Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,6,Mod(49,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.62302918878\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 373x^{4} + 33732x^{2} + 186624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{4}\cdot 5^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.5 | ||
Root | \(15.1546i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.49 |
Dual form | 60.6.d.a.49.2 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −20.3651 | − | 52.0602i | −0.364302 | − | 0.931281i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 121.510i | 0.937278i | 0.883390 | + | 0.468639i | \(0.155256\pi\) | ||||
−0.883390 | + | 0.468639i | \(0.844744\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −699.623 | −1.74334 | −0.871670 | − | 0.490093i | \(-0.836963\pi\) | ||||
−0.871670 | + | 0.490093i | \(0.836963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 436.743i | − | 0.716749i | −0.933578 | − | 0.358375i | \(-0.883331\pi\) | ||
0.933578 | − | 0.358375i | \(-0.116669\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 468.542 | − | 183.286i | 0.537675 | − | 0.210330i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1610.09i | − | 1.35122i | −0.737258 | − | 0.675611i | \(-0.763880\pi\) | ||
0.737258 | − | 0.675611i | \(-0.236120\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2778.55 | −1.76577 | −0.882884 | − | 0.469590i | \(-0.844402\pi\) | ||||
−0.882884 | + | 0.469590i | \(0.844402\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1093.59 | −0.541138 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1469.98i | 0.579420i | 0.957115 | + | 0.289710i | \(0.0935588\pi\) | ||||
−0.957115 | + | 0.289710i | \(0.906441\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2295.52 | + | 2120.42i | −0.734567 | + | 0.678536i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 729.000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2233.05 | −0.493063 | −0.246532 | − | 0.969135i | \(-0.579291\pi\) | ||||
−0.246532 | + | 0.969135i | \(0.579291\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4632.47 | 0.865781 | 0.432891 | − | 0.901446i | \(-0.357494\pi\) | ||||
0.432891 | + | 0.901446i | \(0.357494\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 6296.60i | − | 1.00652i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6325.85 | − | 2474.58i | 0.872869 | − | 0.341453i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5109.62i | 0.613598i | 0.951774 | + | 0.306799i | \(0.0992579\pi\) | ||||
−0.951774 | + | 0.306799i | \(0.900742\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3930.68 | 0.413815 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7683.61 | 0.713848 | 0.356924 | − | 0.934133i | \(-0.383826\pi\) | ||||
0.356924 | + | 0.934133i | \(0.383826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20417.9i | 1.68399i | 0.539484 | + | 0.841996i | \(0.318619\pi\) | ||||
−0.539484 | + | 0.841996i | \(0.681381\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1649.58 | + | 4216.87i | 0.121434 | + | 0.310427i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 21018.3i | − | 1.38788i | −0.720030 | − | 0.693942i | \(-0.755872\pi\) | ||
0.720030 | − | 0.693942i | \(-0.244128\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2042.21 | 0.121510 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14490.8 | 0.780129 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6033.60i | 0.295044i | 0.989059 | + | 0.147522i | \(0.0471297\pi\) | ||||
−0.989059 | + | 0.147522i | \(0.952870\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14247.9 | + | 36422.5i | 0.635103 | + | 1.62354i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 25006.9i | − | 1.01947i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 27762.7 | 1.03832 | 0.519160 | − | 0.854677i | \(-0.326245\pi\) | ||||
0.519160 | + | 0.854677i | \(0.326245\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −48757.3 | −1.67770 | −0.838852 | − | 0.544359i | \(-0.816773\pi\) | ||||
−0.838852 | + | 0.544359i | \(0.816773\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 9842.35i | − | 0.312426i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22736.9 | + | 8894.32i | −0.667495 | + | 0.261113i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 11289.5i | − | 0.307246i | −0.988130 | − | 0.153623i | \(-0.950906\pi\) | ||
0.988130 | − | 0.153623i | \(-0.0490942\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13229.9 | −0.334528 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15381.5 | −0.362121 | −0.181061 | − | 0.983472i | \(-0.557953\pi\) | ||||
−0.181061 | + | 0.983472i | \(0.557953\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 24443.1i | 0.536845i | 0.963301 | + | 0.268422i | \(0.0865023\pi\) | ||||
−0.963301 | + | 0.268422i | \(0.913498\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −19083.8 | − | 20659.7i | −0.391753 | − | 0.424103i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 85011.4i | − | 1.63399i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −23718.9 | −0.427589 | −0.213794 | − | 0.976879i | \(-0.568582\pi\) | ||||
−0.213794 | + | 0.976879i | \(0.568582\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 18970.7i | − | 0.302266i | −0.988513 | − | 0.151133i | \(-0.951708\pi\) | ||
0.988513 | − | 0.151133i | \(-0.0482921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −83821.4 | + | 32789.6i | −1.25837 | + | 0.492254i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 20097.4i | − | 0.284670i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −57532.2 | −0.769902 | −0.384951 | − | 0.922937i | \(-0.625782\pi\) | ||||
−0.384951 | + | 0.922937i | \(0.625782\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 53068.8 | 0.671793 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 41692.2i | 0.499859i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 56585.5 | + | 144652.i | 0.643274 | + | 1.64443i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 173854.i | − | 1.87610i | −0.346499 | − | 0.938050i | \(-0.612629\pi\) | ||
0.346499 | − | 0.938050i | \(-0.387371\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 56669.4 | 0.581113 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −77773.0 | −0.758622 | −0.379311 | − | 0.925269i | \(-0.623839\pi\) | ||||
−0.379311 | + | 0.925269i | \(0.623839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 123836.i | 1.15015i | 0.818102 | + | 0.575073i | \(0.195026\pi\) | ||||
−0.818102 | + | 0.575073i | \(0.804974\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 22271.2 | + | 56932.7i | 0.197138 | + | 0.503951i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 92949.4i | − | 0.784851i | −0.919784 | − | 0.392426i | \(-0.871636\pi\) | ||
0.919784 | − | 0.392426i | \(-0.128364\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 53772.7 | 0.433506 | 0.216753 | − | 0.976226i | \(-0.430453\pi\) | ||||
0.216753 | + | 0.976226i | \(0.430453\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −45986.5 | −0.354261 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 37540.9i | 0.276572i | 0.990392 | + | 0.138286i | \(0.0441594\pi\) | ||||
−0.990392 | + | 0.138286i | \(0.955841\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 76527.6 | − | 29936.4i | 0.539602 | − | 0.211084i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 35376.1i | 0.238916i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 195642. | 1.26647 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 328421. | 2.03923 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 69152.5i | 0.412140i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 157138. | + | 76322.6i | 0.899512 | + | 0.436896i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 154211.i | − | 0.848409i | −0.905566 | − | 0.424204i | \(-0.860554\pi\) | ||
0.905566 | − | 0.424204i | \(-0.139446\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −183761. | −0.972253 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −136783. | −0.696391 | −0.348196 | − | 0.937422i | \(-0.613206\pi\) | ||||
−0.348196 | + | 0.937422i | \(0.613206\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 337623.i | − | 1.65502i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −37951.9 | + | 14846.2i | −0.179225 | + | 0.0701100i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 303547.i | 1.38173i | 0.722982 | + | 0.690867i | \(0.242771\pi\) | ||||
−0.722982 | + | 0.690867i | \(0.757229\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −139766. | −0.613572 | −0.306786 | − | 0.951779i | \(-0.599254\pi\) | ||||
−0.306786 | + | 0.951779i | \(0.599254\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 189165. | 0.801296 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 305555.i | 1.24954i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 45476.3 | + | 116253.i | 0.179624 | + | 0.459180i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 18379.9i | 0.0701537i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −160751. | −0.593184 | −0.296592 | − | 0.955004i | \(-0.595850\pi\) | ||||
−0.296592 | + | 0.955004i | \(0.595850\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −274592. | −0.980045 | −0.490022 | − | 0.871710i | \(-0.663011\pi\) | ||||
−0.490022 | + | 0.871710i | \(0.663011\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 130417.i | 0.450408i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −94340.8 | − | 241167.i | −0.315406 | − | 0.806285i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 333596.i | − | 1.08012i | −0.841627 | − | 0.540059i | \(-0.818402\pi\) | ||
0.841627 | − | 0.540059i | \(-0.181598\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −54302.4 | −0.170344 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −178618. | −0.543077 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 159791.i | − | 0.471067i | −0.971866 | − | 0.235533i | \(-0.924316\pi\) | ||
0.971866 | − | 0.235533i | \(-0.0756837\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −327802. | + | 128231.i | −0.937351 | + | 0.366677i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 549868.i | − | 1.52569i | −0.646579 | − | 0.762847i | \(-0.723801\pi\) | ||
0.646579 | − | 0.762847i | \(-0.276199\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 180549. | 0.486271 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 225062. | 0.588590 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 85278.5i | − | 0.216633i | −0.994116 | − | 0.108316i | \(-0.965454\pi\) | ||
0.994116 | − | 0.108316i | \(-0.0345459\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −257654. | − | 278930.i | −0.635977 | − | 0.688494i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 249864.i | 0.599474i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −378124. | −0.882066 | −0.441033 | − | 0.897491i | \(-0.645388\pi\) | ||||
−0.441033 | + | 0.897491i | \(0.645388\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 74902.5 | 0.169942 | 0.0849708 | − | 0.996383i | \(-0.472920\pi\) | ||||
0.0849708 | + | 0.996383i | \(0.472920\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 438816.i | − | 0.968623i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 266007. | − | 104058.i | 0.571432 | − | 0.223535i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.12645e6i | 2.35564i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 88581.1 | 0.180379 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −810880. | −1.60832 | −0.804161 | − | 0.594412i | \(-0.797385\pi\) | ||||
−0.804161 | + | 0.594412i | \(0.797385\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 120513.i | − | 0.232884i | −0.993197 | − | 0.116442i | \(-0.962851\pi\) | ||
0.993197 | − | 0.116442i | \(-0.0371489\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −80048.9 | − | 204632.i | −0.150754 | − | 0.385378i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.04311e6i | 1.91499i | 0.288456 | + | 0.957493i | \(0.406858\pi\) | ||||
−0.288456 | + | 0.957493i | \(0.593142\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −87715.4 | −0.157016 | −0.0785079 | − | 0.996913i | \(-0.525016\pi\) | ||||
−0.0785079 | + | 0.996913i | \(0.525016\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 101605. | 0.177389 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 271338.i | − | 0.462137i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −156478. | − | 400010.i | −0.260056 | − | 0.664793i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 119069.i | − | 0.193140i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.94393e6 | 3.07834 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 530246. | 0.819919 | 0.409959 | − | 0.912104i | \(-0.365543\pi\) | ||||
0.409959 | + | 0.912104i | \(0.365543\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 138434.i | − | 0.209071i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.06296e6 | − | 415813.i | 1.56827 | − | 0.613482i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 562893.i | 0.811478i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −219988. | −0.309948 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −703193. | −0.968488 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.27008e6i | 1.71028i | 0.518397 | + | 0.855140i | \(0.326529\pi\) | ||||
−0.518397 | + | 0.855140i | \(0.673471\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 185937. | − | 171754.i | 0.244856 | − | 0.226179i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 127005.i | 0.163590i | 0.996649 | + | 0.0817948i | \(0.0260652\pi\) | ||||
−0.996649 | + | 0.0817948i | \(0.973935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −548288. | −0.690908 | −0.345454 | − | 0.938436i | \(-0.612275\pi\) | ||||
−0.345454 | + | 0.938436i | \(0.612275\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 765103. | 0.943387 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 794504.i | − | 0.958752i | −0.877610 | − | 0.479376i | \(-0.840863\pi\) | ||
0.877610 | − | 0.479376i | \(-0.159137\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.09422e6 | + | 428041.i | −1.29251 | + | 0.505610i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 213470.i | − | 0.246868i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 584107. | 0.661451 | 0.330725 | − | 0.943727i | \(-0.392707\pi\) | ||||
0.330725 | + | 0.943727i | \(0.392707\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.64168e6 | 1.82073 | 0.910365 | − | 0.413805i | \(-0.135801\pi\) | ||||
0.910365 | + | 0.413805i | \(0.135801\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −41589.9 | − | 106318.i | −0.0442663 | − | 0.113160i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.21351e6i | 1.26561i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 170737. | 0.174513 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −569849. | −0.570920 | −0.285460 | − | 0.958391i | \(-0.592146\pi\) | ||||
−0.285460 | + | 0.958391i | \(0.592146\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.02843e6i | − | 1.01013i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −295107. | − | 754393.i | −0.284203 | − | 0.726519i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 499302.i | 0.471553i | 0.971807 | + | 0.235776i | \(0.0757633\pi\) | ||||
−0.971807 | + | 0.235776i | \(0.924237\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −620872. | −0.575112 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 180877. | 0.164354 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 716870.i | − | 0.639074i | −0.947574 | − | 0.319537i | \(-0.896473\pi\) | ||
0.947574 | − | 0.319537i | \(-0.103527\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 314110. | − | 122875.i | 0.274769 | − | 0.107485i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 517789.i | − | 0.444503i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.19836e6 | −1.85233 | −0.926163 | − | 0.377124i | \(-0.876913\pi\) | ||||
−0.926163 | + | 0.377124i | \(0.876913\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −253384. | −0.209583 | −0.104792 | − | 0.994494i | \(-0.533418\pi\) | ||||
−0.104792 | + | 0.994494i | \(0.533418\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 477619.i | 0.387860i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.60600e6 | − | 1.48350e6i | 1.28060 | − | 1.18292i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.15596e6i | 0.905199i | 0.891714 | + | 0.452600i | \(0.149503\pi\) | ||||
−0.891714 | + | 0.452600i | \(0.850497\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −375230. | −0.288594 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.37453e6 | −1.79396 | −0.896979 | − | 0.442074i | \(-0.854243\pi\) | ||||
−0.896979 | + | 0.442074i | \(0.854243\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.56745e6i | 1.16340i | 0.813405 | + | 0.581698i | \(0.197611\pi\) | ||||
−0.813405 | + | 0.581698i | \(0.802389\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.30187e6 | + | 509269.i | −0.949410 | + | 0.371394i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 933639.i | 0.669074i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.17252e6 | −0.825803 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.56469e6 | 1.08317 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.74262e6i | − | 1.18586i | −0.805254 | − | 0.592930i | \(-0.797971\pi\) | ||
0.805254 | − | 0.592930i | \(-0.202029\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −565390. | − | 1.44533e6i | −0.378262 | − | 0.966967i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 510025.i | 0.335506i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 642005. | 0.415298 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.48099e6 | −1.57837 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 699957.i | − | 0.437991i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 992949. | + | 2.53832e6i | 0.611192 | + | 1.56241i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.02826e6i | − | 1.83378i | −0.399137 | − | 0.916891i | \(-0.630690\pi\) | ||
0.399137 | − | 0.916891i | \(-0.369310\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.11452e6 | −0.664037 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 139928. | 0.0820356 | 0.0410178 | − | 0.999158i | \(-0.486940\pi\) | ||||
0.0410178 | + | 0.999158i | \(0.486940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.76332e6i | − | 1.59430i | −0.603782 | − | 0.797149i | \(-0.706340\pi\) | ||
0.603782 | − | 0.797149i | \(-0.293660\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −512394. | + | 200441.i | −0.290956 | + | 0.113818i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.81991e6i | − | 1.01719i | −0.861006 | − | 0.508595i | \(-0.830165\pi\) | ||
0.861006 | − | 0.508595i | \(-0.169835\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.56229e6 | 0.859577 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 836545. | 0.453134 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.47370e6i | 2.38595i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 926079. | + | 1.00255e6i | 0.486340 | + | 0.526501i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 483954.i | 0.250285i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.55395e6 | 1.30083 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.72290e6 | 1.36603 | 0.683017 | − | 0.730403i | \(-0.260668\pi\) | ||||
0.683017 | + | 0.730403i | \(0.260668\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 413879.i | − | 0.204533i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −587732. | + | 229911.i | −0.286132 | + | 0.111931i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.95014e6i | − | 0.935385i | −0.883891 | − | 0.467693i | \(-0.845085\pi\) | ||
0.883891 | − | 0.467693i | \(-0.154915\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −337868. | −0.159679 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.24098e6 | −1.50935 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.29038e6i | 1.05117i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 269428. | + | 688749.i | 0.121869 | + | 0.311539i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 1.57423e6i | − | 0.701852i | −0.936403 | − | 0.350926i | \(-0.885867\pi\) | ||
0.936403 | − | 0.350926i | \(-0.114133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 723241. | 0.317848 | 0.158924 | − | 0.987291i | \(-0.449197\pi\) | ||||
0.158924 | + | 0.987291i | \(0.449197\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −318385. | −0.137938 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.94949e6i | 0.832694i | 0.909206 | + | 0.416347i | \(0.136690\pi\) | ||||
−0.909206 | + | 0.416347i | \(0.863310\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 313247. | + | 800766.i | 0.131922 | + | 0.337236i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.76078e6i | 0.731198i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.57967e6 | 0.646891 | 0.323445 | − | 0.946247i | \(-0.395159\pi\) | ||||
0.323445 | + | 0.946247i | \(0.395159\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.24423e6 | 2.11794 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.95579e6i | 1.17735i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.27251e6 | − | 497787.i | 0.499953 | − | 0.195574i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 549351.i | − | 0.212904i | −0.994318 | − | 0.106452i | \(-0.966051\pi\) | ||
0.994318 | − | 0.106452i | \(-0.0339491\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −622372. | −0.237949 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −733145. | −0.276538 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.11946e6i | − | 1.53309i | −0.642189 | − | 0.766546i | \(-0.721974\pi\) | ||
0.642189 | − | 0.766546i | \(-0.278026\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −686904. | + | 1.41424e6i | −0.252242 | + | 0.519333i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 975266.i | 0.353403i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 481024. | 0.172016 | 0.0860079 | − | 0.996294i | \(-0.472589\pi\) | ||||
0.0860079 | + | 0.996294i | \(0.472589\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.38790e6 | 0.489829 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 74246.2i | − | 0.0258629i | −0.999916 | − | 0.0129314i | \(-0.995884\pi\) | ||
0.999916 | − | 0.0129314i | \(-0.00411632\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.42571e6 | + | 1.73127e6i | −1.52171 | + | 0.595268i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 1.65385e6i | − | 0.561331i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 373796. | 0.125245 | 0.0626225 | − | 0.998037i | \(-0.480054\pi\) | ||||
0.0626225 | + | 0.998037i | \(0.480054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.36680e6 | 0.782925 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1.23105e6i | − | 0.402062i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 483038. | + | 1.23481e6i | 0.155772 | + | 0.398205i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.50136e6i | − | 1.11496i | −0.830189 | − | 0.557482i | \(-0.811767\pi\) | ||
0.830189 | − | 0.557482i | \(-0.188233\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.03860e6 | 0.955524 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.45598e6 | −0.452162 | −0.226081 | − | 0.974109i | \(-0.572591\pi\) | ||||
−0.226081 | + | 0.974109i | \(0.572591\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 2.02320e6i | − | 0.620548i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −133616. | − | 341567.i | −0.0404781 | − | 0.103476i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.57480e6i | − | 1.06971i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −55982.6 | −0.0165480 | −0.00827398 | − | 0.999966i | \(-0.502634\pi\) | ||||
−0.00827398 | + | 0.999966i | \(0.502634\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.73192e6 | −0.797745 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.37345e6i | 0.973194i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −987620. | + | 386341.i | −0.281494 | + | 0.110116i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.25790e6i | − | 0.354246i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.15797e6 | −0.878765 | −0.439382 | − | 0.898300i | \(-0.644803\pi\) | ||||
−0.439382 | + | 0.898300i | \(0.644803\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.18745e6 | −1.15145 | −0.575725 | − | 0.817644i | \(-0.695280\pi\) | ||||
−0.575725 | + | 0.817644i | \(0.695280\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.70248e6i | 0.462628i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.41407e6 | + | 3.69599e6i | 0.916853 | + | 0.992564i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5.92453e6i | − | 1.57248i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.74999e6 | −0.721421 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.00857e6 | −1.29873 | −0.649367 | − | 0.760475i | \(-0.724966\pi\) | ||||
−0.649367 | + | 0.760475i | \(0.724966\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.43666e6i | 1.64984i | 0.565253 | + | 0.824918i | \(0.308779\pi\) | ||||
−0.565253 | + | 0.824918i | \(0.691221\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.04627e6 | + | 409286.i | −0.265108 | + | 0.103706i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 4.08442e6i | − | 1.02312i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.41638e6 | −1.09372 | −0.546859 | − | 0.837225i | \(-0.684177\pi\) | ||||
−0.546859 | + | 0.837225i | \(0.684177\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −165419. | −0.0405032 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 1.58430e6i | − | 0.383555i | −0.981438 | − | 0.191778i | \(-0.938575\pi\) | ||
0.981438 | − | 0.191778i | \(-0.0614252\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.17165e6 | + | 2.99513e6i | 0.280477 | + | 0.716995i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1.44676e6i | − | 0.342475i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 654015. | 0.153099 | 0.0765494 | − | 0.997066i | \(-0.475610\pi\) | ||||
0.0765494 | + | 0.997066i | \(0.475610\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.37563e6 | −1.24448 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 2.47133e6i | − | 0.565829i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.08075e6 | − | 2.76277e6i | −0.244736 | − | 0.625628i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.54972e6i | 1.01905i | 0.860457 | + | 0.509523i | \(0.170178\pi\) | ||||
−0.860457 | + | 0.509523i | \(0.829822\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.17375e6 | −0.260043 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.13272e6 | 1.34400 | 0.672002 | − | 0.740549i | \(-0.265434\pi\) | ||||
0.672002 | + | 0.740549i | \(0.265434\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.80795e6i | 1.04233i | 0.853455 | + | 0.521167i | \(0.174503\pi\) | ||||
−0.853455 | + | 0.521167i | \(0.825497\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.17050e6 | − | 849067.i | 0.465509 | − | 0.182100i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.52182e6i | 1.17163i | 0.810445 | + | 0.585815i | \(0.199225\pi\) | ||||
−0.810445 | + | 0.585815i | \(0.800775\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.37179e6 | 0.287975 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.00236e6 | 0.623607 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.42848e7i | − | 2.93577i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.37822e6 | − | 5.89170e6i | 1.29708 | − | 1.19814i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 488722.i | − | 0.0983480i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.10086e6 | −0.816650 | −0.408325 | − | 0.912837i | \(-0.633887\pi\) | ||||
−0.408325 | + | 0.912837i | \(0.633887\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.23159e6 | 0.439796 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.60757e6i | − | 0.313546i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.05089e6 | + | 3.54057e6i | −1.74718 | + | 0.683468i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.67945e6i | 0.320882i | 0.987045 | + | 0.160441i | \(0.0512917\pi\) | ||||
−0.987045 | + | 0.160441i | \(0.948708\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.43812e6 | 0.271971 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.85817e6 | 0.722234 | 0.361117 | − | 0.932521i | \(-0.382396\pi\) | ||||
0.361117 | + | 0.932521i | \(0.382396\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.59540e6i | 0.666238i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.15408e6 | − | 2.95022e6i | −0.211701 | − | 0.541180i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.86902e6i | − | 0.339408i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.53067e6 | −0.634755 | −0.317378 | − | 0.948299i | \(-0.602802\pi\) | ||||
−0.317378 | + | 0.948299i | \(0.602802\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.94881e6 | 0.880860 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.46451e6i | 1.49170i | 0.666113 | + | 0.745851i | \(0.267957\pi\) | ||||
−0.666113 | + | 0.745851i | \(0.732043\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.58386e6 | + | 4.04888e6i | 0.276368 | + | 0.706490i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.62494e6i | 0.280749i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.12223e6 | 1.38957 | 0.694785 | − | 0.719217i | \(-0.255499\pi\) | ||||
0.694785 | + | 0.719217i | \(0.255499\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.97009e6 | −0.503173 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.02556e6i | 0.339822i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.44691e6 | − | 2.52193e6i | 1.07111 | − | 0.419001i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.47049e7i | 2.41956i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 767506. | 0.125073 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.20656e6 | 1.16314 | 0.581572 | − | 0.813495i | \(-0.302438\pi\) | ||||
0.581572 | + | 0.813495i | \(0.302438\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.08544e6i | − | 0.333384i | −0.986009 | − | 0.166692i | \(-0.946691\pi\) | ||
0.986009 | − | 0.166692i | \(-0.0533085\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.51037e6 | − | 2.31888e6i | 0.397502 | − | 0.367181i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 7.45868e6i | − | 1.16986i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.27549e6 | 0.664273 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.24877e6 | −0.346106 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.35576e6i | − | 0.511650i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.83896e6 | + | 1.89293e6i | −0.730917 | + | 0.285923i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 3.40311e6i | − | 0.509261i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.42878e6 | −0.211833 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.54682e6 | −0.227220 | −0.113610 | − | 0.993525i | \(-0.536241\pi\) | ||||
−0.113610 | + | 0.993525i | \(0.536241\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 674122.i | 0.0981159i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.09509e6 | − | 2.79941e6i | −0.157927 | − | 0.403716i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 882763.i | 0.126147i | 0.998009 | + | 0.0630734i | \(0.0200902\pi\) | ||||
−0.998009 | + | 0.0630734i | \(0.979910\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.94934e6 | 0.559235 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.20463e6 | 0.870636 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.88209e6i | − | 0.400770i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 936522. | + | 2.39407e6i | 0.129058 | + | 0.329916i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.32281e7i | 1.80659i | 0.429022 | + | 0.903294i | \(0.358858\pi\) | ||||
−0.429022 | + | 0.903294i | \(0.641142\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.91737e6 | 1.20700 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.01381e7 | −1.36003 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.71554e6i | 0.228102i | 0.993475 | + | 0.114051i | \(0.0363828\pi\) | ||||
−0.993475 | + | 0.114051i | \(0.963617\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.95439e6 | − | 764526.i | 0.257567 | − | 0.100756i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 797230.i | 0.104142i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.06624e7 | −1.38062 | −0.690312 | − | 0.723512i | \(-0.742527\pi\) | ||||
−0.690312 | + | 0.723512i | \(0.742527\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.13322e6 | 0.273807 | 0.136904 | − | 0.990584i | \(-0.456285\pi\) | ||||
0.136904 | + | 0.990584i | \(0.456285\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 7.29792e6i | − | 0.928565i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.11699e6 | − | 3.37438e6i | −0.393157 | − | 0.425623i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.90217e6i | 0.362897i | 0.983400 | + | 0.181448i | \(0.0580785\pi\) | ||||
−0.983400 | + | 0.181448i | \(0.941921\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.08461e6 | 0.134456 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.30514e6 | 0.283307 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.22124e6i | − | 0.514362i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.84169e6 | − | 720440.i | 0.222498 | − | 0.0870378i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.38744e7i | 1.66195i | 0.556310 | + | 0.830975i | \(0.312217\pi\) | ||||
−0.556310 | + | 0.830975i | \(0.687783\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.28715e7 | −1.52877 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.38801e6 | −1.10562 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.05925e6i | 0.123697i | 0.998086 | + | 0.0618487i | \(0.0196996\pi\) | ||||
−0.998086 | + | 0.0618487i | \(0.980300\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.98428e6 | − | 1.01852e7i | −0.461379 | − | 1.17944i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 789439.i | − | 0.0906531i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 821292. | 0.0935256 | 0.0467628 | − | 0.998906i | \(-0.485110\pi\) | ||||
0.0467628 | + | 0.998906i | \(0.485110\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.26399e6 | −0.933262 | −0.466631 | − | 0.884452i | \(-0.654532\pi\) | ||||
−0.466631 | + | 0.884452i | \(0.654532\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 914447.i | 0.102415i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.68833e6 | − | 1.70976e7i | −0.742898 | − | 1.89910i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 252816.i | − | 0.0278505i | −0.999903 | − | 0.0139252i | \(-0.995567\pi\) | ||
0.999903 | − | 0.0139252i | \(-0.00443269\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.44205e6 | 0.266815 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.17960e6 | −0.994765 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5.25712e6i | − | 0.565062i | −0.959258 | − | 0.282531i | \(-0.908826\pi\) | ||
0.959258 | − | 0.282531i | \(-0.0911741\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.60009e6 | − | 1.40830e6i | 0.383818 | − | 0.150144i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.60527e6i | − | 0.698518i | −0.937026 | − | 0.349259i | \(-0.886433\pi\) | ||
0.937026 | − | 0.349259i | \(-0.113567\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.53364e7 | 1.60878 | 0.804392 | − | 0.594100i | \(-0.202491\pi\) | ||||
0.804392 | + | 0.594100i | \(0.202491\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.07162e6 | 0.111509 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 6.99076e6i | − | 0.721613i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 773229. | − | 9.73497e6i | 0.0791786 | − | 0.996860i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.74954e7i | 1.77728i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.22692e6 | 0.829108 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.10137e6 | −0.410068 | −0.205034 | − | 0.978755i | \(-0.565730\pi\) | ||||
−0.205034 | + | 0.978755i | \(0.565730\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.77221e6i | 0.473380i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.02824e6 | + | 3.14052e6i | −0.790107 | + | 0.309077i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 891922.i | − | 0.0870920i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.24590e6 | 0.120707 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.80263e6 | −0.269414 | −0.134707 | − | 0.990885i | \(-0.543009\pi\) | ||||
−0.134707 | + | 0.990885i | \(0.543009\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.05243e7i | − | 1.00384i | −0.864914 | − | 0.501920i | \(-0.832627\pi\) | ||
0.864914 | − | 0.501920i | \(-0.167373\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.74232e6 | + | 9.56664e6i | 0.354194 | + | 0.905441i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.43484e6i | 0.792166i | 0.918215 | + | 0.396083i | \(0.129631\pi\) | ||||
−0.918215 | + | 0.396083i | \(0.870369\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.94234e7 | −1.81014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.06604e6 | −0.468507 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.31348e6i | 0.487637i | 0.969821 | + | 0.243818i | \(0.0784001\pi\) | ||||
−0.969821 | + | 0.243818i | \(0.921600\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.78560e6 | + | 7.12094e6i | 0.253697 | + | 0.648536i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.97989e6i | − | 0.178948i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.80659e7 | −1.62049 | −0.810246 | − | 0.586091i | \(-0.800666\pi\) | ||||
−0.810246 | + | 0.586091i | \(0.800666\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.01234e6 | 0.624251 | 0.312125 | − | 0.950041i | \(-0.398959\pi\) | ||||
0.312125 | + | 0.950041i | \(0.398959\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 6.32874e6i | − | 0.559157i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.75767e7 | + | 6.87573e6i | −1.54128 | + | 0.602927i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.28254e6i | − | 0.285691i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.14307e7 | −0.987431 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.41117e7 | 2.92481 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.39367e6i | 0.288823i | 0.989518 | + | 0.144412i | \(0.0461289\pi\) | ||||
−0.989518 | + | 0.144412i | \(0.953871\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.54579e6 | + | 1.67344e6i | 0.130584 | + | 0.141368i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.77774e6i | 0.568347i | 0.958773 | + | 0.284173i | \(0.0917191\pi\) | ||||
−0.958773 | + | 0.284173i | \(0.908281\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.11251e7 | 1.75843 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.14304e6 | −0.0944484 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.91859e6i | 0.813576i | 0.913523 | + | 0.406788i | \(0.133351\pi\) | ||||
−0.913523 | + | 0.406788i | \(0.866649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.58027e7 | − | 6.18178e6i | 1.28678 | − | 0.503369i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 4.93460e6i | − | 0.398896i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.63513e6 | 0.211473 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46476.2 | 0.00370285 | 0.00185142 | − | 0.999998i | \(-0.499411\pi\) | ||||
0.00185142 | + | 0.999998i | \(0.499411\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.88593e6i | 0.544665i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.84636e6 | + | 7.27625e6i | 0.223526 | + | 0.571407i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.23713e7i | − | 0.964567i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.15054e6 | 0.553536 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.23937e7 | 0.952589 | 0.476294 | − | 0.879286i | \(-0.341980\pi\) | ||||
0.476294 | + | 0.879286i | \(0.341980\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.41973e7i | − | 1.08347i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.85237e6 | − | 9.84796e6i | −0.291914 | − | 0.746231i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 9.45023e6i | − | 0.711040i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.73930e6 | 0.727632 | 0.363816 | − | 0.931471i | \(-0.381474\pi\) | ||||
0.363816 | + | 0.931471i | \(0.381474\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.92123e6 | 0.142530 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.80966e6i | 0.501651i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.59072e7 | − | 6.22267e6i | 1.16367 | − | 0.455210i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.25696e6i | 0.381889i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.67144e7 | −1.20578 | −0.602891 | − | 0.797823i | \(-0.705985\pi\) | ||||
−0.602891 | + | 0.797823i | \(0.705985\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.50473e7 | −1.07801 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.47751e7i | 1.05120i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.12601e6 | − | 4.73500e6i | 0.362188 | − | 0.334561i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.21859e7i | 0.855109i | 0.903990 | + | 0.427555i | \(0.140625\pi\) | ||||
−0.903990 | + | 0.427555i | \(0.859375\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.28746e7 | 2.27545 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.90166e6i | 0.130729i | 0.997861 | + | 0.0653647i | \(0.0208211\pi\) | ||||
−0.997861 | + | 0.0653647i | \(0.979179\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 956862. | − | 374309.i | 0.0653327 | − | 0.0255571i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.89837e6i | 0.535635i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.24528e6 | 0.622743 | 0.311372 | − | 0.950288i | \(-0.399212\pi\) | ||||
0.311372 | + | 0.950288i | \(0.399212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.09216e7 | −0.730702 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.62223e6i | − | 0.572991i | −0.958082 | − | 0.286495i | \(-0.907510\pi\) | ||
0.958082 | − | 0.286495i | \(-0.0924903\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.27372e6 | + | 8.36875e6i | 0.216098 | + | 0.552420i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.53663e6i | 0.100755i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.12943e7 | 0.735624 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.53525e7 | −1.64029 | −0.820146 | − | 0.572154i | \(-0.806108\pi\) | ||||
−0.820146 | + | 0.572154i | \(0.806108\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 5.12864e6i | − | 0.329621i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.59211e6 | + | 1.42953e7i | 0.357033 | + | 0.912697i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 156645.i | − | 0.00993522i | −0.999988 | − | 0.00496761i | \(-0.998419\pi\) | ||
0.999988 | − | 0.00496761i | \(-0.00158125\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.25591e6 | 0.583196 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.56741e7 | −0.981118 | −0.490559 | − | 0.871408i | \(-0.663207\pi\) | ||||
−0.490559 | + | 0.871408i | \(0.663207\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.53394e6i | 0.406316i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.78953e6 | − | 2.65596e6i | 0.419456 | − | 0.164085i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1.21251e7i | − | 0.744214i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.84095e6 | −0.295199 | −0.147600 | − | 0.989047i | \(-0.547155\pi\) | ||||
−0.147600 | + | 0.989047i | \(0.547155\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.49372e6 | −0.272251 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.85997e6i | − | 0.111958i | −0.998432 | − | 0.0559792i | \(-0.982172\pi\) | ||
0.998432 | − | 0.0559792i | \(-0.0178281\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.06339e7 | + | 9.82280e6i | −0.635975 | + | 0.587464i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 5.58784e6i | − | 0.332041i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.13493e7 | −1.26049 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.07613e7 | 0.631300 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.62789e6i | 0.0948901i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.73670e7 | + | 6.79372e6i | −1.00589 | + | 0.393490i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.38288e7i | − | 0.795881i | −0.917411 | − | 0.397940i | \(-0.869725\pi\) | ||
0.917411 | − | 0.397940i | \(-0.130275\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.45183e6 | 0.368970 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.56161e6 | −0.259225 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.12944e7i | 1.20249i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.10588e6 | + | 2.82699e6i | 0.0620567 | + | 0.158638i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 9.71374e6i | − | 0.541677i | −0.962625 | − | 0.270839i | \(-0.912699\pi\) | ||
0.962625 | − | 0.270839i | \(-0.0873010\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.38413e7 | −1.87534 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.66011e6 | 0.256634 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.71009e7i | − | 0.935903i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.63759e6 | + | 9.29891e6i | 0.197844 | + | 0.505757i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 1.97852e7i | − | 1.06944i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.71666e6 | −0.0922175 | −0.0461088 | − | 0.998936i | \(-0.514682\pi\) | ||||
−0.0461088 | + | 0.998936i | \(0.514682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.83595e7 | 0.980188 | 0.490094 | − | 0.871670i | \(-0.336962\pi\) | ||||
0.490094 | + | 0.871670i | \(0.336962\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 2.28046e6i | − | 0.121003i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.31873e6 | + | 3.25416e6i | −0.438695 | + | 0.171611i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 5.67321e7i | − | 2.97354i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.29857e6 | −0.223931 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.04696e7 | −0.542092 | −0.271046 | − | 0.962566i | \(-0.587370\pi\) | ||||
−0.271046 | + | 0.962566i | \(0.587370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.62514e7i | 1.86563i | 0.360355 | + | 0.932815i | \(0.382656\pi\) | ||||
−0.360355 | + | 0.932815i | \(0.617344\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.33515e7 | + | 1.44540e7i | 0.682958 | + | 0.739355i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 2.44656e7i | − | 1.24392i | −0.783050 | − | 0.621959i | \(-0.786337\pi\) | ||
0.783050 | − | 0.621959i | \(-0.213663\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.38073e7 | 0.697789 | 0.348894 | − | 0.937162i | \(-0.386557\pi\) | ||||
0.348894 | + | 0.937162i | \(0.386557\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.04037e7 | −0.522617 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.28814e6i | − | 0.164187i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.86262e7 | + | 1.11981e7i | −1.42085 | + | 0.555814i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 3.37707e6i | − | 0.166620i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.90471e7 | 0.934164 | 0.467082 | − | 0.884214i | \(-0.345305\pi\) | ||||
0.467082 | + | 0.884214i | \(0.345305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.55247e7 | −0.756889 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 2.13708e7i | − | 1.03574i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.67690e6 | − | 9.39941e6i | −0.177150 | − | 0.452855i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.99066e7i | 1.91133i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.41070e7 | −0.671687 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.51106e6 | −0.355531 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.14111e6i | 0.430156i | 0.976597 | + | 0.215078i | \(0.0690006\pi\) | ||||
−0.976597 | + | 0.215078i | \(0.930999\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.58342e6 | − | 1.17168e7i | −0.214425 | − | 0.548142i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 3.39276e7i | − | 1.57798i | −0.614407 | − | 0.788989i | \(-0.710605\pi\) | ||
0.614407 | − | 0.788989i | \(-0.289395\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.26635e7 | −1.04796 | −0.523979 | − | 0.851731i | \(-0.675553\pi\) | ||||
−0.523979 | + | 0.851731i | \(0.675553\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.40275e6 | −0.386290 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.01189e7i | − | 0.919555i | −0.888034 | − | 0.459777i | \(-0.847929\pi\) | ||
0.888034 | − | 0.459777i | \(-0.152071\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.43961e6 | + | 1.73671e6i | −0.201746 | + | 0.0789198i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1.05527e7i | − | 0.476778i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.65943e7 | 0.745433 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.93059e6 | −0.220218 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.40822e7i | 0.625367i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.27400e6 | + | 1.90939e7i | −0.409493 | + | 0.843093i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.99763e7i | 1.31607i | 0.752988 | + | 0.658035i | \(0.228612\pi\) | ||||
−0.752988 | + | 0.658035i | \(0.771388\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.56836e7 | 0.684657 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.74388e7 | 1.62511 | 0.812554 | − | 0.582886i | \(-0.198077\pi\) | ||||
0.812554 | + | 0.582886i | \(0.198077\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2.86458e7i | − | 1.23640i | −0.786021 | − | 0.618200i | \(-0.787862\pi\) | ||
0.786021 | − | 0.618200i | \(-0.212138\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.30080e7 | − | 5.08851e6i | 0.558279 | − | 0.218390i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.81325e7i | 1.20060i | 0.799775 | + | 0.600300i | \(0.204952\pi\) | ||||
−0.799775 | + | 0.600300i | \(0.795048\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.87382e7 | 0.795195 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.59022e6 | −0.193704 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.84004e7i | 2.45068i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.70053e6 | + | 1.96852e7i | 0.321339 | + | 0.821451i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.77804e6i | 0.239773i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.03445e7 | −0.426885 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.71462e6 | 0.398670 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.23289e7i | − | 0.911272i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.52540e6 | − | 3.89944e6i | −0.0619102 | − | 0.158263i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.20623e7i | − | 0.890498i | −0.895407 | − | 0.445249i | \(-0.853115\pi\) | ||
0.895407 | − | 0.445249i | \(-0.146885\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.29961e6 | 0.252874 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.25081e7 | −0.499340 | −0.249670 | − | 0.968331i | \(-0.580322\pi\) | ||||
−0.249670 | + | 0.968331i | \(0.580322\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.32724e7i | 0.526952i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.28448e7 | + | 8.93654e6i | −0.902060 | + | 0.352872i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1.66205e7i | − | 0.652712i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.06659e6 | 0.119775 | 0.0598877 | − | 0.998205i | \(-0.480926\pi\) | ||||
0.0598877 | + | 0.998205i | \(0.480926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.72544e7 | 1.05873 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.71777e6i | 0.259550i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.08346e7 | − | 1.17292e7i | −0.416348 | − | 0.450729i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1.00307e7i | − | 0.383382i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.08272e7 | 1.55206 | 0.776032 | − | 0.630693i | \(-0.217229\pi\) | ||||
0.776032 | + | 0.630693i | \(0.217229\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.67439e6 | −0.214558 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.25935e6i | 0.0473633i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.86433e7 | − | 2.29404e7i | 2.19376 | − | 0.858166i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.07349e6i | 0.114362i | 0.998364 | + | 0.0571812i | \(0.0182113\pi\) | ||||
−0.998364 | + | 0.0571812i | \(0.981789\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.48698e7 | 0.920469 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.32976e6 | 0.0857702 | 0.0428851 | − | 0.999080i | \(-0.486345\pi\) | ||||
0.0428851 | + | 0.999080i | \(0.486345\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.12948e7i | 0.413617i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.80397e6 | − | 4.61155e6i | −0.0657126 | − | 0.167984i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 2.11096e7i | − | 0.764902i | −0.923976 | − | 0.382451i | \(-0.875080\pi\) | ||
0.923976 | − | 0.382451i | \(-0.124920\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.06753e7 | 0.384783 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.63792e7 | 0.587275 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.66559e7i | 0.950738i | 0.879787 | + | 0.475369i | \(0.157685\pi\) | ||||
−0.879787 | + | 0.475369i | \(0.842315\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.65137e7 | + | 4.22145e7i | 0.585916 | + | 1.49780i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.40606e7i | 0.496277i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.68841e7 | −1.29507 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.16939e6 | −0.250423 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.52890e6i | 0.261617i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.27391e6 | + | 2.45426e6i | −0.216880 | + | 0.0848402i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.22706e6i | 0.145369i | 0.997355 | + | 0.0726846i | \(0.0231566\pi\) | ||||
−0.997355 | + | 0.0726846i | \(0.976843\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.02633e7 | −1.37753 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 755839. | 0.0257265 | 0.0128633 | − | 0.999917i | \(-0.495905\pi\) | ||||
0.0128633 | + | 0.999917i | \(0.495905\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.69831e7i | − | 0.575087i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.02297e6 | + | 8.33471e6i | −0.303975 | + | 0.280788i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 239167.i | 0.00801613i | 0.999992 | + | 0.00400806i | \(0.00127581\pi\) | ||||
−0.999992 | + | 0.00400806i | \(0.998724\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.02508e7 | 1.34220 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.35559e6 | −0.144502 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 3.78483e7i | − | 1.24929i | −0.780910 | − | 0.624644i | \(-0.785244\pi\) | ||
0.780910 | − | 0.624644i | \(-0.214756\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.43046e7 | − | 2.12431e7i | 1.78339 | − | 0.697634i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.29855e7i | 0.751037i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.00140e7 | −0.975738 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.04454e7 | −0.661321 | −0.330661 | − | 0.943750i | \(-0.607272\pi\) | ||||
−0.330661 | + | 0.943750i | \(0.607272\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.45061e7i | 0.788680i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.78634e6 | + | 4.56648e6i | 0.0572012 | + | 0.146226i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.20062e6i | 0.0382532i | 0.999817 | + | 0.0191266i | \(0.00608855\pi\) | ||||
−0.999817 | + | 0.0191266i | \(0.993911\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.72491e6 | 0.118087 |
(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 | 60.6.d.a.49.5 | yes | 6 | |
3.2 | odd | 2 | 180.6.d.d.109.4 | 6 | |||
4.3 | odd | 2 | 240.6.f.d.49.2 | 6 | |||
5.2 | odd | 4 | 300.6.a.j.1.1 | 3 | |||
5.3 | odd | 4 | 300.6.a.i.1.3 | 3 | |||
5.4 | even | 2 | inner | 60.6.d.a.49.2 | ✓ | 6 | |
12.11 | even | 2 | 720.6.f.m.289.4 | 6 | |||
15.2 | even | 4 | 900.6.a.x.1.1 | 3 | |||
15.8 | even | 4 | 900.6.a.w.1.3 | 3 | |||
15.14 | odd | 2 | 180.6.d.d.109.3 | 6 | |||
20.19 | odd | 2 | 240.6.f.d.49.5 | 6 | |||
60.59 | even | 2 | 720.6.f.m.289.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.6.d.a.49.2 | ✓ | 6 | 5.4 | even | 2 | inner | |
60.6.d.a.49.5 | yes | 6 | 1.1 | even | 1 | trivial | |
180.6.d.d.109.3 | 6 | 15.14 | odd | 2 | |||
180.6.d.d.109.4 | 6 | 3.2 | odd | 2 | |||
240.6.f.d.49.2 | 6 | 4.3 | odd | 2 | |||
240.6.f.d.49.5 | 6 | 20.19 | odd | 2 | |||
300.6.a.i.1.3 | 3 | 5.3 | odd | 4 | |||
300.6.a.j.1.1 | 3 | 5.2 | odd | 4 | |||
720.6.f.m.289.3 | 6 | 60.59 | even | 2 | |||
720.6.f.m.289.4 | 6 | 12.11 | even | 2 | |||
900.6.a.w.1.3 | 3 | 15.8 | even | 4 | |||
900.6.a.x.1.1 | 3 | 15.2 | even | 4 |