288i | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 8263.00i | 0.690852i | 0.938446 | + | 0.345426i | \(0.112266\pi\) | ||||
−0.938446 | + | 0.345426i | \(0.887734\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 6118.00i | − 0.505701i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10051.0 | 0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1746.00 | 0.142693 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 84.0000i | − 0.00682635i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11154.0i | 0.896333i | ||||||||
\(538\) | 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 | ||||||||
\(543\) | − 4917.00i | − 0.388598i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4048.00i | 0.316417i | 0.987406 | + | 0.158208i | \(0.0505718\pi\) | ||||
−0.987406 | + | 0.158208i | \(0.949428\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 153.000 | 0.0118941 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −266.000 | −0.0205662 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2760.00i | 0.212237i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 6758.00i | − 0.514086i | −0.966400 | − | 0.257043i | \(-0.917252\pi\) | ||||
0.966400 | − | 0.257043i | \(-0.0827481\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −167.000 | −0.0126357 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1932.00 | 0.145399 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24506.0i | 1.83447i | 0.398350 | + | 0.917233i | \(0.369583\pi\) | ||||
−0.398350 | + | 0.917233i | \(0.630417\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 405.000i | − 0.0299972i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1430.00 | 0.105358 | 0.0526790 | − | 0.998611i | \(-0.483224\pi\) | ||||
0.0526790 | + | 0.998611i | \(0.483224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3691.00 | −0.270514 | −0.135257 | − | 0.990811i | \(-0.543186\pi\) | ||||
−0.135257 | + | 0.990811i | \(0.543186\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 7230.00i | − 0.527116i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4571.00i | 0.329798i | 0.986310 | + | 0.164899i | \(0.0527298\pi\) | ||||
−0.986310 | + | 0.164899i | \(0.947270\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7863.00 | −0.564378 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 710.000 | 0.0506984 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6384.00i | 0.453513i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 14808.0i | − 1.04121i | −0.853797 | − | 0.520606i | \(-0.825706\pi\) | ||||
0.853797 | − | 0.520606i | \(-0.174294\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2527.00 | −0.176780 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14862.0 | 1.03442 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24588.0i | 1.70271i | 0.524588 | + | 0.851356i | \(0.324219\pi\) | ||||
−0.524588 | + | 0.851356i | \(0.675781\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5217.00i | 0.357651i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27564.0 | −1.88019 | −0.940096 | − | 0.340911i | \(-0.889265\pi\) | ||||
−0.940096 | + | 0.340911i | \(0.889265\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10987.0 | 0.745706 | 0.372853 | − | 0.927891i | \(-0.378380\pi\) | ||||
0.372853 | + | 0.927891i | \(0.378380\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5877.00i | 0.396899i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13200.0i | 0.882655i | 0.897346 | + | 0.441327i | \(0.145492\pi\) | ||||
−0.897346 | + | 0.441327i | \(0.854508\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −210.000 | −0.0139731 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −410.000 | −0.0271470 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 21066.0i | − 1.38801i | −0.719972 | − | 0.694003i | \(-0.755845\pi\) | ||||
0.719972 | − | 0.694003i | \(-0.244155\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12336.0i | 0.804909i | 0.915440 | + | 0.402454i | \(0.131843\pi\) | ||||
−0.915440 | + | 0.402454i | \(0.868157\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1441.00 | −0.0935681 | −0.0467841 | − | 0.998905i | \(-0.514897\pi\) | ||||
−0.0467841 | + | 0.998905i | \(0.514897\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1242.00 | −0.0802572 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 5520.00i | − 0.354983i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 798.000i | − 0.0508278i | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 13575.0i | 0.852382i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 318.000i | − 0.0197796i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 8604.00i | 0.527696i | 0.964564 | + | 0.263848i | \(0.0849918\pi\) | ||||
−0.964564 | + | 0.263848i | \(0.915008\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 3444.00i | − 0.209270i | −0.994511 | − | 0.104635i | \(-0.966633\pi\) | ||||
0.994511 | − | 0.104635i | \(-0.0333674\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2716.00 | 0.164272 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1995.00 | −0.120108 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3518.00i | 0.210827i | 0.994428 | + | 0.105413i | \(0.0336166\pi\) | ||||
−0.994428 | + | 0.105413i | \(0.966383\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5130.00i | 0.304628i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12612.0 | −0.745514 | −0.372757 | − | 0.927929i | \(-0.621588\pi\) | ||||
−0.372757 | + | 0.927929i | \(0.621588\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27090.0 | 1.59407 | 0.797034 | − | 0.603935i | \(-0.206401\pi\) | ||||
0.797034 | + | 0.603935i | \(0.206401\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 138.000i | 0.00808367i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 644.000i | 0.0373850i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9633.00 | 0.556701 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 238.000 | 0.0136928 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5442.00i | 0.311699i | 0.987781 | + | 0.155850i | \(0.0498115\pi\) | ||||
−0.987781 | + | 0.155850i | \(0.950188\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 15226.0i | − 0.864376i | −0.901783 | − | 0.432188i | \(-0.857742\pi\) | ||||
0.901783 | − | 0.432188i | \(-0.142258\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4205.00 | 0.237663 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7452.00 | −0.419326 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 552.000i | − 0.0309249i | −0.999880 | − | 0.0154624i | \(-0.995078\pi\) | ||||
0.999880 | − | 0.0154624i | \(-0.00492204\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5541.00i | 0.307718i | ||||||||
\(688\) | 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 | ||||||||
\(693\) | − 630.000i | − 0.0345335i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3864.00i | 0.209985i | ||||||||
\(698\) | 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 | ||||||||
\(703\) | 4902.00i | 0.262991i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2760.00i | − 0.146818i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28985.0 | −1.53534 | −0.767669 | − | 0.640847i | \(-0.778583\pi\) | ||||
−0.767669 | + | 0.640847i | \(0.778583\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4968.00 | 0.262046 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6118.00i | 0.321348i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3528.00i | 0.183760i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15722.0 | 0.815482 | 0.407741 | − | 0.913098i | \(-0.366317\pi\) | ||||
0.407741 | + | 0.913098i | \(0.366317\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1540.00 | −0.0795459 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 20901.0i | − 1.07513i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32611.0i | 1.66365i | 0.555036 | + | 0.831826i | \(0.312704\pi\) | ||||
−0.555036 | + | 0.831826i | \(0.687296\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7682.00 | 0.388685 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 8358.00i | − 0.421159i | −0.977577 | − | 0.210580i | \(-0.932465\pi\) | ||||
0.977577 | − | 0.210580i | \(-0.0675351\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9142.00i | 0.456920i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20604.0 | 1.02562 | 0.512808 | − | 0.858503i | \(-0.328605\pi\) | ||||
0.512808 | + | 0.858503i | \(0.328605\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 57.0000 | 0.00282584 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 19476.0i | − 0.961649i | −0.876817 | − | 0.480824i | \(-0.840337\pi\) | ||||
0.876817 | − | 0.480824i | \(-0.159663\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1278.00i | − 0.0625965i | ||||||||
\(748\) | 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 | ||||||||
\(753\) | − 4140.00i | − 0.200359i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 18871.0i | − 0.906048i | −0.891498 | − | 0.453024i | \(-0.850345\pi\) | ||||
0.891498 | − | 0.453024i | \(-0.149655\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | − 9215.00i | − 0.437229i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 194.000i | 0.00913290i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4603.00 | −0.215850 | −0.107925 | − | 0.994159i | \(-0.534421\pi\) | ||||
−0.107925 | + | 0.994159i | \(0.534421\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20772.0 | 0.970279 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.0000i | 0.00167507i | 1.00000 | 0.000837536i | \(0.000266596\pi\) | |||||
−1.00000 | 0.000837536i | \(0.999733\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3870.00i | 0.178681i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1596.00 | 0.0734052 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11592.0 | 0.531107 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 378.000i | 0.0172524i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20281.0i | 0.918602i | 0.888281 | + | 0.459301i | \(0.151900\pi\) | ||||
−0.888281 | + | 0.459301i | \(0.848100\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5652.00 | −0.255027 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4380.00 | −0.196884 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.0000i | 0 0.000761271i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 37524.0i | − 1.66771i | −0.551980 | − | 0.833857i | \(-0.686128\pi\) | ||||
0.551980 | − | 0.833857i | \(-0.313872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18860.0 | 0.835067 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9936.00 | −0.438291 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7980.00i | 0.350695i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 10830.0i | − 0.472409i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31224.0 | −1.35696 | −0.678478 | − | 0.734621i | \(-0.737360\pi\) | ||||
−0.678478 | + | 0.734621i | \(0.737360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32579.0 | −1.41061 | −0.705304 | − | 0.708905i | \(-0.749190\pi\) | ||||
−0.705304 | + | 0.708905i | \(0.749190\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18216.0i | 0.785809i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 3173.00i | − 0.135874i | ||||||||
\(818\) | 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 | ||||||||
\(823\) | 10273.0i | 0.435108i | 0.976048 | + | 0.217554i | \(0.0698079\pi\) | ||||
−0.976048 | + | 0.217554i | \(0.930192\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 16656.0i | − 0.700346i | −0.936685 | − | 0.350173i | \(-0.886123\pi\) | ||||
0.936685 | − | 0.350173i | \(-0.113877\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4790.00 | 0.200680 | 0.100340 | − | 0.994953i | \(-0.468007\pi\) | ||||
0.100340 | + | 0.994953i | \(0.468007\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8409.00 | 0.351029 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14628.0i | 0.608440i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3591.00i | 0.148295i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7414.00 | 0.305077 | 0.152539 | − | 0.988298i | \(-0.451255\pi\) | ||||
0.152539 | + | 0.988298i | \(0.451255\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24193.0 | −0.991964 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 20082.0i | − 0.820475i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5675.00i | 0.230219i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19443.0 | 0.785962 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11868.0 | 0.478061 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 30155.0i | − 1.21042i | −0.796066 | − | 0.605210i | \(-0.793089\pi\) | ||||
0.796066 | − | 0.605210i | \(-0.206911\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 8244.00i | − 0.328599i | −0.986410 | − | 0.164300i | \(-0.947464\pi\) | ||||
0.986410 | − | 0.164300i | \(-0.0525364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17552.0 | 0.697167 | 0.348584 | − | 0.937278i | \(-0.386663\pi\) | ||||
0.348584 | + | 0.937278i | \(0.386663\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1260.00 | 0.0498730 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 34104.0i | − 1.34521i | −0.740003 | − | 0.672604i | \(-0.765176\pi\) | ||||
0.740003 | − | 0.672604i | \(-0.234824\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8391.00i | 0.328689i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7728.00 | 0.301674 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −653.000 | −0.0254031 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 7569.00i | − 0.293439i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 46229.0i | − 1.77998i | −0.455980 | − | 0.889990i | \(-0.650711\pi\) | ||||
0.455980 | − | 0.889990i | \(-0.349289\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − 17143.0i | − 0.653350i | −0.945137 | − | 0.326675i | \(-0.894072\pi\) | ||||
0.945137 | − | 0.326675i | \(-0.105928\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23626.0i | 0.894344i | 0.894448 | + | 0.447172i | \(0.147569\pi\) | ||||
−0.894448 | + | 0.447172i | \(0.852431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11880.0 | −0.448192 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1134.00 | −0.0426380 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 7790.00i | − 0.291918i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 138.000i | − 0.00513677i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1862.00 | 0.0690781 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20976.0 | 0.775596 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 2505.00i | − 0.0923158i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11268.0i | 0.412511i | 0.978498 | + | 0.206256i | \(0.0661279\pi\) | ||||
−0.978498 | + | 0.206256i | \(0.933872\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | − 1988.00i | − 0.0720626i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5280.00i | 0.190143i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15359.0 | 0.551302 | 0.275651 | − | 0.961258i | \(-0.411107\pi\) | ||||
0.275651 | + | 0.961258i | \(0.411107\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16107.0 | −0.576269 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 828.000i | 0.0295276i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2772.00i | 0.0982141i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39790.0 | 1.40524 | 0.702620 | − | 0.711565i | \(-0.252014\pi\) | ||||
0.702620 | + | 0.711565i | \(0.252014\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6042.00 | 0.212694 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 14538.0i | − 0.510132i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 17009.0i | − 0.593020i | −0.955030 | − | 0.296510i | \(-0.904177\pi\) | ||||
0.955030 | − | 0.296510i | \(-0.0958228\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | − 3864.00i | − 0.133435i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 6026.00i | − 0.206778i | −0.994641 | − | 0.103389i | \(-0.967031\pi\) | ||||
0.994641 | − | 0.103389i | \(-0.0329686\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −570.000 | −0.0194973 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22896.0 | 0.780708 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14088.0i | 0.478862i | 0.970913 | + | 0.239431i | \(0.0769608\pi\) | ||||
−0.970913 | + | 0.239431i | \(0.923039\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 588.000i | 0.0198614i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3890.00 | −0.130985 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12102.0 | −0.406230 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8856.00i | 0.296345i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11208.0i | 0.372725i | 0.982481 | + | 0.186362i | \(0.0596699\pi\) | ||||
−0.982481 | + | 0.186362i | \(0.940330\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | − 8460.00i | − 0.278741i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 26870.0i | − 0.879885i | −0.898026 | − | 0.439942i | \(-0.854999\pi\) | ||||
0.898026 | − | 0.439942i | \(-0.145001\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15456.0 | −0.504572 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16587.0 | −0.539839 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 23388.0i | − 0.758862i | −0.925220 | − | 0.379431i | \(-0.876120\pi\) | ||||
0.925220 | − | 0.379431i | \(-0.123880\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 6150.00i | − 0.198335i | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 20340.0i | 0.650021i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 25998.0i | − 0.825842i | −0.910767 | − | 0.412921i | \(-0.864508\pi\) | ||||
0.910767 | − | 0.412921i | \(-0.135492\pi\) | |||||||
\(998\) | 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.f.i.49.2 | 2 | ||
4.3 | odd | 2 | 600.4.f.e.49.1 | 2 | |||
5.2 | odd | 4 | 1200.4.a.bd.1.1 | 1 | |||
5.3 | odd | 4 | 1200.4.a.g.1.1 | 1 | |||
5.4 | even | 2 | inner | 1200.4.f.i.49.1 | 2 | ||
12.11 | even | 2 | 1800.4.f.l.649.2 | 2 | |||
20.3 | even | 4 | 600.4.a.n.1.1 | yes | 1 | ||
20.7 | even | 4 | 600.4.a.e.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 600.4.f.e.49.2 | 2 | |||
60.23 | odd | 4 | 1800.4.a.v.1.1 | 1 | |||
60.47 | odd | 4 | 1800.4.a.m.1.1 | 1 | |||
60.59 | even | 2 | 1800.4.f.l.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.4.a.e.1.1 | ✓ | 1 | 20.7 | even | 4 | ||
600.4.a.n.1.1 | yes | 1 | 20.3 | even | 4 | ||
600.4.f.e.49.1 | 2 | 4.3 | odd | 2 | |||
600.4.f.e.49.2 | 2 | 20.19 | odd | 2 | |||
1200.4.a.g.1.1 | 1 | 5.3 | odd | 4 | |||
1200.4.a.bd.1.1 | 1 | 5.2 | odd | 4 | |||
1200.4.f.i.49.1 | 2 | 5.4 | even | 2 | inner | ||
1200.4.f.i.49.2 | 2 | 1.1 | even | 1 | trivial | ||
1800.4.a.m.1.1 | 1 | 60.47 | odd | 4 | |||
1800.4.a.v.1.1 | 1 | 60.23 | odd | 4 | |||
1800.4.f.l.649.1 | 2 | 60.59 | even | 2 | |||
1800.4.f.l.649.2 | 2 | 12.11 | even | 2 |